The Indian Ocean Tsunami

Downloaded by [INFLIBNET Centre] at 07:51 27 August 2012 Downloaded by [INFLIBNET Centre] at 07:51 27 August 2012 The...

Author: Tad S. Murty | U. Aswathanarayana | Niru Nirupama

222 downloads 2516 Views 14MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

Downloaded by [INFLIBNET Centre] at 07:51 27 August 2012


The Indian Ocean Tsunami


BALKEMA – Proceedings and Monographs in Engineering, Water and Earth Sciences


The Indian Ocean Tsunami

Edited by Tad S. Murty Department of Civil Engineering, University of Ottawa Ottawa, Canada

U. Aswathanarayana Mahadevan International Centre for Water Resources Management Hyderabad, India

N. Nirupama Atkinson School of Administrative Studies, York University, Toronto, Canada

LONDON / LEIDEN / NEW YORK / PHILADELPHIA / SINGAPORE


Taylor & Francis is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2007. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.”

© 2007 Taylor & Francis Group, London, UK All rights reserved. No part of this publication or the information contained herein may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, by photocopying, recording or otherwise, without written prior permission from the publishers. Although all care is taken to ensure integrity and the quality of this publication and the information herein, no responsibility is assumed by the publishers nor the author for any damage to the property or persons as a result of operation or use of this publication and/or the information contained herein. Published by: Taylor & Francis/Balkema P.O. Box 447, 2300 AK Leiden, The Netherlands e-mail: [email protected] www.balkema.nl, www.taylorandfrancis.co.uk, www.crcpress.com Library of Congress Cataloging-in-Publication Data The Indian Ocean Tsunami / editors, Tad S. Murty, U. Aswathanarayana, N. Nirupama. p. cm. Includes index. ISBN-13 978-0-415-40380-1 (hardcover : alk. paper) 1. Indian Ocean Tsunami, 2004. 2. Tsunamis–Indian Ocean. 3. Tsunamis. I. Murty, T. S. (Tadepalli Satyanaraynan), 1938- II. Aswathanarayana, U. III. Nirupama, N. GC222.I45I53 2006 551.46’37156–dc22 2006020259 ISBN 0-203-96443-8 Master e-book ISBN

ISBN-13: 978 0 415 40380 1 (Print Edition)

Cover Illustration


Schematic sketch map showing the pathway of the tsunami (thicker lines indicate higher intensity), and the projected location of the automated Deep Ocean Tsunami buoys (courtesy: Prem Kumar, NIOT, Chennai, India).


In Remembrance


To remember the enormity of the human suffering involving the families of hundreds of thousands of people killed in the tsunami, the Editors could do no better than to reproduce the poignant note of Carol Amaratunga and the photograph (courtesy: Dr. Paul Gully) of the physical destruction wrought by the tsunami.


A Note of Reflection and Dedication

A few days before the Asian Tsunami of December 26, 2004, I was in southern Sri Lanka attending a conference on Sri Lankan Studies at the University of Ruhuna. I took a few quiet moments at sunrise to observe artisanal fishing boats negotiating the waves near the Matara Rest House – an old colonial beach bungalow less than 30 m from the sea. The wrap-around Sea and azure sky that early morning were breath-taking. Nevertheless, for a fleeting moment, I was chilled by the realization of how completely exposed we were to a vast ocean stretching from the southern tip of Sri Lanka to Antarctica. The moment passed, and I rationalized that the bungalow had occupied this shoreline for the better part of a century. Five days later, the Matara Rest House was hit by one of the strongest tsunamis ever recorded, along with hundreds of homes, schools, businesses, and places of worship. The coastal devastation stretched for virtually hundreds of kilometers. In the weeks following the tsunami, Sri Lanka reported 31,229 confirmed deaths, 4093 people missing and more than 15,686 people injured. In this age of globalization and holiday eco tourism, nationals from 73 countries died. Millions of coastal residents were displaced in the 12 countries directly affected by the tsunami. The long-term psychosocial and intergenerational impact of the Asian Tsunami will be experienced for decades. This book is dedicated to the memory of citizens of Matara, Sri Lanka, and to the thousands of women, children and men whose lives were lost that day. This work is also dedicated to those who survived and prevailed. It is with great courage and resiliency that they rebuild their lives, families and communities. Carol Amaratunga University of Ottawa, Canada

Dedication


Dedicated to Dr. R.A. Mashelkar, F.R.S., in appreciation of his indefatigable services in advancing applied science in India and the Developing countries.



Contents

List of figures List of tables Foreword Prologue Preface

xv xxvii xxix xxxi xxxiii

PART 1

1

1 A Historical Account of the Earthquakes and Tsunamis in the Indian Ocean b.k. rastogi

3

Geostructural Environment of Tsunami Genesis

2

Impact of Coastal Morphology, Structure and Seismicity on the Tsunami Surge k.s.r. murthy, v. subrahmanyam, g.p.s. murty, and k. mohana rao

19

3 Tsunamigenic Sources in the Indian Ocean: Factors and Impact on the Indian Landmass r.k. chadha

33

4

Paleo-Tsunami and Storm Surge Deposits k. arun kumar, h. achyuthan, and n. shankar

49

5

Overview and Integration of Part 1 u. aswathanarayana (editor)

57

PART 2

61

6 A Review of Classical Concepts on Phase and Amplitude Dispersion: Application to Tsunamis n. nirupama, t.s. murty, i. nistor, and a.d. rao

63

Modelling of Tsunami Generation and Propagation

7 A Partial Explanation for the Initial Withdrawal of the Ocean during a Tsunami n. nirupama, t.s. murty, a.d. rao, and i. nistor 8 The Energetics of the Tsunami of 26 December 2004 in the Indian Ocean: A Brief Review n. nirupama, t.s. murty, i. nistor, and a.d. rao

73

81

xii


9

Contents Possible Amplification of the Tsunami Through Coupling with Internal Waves n. nirupama, t.s. murty, i. nistor, and a.d. rao

91

10

Numerical Modeling of the Indian Ocean Tsunami z. kowalik, w. knight, t. logan, and p. whitmore

97

11

Modelling Techniques for Understanding the Indian Ocean Tsunami Propagation v.p. dimri and k. srivastava

123

12 Validation of Tsunami Beach Run-up Height Predictive Model Based on Work–Energy Theorem g. muraleedharan, a.d. rao, t.s. murty, and m. sinha

131

13

Normal Modes and Tsunami Coastal Effects n. nirupama, t.s. murty, a.d. rao, and i. nistor

143

14

Helmholtz Mode and K–S–P Waves: Application to Tsunamis n. nirupama, t.s. murty, i. nistor, and a.d. rao

151

15

Numerical Models for the Indian Ocean Tsunami of 26 December 2004: A Brief Review p. chittibabu and t.s. murty

159

16 The Cauchy–Poisson Problem: Application to Tsunami Generation and Propagation n. nirupama, t.s. murty, i. nistor, and a.d. rao

175

17 A Review and Listing of Tsunami Heights and Travel Times for the 26 December 2004 Event i. nistor, k. xie, n. nirupama, and t.s. murty

185

18

209

Overview and Integration of Part 2 n. nirupama (editor)

PART 3

Tsunami Detection and Monitoring Systems

213

19

Satellite Detection of Pre-Earthquake Thermal Anomaly and Sea Water Turbidity Associated with the Great Sumatra Earthquake a.k. saraf, s. choudhury, s. dasgupta, and j. das

215

20

Possible Detection in the Ionosphere of the Signals from Earthquake and Tsunamis t.s. murty, n. nirupama, a.d. rao, and i. nistor

227

21

Seismo-electromagnetic Precursors Registered by DEMETER Satellite a.k. gwal, s. sarkar, s. bhattacharya, and m. parrot

22 Web-Enabled and Real-Time Reporting: Cellular Based Instrumentation for Coastal Sea Level and Surge Monitoring a. joseph and r.g. prabhudesai

235

247

Contents xiii


23

Methodologies for Tsunami Detection t.s. murty, n. nirupama, a.d. rao, and i. nistor

259

24 Tsunami Travel Time Atlas for the Indian Ocean p.k. bhaskaran, s.k. dube, t.s. murty, a. gangopadhyay, a. chaudhuri, and a.d. rao

273

25

293


PART 4

Biophysical and Socio-Economic Dimensions of Tsunami Damage

295

26

Performance of Structures Affected by the 2004 Sumatra Tsunami in Thailand and Indonesia m. saatcioglu, a. ghobarah, and i. nistor

297

27

Field Observations on the Tsunami Impact Along the Kerala Coast, Southwest India n.p. kurian, t.n. prakash, and m. baba

323

28

Ecological Impact of Indian Ocean Tsunami c.s.p. iyer

339

29 Tsunami Damage to the South Eastern Coast of India n. chandrasekar and r. ramesh

351

30

365

Hydrophysical Manifestations of the Indian Ocean Tsunami y. sadhuram, t.v. ramana murthy, and b.p. rao

31 Tsunamis and Marine Life d.v. subba rao, b. ingole, d. tang, b. satyanarayana, and h. zhao

373

32 Tsunami Impact on Coastal Habitats of India p.n. sridhar, a. surendran, s. jain, and b. veera narayan

393

33

405

Overview and Integration of Part 4 u. aswathanarayana (editor)

PART 5

Quo Vadis

409

34

Protection Measures Against Tsunami-type Hazards for the Coast of Tamil Nadu, India v. sundar

411

35

Protective Role of Coastal Ecosystems in the Context of the Tsunami in Tamil Nadu Coast, India: Implications for Hazard Preparedness a. mascarenhas and s. jayakumar

423


xiv

Contents

36

Integrated Preparedness Systems u. aswathanarayana (editor)

37

Social and Political Aspects of Tsunami Response, Recovery, and Preparedness Planning: A Transdisciplinary Approach from Canada c. amaratunga and h. smith fowler

437

445

38 An Ideal Conceptual Tsunami Warning System for the Indian Ocean t.s. murty, n. nirupama, a.d. rao, and i. nistor

455

39

475


Author Index Subject Index

477 487

Figures


1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4 2.5 2.6

2.7

3.1

3.2 3.3

3.4

Rupture areas of great earthquakes of Mw 7.7 or greater and inferred seismic gap areas that could be sites of future tsunamigenic great earthquakes in the Indian Ocean. Source zones of 2004 and 2005 earthquakes in Sumatra–Andaman zone. Rupture areas of past great earthquakes along Sumatra. The southern Sumatra zone is a possible site for future great earthquake. Krakatau volcanic eruption, 1883 (Source: Simkin & Fiske, 1983). Geophysical data coverage over the ECMI (thin solid lines represent cruise tracks over ECMI and Bengal Fan). Bathymetry map of ECMI. Bathymetry sections of ECMI. (a) Magnetic anomaly map of Cauvery basin, with structural interpretation (contour interval: 20 nT). (b) Schematic cross section of basement along Profile A–B of Cauvery Basin. Free air gravity anomaly map of Cauvery offshore basin (contour interval 10 mGal). FZ1 and FZ2 are the inferred faults. Location and focal mechanism of the Pondicherry earthquake are shown (Murty et al., 2002). (a) Bathymetry map of Cauvery offshore basin (F1 and F2 are fault trends inferred from Figure 4(a)). (b) Bathymetry sections of Cauvery offshore basin (horizontal scale: 1 cm = 15 km) (horizontal distance in cms as measured from Figure 4(a)). Bathymetry map of Cauvery offshore basin (Murty et al., 2002), dashed lines indicate ship tracks along which bathymetry and gravity data were acquired. Black dot in the offshore indicates the location of Pondicherry earthquake (Mw 5.5) of 25 September 2001. MBA: Moyar–Bhavani–Attur lineament; PCL: Palghat–Cauvery Lineament. Map of Indian Ocean rim countries affected by the December 26, 2004 Indian Ocean Tsunami due to M9.3 earthquake off the coast of Sumatra. M8.7 earthquake on March 28, 2005 which occurred 250 km south of December 26 event is also shown. (Source: http://www.USGS.gov, adapted and modified.) Map showing different tectonic plates and locations of subduction zones (solid lines) and mid-oceanic ridges (zig-zag lines). Red dots are volcanoes. (Source: www.usgs.gov) Epicenters of the earthquakes of M > 7.0 for the Indian Ocean are shown with different colors of varying depths. Two sources of tsunami generation, Andaman–Sumatra in the east and Makran coast in the west are shown by ellipses. (Source: http://www.USGS.gov, adapted and modified.) Map showing tectonics of the Indo-Australian plate viz-a-viz Burma and Sunda plates. Yellow and Red stars show the epicenter of M9.3 earthquake on

4 5 6 12 20 21 22 25 26

27

29

33 35

36


xvi

Figures

December 26, 2004 and M8.7 on March 28, 2005. Solid arrows are direction of the movement of the Indo-Australian plate. Aftershocks are shown in yellow circles. (Source: http://www.USGS.gov) 3.5 (a) Reference map showing the locations of the principal geological features in the Indian Ocean. The red star marks the location of the initiation of rupture of the great Sumatra–Andaman earthquake. Brown lines show active and fossil plate boundaries. Arrows show the relative plate motions. The age of the incoming oceanic plate is shown with colors in millions of years. (b) Distribution of the apparent thermal age which results from the seismic inversion using the thermal parameterization. It is defined as the lithospheric age at which a purely conductive temperature profile would most closely resemble the observed thermal structure (after Ritzwoller et al., 2005). 3.6 Map showing rupture areas of four great earthquakes in the subduction zone from Andaman and Nicobar Islands to Sunda trench. Star shows epicenter of December 26, 2004 earthquake of M9.3 (figure from http://www.drgeorgepc.com). 3.7 (a) Makran subduction zone west of Karachi, Pakistan. (b) Vulnerability of the Indian west coast to the tsunami generated in Makran coast (figures from http://www.drgeorgepc.com). 3.8 Tsunami run-up heights along the east coast of Tamil Nadu. Numbers in the figure are tsunami heights in meters. 3.9 A shore-normal beach profile at Devanaampatnam (11◦ 44.589 N 79◦ 47.289 E). The sea level shown in the figure is the level at 9 a.m. IST on December 26, 2004, the time of tsunami attack. 3.10 Water marks in house in Devanaampatnam (photograph: R.K. Chadha). 3.11 A Bathymetry profile along 13◦ N, south of Pulicat lake. 7.1 Tide gauge record at Hanasaki, Japan, showing a tsunami forerunner (Nakamura and Watanabe, 1961). 7.2 Tide gauge records showing tsunami forerunners at some locations on the Pacific coast of Canada for the 1960 Chilean and the 1964 Alaska earthquake tsunamis (Murty, 1977). 8.1 The four global oceans. 8.2 The area in the Indian Ocean in which the tsunami energy propagated on 26 December 2004. 8.3 The rupture process according to Stein and Okal (2005). 8.4 Spheroidal normal mode 0 S3 . The amplitude of the mode is greatly exaggerated (from Lomnitz and Nilsen-Hofseth, 2005). 8.5 The directions of minimum and maximum energy (from Lomnitz and Nilsen-Hofseth, 2005). 8.6 Simulated snapshot of tsunami consisting of reconstructed peaks and troughs that formed in the Indian Ocean at a moment 1 h, 55 min after the earthquake struck (from Wilson (June 2005) http://www.physicstoday.org). 9.1 Definition sketch for two-layers profile. 9.2 Sketch of initial and boundary (periodic) conditions. 10.1 Spatial grid distribution in the spherical system of coordinates. 10.2 Ocean bathymetry. Computational domain extends from 80◦ S to 69◦ N. 10.3 History of tsunami propagation. Generated by bottom deformation at T = 40 s this tsunami experiences significant transformations and reflections. Black dashed lines denote bathymetry in meters. Numbers for the bathymetry in the figure should be multiplied by 10.

37

38

39 40 41 42 43 44 74 75 82 83 83 85 85 86 92 94 99 101

103

Figures 10.4 10.5 10.6


10.7 10.8 10.9 10.10 10.11

10.12 10.13 10.14 10.15 10.16 10.17 10.18 10.19 10.20 10.21 10.22 11.1 11.2 12.1 12.2 12.3 12.4

Tsunami signal propagating from the generation domain into the open ocean. Initial box signal of 20-min period is followed by the signal reflected from the shelf break and signal radiated from the shelf domain. December 26, 2004 Sumatra earthquake uplift as constrained by tsunami travel times. The source function. Maximum uplift is 507 cm and maximum subsidence approximately 474 cm. Coordinates are given in geographical degrees. Point (0,0) is located at 89◦ E and 1◦ N. Distribution of the tsunami amplitude in the Indian Ocean at 2 h 50 min from the tsunami onset. The wave reflected from the India and Sri Lanka propagates back to the source region. Distribution of the tsunami amplitude in the Indian Ocean at hour 4 from the tsunami onset. Along with the reflection shown in Figure 10.7, the reflection from the Maldives also sends energy eastward. Sea level recorded at Cocos Island on December 26, 2004. A birds-eye view of the IOT at time 9 h 25 min from the tsunami onset, looking from Africa toward India and Indonesia. Trapped tsunamis around continents and islands still display a strong signal. Sea level pattern generated by the IOT of December 26, 2004 at 30 h 40 min from the onset. Tsunami signals in the Northern Atlantic and Southern Pacific have been reorganized into coherent waves after passing through the narrows between Africa and South America, and Australia and Antarctica. Maximum modeled tsunami amplitude in the Indian Ocean. Maximum modeled tsunami amplitude in World Ocean. Residual maximum amplitude in World Ocean. Energy flux vectors over the South Pacific ridge at time 26 h 20 min. Colors denote sea level. Dark-brown lines denote the ridge depth – 3000 m depth contour. Southward directed energy flux through the E–W cross-section located in the Indian Ocean along 10◦ S from 80◦ E to 105◦ E. Energy flux through the cross-sections located between Antarctic and major continents. Along 20E from Antarctica to South Africa (AS) (light shading); along 140◦ E, from Antarctic to Australia (AA) (dark shading). Travel time (in hours) for the tsunami of 0.1 cm amplitude. Travel time (in hours) for the tsunami of 0.5 cm amplitude. Observations and computations from the four stations in the Indian Ocean. Ground track of Jason-I and computed tsunami amplitude at 2:55 UT on December 26, 2004 in the Indian Ocean. Computed and observed tsunami amplitude along the Jason-I track. Upper panel: source function given in Figure 10.1. Lower panel: source function orientation and width adjusted. The sea state at 5, 30, 60, 120, 180, 240, 300, 360, 420, 480, 600 min in Indian Ocean (Yalciner et al., 2005). The observed run-up distributions along the east coast of India and comparison with model results (Yalciner et al., 2005). Map of Indonesia (www.worldatlas.com). Andaman and Nicobar Group of Islands (map by ANCOST, NIOT, Chennai). (a)–(d) Real shore profiles of a few Andaman and Nicobar Group of Islands (by ANCOST, NIOT, Chennai). Location map of the study area of the Tamil Nadu coasts (www.sthjournal.org/241/chand.pdf).

xvii

104 105 106 107 107 108 108

109 110 110 111 112 113 114 115 116 117 118 119 127 128 132 133 134 136

xviii

Figures

14.1

Resonance characteristics of a system with a single degree of freedom (Raichlen, 1966). Tsunami travel times in hours (annotation “s” does not stand for second) Yalciner (2005). Maximum wave amplitude for the Global Ocean. Arrival time of first wave of the tsunami for the Global Ocean. Maximum tsunami wave height (cm) in the Indian Ocean. Arrival time of first wave in the Indian Ocean. Observed versus model wave arrival times. Computed and observed inundation in Banda Aceh Indonesia from http://www.wldelft.nl/cons/area/ehy/flood/tsunami.html. Tsunami amplitudes at Banda Aceh (Indonesia), Galle (Sri Lanka), Madras (now Chennai, India). Maximum water elevation. Grids used in the model. Computed maximum water elevation in the Indian Ocean. Geographical map of the Indian Ocean (Source: http://mapsherpa.com/tsunami/). Illustration of the antinode with highest positive amplitude at quarter wavelength of a sine wave. Illustration of the phenomena of Helmholtz resonance in harbours. (a) Tsunami waves reaching Kerala after first diffracting around Sri Lanka and travelling northward and getting reflected from Lakshadweep Islands (for illustrative purposes only, not to scale; basemap adapted from www.mapsofindia.com). (b) Tsunami waves reaching Kerala after being reflected from the coast of Somalia (for illustrative purposes only, not to scale; basemap adapted from www.wikipedia.com). Tsunami tidal interaction (personal communication, Prof. Z. Kowalik, 2006). Amplification of the tsunami at the ocean surface through coupling with internal waves. Tidal amphidromic point in the Arabian Sea. Maximum tsunami amplitudes (m) in Sabang and Banda Aceh area. Maximum tsunami amplitudes (m) in centre of Banda Aceh area. Maximum tsunami amplitudes (m) in West Coast of Banda Aceh area. Maximum tsunami amplitude (m) in Sigli area of Banda Aceh. Maximum tsunami amplitude (m) in Khao Lak (north part) in Thailand. Maximum tsunami amplitude (m) in Phuket beach area in Thailand. Maximum tsunami amplitude (m) in Phi Phi Don area in Thailand. Maximum tsunami amplitudes (m) in Sri Lanka. Maximum tsunami amplitudes (m) in Indian east coast area. Maximum tsunami amplitudes (m) in the Maldives. Location of the epicenter of the main shock of the 26 December 2004 mega-thrust earthquake in Banda-Aceh, Sumatra and the aftershocks. Also shows past seismicity of the region. Tectonics of the region around the epicenter of the devastating earthquake on 26 December 2004, the plate margin, where the India plate is being subducted beneath the Burma plate, along the Sunda trench. This active plate movement generates numerous earthquakes along the entire plate margin. The zone of plate movement stretches up to the Himalayan belt and results in the uplift of the Himalayan range.

15.1


15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 15.11 17.1 17.2 17.3 17.4

17.5 17.6 17.7 17.8 17.9 17.10 17.11 17.12 17.13 17.14 17.15 17.16 17.17 19.1 19.2

152 160 161 162 162 163 163 164 167 168 169 170 186 186 187

187 188 189 190 200 201 202 203 204 205 206 207 207 208 216

217

Figures xix


19.3

Schematic model showing the generation of pre-earthquake thermal anomaly and detection by thermal remote sensing and meteorological stations in the ground. 19.4 Concentration of positive charges (denoted by “+” sign) on the surface of the butterfly net, especially at the apex (maximum positive curvature). If the net is inverted by pulling up the thread, charges have the tendency to move towards the new outer surface. 19.5 NOAA–AVHRR data derived LST time series maps for the region around the epicentral region of the 26 December 2004 Sumatra earthquake. A thermal anomaly developed before the earthquake and went away along with the event. The LST was seen to be maximum on 25 December 2004, just one day before the earthquake. 19.6 Seawater turbidity observed through NOAA–AVHRR data sets induced by the almost 1300 km fault rupture, which caused the great earthquake on 26 December 2004. 19.7 Turbidity observed through MODIS data sets near coasts in Sumatra induced by the tsunami after the great earthquake on 26 December 2004. 20.1 Standard and extreme ARDC atmospheres (Harkrider, 1964). 21.1 Track of DEMETER orbit on March 23, 2005 when the satellite was above the Sumatra region. Stars indicate the epicenters of the earthquakes. 21.2 From top to bottom the panels successively show the electron density, electron temperature, spectrogram of an electric component between 0 and 2 kHz and earthquakes seen by DEMETER along the orbit. The data are presented as a function of the universal time (UT), The local time (LT), geographic latitude and longitude values are also given. 21.3 Spectrogram of ELF electric waveform above the latitude in which earthquake occurred obtained using Level 1 burst mode data for the orbit shown in Figure 21.1. 21.4 Three hourly Kp values for March 23, 2005. 21.5 Track of DEMETER orbit on March 26, 2005 when the satellite was close to the Sumatra region. 21.6 Data recorded by DEMETER along the orbit shown in Figure 21.5. The top panel shows the electron density, the middle panel shows the ion density and the bottom panel gives the earthquakes “seen” by the satellite. At the bottom, UT, LT, geographic latitude and longitude values are indicated. 21.7 Three hourly Kp values for March 26, 2005. 21.8 Track of DEMETER orbit on July 6, 2005 when the satellite was above the Indonesian region. Stars indicate the epicenters of the earthquakes. 21.9 The top panel gives the spectrogram of an electric component between 0 and 400 Hz and the bottom panel gives the earthquake information. At the bottom, UT, LT, geographic latitude and longitude values are indicated. 21.10 Spectrogram of ULF/ELF electric waveform above the latitude in which earthquake occurred obtained using Level 1 burst mode data for the orbit shown in Figure 21.8. 21.11 Three hourly Kp values for July 6, 2005. 22.1 (a) Top portion of the gauge’s mounting structure, where battery, electronics, solar panel, and cellular modem are fixed (after Prabhudesai et al., 2006). and (b) Illustration of NIO sea-level gauge installed at Verem Jetty, Mandovi estuary, Goa, India (after Prabhudesai et al., 2006). 22.2 Schematic diagram illustrating implementation of realtime coastal sea-level data reception utilizing GPRS technology (after Prabhudesai et al., 2006).

219

220

222 223 224 229 237

238 239 240 240

241 242 242 243 244 244

252 254

xx

Figures

22.3 22.4


23.1 23.2 23.3 23.4 23.5 23.6 24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8 26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9 26.10

26.11 26.12 26.13 26.14

Display of predicted fair-weather sea-level, observed real-time sea levels, and residuals from Verem jetty (Mandovi estuary), Goa, India (after Prabhudesai et al., 2006). FTP up-load time during a period of 24 h for a 100 kb test data (after Prabhudesai et al., 2006). Sea level gauge network for the PTWS (McCreery, 2005). Tsunami run-up detectors used by the PTWC (McCreery, 2005). DART systems that were in operation for the Pacific Ocean (Bernard, 2005). The DART system as deployed in the ocean (Bernard, 2005). Schematic diagram of plane-wave incident on a cylindrical island. Input is trace X , response is trace Y . (Reid and Knowles, 1970). A simulated satellite picture of the Indian Ocean tsunami of 26 December 2004 (Wilson (June 2005) http://www.physicstoday.org). 250 locations in 35 countries for which tsunami travel time charts are prepared. Epicenter locations of the past earthquakes that generated tsunamis, which had some impact in the Indian Ocean. Tsunami travel time chart for a location in the Rann of Kutch in India. Tsunami travel time chart for a location off the coast of Sri Lanka. Tsunami travel time chart for a location in the Bay of Bengal. Tsunami travel time chart for a location in the Andaman Sea. Tsunami travel time chart for the city of Cota Raja, Banda Aceh in Indonesia. Tsunami travel time chart for a location in the Indian Ocean. (a) Phuket, Thailand and (b) Khao Lak, Thailand, visited during reconnaissance investigations. (Figures reprinted from Mapsoft world, 2005, Khao Lak Promotions.) Coastal erosion in Rawai Beach on Phuket Island, Thailand. Damage to (a) roof tiles and (b) timber columns, Kata Beach on Phuket Island, Thailand. Damage to first-story masonry walls, Patong Beach on Phuket Island, Thailand. Damage to buildings in Nai Thon Beach on Phuket Island, Thailand. Extensive damage to columns, masonry walls and roofs of low-rise buildings in Khao Lak Beach, Thailand. (a) Damage to the harbor and (b) boat floated inland, just north of Khao Lak Beach, Thailand. Damage to buildings in Phi Phi Island, Thailand. Wave pressure as per: (a) equation (26.1) (Goda, 1995) and (b) equation (26.2) (Hiroi, 1919). Comparisons of lateral forces due to earthquake, wind, and tsunami for an interior frame of a 6-story reinforced concrete building in Vancouver, Canada for 5.0 m tsunami water height, 6.0 m transverse span length and seismic force reduction factor of R = 4.0. Damage to timber frame structures in Thailand. (a) Damaged wall exposing masonry units in Patong Beach; (b) typical 50 mm thick concrete block masonry units; (c) and (d) construction of confined masonry in Khao Lak harbor town. Typical punching failure of masonry walls: (a) Kamala Beach and (b) Phi Phi Island. (a) Column failures in a 2-story reinforced concrete frame units in Khao Lak Beach and (b) Nominal moment-axial force interaction diagram for a 200 mm square column with 0.5% reinforcement and approximate moments imposed due to assumed tsunami pressure.

255 255 260 261 262 263 265 267 274 282 288 288 289 289 290 290 298 298 299 299 300 300 301 301 302

303 304 304 305

305


Figures xxi 26.15 (a) and (b) Column failures in Khao Lak Beach; (c) and (d) frame damage on Phi Phi Island. 26.16 Non-engineered concrete frames that survived the tsunami in Khao Lak Beach. 26.17 Engineered reinforced concrete frame buildings: (a) and (b) on Phi Phi Island; (c) in Nai Thon Beach; (d) in Khao Lak Beach, that survived the tsunami without structural damage. 26.18 Damage to reinforced concrete frame buildings in Nai Thon Beach. 26.19 Damage to reinforced concrete frame building under construction in Nai Thon Beach. 26.20 (a) and (b) Damage to precast slab strips in Phaton Beach shopping center; (c) Close-up view of a precast slab strip; (d) lifting of precast concrete slab due to water pressure in Nai Thon Beach. 26.21 Damage to precast slab strips of the concrete dock in Khao Lak. 26.22 Soil erosion and related foundation problems: (a) buildings in Kamala Beach and (b) a building in Nai Thon Beach. 26.23 Destruction of residential timber framed construction in Banda Aceh. 26.24 Tsunami damage to non-engineered reinforced concrete buildings in central Banda Aceh. 26.25 Impact loading on columns due to floating debris, Banda Aceh. 26.26 Impact of fishing boats on buildings, Banda Aceh. 26.27 Power generating vessel that floated 3.5 km inland in Banda Aceh. 26.28 Timber framed structures in Banda Aceh. 26.29 Punching failure of masonry infill walls under tsunami pressure, Banda Aceh. 26.30 Damage to non-engineered reinforced concrete framed buildings, Banda Aceh. 26.31 Non-engineered reinforced concrete framed buildings that survived the tsunami. 26.32 Engineered reinforced concrete framed buildings that survived tsunami in downtown Banda Aceh, away from the coastal region. 26.33 A single-story house, displaced by water pressure due to lack of proper anchorage, Banda Aceh. 26.34 Displaced fuel tanks due to tsunami water pressure that were swept by half a kilometer, also destroying houses in their way, Banda Aceh. 26.35 The failure of a steel truss bridge in eastern Banda Aceh. 26.36 (a) and (b) The failure of a precast concrete bridge near downtown Banda Aceh and replacement by a temporary bridge. 26.37 Multi-span reinforced concrete bridges in eastern Banda Aceh, crossing the same river; (a) a bridge close to the ocean that was completely swept off by the tsunami and (b) a bridge approximately 3 km away from the ocean that survived the tsunami. 26.38 (a) A 3-span reinforced concrete bridge in Banda Aceh that was displaced on its abutments due to tsunami and/or seismic ground shakings and (b) close-up view of the separation of girders at a pier. 27.1 Location map. 27.2 Run-up level along the Kerala coast (after Kurian et al., 2006). 27.3 Beach profile stations. 27.4 SLED profiles across two stations off Chavara. 27.5 Bathymetric changes along Arattupuzha–Thangasseri coast. 27.6 Distribution of sand in the inner shelf (a) during 1987 and (b) during 2005. 27.7 Bathymetric changes along the TS canal.

306 307 307 308 309 310 310 311 312 312 313 313 314 314 315 316 317 317 318 318 319 319

319 320 324 326 328 328 329 333 334

xxii 28.1 28.2 28.3


28.4

28.5 28.6 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 30.1 30.2

30.3 30.4 30.5 30.6 30.7 30.8 31.1

Figures Indian Remote Sensing Satellite (IRS) imageries of the Kerala coast, captured before and after tsunami. (a) During January 2004 using IRS 1D and (b) December 27, 2004. (a) Selected transects and stations. (b) Isolines of various physical parameters, January 2005: (i) temperature in ◦ C, (ii) pH, (iii) salinity, and (iv) dissolved oxygen. Isolines of various nutrients. (µmol/l). (a) Nitrite – January 2005, (b) nitrite – May 2005, (c) nitrate – January 2005, (d) nitrate – May 2005, (e) phosphate – January 2005, and (f) phosphate – May 2005. Isolines of various biological parameters. Primary productivity in mgC/m3 /h for (a) pre-tsunami, (b) January 2005, and (c) May 2005. Chlorophyll-a in mg/m3 for (d) pre-tsunami, (e) January 2005, and (f) May 2005. Zooplankton biomass in ml/m3 for (g) pre-tsunami, (h) January 2005, and (i) May 2005 periods. Textural variations in sediments off 25 km – Vizhinjam. Latitudinal depth profile along Muttam to Kolachel transect, note the channelized flow at 8.03 latitude. Location map. Coastal geomorphology of the Kanyakumari District. (a) Map showing the inundation between Arokiapuram to Dharmapuram, (b) Map showing the inundation between Rajakkamangalam to Colachel. Impact of tsunami on the beach profile along the study area. Proportion of erosion and accretion of beach volume due to tsunami along the study area. Physical damages along the Kanyakumari District. (a) Impact of tsunami in the pH level along the Kanyakumari District, (b) Impact of tsunami in the TDS level along the Kanyakumari District. Tsunami vulnerability map of the study area. Time series (hourly) data on (a) temperature (◦ C) and (b) salinity (psu). Average profiles of (a) temperature (◦ C), (b) salinity (psu), (c) density (kg/m3 ), (d) sound velocity (m/s) and (e) Brunt Vaisala frequency (N 2 ; cph) based on the above data (solid line). Profiles from Levitus for the month of January are plotted (dotted line). Variations of (a) temperature (◦ C), (b) salinity (psu) and (c) density (kg/m3 ) along the transect off Visakhapatnam harbour on 8 January 2005. Variations of (a) temperature (◦ C), (b) salinity (psu) and (c) density (kg/m3 ) before (20 December 2004) (solid line) and after (7 January 2005) (dotted line) tsunami. Time series data (2 min interval) on temperature (◦ C) direction and speed (m/s) of the current, U and V components at (a) 10 m and (b) 60 m below surface. Spectral analysis of temperature (2 min interval) at (a) 10 m and (b) 60 m depths at the above location. Changes in temperature (◦ C) and salinity (psu) in the top layer as seen from the Argo data before (20 December 2004) (solid line) and after (26 December 2004) (dotted line) tsunami. Vulnerability of the Indian coast for the damages due to tsunamis/storm surges, inferred from the shoreline displacement for 1 m rise in sea level (Shetye et al., 1990). Schematic representation of the duration of a natural hazard and its impact on life and property per unit time (based on Krishna, 2005).

340 341 344

345 347 347 352 353 354 357 357 358 360 361 366

366 367 368 368 369 370 371 374

Figures xxiii


31.2

(a) Study area (box-S) showing southeast Asian countries affected by tsunami on 26 December 2004. (b) Study area in detail. The epicentres of earthquakes are marked with star/numbers – 1 for the disaster on 26 December 2004 and 2 for 28 March 2005. Box-T is the region for which time-series data (daily and 8-day) of and SST were examined. Provinces of Indonesia labelled: Aceh, N.S: North Sumatra, S.S.: South Sumatra, W.S.: West Sumatra, Riau and Jambi. 31.3 Cruise track and sample location map of the study area (based on Murthy, 2005). 31.4 Spatial distribution of chlorophyll a (mg/m3 ) (derived from MODIS) in the Indian Ocean during December 2004. Position of the earthquake on 26 December 2004 was indicated with red star in Figure 31.4(d). The circles in Figure 31.4(a,b) show high on northeast of Sumatra Island. Regions X and Y (Fig. 31.4(d)) represent changes in the coastal chlorophyll associated with tsunami waves. The interruption of satellite coverage (white patches over sea surface area) is due to cloud cover. 31.5 Spatial distribution of chlorophyll a (mg/m3 ) during January 2005. Circles 1 and 2 are the phytoplankton blooms. 31.6 Time-series data: (a) Daily concentrations of chlorophyll a derived from MODIS. Line-T passing through the bars is the trend line. Discontinuity of graph could be noticed due to missing values. Numbers 1, 2, 3, and 4 are the peaks of concentration during the events of earthquakes. (b) Comparison of (8-day average) among 3 years. P is the maximum encountered between mid of January and February during 2002–2003 and 2003–2004. (c) and SST during October 2004–May 2005. The dates of earthquakes are indicated with down arrows in all panels. 31.7 SST in the period of tsunami. The position of earthquake was indicated with red star in Figure 31.7(b). Downward arrow (Fig. 31.7(c)) denotes the gradient of lowering temperature from northeast to the southeast coast of India in Bay of Bengal. Variation of temperature close to the epicentre of earthquake was pointed with straight arrows. 31.8 Submerged coral beds, beach and forest area along the eastern coast of Southern Andaman Island near Baratang Island. 31.9 Map showing Malacca in Car Nicobar and settlement areas close to coast. 31.10 Returning wave of tsunami at Chennai, India. 31.11 Schematic representation of impact of tsunami on the various marine biotopes. 32.1 Circled areas indicate the severely affected coastal areas in (1). Andaman–Nicobar Islands and (2) southern east coast of India and north coast of Sri Lanka. 32.2 AWiFs data showing pre- (A) and post-tsunami (B) scenario in Nicobar Islands (a) Katchal, (b) Kamorta and (c) Trankati. 32.3 IRS-LISS III data showing north Chennai coast affected by tsunami waves. 32.4 Quick Bird data showing inundation of tsunami devastated Nagapattanam. 32.5 False color image showing high turbidity in the coastal waters of Andaman Islands on 27th December 2004. 32.6 The pre- and post-tsunami ocean color data showing increase in suspended particulate in coral reef areas of Andaman Islands on 27 December 2004. 32.7 Oceansat-OCM derived suspended sediment concentration along Pulicat Lake, Chennai coast during pre-tsunami (25 December 2004) and post-tsunami (27 and 31 December 2004).

375 375

376 377

378

379 381 382 383 383 394 394 395 395 396 396 397

xxiv

Figures


32.8

IRS-LISS III data showing the opening of Pichavaram inlet (2 and 4) and reaching of Vellar and Kollidam mouths (1 and 3) during pre- and post-tsunami. 32.9 The field photography showing damage to the coastal geomorphology and dunes erosion in MGR Tittu in Pichavaram due to tsunami wave runoff. 32.10 (A) Fishermen village houses damaged by tsunami waves in Pichavaram, (B) Tiruchendur, a temple town experienced retreat of sea during tsunami, (C and D) Along the coast of Mannakkudi (Kanyakumari District), the church and the bridges suffered damage where there was no seawall to protect them from tsunami waves. 32.11 Post-tsunami vulnerability ranking of coastal stretch of Tamil Nadu based on the slope, type of coast, presence of barriers and relative elevation, etc. 34.1 System of groins in the Chennai area. 34.2 Satellite imagery showing the shoreline advancement due to groin field in Kanyakumari district. 34.3 Suggested protection measure for the stretch of the coast at Pudukuppam in Parangipettai. 34.4 Proposed groins (thoondil valaivu) at Colachel jetty. 34.5 Proposed layout of groins from Nagore to Keechankuppam. 34.6 Rehabilitation of existing groins at Tranquebar coast. 34.7 Proposed shape of the sand dune at Palayur. 34.8 Proposed coastal protection measure at Palayur. 34.9 Proposed coastal protection measure at Thirumalaivasal. 35.1 Location of 24 stations along Tamil Nadu coast where post-tsunami surveys and beach profiles were carried out. 35.2 Map of Nagore–Velankanni stretch showing some of the coastal geomorphic and vegetal features. 35.3 Landscape changes before (November 1998) and after (April 2005) the tsunami: (a), Human occupation of dunes at Nagore (November/1998). (b) All huts and shacks flattened by the tsunami; only coconut groves survived (April/2005). (c), Crowded improvised structures on the beach opposite the shrine at Velankanni (November/1998). (d) Make-shift structures washed off in totality by violent waves (April/2005). 35.4 Profiles of the beach at five stations along Tamil Nadu coast. The arrow indicates run-up heights at each location. 35.5 Casuarina plantations served as excellent buffers against the tsunami onslaught at Nanjalingampettai (a) and at Karaikal (b); these trees remained intact all along the Tamil Nadu coast (April 2005). 36.1 Risk adequate premiums as a function of the size of the risk community. (Source: Menzinger and Brauner, 2002.) 36.2 Institutional structure for a catastrophe bond (cat bond). (Source: Stipple, 1998.) 37.1 The population health model. 37.2 Suggested schemata for the application of an eco-health approach to development. 37.3 Iterative research strategy for improving human health using a participatory and transdisciplinary approach (Forget, 1997). 38.1 The four global oceans. 38.2 The countries in and around the Indian Ocean. 38.3 250 locations in the Indian Ocean and adjoining region for which tsunami travel time charts have been prepared (Bhaskaran et al., 2005).

399 399

400 401 413 414 416 417 418 419 419 420 421 424 425

428 431 432 440 440 449 451 452 455 456 457

Figures xxv 38.4 38.5 38.6


38.7 38.8 38.9 38.10 38.11 38.12 38.13

Tsunami travel time chart for Rann of Kutch, India. Latitude 23.583◦ N; Longitude 68.367◦ E (from Bhaskaran et al., 2005). Tsunami travel time chart for a location off Sri Lanka: Latitude 8.570◦ N; Longitude 81.230◦ E (from Bhaskaran et al., 2005). Irregular triangular grid for a finite element model for a part of the Pacific coast of Canada and USA. Irregular triangular grid for a finite element model of the Queen Charlotte Islands of Canada. The Marching problem (Hyperbolic) (from Crandall, 1956). The Jury problem (Elliptic) (from Crandall, 1956). Method of characteristics (from Crandall, 1956). Schematic illustration of the tsunami numerical modelling concept for the Pacific Ocean. Schematic illustration of the tsunami numerical modelling concept for the Atlantic Ocean. Schematic illustration of the tsunami numerical modelling concept for the Indian Ocean.

458 458 460 460 462 462 465 467 467 468



Tables

1.1 1.2 2.1

List of tsunamis in Sumatra–Java region. List of tsunamis that affected Indian region and vicinity. Shelf/slope characteristics off selected places over the ECMI (Murthy et al., 1993). 3.1 Details of tsunami run-up surveys along the coast of Tamil Nadu. 8.1 Some of the fault parameters (from Kowalik et al., 2005). 10.1 Fault parameters used to generate vertical sea floor movement. 10.2 Observed and calculated travel time. 11.1 Some of the world’s destructive tsunamis of the Pacific and Indian Ocean. 12.1 Maximum water height and maximum inundation distance along the coasts of Indonesia during historical tsunamis. 12.2 Predicted time (t) required to travel from 1 m depth to 0 m depth and tsunami height (Hs ) near coastlines of Indonesia. 12.3 Maximum run-up level distance up to which seawater inundated inland during boxing day tsunami in Andaman and Nicobar Islands. 12.4 Predicted tsunami travel time (t) from 1 m depth to 0 m depth and tsunami height (Hs ) near coastline of Andaman and Nicobar Islands. 12.5 Few examples in Andaman and Nicobar Islands to show the improvement in tsunami height (Hs ) predictions when different slopes on land (Figure 12.3(a)–(d)) are considered. 12.6 Run-up level of sea water during 26 December 2004 Indian Ocean Tsunami at selected locations along Tamil Nadu coasts. 12.7 Prediction of travel time (t) from 1 m depth to 0 m depth and tsunami height near coastline for Tamil Nadu coasts for 26 December 2004 Indian Ocean Tsunami. 12.8 Inundation distance extent along the study area. 12.9 Predicted time (t) required to travel from 1 m depth to 0 m depth and tsunami height (Hs ) near coastline for 26 December 2004 Indian Ocean Tsunami. 12.10 Historical tsunami events and run-up levels in the Pacific and Atlantic oceans. 12.11 Predicted tsunami travel time (t) from 1 m depth to 0 m depth near coastlines and tsunami heights (Hs ) of historical tsunamis of Pacific and Atlantic oceans. 15.1 The fault data used to compute the tsunami source for simulation. 15.2 Fault parameters as used in the DCRC model. 15.3 Model parameters. 15.4 Fault parameters used to generate vertical sea floor movement. 15.5 Observed and calculated travel time. 17.1 Length of pendulum day at different latitudes. 17.2 Listing of observed tsunami arrival times and run-up. 19.1 Time of acquisition of NOAA–AVHRR GAC data used to prepare LST time series maps to study pre-earthquake thermal anomaly.

8 14 23 43 84 105 116 125 132 133 135 136 137 138 138 139 139 140 141 160 166 168 170 171 189 191 221

xxviii Tables 19.2 19.3 21.1


21.2 23.1 24.1 24.2 24.3 27.1 27.2 28.1 28.2 28.3 29.1 29.2 29.3 29.4 31.1 31.2 31.3 31.4 34.1 34.2 35.1 35.2 36.1 36.2 38.1

Time of acquisition of NOAA–AVHRR GAC data, used for analysis of seismically induced turbidity in the seawater by the mega-thrust earthquake of 26 December 2004. Time of acquisition of terra-MODIS data, used for analysis of tsunami induced turbidity in the seawater by the mega-thrust earthquake of 26 December 2004. Time, locations, depth and region of the earthquakes that occurred in the Sumatra region (from the web server http://www.iris.edu/seismon). Time, locations, depth and region of the earthquakes that occurred in the Indonesian region (from the web server http://www.iris.edu/seismon). Use of the data from DART systems in tsunami warning (Gonzalez et al., 2005). Number of locations in each country for which tsunami travel time charts are prepared. Locations in each country for which tsunami travel time charts have been prepared. Geographical coordinates and the source region of the epicenters used for the study. All longitudes are east and negative latitudes denote southern hemisphere. Run-up level and maximum inundation time along Kerala coast (after Kurian et al., 2006). Volume changes at different stations adjoining the Kayamkulam inlet (after Kurian et al., 2006). Comparison of physico-chemical parameters. Comparison of biological parameters. Granulometric data on sediments. Inundation extent and run-up level along the study area. Amount of accretion/erosion of beach volume (m3 ) due to the tsunami. Loss of life and properties due to the tsunami. Criteria adopted for the preparation of vulnerability map. Satellite based data on inundation of seawater in Nicobar Islands during tsunami. Impact of tsunami on mangrove stands of Andamans (based on Roy and Krishnan, 2005). Summary of observations made by dives on coral reefs. Impact of tsunami on aquaculture in peninsular India. Rate of erosion along the Tamil Nadu coast (Public Work Department, Tamil Nadu, 2002). Area of beach in-between groins 5 and 6. State of coastal landforms along Nagore–Velankanni sea front of Tamil Nadu in November 1998, and landscape changes and impacts recorded after the tsunami of December 2004. Monetary loss (crops, property and infrastructure) incurred and deaths reported as a consequence of some of the extreme events along the Indian coasts during the last 53 years. Populations affected by the tsunami. Science-based and people-based preparedness systems. Tsunami characteristics of the four oceans.

221 221 237 242 264 274 275 282 330 331 343 346 346 355 355 359 361 382 386 387 388 412 414 426 429 437 443 466


Foreword

The tsunami of 26 of December of 2004 in the Indian Ocean, with its sequel of death and destruction, showed us nature at its horrendous worst. It will take years, if not decades, for the region to recover fully from the loss of livelihoods and the negative effects on development efforts. But the tragedy also gave us the opportunity to see human nature at it best. Immediately after the disaster, the Secretary General of the UN, Kofi Annan, issued an appeal to the solidarity of the world. The response to this call was unprecedented in the record of humanitarian missions of the UN. Nations, International Organizations, private industries, individual citizens, rich and poor – all did contribute to this magnanimous response. We have the knowledge; we have the science and the technology to mitigate the impact of this and other natural disasters. If a tsunami warning system, like the one existing in the Pacific Ocean since 1965,would had been in place, much of that damage would have been prevented. This is the hard lesson of the Tsunami of 2004. The Science of tsunami is still growing, as all science does. The learning never ends or stops. It is the role and mission of scientists, to constantly push the outer boundary of knowledge. But at any given time, science, what we know from theory and experience, can always be applied for the benefit of humankind. The application itself may not constitute science sensu stricto; it may be something else – it is designing a tool to do a job. The more we know, the better will be the tool, but the will to build the tool must be there. For that we need scientists, engineers and technicians that humbly assume this less glamorous task of putting science to work. The architecture of the international tsunami warning system now being put in place in the Indian Ocean under the leadership of the Intergovernmental Oceanographic Commission of UNESCO, is composed of two different networks: the upstream detection network of instruments, seismographs, sea-level gauges and deep ocean pressures sensors, and the downstream network of national tsunami centres, in charge of delivering the warnings to the people at risk with at least one national centre in each participating nation. In a minimal configuration, the national tsunami centre must have the operational capability of receiving warnings 24 hours a day, 7 days a week, and of disseminating these warnings both to the responsible authorities and to the general public. National tsunami centres must also be capable of defining national preparedness procedures and of putting in place national education and awareness plans. A timely, cent-per-cent accurate and precise warning will not provide any protection if the information doesn’t reach in time the people at risk and the people do not know how to respond to the emergency. Early warning is thus as much an issue of “soft” organizational technology, communication and community based systems, as it is of “hard” science and technology, numerical modelling and instrumental networks. In our experience, the real effectiveness of such a system is achieved when national centres move away from this minimal configuration, and start to develop their own national detection networks and risk-assessment protocols. These developments take time and require sustained efforts at both the national and international levels. One of the editors of this book, Tad S. Murty, published in 1977 a pioneering book entitled “Seismic Sea Waves: Tsunamis”, that has been extensively used in many parts of the world as a


xxx

Foreword

training tool. What has happened in the Indian Ocean in recent months furnishes many examples of actions taken at the community level, with the support of a wide variety of national and international organizations, many of them NGOs. But we must recognize that building national preparedness is the most difficult part of establishing early warning systems. In this new book “The Indian Ocean tsunami”, co-edited with U. Aswathanarayana and N. Nirupama, these scholars are giving us further demonstration of their deep-rooted concern on the importance of using science for the public good. The many contributions collected in this volume, give a thorough account of the different aspects of Indian Ocean Tsunami of December 2004. The wealth of information contained in these pages will certainly contribute to improve the design of the end-to-end systems needed for providing true protection from tsunami hazard to the populations living around the Indian Ocean rim. Through the acknowledgement to all those contributing to make this book, we also wish to thank all the scientists, technicians, professionals and engineers that during the last 18 months have volunteered their work to this noble cause. Patricio A. Bernal Executive Secretary of IOC Assistant Director-General of UNESCO Paris, July 2006.


Prologue

The 2004 Indian Ocean Tsunami was a great catastrophe. The tsunami directly affected the coastlines of the Indian Ocean, and the event was recorded by coastal tide gauges around the world. The loss of life, property and livelihoods was horrific. But, the response to the disaster has been dramatic, both in terms of support from individuals and nations from around the world and by scientists around the Indian Ocean and elsewhere. In the immediate aftermath of the tsunami, scientists worked together to find support and launch field surveys around the Indian Ocean. Scientists made field observations and surveyed run-up and inundation to provide important constraints for numerical modeling of the tsunami, then underway. Engineers visited sites of destruction along the coastlines of many countries and observed the destruction of man-made structures brought by a major tsunami. And, unfortunately many individuals lost their lives, particularly women and children, and others were permanently affected by the trauma associated with the loss of lives, injuries, loss of homes and property and the loss of their livelihood. This volume is the product of the energy and talent of many scientists within the region and outside the region who are dedicated to achieving a better understanding the phenomena of tsunami. Expertise involves specialists in the areas of: seismology, oceanography, tsunami science, structural geology, tectonics, sedimentology, geomorphology, hydrology, and many related fields of study. Their aim is the same: to better understand how tsunami are generated, how they propagate across the ocean, how the tsunami waves change when they reach shallow water and how they flood onto the coastline and inundate the land. These studies aim at increasing our understanding of tsunami, improving our capability to predict tsunami, identify ways to mitigate damage, and ultimately to save lives. It is very rewarding to see Indian Scientists writing about the Indian Ocean Tsunami. We hope the collaborations between scientists will continue in the future. The reports in this volume are integrated and reviewed by the editors. All tsunami scientists will benefit from the work described in this volume. I thank all of the contributors to this volume and the editors for a job well done. Your work will save lives during the next tsunami. Aloha, Dr. Barbara H. Keating University of Hawaii, Marine Geologist and President of the Tsunami Society June 5, 2006



Preface

The purpose of the volume is to develop methodologies for the prediction of, and preparedness for, the tsunamis per se, on the basis of the knowledge obtained from a study of the Indian Ocean Tsunami (also known as the Asian Tsunami or the Sumatra Tsunami) of December 26, 2004. On the basis of the analysis of seismological data, hydroacoustic signals, geodynamic environment of genesis, magnetic images of the crust of the Sumatra region, Global Position System (GPS) analyses, etc., it has been found that the Sumatra earthquake which had a magnitude Mw of 9.3, energy of 1.1 × 1017 Nm, occurred at a depth of 20–30 km. close to Indonesian forearc. The earthquake rupture had a maximum length of 1200 km along the interface between the IndoAustralian and Burmese plates. There was a 20 m displacement of the fault plane, and the sea floor thrusted up several metres. The earthquake appears to have produced a recognizable pole shift, and a small change in the length of the day, and oblateness of the earth. Jason I altimetry satellite could detect the tsunami wave. The tsunami affected 12 countries from Indonesia to Somalia, and killed 176,260 people. The number of people missing is 49,682, and the number of persons displaced is 1,726,270 (Science, August 12, 2005). The tsunami destroyed billions of dollars worth of property, and caused horrendous human suffering. Indonesia suffered the greatest damage as the epicenter of the earthquake, and area of initiation of the tsunami are located there. There is a scientific explanation for the linear path of the tsunami – why it affected Sri Lanka and the Tamilnadu coasts, but not Bangladesh and Orissa coasts. Singh (Nature, 2005) showed that as a consequence of the existence of a lithosphere-scale boundary around the Simeulue Island which continues upto the east of Nicobar Island, the December 26, 2004 earthquake rupture which seems to have been initiated west of this boundary, did not cross the boundary to the east, but got propagated northwards upto the Andaman Islands. The same boundary also explains why the after shocks of Mw 9.3 earthquake of December 26, 2004 and Mw 8.6 earthquake of March 28, 2005 did not overlap. The design of a cost-effective strategy for the warning and preparedness for tsunamis has to take into account two attributes of the tsunami, namely, its genesis and its impact. Tsunami is triggered by earthquakes, volcanism, submarine landslides, etc., and hence it can be conveniently dovetailed with the existing administrative structures for earthquake disaster management. A tsunami is akin to a tidal wave in its impact on the coasts, and can hence be treated as an add-on to tidal wave warning systems. The volume seeks to provide the knowledge base needed for the purpose. In order to predict the future occurrence of tsunami, and to design warning and preparedness systems for the purpose, we need to understand why the tsunami got generated where, when and how it got generated, and why and how it could cause so much devastation as it did. The volume is structured to seek answers to these questions: Part 1: Geostructural environment of tsunami genesis – the sites wherefrom the future tsunami could be generated; Part 2: Modeling of the tsunami generation and propagation – how will such tsunamis be expected to move, Part 3: Tsunami detection and monitoring systems – how to use the precursors to enhance the advance warning time, how to detect the tsunami when it occurs, how to communicate the warning to the


xxxiv

Preface

populations likely to be affected, and how to get it implemented; Part 4: Biophysical and socioeconomic dimensions of tsunami damage – how the variation in the severity of tsunami damage at various sites is determined by the geophysical, ecological and socioeconomic ambiences of the sites and Part 5: Quo Vadis – Where do we go from here. Preparedness systems based on dual-use technologies. The Editors are grateful to Dr. Patricio Bernal, Executive Secretary, Intergovernmental Oceanographic Commission andAssistant Director General of Unesco, Paris, for his perceptive Foreword, and to Dr. Barbara Keating, President of the Tsunami Society, Honolulu, for her appreciative Prologue. The knowledge base contained in the volume is relevant not only to the Indian Ocean countries, but also globally. It will be useful to university students, professionals and administrators concerned with seismology, ocean science, meteorology, disaster management, coastal management, etc. The impetus for the volume came from the Brain Storming Session (regarding the Indian Ocean Tsunami of December 26, 2004), New Delhi, India, January 21 and 22, 2005, organized by the Department of Science and Technology and the Department of Ocean Development, Government of India, under the aegis of the Indian National Science Academy. One of us (TSM) is grateful to the Government of Canada for associating him with the various authorities concerned with the Indian Ocean Tsunami. Tad S. Murty U. Aswathanarayana N. Nirupama


Part 1

Geostructural environment of tsunami genesis


CHAPTER 1

A Historical Account of the Earthquakes and Tsunamis in the Indian Ocean


B.K. Rastogi National Geophysical Research Institute, Hyderabad, India

1.1

INTRODUCTION

A catalog of tsunamis in the Indian Ocean during the period 326 BC to 2005 AD has been compiled. Possible source zones of large tsunamigenic earthquakes in the Indian Ocean have been identified. Repeat periods of strong earthquakes in these zones are also assessed. Tsunamis are not as common in the Indian Ocean as in the Pacific. As compared to average eight tsunamis per year in the Pacific, Indian Ocean has no more than one in 3 years or so. Eighty percent of the tsunamis of the Indian Ocean originate in the Sunda arc covering Java and Sumatra. A catalog of tsunamis presented here includes about 70 tsunamis from Sunda arc and about 20 tsunamis from the rest of the Indian Ocean. The same belt extends northward to Andaman–Nicobar Islands where a few tsunamis have originated. Further north, Bangladesh– Myanmar coast has produced some well-documented tsunamis. Makran coast in the northwest is known to have generated at least one major tsunami. Karachi–Kutch coast region is a possible source zone. Other regions like Chagos Ridge can give rise to local tsunamis. Tsunamis are mostly caused by thrust-type subduction zone earthquakes which are sometimes associated with landslides. The seismic gap areas along the subduction zones are possible sites of future great earthquakes. Along the Sunda arc, great earthquakes of M8.5 or greater can be repeated every two centuries at a site but smaller tsunamigenic earthquakes can be repeated every few decades. Along Sunda arc volcanic eruptions have also given rise to large tsunamis. There appears to have been a hiatus in tsunami generation in this region, with a significant gap in events occurring from around 1909 through 1967 (Tsunami Laboratory, Novosibirsk, Russia). Tsunamis from the Java region are not described in detail as their effects are restricted to Indonesia. 1.2 TSUNAMIGENIC EARTHQUAKE SOURCE ZONES IN THE INDIAN OCEAN Thrust-type earthquakes occurring along subduction zones that cause vertical movement of ocean floor tend to be tsunamigenic. During rupture of a subduction megathrust, for example along the Sumatra arc, the portion of southeast Asia that overlies the megathrust jumps westward (toward the trench) and upward by several meters. This raises the overlying ocean, so that there is briefly a “hill” of water overlying the rupture. The flow of water downward from this hill triggers a series of broad ocean waves that are capable of traversing the entire Bay of Bengal. When the waves reach shallow water they slow down and increase greatly in height – from a few meters to some tens of meters – and thus are capable of inundating low-lying coastal areas. The maximum tsunami run-up is generally twice the vertical movement of the ocean floor and its power depends on the rupture area. Landslide of the ocean floor associated with earthquakes adds to the power of tsunami. 3


4

B.K. Rastogi

Figure 1.1.

Rupture areas of great earthquakes of Mw 7.7 or greater and inferred seismic gap areas that could be sites of future tsunamigenic great earthquakes in the Indian Ocean.

In the near future, earthquakes along southern Sumatra, Makran coast, Indus Delta, Kutch– Saurashtra coast, Bangladesh and southern Myanmar might cause tsunamis which can affect India (Figures 1.1–1.3). The seismic gap areas along subduction zones like Andaman–Sumatra and Makran can be assessed as possible future source zones of tsunami-generating earthquakes in the Indian Ocean and the repeat periods of great earthquakes can be assessed from past seismicity. Along the Andaman–Sumatra trench, the convergence rate is 40–50 mm/year yielding return periods of 150–200 years for great to giant earthquakes of M8.5 or greater. Major tsunamigenic earthquakes of M < 8.0 have been repeated more frequently at intervals of over a few decades. Occurrence of M8.5 earthquake of 2005 at the rupture zone of M8.5 earthquake of 1861 matches with the estimated recurrence rate. However, some great earthquakes have occurred more frequently: rupture zone of 1833 M8.7 earthquake overlapped 1797 M8.2 rupture zone (i.e. within 36 years). Smaller but tsunamigenic earthquakes, of M7.5–8.0 have been repeated more frequently at intervals of over a few decades like 1907 (Ms7.6) and 1935 (Mw 7.7) major earthquakes that occurred near the 1861 (Mw 8.5) source zone. The Sumatran subduction zone is one of the most active plate tectonic margins in the world, accommodating over 50 mm/year of oblique northward convergence between the south Asian and India–Australian plates, which arcs 5500 km from Myanmar past Sumatra and Java toward Australia. The plates meet 5 km beneath the sea at the Sumatran trench, on the floor of the Indian Ocean. The trench runs roughly parallel to the western coast of Sumatra, about 200 km offshore. At the trench, the Indian–Australian plate gets subducted; that is, it is plunging into the earth’s interior and being overridden by southeast Asia. The contact between the two plates is a “megathrust”. The two plates do not glide smoothly past each other along the megathrust

5


A historical account of the earthquakes and tsunamis in the Indian Ocean

Figure 1.2.

Source zones of 2004 and 2005 earthquakes in Sumatra–Andaman zone.

but move in “stick-slip” fashion. This means that the megathrust remains locked for centuries, and then slips suddenly a few meters, generating a large earthquake. Some coastal areas east of the megathrust sink by a meter or so, leading to permanent swamping of previously dry, habitable ground. Islands above the megathrust rise 1–3 m, so that shallow coral reefs emerge from the sea.


6

B.K. Rastogi

Figure 1.3.

Rupture areas of past great earthquakes along Sumatra. The southern Sumatra zone is a possible site for future great earthquake.

Sunda arc extends further north to the Andaman–Nicobar group of islands which is also seismically active zone and generates frequent large earthquakes. Large earthquakes occurred in 1847 (Mw > 7.5), 1868, 1881 (Mw 7.9) and 1941 (M7.7). Future locales are seismic gap areas that have remained unruptured in the past few decades. The 2004 Sumatra earthquake of M9.3 occurred in one such gap. The 28 March 2005 earthquake of M8.7 has occurred in a gap area south of the 2004 rupture identified by Kerry Sieh of Caltech. The 2005 earthquake was probably triggered by the 2004 Sumatra earthquake. Further south along Sumatra trench large and great earthquakes can be expected within a few decades. Mw 7.8 earthquake of 2000 has occurred along the southernmost tip of Sumatra. Northern Sumatra and Andaman regions are assessed to be probably free from great earthquakes for a few decades due to occurrence of 2004 Mw 9.3 and 2005 Mw 8.7 earthquakes. Southern Sumatra has potential for a great earthquake. However, the effect of tsunami due to this in India and Sri Lanka may be a limited one as the path of tsunami will be oblique to the rupture zone.



7

The Makran subduction zone of southern Pakistan and Iran is seismically less active, but has produced great earthquakes. The 28 November 1945 (Mw 8.0) earthquake generated the last major tsunami in the Arabian Sea. More than 4000 people were killed on the Makran coast by both the earthquake and the tsunami. The tsunami caused damage in Mumbai with 2-m run-up and affected Karwar (Karnataka). This earthquake occurred in the eastern part of the Makran zone, two sides of which remain potential zones for great earthquakes. Indus Delta and probably the coasts of Kutch and Saurashtra are also potential zones for great earthquakes and tsunami. Tsunami was generated by an earthquake in 1762 in Myanmar and possibly in 1874 by an earthquake near Bangladesh. Some earthquakes in future also in these regions can possibly generate tsunamis. Normal fault-type earthquakes can also generate moderate tsunami. Strike-slip earthquakes that cause horizontal movement of ocean floor are not tsunamigenic but oblique-slip/dip-slip component in them can generate weak tsunamis. Spreading zones like Carlsberg ridge, NinetyEast ridge, etc. are sites of such earthquakes. The Chagos ridge east of Carlsberg ridge had given rise to a local tsunami due to thrust component of motion for a major earthquake of Mw 7.7 earthquake of 30 November 1983 near Diego Garcia.

1.3

EARTHQUAKES AND TSUNAMIS FROM SUNDA ARC REGION

Newcomb and McCann (1987) compiled historic records of earthquakes and tsunamis from Sunda arc region. An updated list is given in Table 1.1. The Sumatra part of the Sunda arc had been much more active than Java part. Detailed description of some of the significant earthquakes and the tsunamis caused by them are given below. 1.3.1

Earthquakes in Sumatra

11 December 1681

“Strong earthquake” shook the Sumatra mountains near Mentawai Archipelago and a seaquake was observed. 3 November 1756 Many houses collapsed in several towns of Sumatra near to Engano Island. No tsunami was reported. No date, 1770 Severe damage in the same general area as the 1756 event, but a tsunami was reported. 10–11 February 1797, A large earthquake and tsunami was observed in ports on the coast of Mw 8.2 the mainland and on the Batu Island. Waves of great force hit the area near Padang (0.99◦ S 100.37◦ E), the town was inundated and more than 300 fatalities occurred (Heck, 1947). 18 March 1818 A very strong shock associated with both tsunami and seaquake near to Engano Island. 24 November 1833 The great earthquake of M > 8.7 had maximum intensities and generated a tsunami over 550 km along the south central coast of Sumatra that also caused much damage to the coast. Numerous deaths occurred in western Sumatra. This earthquake ruptured the plate margin from the southern island of Enggano to Batu. 5–6 January 1843, The earthquake caused severe damage, liquefaction and many fatalities Mw 7.2 in Nias Island. A tremendous tsunami wiped out towns on the east coast of Nias and mainland. The damage and associated tsunami were much localized. The village of Barus (2◦ N 98.38◦ E) and Palan Nias (Nias Island 1.1◦ N 97.55◦ E) reported large waves on 2 days. 11 November 1852 Earthquake near Nias generated seaquake.

Year

416.09.10 1681.12.11 1768.06.22 1770 1797.02.10 1799 1815.04.10 1815.11.22 1816.04.29 1818.03.18 1818.11.08 1820.12.29 1823.09.09 1833.01.29 1833.11.24

Sep. 1837 1843.01.05 1843.01.06 1852.11.11 1856.07.25 1857.05.13 1859.10.20 1861.02.16 1861.03.09 1861.04.26 1861.06.05 1861.06.17 1861.09.25 1864 1883.08.26 1883.08.27

1 2 3 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Banda Ache Southwest Sumatra Southwest Sumatra Sibolga, Sumatra Java-Flores sea Bali Sea Southern Java sea Southwest Sumatra Southwest Sumatra Southwest Sumatra Java Southwest Sumatra Southwest Sumatra Sumatra Krakatau Krakatau (Volcano)

Java-S Sumatra Bali Sea Southwest Sumatra Southwest Sumatra Southeast Sumatra Java-Flores Sea Bali Sea Penang Island Bengkulu, Sumatra Bali Sea Flores Sea Java Bengkulu, Sumatra Southwest Sumatra

Location

−6.10 −6.06

105.423 105.25

−3.5

102.2 5.5 1.5 1.05 1.7 −8.5 −8 −9 −1 0.3 1 −6.3 1 −1.5

−7 −5 −1 −2.983 −8.2 −8 5.383 −3.767 −7 −7 −6.5

115 102 99 104.75 118 115.2 100.25 102.267 117 119 108.5

96 98 97.33 98.8 116 115.5 111 97.5 99.37 97.5 107.3 97.5 100

−10

Lat.

120

Long.

List of tsunamis in Sumatra–Java region.

S.N.

Table 1.1.

1 1

Ms 6.8 Ms 6.5

Ms 8.5 Ms 7 Ms 7

6 6

1 1 1 1 1 1 1

Ms 6.8 Ms 7

4 1

1

6 1 1 1 1 1 6 3 1 3 1 1 1

Ca.

Ms 7.2 Ms 7.2

Mw 8.7

Ms 7 Ms 8.5 Ms 7.5 Ms 6.8

Ms 7

Ms 7.5 Ms 7 Ms 8

Mag.

3 4

1 2 4 2 4 4 4 2 3 3

2 4

4

2 4 4 3 4 2 4 3 2 3 2 4 2

Pro.

(1) (3)

0.5 3.0

(1) (8) 35 (67)

1.0 4.5

(2) (1) (9) (4) (1) 1.5

3.0 2.0 1.5

(3)

2.5

(1)

(1) (1)

(1) (1)

Max. run-up (run-ups)

1.5

0.5 3.0

I

NOAA/NESDIS Newcomb and McCann (1987) NOAA/NESDIS NGDC/NOAA Berninghausen (1966) Berninghausen (1966) NOAA/NESDIS NOAA/NESDIS NGDC/NOAA Berninghausen (1966) NOAA/NESDIS NOAA/NESDIS NOAA/NESDIS Berninghausen (1966) NGDC/NOAA, Newcomb and McCann (1987) NGDC/NOAA Berninghausen (1966), Heck (1947) Berninghausen (1966), Heck (1947) NGDC/NOAA NOAA/NESDIS NOAA/NESDIS Berninghausen (1966) Berninghausen (1966) NGDC/NOAA NGDC/NOAA NOAA/NESDIS NOAA/NESDIS Berninghausen (1966) Berninghausen (1966) Berninghausen (1966) Berninghausen (1966)

References

Downloaded by [INFLIBNET Centre] at 07:51 27 August 2012 8 B.K. Rastogi

Feb. 1884 1885.07.29 1889.08.16 1892.05.17 1896.10.10 1904.07.04 1907.01.04

1908.02.06 1909.06.03 1914.06.25

1917.01.21 1921.09.11

1922.07.08 1926.06.28 1928.03.26 1930.03.17 1930.06.19 1930.07.19 1931.09.25 1935.12.28 1936.08.23 1948.06.02 1949.05.09 1955.05.17 1957.09.26 1958.04.22 1963.12.16 1964.04.02

31 32 33 34 35 36 37

38 39 40

41 42

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Lhoknga, Ache Southwest Sumatra Krakatau Java-south Java-south Southern Java Sea Southwest Sumatra Southwest Sumatra Malay Peninsula Malay Peninsula Malay Peninsula Malay Peninsula Southern Java Sea Southwest Sumatra Java Off northwest coast of Indonesia

Southwest Sumatra Sumatra West coast of South Sumatra Bali Sea Southern Java Sea

Krakatau Ajerbangis Java, Indonesia Malay Peninsula Southwest Sumatra Sumatra Southwest Sumatra

95.233 99.5 105.423 105.4 105.3 114.3 102.7 98.25 95 94 95 94 107.3 104 105.4 95.7

115.4 111 5.467 −1.5 −6.102 −6.1 −5.6 −9.3 −5 .001 6 5.5 5 6.5 −8.2 −4.5 −6.2 5.9

−8 −11

−5 −2 −4.5

2

94.5 100 101 102.5

−6.10 0.2 −6 2.5 −3.5

105.423 99.383 106 99.5 102.5

Ms 6 Ms 6.5 Ms 7.5 Ms 8.1 Ms 7.3 Ms 6.5 Ms 6.7 Ms 7.2 Ms 5.5 Ms 6.5 6.5 Ms 7.0

Ms 6.7

Ms 6.5 Ms 7.5

Ms 7.5 Ms 7.7 Ms 8.1

Ms 7.6

Ms 6.8 Ms 6 Ms 7.5 Ms 6.8

3 4 1 0 1 1 3 2 3 1 2 2 2 2 3 2 2 3

1 1 6 6 1 1 1 1 1 1 1 1 1 1 1 8

4 2 0

4

2 2 3 3 2

1 1

1 1 1

1

1 1 1 1 1

1.4 (1) 1.4

1.0 1.0

0.7 1 0.7 0.7

0.7

0.7 0.1 31.4

2 0.2

2.8 (7)

4 (4) 1 (1)

2.0

1.0


(Continued )

NGDC/NOAA NGDC/NOAA/Newcomb and McCann (1987) NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA NOAA/NESDIS

NGDC/NOAA/Newcomb and McCann (1987) NGDC/NOAA NGDC/NOAA NGDC/NOAA

Murty et al. (1999) NGDC/NOAA NGDC/NOAA NGDC/NOAA NGDC/NOAA

A historical account of the earthquakes and tsunamis in the Indian Ocean 9

1964.04.02 1967.04.12 1977.08.19 1982.02.24 1984

1985.04.13 1994.02.15 1994.06.02 2000.06.04

2000.06.18 2004.12.26

2005.03.28

2005.04.10

59 60 61 62 63

64 65 66 67

68 69

70

71

Malay Peninsula Malay Peninsula Sunda Islands Java trench Off west coast of Sumatra Bali Island, Indonesia Southern Sumatra Java, Indonesia Off west coast of Sumatra South Indian Ocean Off west coast of Sumatra Off west coast of Sumatra Kepulauanmentavia

Location

99.607

97.013

97.45 95.947

114.2 104.3 112.8 102.09

95.7 97.3 118.4 97.7 97.955

Long.

−1.64

2.074

−13.8 3.307

−9.2 −5 −10.5 −4.72

5.9 5.5 −11 4.37 0.18

Lat.

Ms 6.7

Mw 8.7

Ms 7.8 Mw 9.3

Ms 6.2 Ms 7.0 Ms 7.2 Ms 7.8

Ms 7.0 Ms 7.5 Ms 8 Ms 5.4 7.2

Mag.

1

1

1 1

1 1 1

1 1 1 1

Ca.

4

4

4 4

4

2

3 3 4 4

Pro.

3.0

1.5

I

NOAA/NESDIS NGDC/NOAA NOAA/NESDIS NOAA/NESDIS

13 (15) (1) 0.3 24 (302 4 (2) 1 (1)

NOAA/NESDIS NGDC/NOAA NOAA/NESDIS NGDC/NOAA Engdahl et al. (1998)

References

NGDC/NOAA NGDC/NOAA NGDC/NOAA USGS/NEIC(PDE)

2

Max. run-up (run-ups)

Cause Code: Cause code indicates the cause or source of the tsunamis. Valid values: 1 to 12 1 = earthquake 2 = questionable earthquake 3 = earthquake and landslide 4 = earthquake and volcano 5 = earthquake, volcano and landslide 6 = volcano 7 = volcano and earthquake 8 = volcano and landslide 9 = volcano, earthquake, and landslide

I is tsunami intensity, maximum run-up is in meters, reported number of run-ups are given within brackets. The data are taken from National Geophysical Data Center (NGDC); National Oceanic and Atmospheric Administration (NOAA) and National Environmental Satellite, Data, and Information Service (NESDIS). A “−1” is used as a flag (missing) value in some fields. The cause and probability of the tsunamis are shown by “Ca.” and “Pro.” respectively. The cause and probability of the tsunamis are given by following codes.

Year

(Continued)

S.N.

Table 1.1.

Downloaded by [INFLIBNET Centre] at 07:51 27 August 2012 10 B.K. Rastogi

where “h” is the maximum run-up height of the wave.

I = log2 (21/2 ∗ h)

Some other formulae are also in use. Tsunami Intensity: Tsunami intensity scales have been suggested based on its effect and damage caused by it. There are many formulae for intensity based on tsunami run-ups. Tsunami intensity is defined by Soloviev and Go (1974) as

10 = landslide 11 = meteorological 12 = explosion Event Probability: Probability of actual tsunami occurrence is indicated by a numerical rating of the validity of the reports of that event. Valid values: 0 to 4 4 = definite tsunami 3 = probable tsunami 2 = questionable tsunami 1 = very doubtful tsunami 0 = erroneous entry Tsunami Magnitude: Tsunami magnitude, Mt is defined in terms of tsunami-wave amplitude by Iida et al. (1967) as: Mt = log2 Hmax


A historical account of the earthquakes and tsunamis in the Indian Ocean 11


12

B.K. Rastogi

Figure 1.4.

Krakatau volcanic eruption, 1883 (Source: Simkin & Fiske, 1983).

16 February 1861 A great earthquake of M8.5 ruptured a major segment of the plate boundary in northern Sumatra. The tsunami that was generated extended over 500 km along the arc. Tsunami destroyed southern towns of Batu Island, and a town on the southwest side of Nias experienced a tsunami of height 7 m. The earthquake and tsunami caused thousands of fatalities along the west coast of Sumatra. Two aftershocks on 9 March and 26 April 1861 also caused tsunamis. There was no major shock for almost 50 years. Historic records show that the strongest tsunami was associated with the volcanic eruption of Krakatau in Indonesia on 27 August 1883. The 35 m-high tsunami took a toll of 36,000 lives in western Java and southern Sumatra. The island volcano of Krakatau exploded with devastating fury, blowing its underground magma chamber partly empty so much so that much overlying land and seabed collapsed into it. Figure 1.4 shows the parts of the island that fell into the sea. A series of large tsunami waves was generated from the explosion, some reaching a height of over 35 m above sea level. Tsunami waves were observed throughout the Indian Ocean, the Pacific Ocean, the American west coast, South America and even as far away as the English Channel. On the facing coasts of Java and Sumatra the sea flood went many kilometers inland and caused such vast loss of life that one area was never resettled and is now the Ujung Kulon nature reserve. At its peak, the island of Rakata, which the volcano of Krakatau had formed, had reached a height of 790 m above sea level. Subsequent local tsunamis in the Sunda Strait were generated by the 1927 and 1928 eruptions of the new volcano of Anak Krakatau (Child of Krakatau) that formed in the area. Although large tsunamis were generated from these recent events, the heights of the waves attenuated rapidly away from the source region, because their periods and wavelengths were very short. There was no report of damage from these more recent tsunamis in the Sunda Strait (George, 2003).



1.3.2

13

Krakatau explosive eruption (1883)

According to ancient Japanese scriptures, the first known supercolossal eruption of Krakatau occurred in the year 416 AD – some gave the date as 535 AD. The energy of this eruption is estimated to have been about 400 Mt of TNT, or the equivalent of 20,000 Hiroshima bombs. This violent early eruption destroyed the volcano, which collapsed and created a 7-km-wide submarine caldera. The remnants of this earlier violent volcanic explosion were the three islands of Krakatau, Verlaten and Lang (Rakata, Panjang and Sertung). Undoubtedly the 416 AD eruption/ explosion/collapse must have generated a series of catastrophic tsunamis, damage from which must have been much greater than those generated in 1883. However, there are no records documenting the size of these early tsunamis or the destruction they caused. Subsequent to the 416 AD eruption and prior to 1883, three volcanic cones of Krakatau and at least one older caldera had combined again to form the island of Rakata. The volcanic cones on the island were aligned in a north–south direction. The northernmost was called Poeboewetan and the southernmost was called Rakata. Overall approximate dimensions of the island were 5 km × 9 km (George, 2003). 4 January 1907, This event caused tsunamis that devastated Simeuleu, Nias and Batu Ms 7.6 Islands of Sumatra and extended over 950 km as measured by tide gauges. 25 June 1914, M7.6 This earthquake destroyed buildings in southern Sumatra. No tsunami was reported. 1935, Mw 7.7 Tsunami in southwest Sumatra. The 2004 Sumatra–Andaman earthquake of M9.3 generated 30-m-high tsunami when upward slip of the ocean floor was up to 15 m along a 1300-km long and 160–240-km-wide rupture. It was the deadliest tsunami killing about 300,000 people in 13 countries situated all around the Indian Ocean. The tsunami power was enhanced by large landslides over the rupture zone of 2004 earthquake. The earthquake had created large thrust ridges, about 1500 m high, which collapsed in places to produce large landslides, several kilometers across. The force of displaced water was such that blocks of rocks, massing millions of tons apiece, were dragged as much as 10 km. An oceanic trench several kilometers wide was also formed. The M8.7 great Sumatra earthquake of 28 March 2005 with an upward movement of 2 m of seafloor in an area of 400 km × 100 km generated a locally damaging 4-m-high tsunami that struck nearby islands and coastal Sumatra and was recorded by tidal stations in the Indian Ocean (asc.India.org). The earthquake and tsunami killed 665 people. The tsunami struck Nias Island with wave heights of 4–5 m. A 3–4 m wave struck the islands of Banyak and Simeulue, and the Singkil District of Sumatra. According to the Pacific Tsunami Warning Center (PTWC), tide gauges in the Indian Ocean recorded minor wave activity in the Australian Cocos Island (10–22 cm), the Maldives (10 cm) and Sri Lanka (25–30 cm). 1.4 TSUNAMIS THAT AFFECTED THE INDIAN REGION AND VICINITY Though rare, tsunamis have hit India earlier. The tsunamis in the Indian region and vicinity are listed in Table 1.2. The oldest record of tsunami is available from November 326 BC earthquake near the Indus Delta/Kutch region that set off massive sea waves in the Arabian Sea. Alexander the Great was returning to Greece after his conquest and wanted to go back by a sea route. But a tsunami due to an earthquake of large magnitude destroyed the mighty Macedonian fleet (Lisitzin, 1974). Poompuhar is a town in the southern part of India in the state of Tamil Nadu. It was a flourishing ancient town known as Kaveripattinam that was washed away in what is now recognized as an ancient tsunami in about 500 AD. This time matches with the Krakatau explosion.

326 BC About 500 AD 900 AD 1008 1762.04.12 1819.06.16 1842.11.11 1845.06.19 1847.10.31

1868.08.19 1874 1881.12.31

January 1882 1883.08.27 1884 1935.05.31 1935.11.25 1941.06.26 1945.11.27 1983.11.30 2004.12.26

1 2 3 4 5 6 7 8 9

10 11 12

13 14 15 16 17 18 19 20 21

Sri Lanka Krakatau (Volcanic Eruption) West of Bay of Bengal Andaman–Nicobar Andaman–Nicobar Andaman Islands Makran Coast Chagos ridge Off west coast of Sumatra and Andaman–Nicobar

Andaman Islands Sunderbans (Bangladesh) West of Car Nicobar

Indus Delta/Kutch region Poompuhar, Tamil Nadu Nagapattinam, Tamil Nadu Iranian Coast Bay of Bengal (Bangladesh) Kutch Northern Bay of Bengal Kutch Little Nicobar Island

Location

Note: For footnotes refer Table 1.1.

Date

8.34 −6.06 5.5 12.1 25.2 −6.85 3.307

94 92.5 63.5 72.11 95.947

11.67 22 8.52

11.12 10.46 25 22 71.9 21.5 68.37 7.333

Lat.

81.14E 105.25

92.73 89 92.43

79.52 79.53 60 92 26.6 90 23.6 93.667

Long.

List of tsunamis that affected Indian region and vicinity.

S.N.

Table 1.2.

Mw 7.5 Ms 6.5 Mw 7.7 Mw 8.0 Mw 7.7 Mw 9.3

Mw 7.9

Mw 7.5–7.9

Mw 7.8

Eq. Mag

1 1 1 1 1 3

1 6

1 1 1

4 2 4 4 4 4

3 4

4 2 4

4 4 4 4 4 3 4 3 3

1 1 1 1 1 1 1

Pro.

Cau.

3.0

4.5

I

1.25 11 1.5 (2) 5

(1)

2

1.2

4

(3)

>2 (1)

(run ups)

Max. run-up


Lisitzin (1974) Wikipedia Kalki Krishnamurthy Murty et al. (1999) Mathur (1988) Macmurdo (1821) Oldham (1883) Nelson (1846) Berninghausen (1966), Heck (1947) NGDC/NOAA Mihir Guha, Free Journal Berninghausen (1966), Ortiz and Bilham (2003) Berninghausen (1966) Berninghausen (1966) Murty et al. (1999) NGDC/NOAA NGDC/NOAA Bilham et al. 2005 Murty et al. (1999) NGDC/NOAA NGDC/NOAA

References

14 B.K. Rastogi



15

There is mention in the scriptures of tsunami effect at Nagapattinam in 900 AD that destroyed a Budhist monastery. According to literature available in the library of Thondaiman Kingdom in Pudukottai, Tamil Nadu, it was during the reign of Chola that waves had washed away the monastery and several temples, and killed hundreds of people. There is evidence of this in Kalki Krishnamurthy’s book “Ponniyin Selvan,” The Pinacle of Sacrifice. In the chapter “The Sea Rises”, the author explains how the sea had risen very high and a black mountain of water surged forward. The sea inundated warehouses and sheds, and began to flow into the streets. Ships and boats seemed suspended in mid-air, precariously poised on the water peaks. The book also describes how an elephant was washed away by the gushing water. Tsunami has been observed in the north Indian Ocean on the Iranian coast from a local earthquake between 1 April and 9 May 1008 (Murty et al., 1999). An earthquake occurred during 1524 AD off the coast of Dabhol, Maharashtra, and a resulting large tsunami caused considerable alarm to the Portuguese fleet that was assembled in the area (Bendick and Bilham, 1999). A tsunami is known to have occurred in the Bay of Bengal on 2 April 1762, caused by an earthquake in Bangladesh–Myanmar border region. The epicenter is believed to be 40 km southeast of Chittagong, or 61 km north of Cox’s Bazaar, or 257 km southeast of Dhaka, Bangladesh. The shock caused severe damage at Chittagong and other areas on the eastern seaboard of the Bay of Bengal. The Arakan coast got elevated for a length of more than 160 km. The quake also caused a tsunami in the Bay of Bengal. The water in the Hoogly River in Kolkata rose by 2 m. The rise in the water level at Dhaka was so sudden that hundreds of boats capsized and many people were drowned. This is the earliest well-documented tsunami in the Bay of Bengal (Mathur, 1998). 16 June 1819 in India, Kutch (Mw 7.8) there was a Severe earthquake with large changes in the elevation of the land. The town of Sindri (26.6◦ N 71.9◦ E) and adjoining country were inundated by a tremendous rush of water from the ocean. There was submergence, with the ground apparently sinking by about 5 m (Macmurdo,1821) An earthquake on 11 November 1842 near the northern end of Bay of Bengal caused a tsunami by which waters of the distributaries of the Ganges Delta were agitated. Boats were tossed about as if by waves in a squall of wind (Oldham, 1883). 19 June 1845 in India, Kutch “The sea rolled up the Koree (Kori creek, 23.6◦ N 68.37◦ E) (the east) mouth of the Indus overflowing the country as far westward as the Goongra river, northward to the vicinity of Veyre, and eastward to the Sindree Lake” (Nelson, 1846). On 31 October 1847 the small island of Kondul (7◦ 13 N 93◦ 42 E) near Little Nicobar was inundated (Heck, 1947; Berninghausen, 1966) by an earthquake whose Mw magnitude could have been greater than 7.5 (Bilham et al., 2005). Mihir Guha (http://www.freejournal.net), Former Director General of the India Meteorological Department, reported that a tsunami struck Sunderbans (Bangladesh) in May 1874, killing several hundred-thousand people. It was the result of an earthquake in Bhola district. Earthquake and tsunami both played havoc in vast areas of Sunderbans, 24-Parganas, Midnapore, Barishal, Khulna and Bhola. Even Kolkata felt its impact. It was the same year that the meteorological center in Alipore was set up. However, no written record of such an earthquake or tsunami is available. Other minor tsunamis of height up to 2 m hit the east coast of India in 1842 and 1861 (from Sumatra), 1881 (from Car Nicobar), 1883 (Krakatau), 1907 (Sumatra) and 1941 (Andaman). The 1881 Andaman earthquake of Mw 7.9 caused 1.2-m-high tsunami. Indonesian earthquake of 1907 registered about 1-m-high tsunami in India. Chennai Port Trust recorded a 2-m-high tsunami due to the eruption of the Krakatau volcano in Indonesia on 27 August 1883. Andaman earthquake of Mw 7.7 in 1941 registered a 1.5-m-high tsunami. Some of these tsunamis are described below. An earthquake of magnitude Mw 7.9 occurred at Car Nicobar Island on 31 December 1881. A tsunami was generated by this earthquake in the Bay of Bengal. Though the run-ups and waves


16

B.K. Rastogi

heights were not large, its effects were observed in the Andaman–Nicobar Islands and were recorded on the east coast of India. In the Nicobar Islands, the waves were less than 75-cm high (Ortiz and Bilham, 2003). A 1-m-high wave was recorded (Berninghausen, 1966) at Port Blair on South Andaman Island. On the east coast of India, the tsunami first arrived at Nagapattinam at around 10:15 a.m. local time (LT) in the form of 1.2-m-high waves (Ortiz and Bilham, 2003). Tidal gauges at other locations recorded minor variations from normal tidal changes. The tsunami then struck the rest of the Tamil Nadu coast, first hitting Chennai (Ortiz and Bilham, 2003) at 10:20 LT and then progressing north toward Vishakhapatnam in Andhra Pradesh at 10:43 LT. Waves arrived (Ortiz and Bilham, 2003) at False Point on the Mahanadi delta in Orissa at 11:15 LT and at Pamban in the Gulf of Mannar at 11:32 LT. Waves less than 0.3-m high were recorded later in the day in West Bengal by tidal gauges at Dublat at the mouth of the Hoogly river at 13:00 LT and then in Diamond Harbour at 15:10 LT. Waves attributed (Berninghausen, 1966) to this tsunami were also observed at Batticaloa and Trincomalee on the east coast of Sri Lanka. No tsunami (Ortiz and Bilham, 2003) was reported from tidal gauges in Myanmar. A tsunami was noticed at Dublat (mouth of Hoogly River) near Kolkata due to earthquake in the western part of the Bay of Bengal in 1884 (Murty et al., 1999) that reached up to Port Blair. On 26 June 1941, Andaman had an earthquake that had a moment magnitude Mw 7.7 and was located at 12.1◦ N and 92.5◦ E (Bilham et al., 2005). A tsunami was triggered by this earthquake in the Bay of Bengal. Height of the tsunami was reported to be of the order of 0.75–1.25 m. At the time no tidal gauge was in operation. Mathematical calculations suggest that the height could be of the order of 1 m. This tsunami was witnessed along the eastern coast of India. It is believed that nearly 5000 people were killed by the tsunami on the east coast of India. Local newspapers are believed to have mistaken the deaths and damage to a storm surge; however, a search of meteorological records does not show any storm surge on that day on the Coromandel Coast (Murty, 1984). National dailies like the Times of India, which reported the quake’s shaking effects, did not mention any deaths, either as a result of a storm surge or a tsunami. The deadliest tsunami prior to 2004 in south Asia was in 28 November 1945 that originated off the Makran coast of Pakistan in the Arabian Sea, and caused deaths as far as Mumbai. More than 4000 people were killed on the Makran coast by both the earthquake and the tsunami. The earthquake was also characterized by the eruption of a mud volcano, a few kilometers off the Makran coast, which are common features in western Pakistan and Myanmar. It led to the formation of four small islands. A large volume of gas that erupted from one of the islands sent flames leaping “hundreds of meters” into the sky (Mathur, 1998). The most significant aspect of this earthquake was the tsunamis that it triggered. The tsunami reached a height of 17 m in some Makran ports and caused great damage to the entire coastal region. A good number of people were washed away. The tsunami was also recorded at Muscat and Gwadar. The tsunami had a height of 11.0–11.5 m in Kutch, Gujarat (Pendse, 1945). At 8:15 a.m., it was observed on Salsette Island (i.e. Mumbai) (Newspaper archives, Mumbai). It was recorded in Bombay Harbour, Versova (Andheri), Haji Ali (Mahalaxmi), Juhu (Ville Parle) and Danda (Khar). At Versova (Andheri, Mumbai), five persons who were fishing were washed away. At Haji Ali (Mahalaxmi, Mumbai), six persons were swept into the sea. At Danda and Juhu, several fishing boats were torn off their moorings. The tsunami did not do any damage to Bombay Harbour. Most persons who witnessed the tsunami said that it rose like the tide coming in, but much more rapidly. The height of the tsunami in Mumbai was 2 m. A total of fifteen persons were washed away in Mumbai. The Mw 7.7, 30 November 1983 earthquake in Chagos Archipelago, was one of the strongest earthquakes ever recorded in the Indian Ocean. It occurred at 17:46 p.m. UTC. The earthquake caused some damage (NEIC) to buildings and piers on Diego Garcia, which is part of the Chagos Archipelago. The 1983 earthquake triggered a tsunami in the region. In the lagoon, on Diego Garcia, there was a 1.5-m rise in wave height and there was some significant wave damage near the southeastern tip of the island. A 40-cm wave was also recorded at Victoria, Seychelles. There was a large zone of discolored seawater observed 60–70 km north–northwest of Diego Garcia.


17

Moment-tensor solution indicated normal faulting along an east–west plane at a depth of 10 km with source duration of 34 s.


1.5

CONCLUSIONS

• It is assessed that Sumatra and Andaman regions will probably not generate great earthquakes for a few decades due to occurrence of 2004 Mw 9.3 and 2005 Mw 8.7 earthquakes. Southern Sumatra has potential for a great earthquake. However, the effect of tsunami due to this in India and Sri Lanka may be a limited one as the path of tsunami will be oblique to the rupture zone. • The Makran subduction zone of southern Pakistan is seismically less active, but has produced great earthquakes. The 28 November 1945 (Mw 8.0) earthquake generated the last major tsunami in the Arabian Sea. This earthquake occurred in the eastern part of the Makran zone, two sides of which remain potential zones for great earthquakes that can generate tsunamis in future. • Indus Delta and possibly the coasts of Kutch and Saurashtra are also potential zones for great earthquakes and tsunami. • Tsunami was generated by an earthquake in 1762 in Myanmar and in 1874 by an earthquake near Bangladesh. In future also, some earthquakes in these regions can possibly generate tsunamis. • The Carlsberg ridge, Chagos ridge and Ninety-East ridge can give rise to local tsunami due to normal and thrust component of motion for major earthquakes as happened due to Mw 7.7 earthquake of 30 November 1983 near Diego Garcia along the Chagos ridge. • Eighty percent of the tsunamis in the Indian Ocean are from Sunda arc region where on average tsunamis are generated once in 3 years. In the rest of the Indian Ocean tsunamis can be generated once in 10 years or so. REFERENCES Bendick, R. and Bilham, R. (1999). A Search for Buckling of the SW Indian Coast related to Himalayan Collision. In: A. Macfarlane, R.B. Sorkhabi, and J. Quade, (eds.), Himalaya and Tibet: Mountain Roots to Mountain Tops: Geological Society of American Special paper 328. pp. 313–322. Berninghausen, W.H. (1966). Tsunamis and Seismic Seiches Reported from Regions Adjacent to the Indian Ocean. Bull. Seism. Soc. Am., 56(1), 69–74. Bilham, R., Engdahl, R., Feld, N., and Sayabala, S.P. (2005). Partial and Complete rupture of the IndoAndaman plate Boundary 1847–2004. Seism. Res. Lett., 76(3), 299–311. Engdahl, E.R., van der Hilst, R.D., and Buland, R.P. (1998) Global teleseismic earthquake relocation with improved travel times and procedures for depth determination. Bull. Seis. Soc. Am., 88, 722–743. George, P.-C. (2003). Near and Far-Field Effects of Tsunamis Generated By the Paroxysmal Eruptions, Explosions, Caldera Collapses and Massive Slope Failures of The Krakatau Volcano in Indonesia on August 26–27, 1883. Sci. Tsunami Hazards, 21(4), 191–222. Heck, N.H. (1947). List of Seismic Sea Waves. Bull. Seism. Soc. Am., 37, 269–286. Lisitzin, E. (1974). Sea Level Changes, Elsevier Oceanographic Series, No.8, New York, 273 pp. Macmurdo, C. (1821). Account of the Earthquake which Occurred in India in June 1819. Edinburgh Phil. J., 4, 106–109. Mathur, S.M. (1998). Physical Geology of India. National Book Trust of India, New Delhi. Murty, T.S., Bapat, A., and Prasad, V. (1999). Tsunamis on the Coastlines of India. Sci. Tsunami Hazards, 17(3), 167–172. Murty, T.S. (1984). Storm Surges – Meteorological Ocean Tides. Bull. Fish. Res. Board Can., Ottawa. Nelson, C. (1846). Notice of an Earthquake and a Probable Subsidence of the Land in the District of Cutch, near the Mouth of Koree, or the Eastern Branch of the Indus in June 1845. Quart. J. Geol. Soc. London, 2, 103.

18

B.K. Rastogi


Newcomb, K.R. and McCann, W.R. (1987). Seismic History and Tectonics of the Sunda Arc. J. Geophys. Res., 92(B1), 421–439. Oldham, T.A. (1883). Catalogue of Indian earthquakes. Geo. Surv. Ind. Mem, 19(Pt 3), 163–215. Ortiz, M. and Bilham, R. (2003). Source Area and Rupture Parametres of the 31 December 1881 Mw = 7.9 Car Nicobar Earthquake Estimated from Tsunamis Recorded in the Bay of Bengal. J. Geophys. Res. Solid Earth, 108(4), ESE 11, 1–16. Pendse, C.G. (1945). The Mekran earthquake of the 28th November 1945. India Met. Deptt. Scientific Notes, 10, 141–145. Simkin, T. and Fiske, R.S. (1983). Krakatau 1883: The Volcanic Eruption and its Effects. Smithsonian Institution Press, Washington, DC. 464 pp. Soloviev, S.L., and Go, C.N. (1974) Catalog of tsunamis in the western coast of Pacific Ocean (in Russian), Nauka Publishing Co., Moscow.

CHAPTER 2


Impact of Coastal Morphology, Structure and Seismicity on the Tsunami Surge K.S.R. Murthy, V. Subrahmanyam, G.P.S. Murty and K. Mohana Rao National Institute of Oceanography, Regional Centre, Lawsons Bay, Visakhapatnam, Andhra Pradesh, India

2.1

INTRODUCTION

The Sumatra earthquake (Mw9.3) with its epicenter located southwest of Sumatra island (3.7◦ N, 95◦ E) occurred at the interface of the Indian and Burmese plates, where the former subducts beneath the Burmese plate all along the Andaman–Sumatra–Sunda Arc (McCloskey et al., 2005; Sieh, 2005; Gupta, 2005; Satish Singh, 2005). It is the Fifth largest earthquake since 1990 and the largest since the 1964 Alaska earthquake. In this region the Indian plate moves towards northeast at the rate of 6 cm/year relative to the Burmese plate which results in an oblique convergence at the Sunda trench. The oblique motion is partitioned into thrust faulting and strike-slip faulting which occurs at the plate interface. The 26 December earthquake was the result of such thrust faulting (Radhakrishna, 2005). The earthquake with a focal depth of 30 km has affected a length of nearly 1300 km along the interface, with the rupture mainly propagating towards the north of the epicenter within an average width of 100 km. The average displacement of the fault plane is 15 m. The rupture appears to have occurred in two stages; in the first stage it propagated rapidly to about 400 km followed by a slow rupture of about 500 km. The total duration of the rupture is around 800 s (13 min). Subsequent observations indicate that this catastrophic event made the Earth wobble on its axis. An anticlockwise rotation of the islands of the Andaman and Nicobar region by about 2–3 m has been reported. The southern part of these islands has undergone submergence of about 2 m, whereas the Northern Andaman area has experienced an uplift of about 1 m (Subramanian, 2005; Murthy, 2005a,b). As many as 2000 aftershocks have been reported in this area even after 7 months of the main event, with some of them having magnitudes greater than 7.0 (e.g., Mw 7.3, 26 December 2004; Mw 8.4, 28 March 2005; and Mw 7.2, 24 July 2005). This earthquake appears to have disturbed a water column of nearly 100 × 70 × 1.5 km3 volume (Radhakrishna, 2005), resulting in an unique Indian Ocean Tsunami that has engulfed the coastal area of Indian Ocean rim countries including Indonesia, Thailand, India, Sri Lanka and as far west as Somalia in EastAfrica. The inundation on the coastal stretches is as much as 2 km in some cases, the worst affected being the Andaman and Nicobar Islands and the southern parts of east coast of India. Tidal measurements at Port Blair, Chennai and Visakhapatnam indicate surge heights of the order of 1.5–5.5 m above mean sea level, with maximum height near Nagapattinam and Karaikal (Chadha et al., 2005). The tsunami waves reached the Nicobar Islands, within few minutes, the Andaman Islands within half-an hour and the Indian coast in about 2–2.5 h (Subramanian, 2005; Chadha et al., 2005). Sea level transgression was of the order of 1100–1200 m in case of Andaman coast, 350–1100 m in case of Nicobar and nearly 200–800 m in case of Tamil Nadu coast of India. The twin events of the earthquake and tsunami not only stress the importance of an integrated warning system for the Indian Ocean rim countries but also the need for new disaster management 19

20

K.S.R. Murthy et al.


plans to mitigate such hazards. As far as the Indian coastal regions are concerned, detailed geophysical surveys on the coastal morphology, structure and coastal seismicity are very essential in order to understand the relationship between tsunami run–up heights, inundation extent and the shelf/slope morphology. Studies on coastal structure and seismicity are useful in estimating the seismic hazard risk of the coastal region as well as in understanding the influence of tectonics on the tsunami initiation and surge. In this chapter, we present a detailed analysis on the morphology, structure and seismicity of the Cauvery offshore basin, which includes the tsunami-affected Nagapattinam-Cuddalore shelf of Tamil Nadu margin. 2.2

COASTAL MORPHOLOGY AND STRUCTURE IN RELATION TO TSUNAMI SURGE – A CASE STUDY

The east coast of India is more prone for natural hazards like cyclones, storm surges and now the new hazard in the form of tsunami, in comparison to the west coast. The Eastern Continental

Figure 2.1.

Geophysical data coverage over the ECMI (thin solid lines represent cruise tracks over ECMI and Bengal Fan).


Impact of coastal morphology, structure and seismicity on the tsunami surge

21

Margin of India (ECMI) is a passive margin evolved during the process of breakup of Eastern Gondwanaland in the late Cretaceous (Murthy et al., 1995). In the pre-breakup scenario, the present Krishna–Godavari Basin was conjugate with the Enderbyland of east Antarctica (Murthy et al., 1997). Most of the Indian rivers, having an eastward slope, join the Bay of Bengal, thereby resulting in a mosaic of basinal and non-basinal morphology. The shallow bays associated with the basinal areas are more affected by the crossing of cyclones and storm surges, due to the wider shelf with gentle slope. One of the important parameters to be considered in the context of cyclones/storm surges/tsunami is the seabed morphology, including the shelf/slope characteristics of the margin. In this connection, the Regional Centre, National Institute of Oceanography (NIO), Visakhapatnam, India has collected bathymetry, magnetic and gravity data over the ECMI from Karaikal in the south to Paradip in the north (Figure 2.1). Morphology, stratigraphy, structure and tectonics of ECMI, including the offshore river basins like the Cauvery, Krishna–Godavari and Mahanadi were analyzed from this data by Murthy et al. (1993), Murthy et al. (1995), Subrahmanyam et al. (1995), Murthy et al. (1997) and Murty et al. (2002). In this chapter, we make use of this data to analyze the factors that facilitated the high tsunami surge in case of the Nagapattinam–Cuddalore shelf of Tamil Nadu margin.

Figure 2.2.

Bathymetry map of ECMI.


22


2.3

FACTORS GUIDING THE HIGH TSUNAMI SURGE AT NAGAPATTINAM–CUDDALORE SHELF

It is evident from the bathymetric maps and sections of the eastern continental margin that the shelf is in general steep and narrow in the south (except off Chennai) whereas it is relatively wider and gentle in the north (Figures 2.2 and 2.3 and Table 2.1). However, some of the offshore river basins are associated with shallow bays with a concave coastline (e.g., Cauvery and Krishna– Godavari). There is a significant change in the direction of the coastline at 14◦ N, south of which the coastline is oriented in north–south direction, whereas north of it is northeast–southwest in orientation. The southern part of the eastern continental shelf of India from Karaikal in the south (11◦ N) and Visakhapatnam in the north (approximately 18◦ N) was affected by the tsunami surge caused by the Sumatra earthquake (Figure 2.1). However, the Tamil Nadu shelf, in particular Nagapattinam– Cuddalore part (shown as shaded zone in Figures 2.1–2.6) was the worst affected by the tsunami surge of 26 December 2004. The observed run-up heights in this part are as much as 5.2 m (e.g., Nagapattinam) with inundation to a distance of nearly 800 m into the interior (Chadha et al., 2005). This part of the shelf represents the offshore Cauvery Basin. Qualitative inferences drawn

Figure 2.3.

Bathymetry sections of ECMI.


23

by Raval (2005) and Subrahmanyam et al. (2005) suggest that some of the main reasons for the high Tsunami surge in case of Nagapattinam–Cuddalore shelf of Tamil Nadu margin are:


1 its relative proximity to the source of the tsunami, 2 the configuration of the coastline and the bathymetry of the shelf and 3 the tectonics associated with the offshore Cauvery basin. Earlier analysis from magnetic data of the Cauvery Basin (Subrahmanyam et al., 1995) suggest that the basin is fault controlled, with two major east–west faults (shown as F1 and F2, in Figure 2.4(a)) extending from the land into the offshore. The northern fault is located north off Pondicherry, whereas the southern fault is located north off Vedaranyam. Magnetic and gravity data indicate shallow basement on either side of the main basin, with a down throw underlying major part of the basin (Schematic cross section shown in Figure 2.4(b)). Dyke intrusions, with Table 2.1.

Shelf/slope characteristics off selected places over the ECMI (Murthy et al., 1993).

Location (See Figure 2.1)

Water depth at shelf break (m)

Shelf edge distance from coast (km)

Shelf gradient (ratio)

Slope gradient (ratio)

Depth at which marginal high (M.H.) is recorded (m)

Paradip

100

68

1 : 320

1 : 50

Not clear

Puri

130

56

1 : 300

1 : 43

Not clear

Chilka lake

220

52

1 : 200

1 : 28

800?

South of Chilka lake

220

47

1 : 200

1 : 35

Not clear

South of Gopalpur

220

51

1 : 200

1 : 16

1500–2000

Kalingapatnam

120

44

1 : 280

1 : 16

1800–2000

South of Kalingapatnam Visakhapatnam

130

53

1 : 345

1 : 15

2000–2100

200

54

1 : 250

1 : 12

1900–2100

North of Kakinada

200

57

1 : 225

1 : 12

2400–2600

Krishna river

70

35

1 : 300

1 : 25

Nizampatnam

70

57

1 : 300

1 : 25

Madras

200

55

1 : 200

1:8

Uncertain due to slumping over the slope Uncertain due to slumping over the slope 2700

North of Pondicherry Karaikal

90

51

1 : 400

1:6

3000

70

29

1 : 200

1 : 19

3000

Nagapattinam

70

47

1 : 340

1 : 17

3000

Remarks (only relative terms) Wide shelf, gentle slope Wide shelf, gentle slope Wide shelf, gentle slope Wide shelf, gentle slope Wide shelf, steep slope Narrow shelf, steep slope Wide shelf, steep slope Wide shelf, steep slope Wide shelf, steep slope Narrow shelf, gentle slope Wide shelf, gentle slope Wide shelf, very steep slope Wider shelf, very steep slope Narrow shelf, steep slope Narrow shelf, steep slope


24


north–south trends were inferred north and south of these two east-west fault trends. In the central part of the basin, a minor basement rise representing probable offshore extension of the Kumbakonam Ridge was also delineated (shown as KR in Figure 2.4(a)). Thus the Nagapattinam– Cuddalore part of Tamil Nadu margin is a structurally controlled basin flanked by two major fault lineations. The free-air gravity anomaly map (Figure 2.5) is characterized by a significant north–south trending linear gravity low with major discontinuities, FZ1 and FZ2 along 12◦ 15 N and 11◦ 45 N respectively, indicating major fault zones (Murty et al., 2002). The discontinuity observed in the gravity data (FZ1) correlates well with the major discontinuity observed in the magnetic data (F1). Similar trend has also been evidenced from the bathymetry, which may indicate a major structural trend. The east–west trending lineation F2, (Figure 2.4(a)) which correlates well with the landward Palghat–Cauvery Lineament (PCL) can be considered as its offshore extension. The PCL has been termed as a shear zone. These studies have also revealed a good correlation between land–ocean tectonics and coastal seismicity and the epicenter of a moderate earthquake of magnitude 5.6 that occurred on 26 September 2001 was located over the fault trend FZ1, which was inferred as the offshore extension of the Moyar–Bhavani–Attur (MBA) lineament (Figure 2.5 and Murty et al., 2002) Detailed bathymetry map and sections of the Nagapattinam–Cuddalore shelf (from 10.5◦ N to about 12◦ N, Figures 2.6(a) and (b)) indicate that one of the main reasons for the higher run-up heights and inundation in Nagapattinam–Cuddalore coast could be the concave shape of the shelf with a gentle slope, which might have accelerated the tsunami surge to flush through at a rapid force. Bathymetry sections off Pondicherry (CB3) and Cuddalore (CB4) indicate a gentle continental shelf and slope up to about 3000 m water depth representing the concave nature of the shelf. The sections off Vedaranyam (CB9) in the south and those in the north of Pondicherry (CB1 and CB2) indicate a wider shelf with a steeper slope (Figure 2.6(b)), representing the southern and northern boundaries of the concave shelf. The area within these boundaries is more affected by the tsunami surge. Earliest bathymetry observations over the offshore Cauvery basin revealed the presence of submarine canyons off Cuddalore and Pondicherry (Varadachari et al., 1968). Subsequent geophysical studies also suggested that major valleys off Pondicherry are formed due to the existence of mega lineaments (Rao et al., 1992). The lineament pattern played a major role in shaping the continental slope morphology, besides erosional and depositional processes (Figure 2.5 of Rao et al., 1992). The high run-up heights and inundation in case of Nagapattinam and Cuddalore shelf are therefore the result of a combination of a structurally controlled basin with a favorable seabed morphology. 2.4

COASTAL SEISMICITY

The effect of the Sumatra earthquake is relatively insignificant on the east coast of India, though its southern part, namely the Tamil Nadu coast is severely affected more by the tsunami surge. The Andaman and Nicobar Islands however were affected both by the earthquake and the tsunami. Nevertheless it is important to note that during the months of December 2004 to July 2005, the coastal areas all along the east coast of India have experienced tremors of few seconds duration both due to the main event of 26 December 2004, and by the aftershocks of 28 March 2005 (Mw 8.3) and 24 July 2005 (Mw 7.3). This is a new development and it is quite likely that the aftershocks are likely to continue in the Andaman and Nicobar region with relatively high frequency and with increased amplitude (>5.0). This implies that the coastal regions have to take note of this new seismic hazard. Hitherto the observed seismicity in the coastal regions of the Stable Continental Region (SCR) is mainly due to the reactivation of weak zones due to


(a)

(b)

Figure 2.4.

(a) Magnetic anomaly map of Cauvery basin, with structural interpretation (contour interval: 20 nT). (b) Schematic cross section of basement along Profile A–B of Cauvery Basin.


26


Figure 2.5.

Free air gravity anomaly map of Cauvery offshore basin (contour interval 10 mGal). FZ1 and FZ2 are the inferred faults. Location and focal mechanism of the Pondicherry earthquake are shown (Murty et al., 2002).

the stresses developed as a result of the northward movement of the Indian plate. However there is now a new possibility of reactivation of weak zones of the coastal areas, due to the aftershock, of high amplitude, occurring continuously at the eastern end, that is along the Andaman and Nicobar arc. Under these circumstances, it is very essential to carryout geophysical studies in the coastal region in order to identify the land–ocean tectonic lineaments and their correlation with earlier reported seismicity so that seismic zonation maps can be generated for the Coastal regions. Some attempts were made in this direction particularly over the Tamil Nadu and Andhra Pradesh margin. Geophysical data comprising of bathymetry, magnetic, gravity and in some cases shallow seismic data were collected on the continental shelf region of Tamil Nadu and Andhra Pradesh margin. These data sets were utilized to delineate the offshore extension of the Coastal lineaments. Correlation some of these lineaments with earlier reported seismicity



Figure 2.6.

27

(a) Bathymetry map of Cauvery offshore basin (F1 and F2 are fault trends inferred from Figure 4(a)). (b) Bathymetry sections of Cauvery offshore basin (horizontal scale: 1 cm = 15 km) (horizontal distance in cms as measured from Figure 4(a)).

indicate neotectonic activity associated with these lineaments. As a case study the Cauvery basin study is presented below. 2.5

EVIDENCE OF FAULT REACTIVATION OFF PONDICHERRY COAST FROM MARINE GEOPHYSICAL DATA

Present study is mainly focused on the northern part of the Cauvery offshore basin, between latitudes 10◦ –14◦ N and longitudes 80◦ –82◦ E (Figure 2.7), over which the bathymetry, gravity and magnetic data were collected (Murty et al., 2002). The bathymetry map (Figure 2.7) in general, shows a linear north–south trend, except between latitudes 10◦ 45 N and 12◦ 15 N, where the contours trend coastward indicating a major fault zone. Similar trend is also evidenced by the geophysical anomalies. The free-air gravity anomaly map (Figure 2.5) is characterized by a significant north–south trending linear gravity low with major discontinuities, FZ1 and FZ2 along 12◦ 15 N and 11◦ 45 N respectively, indicating major fault zones. Total field magnetic anomaly map (Figure 2.4) also shows two major discontinuities, F1 and F2 along 12◦ 15 N (off Pondicherry), and 10◦ 45 N (south of Karaikal), respectively (Subrahmanyam et al., 1995). The discontinuity observed in the gravity data (FZ1) correlates well with the major discontinuity observed in the magnetic data (F1). Similar trend has also been evidenced from the bathymetry,

Downloaded by [INFLIBNET Centre] at 07:51 27 August 2012 28 K.S.R. Murthy et al.

Figure 2.6.

(Continued)



Figure 2.7.

29

Bathymetry map of Cauvery offshore basin (Murty et al., 2002), dashed lines indicate ship tracks along which bathymetry and gravity data were acquired. Black dot in the offshore indicates the location of Pondicherry earthquake (Mw 5.5) of 25 September 2001. MBA: Moyar–Bhavani–Attur lineament; PCL: Palghat–Cauvery Lineament.

which may indicate a major structural trend. F1, trending eastnortheast–westsouthwest, which was interpreted earlier as an offshore extension of northeast–southwest trending Kumbum– Pondicherry lineament on land. The east–west trending lineation F2, which correlates well with the landward PCL can be considered as its offshore extension. Another major discontinuity, having eastnortheast–westsouthwest trend (FZ2), as observed in the gravity data, may be spatially correlated to the east–west trending MBA lineament on land. This lineament was interpreted as a shear zone and also been suggested as a suture zone and a steeply dipping thrust fault. It can be suggested that FZ2 may be the offshore extension of the MBA lineament (see Subrahmanyam et al., 1995 for references). An earthquake of M5.5, that occurred on 25 September 2001 off Pondicherry, can be considered as a fairly larger event for the south Indian shield so far. Located at 11.95◦ N and 80.23◦ E, the epicenter falls over the continental slope, about 40 km off Pondicherry at 1900 m water depth with a focal depth of 10 km. The epicenter of the earthquake falls over the reported fault zone FZ2, which has been interpreted as an offshore extension of the MBA lineament. The focal


30


mechanism solution of the earthquake (Figure 2.5) suggests thrust faulting and indicates small strike-slip component with left lateral motion along a northeast striking nodal plane (Rastogi, 2001). The other nodal plane in the solution strikes in the east–west direction and is preferred to be the fault plane on the basis of the seismicity trend in this region along 12◦ N latitude. Chandra (1977) has reviewed the seismicity of Peninsular India and obtained the focal mechanism solutions for some of the prominent earthquakes, including the Bhadrachalam (Mw 5.7, 1969) and Ongole (Mw 5.4, 1967) earthquakes. Some similarities can be drawn between these earthquakes and the Pondicherry earthquake, as they all fall in the vicinity of the 80◦ E longitude, along which the coastline trends nearly north–south in the south Indian shield. The fault-plane solutions suggest that they are of thrust type. Interestingly, the Ongole earthquake also suggests faulting along an east–west trending fault, which is very similar to the Pondicherry earthquake. Based on the qualitative analysis of geophysical data, it is conjectured that the Pondicherry earthquake might have occurred due to the release of compressional stresses along the fault zone FZ2, which may be the offshore extension of east–west trending MBA lineament. This further indicates the recent reactivation of the Precambrian shear zones in the offshore regions of Tamil Nadu, particularly the MBA lineament. Similar studies have been carried out on the land–ocean tectonics and neotectonics associated with some of these lineaments over the Palar basin, Visakhapatnam and Vizianagaram shelf of Andhra Pradesh (Subrahmanyam et al., 1999; Murthy et al., 2001). The results suggest reactivation of some coastal lineaments and thus form part of the seismicity associated with SCR regions, as discussed already. In the context of the seismicity experienced over the coastal regions of east coast of India in the post-Sumatra earthquake scenario, these studies assume significant importance and must be continued for the entire east coast.

ACKNOWLEDGEMENTS The authors are thankful to Dr. Satish R. Shetye, Director, N.I.O, Goa for his encouragement. Thanks are also due to Ms. T. Sridevi, Ms. Sunita Rani Panda, Ms. A. Anuradha and Ms. B. Adilakshmi and for their help in the preparation of the manuscript. REFERENCES Chadha, R.K., Latha, G., Harry, Y., Peterson, C., and Toshctama, K. (2005). The Tsunami of the Great Sumatra Earthquake of M.9.0 on 26, December, 2004 – Impact on the east coast of India. Curr. Sci., 88, 1297–1300. Chandra, U. (1977). Earthquakes of peninsular India – A seismotectonic study. Bull. Seism. Soc. of Am., 67, 1387–1413. Gupta, H.K. (2005). Early warning system for oceanographic disasters in Indian Ocean (tsunami and storm surges): The Indian initiative. J. Geol. Soc. India, 65, 639–646. McCloskey, J., Nalbant, S.S., and Steacy, S. (2005). Scientists issue Indonesia earthquake warning. Nature, 434, 582. Murthy, K.S.R. (1995). Some geodynamic complexities related to the evolution of Bengal Fan and the neotectonic activity of the South Indian Shield. Curr. Sci., 73, 10. Murthy, K.S.R. (2005a). First oceanographic expedition to survey the impact of the Sumatra earthquake and the Tsunami at 26th December 2004. Curr. Sci., 88, 1038–1039. Murthy, K.S.R. (2005b). Oceanographic expedition to study the Post-Tsunami impact in the Bay of Bengal and Andaman and Nicobar Islands, paper presented at the International Symposium on “External Flooding Hazards at Nuclear Power Plant Sites” (IAEA/NPCIL) held at Kalpakkam, Tamilnadu, India, 29th August, 2005.



31

Murthy, K.S.R., Rao, T.C.S., Subrahmanyam, A.S., Malleswara, Rao M.M., and Lakshminarayana, S. (1993). Structural lineaments from magnetic anomaly map of eastern continental margin of India and Bengal Fan. Mar. Geol., 114, 169–183. Murthy, K.S.R., Subrahmanyam, A.S., Lakshminarayana, S., Chandrasekhar, D.V., and Rao, T.C.S. (1995). Some geodynamic aspects of Krishna–Godavari basin, east coast of India. Conti. Shelf Res., 15, 779–788. Murthy, K.S.R., Malleswara Rao, M.M., Venkateswarlu, K., Subrahmanyam, A.S., Lakshminarayana, S., and Rao, T.C.S. (1997). Marine magnetic anomalies as a link between granulite belts of east coast of India and Enderbyland of Antarctica. J. Geol. Soc. India, 49, 153–158. Murthy, K.S.R., Subrahmanyam, A.S., Murty, G.P.S., and Sarma, K.V.L.N.S. (2001). Reactivation of some land–ocean tectonic lineaments of the eastern continental shelf under the compressional stress regime in the South Indian Shield – A Geophysical study, 38th Annual Convention of IGU, Visakhapatnam, pp. 47–48. Murty, G.P.S., Subramanyam, A.S., Murthy, K.S.R., and Sarma, K.V.L.N.S. (2002). Evidence of Fault Reactivation off Pondicherry Coast from Marine Geophysical Data. Curr. Sci., 83, 1446–1449. Radhakrishna, B.P. (2005). Devastating Tsunami strikes coastline of India on 26th December 2004. J. Geol. Soc. India, 65, 129–134. Rao, L.H.J., Rao, T.S., Reddy, D.R.S., Biswas, N.R., Mohapatra, G.P., and Murty, P.S.N. (1992) Morphology and sedimentation of continental slope, rise and abyssal plain of western part of Bay of Bengal. Geol. Surv. of India, Special Publication, 29, 209–217. Rastogi, B.K. (2001). A note on the Focal Mechanism of Pondicherry earthquake. EQ News, Biannu. News Lett., Department of Science and Technology (DST), New Delhi, 2, 3. Raval, U. (2005). Some factors responsible for the devastation in Nagapattinam region due to Tsunami of 26th December 2004. J. Geol. Soc. India, 65, 647–649. Satish Singh (2005). Sumatra earthquake indicate why the rupture propagated Northwards. EOS, 86, 48. Sieh. K. (2005). Aceh-Andaman earthquake: What happened and what next? Nature, 434, 573–574. Subrahmanyam, A.S., Lakshminarayana, S., Chandrasekhar, D.V., Murthy, K.S.R., and Rao, T.C.S. (1995). Offshore Structural trends from magnetic data over Cauvery Basin, east coast of India. J.Geol. Soc.India, 46, 269–273. Subrahmanyam, A.S., Venkateswarlu, K., Murthy, K.S.R., Malleswara Rao, M.M., Mohan Rao, K., and Raju, Y.S.N. (1999). Neotectonism–An offshore evidence from eastern continental off Visakhapatnam, Curr. Sci., 76, 1251–1254. Subrahmanyam, C., Gireesh, R., and Gahalaut, V. (2005). Continental slope characteristics along the Tsunami – affected areas of eastern offshore of India and Sri Lanka, Jour Geol. Soc. India, 65, 778–780. Subramanian, B.R. (2005) – Restricted circulation. Preliminary report on studies of seismic pattern, tidal pattern and submergence to help locate resettlement areas in Andaman and Nicobar Islands, submitted to Department of Science and Technology, New Delhi. Varadachari, V.V.R., Nair, R.R., and Murthy, P.S.N. (1968). Submarine canyons off the Coramandel coast. Bull. Nat. Inst. Science, 38, 457–462.


CHAPTER 3

Tsunamigenic Sources in the Indian Ocean: Factors and Impact on the Indian Landmass


R.K. Chadha National Geophysical Research Institute, Hyderabad, Andhra Pradesh, India

3.1

INTRODUCTION

The Indian Ocean Tsunami of December 26, 2004 was the deadliest ocean related disaster in living memory, claiming about 300,000 human lives. The event was associated with the world’s second largest earthquake of M9.3 which occurred off the coast of Sumatra in Sunda trench. Initially, the magnitude of this earthquake was estimated to be 9.0. This became an extraordinary event due to its magnitude and rarity of this phenomenon in the Indian Ocean region relative to Pacific Ocean, where tsunami are very frequent. The tsunami from Sumatra propagated throughout the oceans on the earth with devastating effects on the Indian Ocean rim countries like Indonesia, Thailand, Malaysia, Myanmar, Bangladesh, India, Sri lanka, Maldives and Africa (Figure 3.1).

Figure 3.1.

Map of Indian Ocean rim countries affected by the December 26, 2004 Indian Ocean Tsunami due to M9.3 earthquake off the coast of Sumatra. M8.7 earthquake on March 28, 2005 which occurred 250 km south of December 26 event is also shown. (Source: http://www.USGS.gov, adapted and modified.)

33

34

R.K. Chadha

Another great earthquake of M8.7 occurred on March 28, 2005 about 150 km further southeast of the December 2004 event, with its hypocenter below Nias Island in the Sunda trench. This earthquake set off alarms leading to tsunami warnings along the Indian east coast and also in parts of Indonesia and Thailand. The tsunami warnings were called off within few hours, as this earthquake did not generate any consequential tsunami. Although this earthquake was 6 times smaller than the December 26, 2004 earthquake, it was still strong enough to generate large tsunami. However, there was only a single report of small tsunami of few tens of centimeters height from Cocos Islands.


3.2

CAUSES OF TSUNAMI

Tsunamis are water waves generated by the disturbance caused by submarine earthquakes, landslides, explosive volcanism and meteorite impact with the ocean. Among these, submarine earthquakes are the major cause for tsunami generation. More than 90% of the tsunamis generated in the Pacific Ocean over the last 200 years were caused due to earthquakes. But, not all earthquakes generate tsunamis. Major factors for tsunami generation are: (i) magnitude, (ii) depth and (iii) the nature of earthquake faulting and rupture of ocean floor. It has been generally observed that the tsunami caused by earthquakes of M7.5–7.8 are local in nature and will not cause great damage at distant regions. However, this type of events can cause secondary effects like triggering submarine landslides or slumps. Most of the earthquakes of magnitude greater than 7.9 cause both destructive local tsunamis near the epicenter and also significant sea level changes leading to high run-up heights causing severe damages at great distances. The second most important factor is the depth of the earthquake. Shallow marine events that deform the seafloor generate tsunami rather than a deeper event. Lastly, earthquakes with thrust or normal fault mechanism are more likely to generate a tsunami than a strike-slip fault where there is only horizontal displacement. Submarine landslides can also generate tsunamis in some cases, provided volume of material moved is substantial and move at a great speed. The characteristics of these tsunamis are different from those of earthquake generated, which displaces seabed. In case of earthquakes the maximum energy is focused perpendicular to the strike of the fault and decreases in intensity along the strike of the fault. The landslide-generated tsunamis are more focused. The slide moves in a down slope direction and the wave propagates both upslope and parallel to the slide. While earthquakegenerated waves are very symmetrical close to their source, landslide generated ones have a shape that is best characterized by N-shaped waves. The wave train is led by a very low crested wave followed by a trough up to 3 times greater in amplitude. The second wave in the wave train has the same amplitude as the trough, but over time, it decays into three or four waves with decreasing wave periods. The initial inequality between the crest of the first wave and the succeeding trough enables landslide-generated tsunami to acquire greater run-up heights than those induced by earthquakes (Bryant, 2001). Submarine eruptions within 500 m of the ocean surface can disturb the water column enough to generate a surface tsunami wave. Below this depth, the weight and volume of the water suppress surface wave formation. Tsunami from this cause rarely propagates more than 150 km from the site of eruption. More significant are submarine explosions that occur when ocean water comes in contact with the magma chamber. This water is converted instantly to steam and in the process produces a violent explosion. Krakatau volcanic explosion during 1883 produced a tsunami of 40 m height killing 36,000 people mostly on the islands of Java and Sumatra. The impact of the meteorite into an ocean can also cause tsunami, but more dangerous will be the splash that travels at high velocity for hundreds of kilometers and fall back to the surface of the earth over equivalent distances. But this is a very rare phenomenon.


Tsunamigenic sources in the Indian Ocean

Figure 3.2.

35

Map showing different tectonic plates and locations of subduction zones (solid lines) and mid-oceanic ridges (zig-zag lines). Red dots are volcanoes. (Source: www.usgs.gov)

3.3 TECTONIC ENVIRONMENT OF TSUNAMI Typically, large earthquakes in the subduction zones or trenches are the main source of tsunami generation through out the world oceans. The tsunami can be generated either by earthquake faulting which deforms the ocean floor or by triggering a huge submarine landslide. The Pacific Ocean is encircled through out with such trenches due to the interaction of the Pacific plate with other plates like, Nazca, Cocos, Indo-Australian, Eurasian, Kamchatka, Philippines, North American and South American plates. Most of the world’s great earthquakes have occurred in these subduction zones, which are seismically very active and often referred to as “Ring of Fire” (Figure 3.2). The Hawaiian Hot Spot is another source of tsunami generation in the Pacific Ocean. During 1900 to 2001, 796 tsunamis were observed or recorded in the Pacific Ocean according to the Tsunami Laboratory in Novosibirsk, Russia. Of them, 117 caused casualties and damage, mostly near the source, and 9 caused widespread destruction throughout the Pacific. The greatest number of tsunamis during any 1 year was 19 in 1938, but all were minor and caused no damage. There was no single year of the period that was free of tsunami. Seventeen percent of the total tsunamis were generated in or near Japan. The distribution of tsunami generation in other areas is as follows: South America, 15% ; New Guinea Solomon Islands, 13%; Indonesia, 11%; Kuril Islands and Kamchatka, 10%; Mexico and Central America, 10%; Philippines, 9%; New Zealand and Tonga, 7%; Alaska and west coasts of Canada and the United States, 7% ; and Hawaii, 3% (www.prh.noaa.gov/ptwc/abouttsunamis.htm). Compared to this, there are a very few tsunami reported in the Indian Ocean during the last 200 years, viz., (i) 1883 due to Krakatau volcanic explosion, (ii) December 31, 1881 due to Mw 7.9 earthquake in the Nicobar Islands, (iii) June 26, 1941 due to Mw 8.1 earthquake in the Andaman Islands, (iv) November 27, 1945 due to M8.3 earthquake in the Makran coast, Arabian Sea and (v) December 26, 2004 due to M9.3 earthquake off the coast of Sumatra.


36

R.K. Chadha

Figure 3.3.

3.4

Epicenters of the earthquakes of M > 7.0 for the Indian Ocean are shown with different colors of varying depths. Two sources of tsunami generation, Andaman–Sumatra in the east and Makran coast in the west are shown by ellipses. (Source: http://www.USGS.gov, adapted and modified.)

INDIAN OCEAN TSUNAMI SOURCES

Indian Ocean exhibits an environment dominated by the presence of mid-oceanic ridges where Indo-Australian and African plates are moving away from the Antarctic plate along these ridges. The earthquakes associated with these ridges are mostly occurring on strike-slip faults where the dominant movement is horizontal along transform faults and hence, not a source for tsunami generation. Due to the movement of the Indian plate in north northeast direction, the subduction zones are confined in the north along the Himalayan region due to the continent–continent collision between Indian and Eurasian plates, in the east along the Andaman–Sumatra Sunda trench where the Indian plate is subducting below the Burmese plate, and a small subduction zone in the west along Makran coast, near Karachi, Pakistan. Thus, the Andaman–Sumatra and Makran subduction zones are the two main sources in the Indian Ocean (Figure 3.3) where earthquakes of magnitudes between 7.9 and above can occur giving rise to tsunamis, which can affect the east and the west coasts of India. 3.4.1 Andaman–Sumatra Tsunami source The M9.3 earthquake off the coast of Sumatra triggered the tsunami (Figure 3.4). The earthquake occurred due to the thrusting of the Burmese plate over the Indian plate. The fracture propagated unidirectionally from Sumatra, toward north along the arcuate plate boundary paralleling the Andaman and Nicobar Islands, at a velocity of about 2.4 km/s for the first 600 km and then it slowed down to about 1.5 km/s (de Groot-Hedin, 2005). The total length of the fracture as seen from the aftershocks distribution is about 1250 km. McCloskey et al. (2005) estimated a maximum displacement of the order of about 20 m, with most of the slip being concentrated in the first 500 km from the epicenter. The 10–20 m of the



Figure 3.4.

37

Map showing tectonics of the Indo-Australian plate viz-a-viz Burma and Sunda plates. Yellow and Red stars show the epicenter of M9.3 earthquake on December 26, 2004 and M8.7 on March 28, 2005. Solid arrows are direction of the movement of the Indo-Australian plate. Aftershocks are shown in yellow circles. (Source: http://www.USGS.gov)

vertical displacement of the ocean floor, up to a distance of about 600 km in the first 3–4 min, caused enormous displacement of water in the Indian Ocean, creating large-scale tsunami which then traveled to several thousands of kilometers in the world oceans. As the tsunami source was large and elongated in the northwardly direction from Sumatra, the east coast of India and Sri Lanka were the worst affected in the west. On March 28, 2005, another great earthquake of M8.7 occurred 150 km further southeast of the December 26, 2004 event. This event also occurred on a thrust fault in Sunda trench at a depth of 30 km. The fracture propagation for this event was also unidirectional but in the southeast direction from the epicenter for a length of about 300 km as seen from the aftershock zone (Figure 3.4). From the modeling of earthquake ruptures of these two earthquakes (Lay et al., 2005; Ammon et al., 2005) and their directions, Singh (2005), showed that a lithosphere-scale boundary around Simeulue Island could have acted as a barrier for rupture propagation on either side of this boundary. Earlier, Ritzwoller et al. (2005) have shown that December 26, 2004 earthquake got initiated where the incoming Indian plate lithosphere is warmest and the dip of the WadatiBenioff zone is least steep along the subduction zone extending from the Andaman trench to the Java trench. Anomalously high temperatures are observed in the supra-slab mantle wedge in the


38

R.K. Chadha

Figure 3.5.

(a) Reference map showing the locations of the principal geological features in the Indian Ocean. The red star marks the location of the initiation of rupture of the great Sumatra– Andaman earthquake. Brown lines show active and fossil plate boundaries. Arrows show the relative plate motions. The age of the incoming oceanic plate is shown with colors in millions of years. (b) Distribution of the apparent thermal age which results from the seismic inversion using the thermal parameterization. It is defined as the lithospheric age at which a purely conductive temperature profile would most closely resemble the observed thermal structure (after Ritzwoller et al., 2005).

Andaman back-arc. The subducting slab is observed along the entire plate boundary to a depth of at least 200 km. These factors contribute to the location of the initiation of rupture, the strength of seismic coupling, the differential rupture speed between the northern and southern segments of the earthquake, and the cause of convergence in the Andaman segment (Figure 3.5(a) & (b)). The subduction zone boundary from Andaman and Nicobar Islands to Sunda trench in the Indian Ocean has experienced several great earthquakes in past which either generated or had the potential to generate tsunami (Ortiz and Bilham, 2003). Figure 3.6 shows rupture areas of four great earthquakes since 1800. From the rupture areas and the damages, these earthquakes could be of M ≥ 8.0. It is seen from the figure that the December 26, 2004 event occurred in the gap between 1861 and 1881 earthquakes in the Sumatra–Nicobar region and ruptured a fault length of about 1250 km from Sumatra to Andaman including areas ruptured in earlier earthquakes during 1881 and 1941. The March 28, 2005 episode, however, ruptured a 300 km fault segment in southeast direction agreeing with typical fault lengths associated with earthquakes with M8.0 or greater. It is now observed that earthquakes with M ≥ 9.0 will have greater fault lengths like, 1960 Chile earthquake of M9.5 with 1000 km, 1964 Alaska earthquake of M9.1 with 700 km and now 2004 Sumatra earthquake of M9.3 with about 1300 km. 3.4.2

Makran Tsunami source

The convergence of the Indian plate with the Arabian and Iranian microplates of the Eurasian tectonic blocks has created an active east–west subduction zone along the Makran coast in southern



Figure 3.6.

39

Map showing rupture areas of four great earthquakes in the subduction zone from Andaman and Nicobar Islands to Sunda trench. Star shows epicenter of December 26, 2004 earthquake of M9.3 (figure from http://www.drgeorgepc.com).

Pakistan. Although large earthquakes along the Makran subduction zone are infrequent, the November 28, 1945 earthquake generated a tsunami which claimed more than 4000 human lives in southern Pakistan, and affected western coast of India, Iran, Oman and possibly elsewhere in other Indian Ocean islands (Figure 3.7). 3.5

IMPACT ON THE INDIAN LANDMASS

The impact of the tsunami was immediate and highest in the Andaman and Nicobar Islands as they were lying on the tsunami source. Small islands were totally inundated and in one case an island was cut up into two parts due to tsunami water, which overran the entire island from one end to the other. A maximum tsunami run-up height of 7.0 m was observed at Malacca in Car Nicobar Islands. The maximum tsunami run-up height is defined as the vertical water-surface elevation reached by the tsunami above sea level. It is measured using the standard surveying techniques and instrumentation.


40

R.K. Chadha

Figure 3.7.

(a) Makran subduction zone west of Karachi, Pakistan. (b) Vulnerability of the Indian west coast to the tsunami generated in Makran coast (figures from http://www.drgeorgepc.com).

The most severe distant effects were observed along the western coast of India, more than 2000 km from the tsunami source. These effects were studied in detail by several workers to understand the impact along the east coast of India (Chadha et al., 2005; Yeh et al., 2005; Peterson et al., 2005). These studies describe the measurements of maximum tsunami run-up heights and inundation distances, flow patterns of tsunami runup and rundown, recording of eyewitness accounts, examination of sediment deposits, observations of structural damages, etc. Because of the distant tsunami, no observation of subsidence, uplift, and landslides was made, although geomorphological changes due to tsunami were examined. The tsunami took about 150 min to reach the east coast of India. The worst affected was the coastline along Tamil Nadu coast from Chennai in the north to Nagapattinam in the south. Relatively, the Andhra Pradesh coast suffered less. The tsunami claimed 106 human lives, with Krishna and Prakasam districts recording 27 and 35 deaths, respectively. Other affected districts were Guntur, Nellore, west Godavari, east Godavari and Vishakapatnam. The tsunami is reported to have encroached 500 m to 2 km inland at various places owing to the flatness of several beaches. Tide gauge recorder at Vishakapatnam port in Andhra Pradesh showed tsunami heights to be about 1.4 m at 09:05 h (IST). Although, eyewitnesses reported tsunami heights up to 5 m, the surveys showed the maximum tsunami run-up height to have reached about 2.5 m along Andhra Pradesh coastline with higher splashes at a few places. However, there was a general agreement amongst



41

Figure 3.8. Tsunami run-up heights along the east coast of Tamil Nadu. Numbers in the figure are tsunami heights in meters.

the people that four waves hit the coast in which the second wave was the strongest claiming most of the lives. Several people reported receding of the sea up to 500 m prior to the arrival of tsunami waves in the region. The 350-km-long stretch of the shoreline of Tamil Nadu state from Pulicat (13.3◦ latitude) in the north to Vedaranniyam (10.3◦ latitude) in the south was affected to varying degrees. The tsunami run-up heights varied between 2.5 and 5.2 m in these regions after applying tidal corrections from tide tables published by Survey of India. Maximum surge elevations were also measured and found to vary between 3.8 and 6.0 m (Mean tidal level). Shore-normal inundation profiles studied at 11 locations to estimate the run-up heights of the tsunami along this section are shown in Figure 3.8. Survey localities were selected on the basis of the reports of maximum damage and loss of lives. The profiles within the survey localities were selected on the basis of representative high-water marks and line-of-sight traverses to beach swash zones. High-water marks were measured from the highest elevations of several different indicators. These indicators include: (i) mud lines on standing structures, i.e., maximum still-water elevation, (ii) physical damage to standing structures, i.e., maximum surge elevation and (iii) flotsam debris on tree branches, roofs and ground slopes, i.e., maximum splash elevations and/or maximum inundation distances. Maximum still-water elevations were preferentially taken from interior wall mud line, which should minimize effects from turbulent flow around structures. Exterior wall mud lines were used where horizontal mud lines could be correlated between buildings. The vertical distance between the highest horizontal mud line and ground elevation, i.e., tripod footings surface was measured to the nearest centimeter with a tape. Maximum surge elevations were estimated from features reflecting apparent large debris damage at elevations above the mud lines. These features included displaced roof tiles, broken masonry, fresh gouges in plaster and heavy woody debris left in broken or bent tree branches. Maximum splash elevations were established from light flotsam hanging in limbs of standing vegetation and/or draped on standing structures such as railings and roofs. Horizontal sighting distances were generally less than 100 m between level and stadia rod. Elevations were measured to the nearest centimeter. Total profile errors of ±0.1 m

42

R.K. Chadha 4

Elevation (m)

Tsunami inundation 3 2 1


Sea level 0 50

0

50

100

150

Inshore distance from the shore (m)

Figure 3.9. A shore-normal beach profile at Devanaampatnam (11◦ 44.589 N 79◦ 47.289 E). The sea level shown in the figure is the level at 9 a.m. IST on December 26, 2004, the time of tsunami attack.

are assumed for the single sighting, single direction, leveling surveys. End points of the profiles were approximately located by 12-channel GPS using the WGS84 datum. Three levels of flow competence were established from maximum landward transport of gravel, sand and flotsam debris. The gravel-size material included large (>2-cm diameter) shells, brick and mortar fragments and road gravel. General lack of gravel source material likely precluded evidence of high-flow competence in some areas. Beach sand (0.06 to 2 mm grain diameter) was present in almost all the profiles. Maximum inundation positions were generally evident from semicontinuous lines of debris that crossed streets, vacant lots, fields and wetland surfaces. Large inundation distances in some locations were related to localized flow through dune-ridge gaps or tidal inlets. Overland flow direction was measured from several different features. These features included vegetation, flop-overs and debris shields wrapped around trunks and sand ripples and linear-scours. Figure 3.9 shows a shore-normal beach profile at Devanaampatnam. The true inundation was measured at the mud line inside the house in Devanaampatnam shown in Figure 3.10 (Yeh et al., 2005). Three zones of flow competence were established from the maximum transport distances of gravel, sand and flotsam in the 11 profiles surveyed. Gravel transport ranged from 30 to 60-m distance from the swash zone in Pattinapakam, Periakalapet, Devanaampatnam and Tarangambadi profiles. The gravel-size clasts were largely derived from tsunami damaged brick walls, foundations and roofing tiles in the region. Maximum sand transport ranged from 90 to 430-m distance from the swash zone in most of the profiles (Table 3.1). Beach width in most of the profiles varies between 30 and 80 m, except at Parangipettai and Nagapattinam where it was about 300 m. With the exception of these profiles, the average sand transport distance is about 100 m beyond the beach backshore. Tsunami sand deposits ranged from coarse upper (700–1000 µ) to very fine upper (88–125 µ) in grain size, based on comparisons with grain-size cards. Sand sheet thickness ranged from several tens of centimeters near beach backshore to 1 cm thickness at the distal end of sand transport. With increasing distance landward, the mean grain size of the sand sheets appeared to decrease. The graded sequence from coarse to fine upwards in each of 2–3 sand layers was observed at the 80 m position at Devanaampatnam. Maximum inundation distances along the profiles were established on the basis of most landward distribution of flotsam in debris lines or of anomalous articles, e.g., clothing mats, fishing floats etc. Maximum inundation ranged between 140 and 800 m from the swash zone. Based on local topography, flow direction indicators and the orientation of debris lines it was apparent that maximum landward



43

Figure 3.10. Water marks in house in Devanaampatnam (photograph: R.K. Chadha). Table 3.1.

Details of tsunami run-up surveys along the coast of Tamil Nadu.

Sl. No.

Location

1

Pulicat

2

Pattinapakam

3

Kovalam

4

Kalpakkam

5

Periakalapet

6

Puttupatnam

7

Devanaampatnam

8

Parangipettai

9

Tarangambadi

10

Nagapattinam

11

Vedaranniyam

Latitude ◦ N/ Longitude ◦ E

Run-up elevation (m)

Lateral inundation (m)

Maximum sand distance (m)

13◦ 23.040 / 80◦ 19.984 13◦ 01.263 / 80◦ 16.722 12◦ 47.455 / 80◦ 15.003 12◦ 30.378 / 80◦ 09.688 12◦ 01.544 / 79◦ 51.888 11◦ 51.618 / 79◦ 48.926 11◦ 44.576 / 79◦ 47.230 11◦ 30.965 / 79◦ 45.947 11◦ 01.620 / 79◦ 51.350 10◦ 45.785 / 79◦ 50.928 10◦ 23.597 / 79◦ 52.014

3.2

160

90

2.7

145

120

4.3

180

120

4.1

360

190

3.9

170

130

2.6

–

–

2.5

340

180

2.8

700

400

4.4

400

150

5.2

800

430

3.6

–

–

R.K. Chadha

inundation occurred by lateral flow at Pulicat, Devanaampatnam, Parangipettai and Tarangambadi. Lateral flows filled interdune-ridge valleys that were landward of shore-parallel dune ridges at Devanaampatnam and Parangipettai. The interdune-ridge valleys at the landward ends of these two profiles were connected to tidal inlet channels. Lateral flow also filled shallow valleys in Pulicat and Tarangambadi where breaches in shore-parallel dune-ridges allowed tsunami to inundate back-ridge areas. Flow features were recorded in most of the profiles that include vegetation flop-over, orientated beams, debris shields around tree trunks and sand ripples. The mean bearing of measured flow direction was observed to be 250◦ from true north. The data suggest an oblique angle of tsunami wave attack, particularly in profiles between 11.5◦ and 12◦ latitude where the shoreline trends north northeast. The tsunami wave attack was observed to be of the order of 30–40◦ from shore normal, in the study area. It is remarkable that the run-up heights are fairly uniform (2.5–5.2 m) along the 600-km long coast of Andhra Pradesh and Tamil Nadu states of the Indian east coast. The energetic and uniform tsunami run-up distribution along the very long coastal stretch must be attributed to its very long tsunami source coinciding with the initial rupture of the fault plane of the December 26, 2004 earthquake. Variations in the run-up heights must be caused by the bathymetry and coastal topography. According to the General Bathymetric Chart of the oceans (GEBCO), depth of the Bay of Bengal is fairly uniform with very gradual inclination toward north. Ninetyeast Ridge is the only major disturbance in the abyssal plain but it is running in the north–south direction, perpendicular to the tsunami propagation and parallel to the Indian coast; hence the wave refraction must be minimal. The topography along the coast is fairly straight without significant features of headlands, sounds and coves. Furthermore, the incident tsunami was very long – approximately 430 km – hence detailed bathymetry in small scale could not cause significant local amplification. The continental shelf along the south-east coast is narrow (ranging less than 20–50 km long), and the continental slope is steep. The exception is the south of 10◦ 30 N, near Palk Straight facing Sri Lanka, where the breadth of continental shelf becomes as wide as 100 km. Figure 3.11 shows a typical bathymetry profile taken from the Marine Chart along 13◦ N (DMA63270), south of Pulicat; the continental shelf is about 40-km wide and the continental slope is approximately 1/10. 0 500

Bathymetry profile along 13°N

1000 Depth (m)


44

1500 2000 2500 3000 3500 4000

0

20

40

60 80 Distance offshore (km)

Figure 3.11. A Bathymetry profile along 13◦ N, south of Pulicat lake.

100

120

140

Tsunamigenic sources in the Indian Ocean 3.6

45

FACTORS OF TSUNAMI IMPACT ON INDIAN COAST

Several factors that are responsible for severe impact on Indian coast line have become obvious from the earthquakes of December 26, 2004 and March 28, 2005. The most critical factors are as follows.


3.6.1

Strike of the fault

The strike of the earthquake fault is one of the most important factors in energy distribution in case of a tsunami. The maximum energy is focused perpendicular to the strike of the fault and decreases in intensity toward the strike direction. The M9.3 earthquake on December 26, 2004 occurred on a mega-thrust with 10–20 m of vertical slip on the fault. The rupture propagated from Sumatra in northwest direction up to Nicobar Islands and then turned toward Andaman Islands in the north. Due to this large earthquake source, the tsunami propagated with maximum energy in the perpendicular direction, toward Sri Lanka, east coast of India, Maldives and African countries that are located in this path. Although, there were few deaths reported from Bangladesh, the impact of tsunami was minimal along the northern coastal regions of India in Orissa and West Bengal where tsunami of few centimeters height were reported. 3.6.2

Energy dissipation

During the propagation of tsunami in the open ocean, the energy gets dissipated whenever there is an obstruction. This is one of the reasons that the coastal regions in the Palk Bay, between India and Sri Lanka viz., Rameswaram, Ramananthapuram and Tuticorin Port along the Tamil Nadu coast did not suffer damage because of the natural protection provided by the presence of Sri Lanka Island in front of them which took the frontal attack of the tsunami. But due to the wrap-up effect, which is caused by focusing of energy into the marginal areas of a bay, the Kanyakumari region, situated at the tip of the Indian landmass and some parts of Kerala on the western coast of India were also affected. The damage was more in some coastal regions of Kerala due to the reflection of tsunami from Maldives in the Indian Ocean. Similarly, the western coast of Sri Lanka suffered less damage compared to the east and southern coast. 3.6.3

Coastal topography

The observations made during tsunami run-up surveys clearly show the role of coastal topography on the impact of a tsunami attack. The run-up heights were found to be in the range from 2.5 to 5.2 along the east coast of India. Most of the loss of life and damage to property was in the first 100 m from the shore where several settlements were washed away. Small differences in local run-up and coastal topography resulted in large differences in tsunami inundation and associated loss of life and damage within the Tamil Nadu coastal areas. However, the combination of local high runup, low topography and dense development apparently accounted for the large loss of lives and property. The surge water elevations, together with surge water depths appear to be other important parameters during a tsunami attack. Another important coastal feature like low valleys behind shore-parallel dune ridges claimed several lives due to lateral flows from tidal inlets or from breaches in the dune ridge. 3.7

SUMMARY

The December 26, 2004 Great Indian Ocean Tsunami is undoubtedly a remarkable event because of its size and the aerial extent of damage caused in several of the Indian Ocean countries. This


46

R.K. Chadha

event has also provided an impetus to explore both basic and applied research in tsunami science and engineering fields in the Indian Ocean, which will lead to better preparedness for the future disaster. Although the causes of tsunami are many, more than 90% of them are generated due to large earthquakes associated with thrust faulting in subduction zones. Unlike the Pacific Ocean where the tsunami sources are several in view of the subduction zones which surround the entire Pacific plate, the Indian Ocean has mainly two such sources, viz., Andaman–Sumatra and Makran subduction zones in the east and west, respectively. Both these sources are distant sources of tsunami generation and hence, the chances of India being affected by the local tsunami are remote. The danger from local tsunami generation is mostly limited to the Andaman and Nicobar Islands. The entire east coast of India is vulnerable to varying degree of tsunami threat from large earthquakes occurring in the Andaman–Sumatra subduction zone. The three primary conditions for earthquakes to generate tsunami are: (i) the magnitude should be ≥7.9, (ii) the nature of faulting should be either thrust or normal and (iii) the earthquake should be shallow enough to cause vertical uplift in the ocean floor. The December 26, 2004 earthquake off the coast of Sumatra fulfills all these three conditions, as the magnitude was M9.3, the faulting was a thrust type, the depth was 30 km or less which deformed the ocean floor by 10–20 m. Although the earthquake of M8.7 below the Nias Island in Sumatra, on March 28, 2005 was strong enough, it did not deform the ocean floor. Further, the focus of the earthquake was below the Nias Island and any displacement of ocean water would not have been significant to create large tsunami, even if there is some deformation of the ocean floor. However, there were reports of few centimeters of tsunami recorded at Cocos Islands. Even if a tsunami was generated due to this earthquake, it must have propagated in the open ocean, as the strike of the earthquake fault is west northwest. This also brings the important factor of focusing of energy in perpendicular direction of the strike of the fault. Similarly, an earthquake of M8.1 which occurred on December 24, 2004, south of Australia, did not generate any tsunami as this earthquake occurred on a strike-slip fault associated with the spreading mid-oceanic ridge. From the Indian point of view, if tsunamis are generated due to the earthquakes occurring on the Andaman–Nicobar section of the subduction zone, which has a north northwest to north– south trend, the impact on the east coast of India will be much severe due to directivity of energy and also lesser distance to the Indian coastline. Conversely, if tsunamis are generated due to earthquakes further south along the Sumatra–Java axis along the Sunda trench, it will not have any damaging effect on the Indian coast, as the strike of the fault in this region changes to west northwest to east–west. On the western side the Indian coast is likely to be affected due to large earthquakes in the Makran subduction zone, southern Pakistan. There are reports of tsunami affecting coastal regions up to Goa on the west coast of India, during the earthquake of November 28, 1945 earthquake in Makran subduction zone. In the recent times, there have been some suggestions about the breakup of Indo-Australian plate into two along an east– west nascent boundary developing in the Indian Ocean (Orman et al., 1995). There have been few earthquakes recorded from this region. At present the tsunami potential of this region is unknown. Earthquakes generating tsunami have occurred in the past, it has occurred now and will continue to occur. To mitigate this hazard, efforts in three directions are needed. On one hand, work has to be done in terms of developing a Tsunami Early Warning System for the Indian Ocean based on online monitoring of damaging earthquakes with all its parameters and tsunami propagation modeling in the Indian Ocean. On the other hand, tsunami hazard maps have to be prepared showing the possible inundation areas in case of a tsunami attack. Lastly, educating people and disseminating information about the impending disaster to the people likely to be affected is another important aspect which should be looked into from the mitigation point of view.


47

ACKNOWLEDGEMENT I am thankful to Profs. Tad Murthy and U.Aswathanarayana for inviting me to contribute this paper to their book on tsunami and also making suggestions during the preparation of this manuscript. I am grateful to the Director, National Geophysical Research Institute, Hyderabad, India for fruitful discussions. The information provided by Dr. George Pararas-Carayannis is gratefully acknowledged.


REFERENCES Ammon, C.J., Chen, J., Thio, H.-K., Robinson, D., Ni, S., Hjorleifsdottir, V., Kanamori, H., Lay, T., Das, S., Helmberger, D., Ichinose, G., Polet, J., and Wald, D. (2005). Rupture process of the 2004 Sumatra–Andaman earthquake. Science, 308, 1133–1139. Bryant, E. (2001). Tsunami – The Underrated Hazard, Cambridge University Press, UK, 320 pp. Chadha, R.K., Latha, G., Yeh, H., Peterson, C., and Katada, T. (2005). The tsunami of the great Sumatra earthquake of M 9.0 on 26 December 2004 – Impact on the east coast of India. Curr. Sci., 88(8), 1297–1300. de Groot-Hedin, C.D. (2005). Estimation of the rupture length and velocity of the Great Sumatra earthquake of December 26, 2004 using hydroacoustic signals. Geophys. Res. Lett., 32, L11303, doi:10.1029/2005GL022695. Lay, T., Kanamori, H., Ammon, J., Nettles, M., Ward, S.N., Aster, R.C., Beck, S.L., Bilek, S.L., Brudzinski, M.R., Butler, R., DeShon, H.R., Ekstrom, G., Satake, K., and Sipkin, S. (2005). The great Sumatra– Andaman earthquake of 26 December 2004. Science, 308, 1127–1132. McCloskey, J., Nalbant, S.S., and Steacy, S. (2005). Earthquake risk from so-seismic stress. Nature, 434, 291. Orman, J., Van Cochran, J.R., Weissel, J.K., and Jestin, F. (1995). Distribution of shortening between the Indian and Australian plates in the central Indian Ocean. Earth Planet. Sci. Lett., 133, 35–46. Ortiz, M., and Bilham, R. (2003). Source area and rupture parameters of the 31 December 1881 Mw 7.9 Car Nicobar earthquake estimated from tsunami recorded in the Bay of Bengal. J. Geophys. Res., 108(B4), 2215, doi:10:1029/2002JB001941. Peterson, C., Chadha, R.K., Cruikshank, K.M., Francis, M., Latha, G., Katada, T., Singh, J.P., and Yeh, H. (2005). Preliminary comparison of December 26, 2004 tsunami records from southeast Indian and southwest Thailand to paleotsunami records of overtopping height and inundation distance from the Central Cascadia margin, USA. Communicated to the 8th NCEE Conference, San Francisco, USA, April 2006. Ritzwoller, M.H., Shapiro, N.M., and Engdahl, E.R. (2005). Structural context of the great Sumatra– Andaman Island earthquake (personal communication). Singh, S.C. (2005). Sumatra Earthquake Research indicates why rupture propagated northward. EOS. Trans. Am. Geophys. Un., 86(48), 497, 502. Yeh, H., Peterson, C., Francis, M., Latha, G., Chadha, R.K., Katada, T., Singh, J.P., and Raghuram, G. (2005). Tsunami survey along the south-east Indian coast, SPECTRA, Earthquake Engineering Research Institute, OR, USA (in press). Yeh, H., Francis, M., Peterson, C.D., Katada, T., Latha, G., Chadha, R.K., Singh, J.P. and Raghuram, G. (2006). Effects of the 2004 Great Sumatra Tsunami: Southeast Indian coast, Jour. Am. Soc. Civil. Engg., (In Press).


CHAPTER 4

Paleo-Tsunami and Storm Surge Deposits


K. Arun Kumar, H. Achyuthan, and N. Shankar Department of Geology, Anna University, Chennai 600 025, Tamil Nadu, India

4.1

INTRODUCTION

Tsunamis are generated by seafloor displacement that occurs during earthquakes, collapse of sub-aerial landmasses into lakes or reservoirs, landslides, and volcanic activity independent of earthquakes. An earthquake recurrence interval is an important factor in seismic hazard assessment, but they are often poorly determined. In areas with low deformation rates, mainly intraplate regions, the recurrence and intervals of strong earthquakes usually exceed the time span covered by historical records, so geological records serve the purpose. Estuarine environment can preserve tsunami records that can be extended beyond the historical record in several ways. Generally, only large tsunamis (>5 m) leave visible deposits, with the identification of smaller events requiring higher-resolution studies. Such deposits are not found in all coastal sites. However they are vital for not only extending the magnitude and frequency record back in time, but also for verification and augmentation of model data and for iteration with model data to ensure realistic inundation scenarios. The records and evidences are difficult to achieve due to the anthropogenic activities in the coastal belts. Rapid industrialization coupled with the population growth makes it difficult to retrieve the evidences of historic tsunamis.

4.2

METHODS FOR IDENTIFICATION OF PALEO-TSUNAMI AND STORM SURGE DEPOSITS

Tsunami deposits are typically thin and fine landward and must contain marine and brackish fossils (Bobrowski et al., 1999). The identification and analysis of tsunamigenic deposits provide insight into their characteristics, including the recurrence interval of the catastrophic events near the shore. The low-elevation lakes less than 5 m above the mean sea level situated close to the sea shore are recent target to study paleo-tsunami deposits (Hutchinson et al., 2000). Tsunami deposits commonly exhibit evidence of rapid deposition, such as grading or massive structure. Tsunami deposits are not uniquely identifiable, and other kinds of deposits share some of their characteristics, but in general will not share all. Storm deposits most closely resemble tsunami deposits, but storm waves will not penetrate the distances of a long wave such as a tsunami. Tsunami deposits will tend to show less contemporaneous reworking than storm deposits. Moreover, in the case of Kamchatka, cyclones are weaker than in Japan, for example, where tsunami deposits have been described to the exclusion of storms at elevations of less than 3 m (Minoura et al., 1994). Compared to tsunami and storm deposits, aeolian sands are typically very well sorted, very fine sand, and form thicker, wedge-shaped layers. Silt and very fine aeolian sand are also disseminated in the peat. Flood deposits are typically browner and muddier, and fluvial sediment less mature than on the beach. Colluvium is poorly sorted, with angular grains. The sites chosen for paleo-tsunami study should not be susceptible to river flooding. 49


50

K. Arun Kumar et al.

A tsunami deposit is usually identified by the sedimentary context (e.g. deposited on soil associated with coseismic subsidence), larger grain size than surrounding sediments indicating higher-energy depositional conditions, spatial distribution of the deposit, and by ruling out other high-energy depositional modes (e.g. storm surges or floods). For example at Cascadia, paleotsunami deposits were identified as being anomalous sand layers in low-energy marsh or lacustrine environments (Peters et al., 2001). Additional information that indicates a seaward source of sediments, such as microfossils (Hemphil-Haley, 1995) or geochemical signature (Schlichting, 2000), are also useful for determining that a deposit was formed by a tsunami. The sedimentation is often such that the thicker deposits with larger grain sizes indicate faster flows. A deposit is formed by spatial gradients in transport (more coming into an area than leaving it), by change in storage of sediment in suspension in the water column, or by a combination of these processes. The variation (both horizontal and vertical) in grain size in the deposit may be used to constrain the relative contributions of transport gradients and sediment storage in the water column to forming the deposit. For example, when sediment settles from suspension (change in storage in the water column) the deposit will have more particles with higher settling velocities near the bottom and more particles with lower settling velocities near the top. When density of particles is similar, larger particles have higher settling velocities. The resulting deposit will have larger particles near the bottom creating a normal grading (Jaffe and Gelfenbaum, in preparation). When deposits are formed by spatial gradients in transport, the bed may or may not be normally graded, depending on sediment source, the time history of sediment transport, and the spatial gradients in transport of each particle size. Foraminiferal assemblages are the best way to study the inundation caused by the tsunamis. When the sediment is characterized as a tsunami deposit the number of broken shell fragments is much lower than the number of foraminiferal assemblages; particularly the deep-sea forams are in abundance. To differentiate a storm surge from the tsunami deposit foraminiferal analyses are the best. A storm surge consists of foraminifera, which are characteristic to the beach environment, but a tsunami deposit contains more of deep-sea foraminifers. In a lacustrine environment, plant detritus of diverse sizes and reworked submarine shelf or intertidal material can also be encountered within the sand sheet and or towards the top. Cataloging and assessing tsunami records are important for long-term tsunami prediction and for tsunamihazard mapping. Historical records of tsunamis are too short to develop a predictive chronology of events using only historical data. The way to obtain long-term data is to study paleo-tsunami, that is, to identify, map, and date prehistoric and historical tsunami deposits. These deposits provide a proxy record of large earthquakes. Paleo-tsunami sediments can be chronologically dated using radiocarbon, optically stimulated luminescence, and thermoluminescence dating method and these are being carried out in several sites along the east coast of India. This chapter deals with several occurrences of past tsunami that occurred in the Indian Ocean and elsewhere. Scientists have known that for some 50 million years, the Indian subcontinent has been pushing northward into Eurasia, forcefully raising the Tibetan Plateau and the Himalayan Mountains. The new research suggests that starting about 8 million years ago, the accumulated mass became so great that the Indo-Australian Plate buckled and broke under the stress. The world’s largest recorded earthquakes were all megathrust events and occur where one tectonic plate subducts beneath another. These include: the magnitude 9.5, 1960 Chile earthquake; the magnitude 9.2, 1964 Prince William Sound, Alaska earthquake; the magnitude 9.1, 1957 Andrean of Alaska earthquake, and the magnitude 9.0, 1952 Kamchatka earthquake. Megathrust earthquakes often generate large tsunamis that cause damage over a much wider area than is directly affected by ground shaking near the earthquake’s rupture. In the Pacific Ocean where the majority of these waves have been generated, the historical record shows tremendous destruction. There is also a history of tsunami destruction in Alaska, in the Hawaiian Islands in South America and elsewhere in the Pacific, although the historic records


Paleo-tsunami and storm surge deposits

51

for these areas do not go back sufficiently in time. Historical records also document considerable loss of life and destruction of property on the western shores of the North and South Atlantic, the coastal regions of northwestern Europe, and in the seismically active regions around the eastern Caribbean. Fortunately tsunami in the Indian Ocean, Atlantic, and the Caribbean do not occur as frequently as in the Pacific. Destructive tsunamis have also occurred in the Indian Ocean and in the Mediterranean Sea. The most notable tsunami in the region of the Indian Ocean was that associated with the violent explosion of the volcanic island of Krakatoa in August 1883 that it forced much of the seabed below to collapse. A 30-m (100 ft) tsunami resulting from this explosion killed 36,500 people in Java and Sumatra. Japan is very vulnerable to the tsunami hazard. In Japan, which has one of the most populated coastal regions in the world and a long history of earthquake activity, tsunamis have destroyed entire coastal populations. All the major Japanese islands have been struck by devastating tsunamis. A total of 68 destructive tsunami have struck Japan between AD 684 and 1984 with thousands of lives lost and with the destruction of hundreds of villages. In this century alone, at least six major destructive tsunamis have hit Japan. On March 3, 1933 a tsunami in the Sanriku area reached a height of about 30 m and killed over 3000 people, injured hundreds more, and destroyed approximately 9000 homes and 8000 boats. Other similarly destructive tsunami occurred in 1944, 1946, 1960, and in 1983. The 1983 event, although not very destructive in terms of lives lost and property damage, occurred in the Sea of Japan in an area not known before for seismic or tsunami activity. In the Hawaiian Islands, tsunamis have struck repeatedly, causing great loss of life and immense damage to property. Most noteworthy of the recent Hawaiian tsunami is that of April 1, 1946 which inundated and destroyed the city of Hilo, killing 159 people. Other recent tsunamis that have hit Hawaii occurred in 1952, 1957, 1960, 1964, and 1975. A large earthquake in the Moro Gulf in the Philippines on August 16, 1976 generated one of the most devastating recent tsunami. The tsunami waves killed over 8000 people in Mindanao, leaving 10,000 injured and 90,000 more homeless. In August 1977 a large earthquake in the Lesser Sunda Islands, Indonesia, generated a destructive tsunami, which killed hundreds of people on Lombok and Sumbawa Islands along the eastern side of the Indian Ocean. Another devastating tsunami occurred on December 12, 1979 in the southwest corner of Colombia destroying several fishing villages, taking the lives of hundreds of people and creating economic chaos in an already economically depressed region of that country. Many more events have occurred in the last 20 years. 4.3 TSUNAMI CAUSED DUE TO FALL OF VOLCANO INTO THE SEA On the early morning of March 13, 1888, about 5 km3 of the Ritter Island volcano fell violently into the sea northeast of Papua New Guinea. This event, the largest lateral collapse of a volcanic island in historical time, flung devastating tsunamis tens of meters high onto adjacent shores (Cooke, 1981). During the recent research cruise, the debris avalanche and associated debris flows off Ritter were studied using a hull-mounted Em120 multibeam system, which gave both bathymetry and acoustic reflectivity, or “backscatter” data. The survey also deployed an mr1 towed vehicle to collect higher-quality backscatter images, an underway 3.5-kHz sonar, and an Sio EdgeTech chirp 2–6 kHz seismic system. The latter two provided sub-bottom sediment profiles to depths of tens of meters, and thus thickness estimates for large areas of the debris deposits. 4.4

OTHER VOLCANO COLLAPSES IN THE BISMARCK SEA

Collapse is known to be a major process of volcano denudation in the Hawaiian (Moore et al., 1989) and Canary Islands (Urgeles et al., 1997) and in the Lesser Antilles island arc (Deplus et al.,

52



2001). In addition to the well documented collapse of Ritter Island, 10–12 additional debris avalanche deposits related to collapse were discovered throughout the Bismarck volcanic arc. The older debris avalanches are exposed off Tolokiwa and Sakar islands near Ritter, Garove, and Unea islands in the Witu group (north of west New Britain), Dakataua volcano (the northernmost of a north–south volcanic peninsula on central New Britain), Crown, Long, and Karkar volcanoes north of Madang, and Manam and Bam volcanoes off northwestern Papua New Guinea. The Tolokiwa deposit is especially impressive, with large blocks (hundreds of meters long) individually imaged as far as 20 km from its north coast. The debris avalanche off the breached caldera Garove island, expansive enough for the Kilo Moana to sail in, extends 20 km from the breach along the south side of the caldera. A prominent debris field can be seen to a distance of 15 km north of Crown island. Several of the volcanoes show multiple collapse events. 4.5

PALEO-TSUNAMI DEPOSITS FORMED DUE TO VOLCANIC ERUPTIONS

The geological record suggests that megatsunamis are rare, but due to their size and power, can produce immensely devastating effects. However as with Lituya Bay, this is often localized. A megatsunami that is known to have a widespread impact which reshaped an entire coastline occurred approximately 4000 years ago on Reunion Island, to the east of Madagascar. Extensive geological investigations indicate that the risk of a re-occurrence is minimal. There are indications that a giant tsunami was generated by the bolide impact that created the Chesapeake Bay impact crater, a shallow-water near-shore impact off the eastern North American coastline about 35.5 million years ago, in the late Eocene Epoch. Around Kamchatka more than 24 Holocene key marker tephra layers from 11 different volcanic centers have been identified (Braitseva et al., 1997). Ages of prehistoric marker tephra have been determined by multiple radiocarbon dates of enclosing strata, calibrated to calendar ages (Braitseva et al., 1997). These dated tephra layers have provided a record of the most voluminous explosive events. Each marker tephra has been traced for tens to hundreds of kilometers away from the volcanic source and characterized by stratigraphic position, area of dispersal, radiocarbon age, typical grain-size distribution, and chemical and mineral composition. They occur as patchy deposits and do not occur over the entire inundated surface. In Cascadia, Darienzo and Peterson (1990) have dated a series of tsunami deposits and determined the recurrence interval for subduction zone earthquakes and associated tsunamis is from 200 to 600 years. Darienzo and Peterson (1990) provided evidence for paleo-tsunami deposition across a series of salt marshes along the northern Oregon coastline. They described a series of sediment sheets occasionally containing clay/silt units, marine brackish diatoms, and generally massive structure. These authors argued that the sands were transported and deposited out of turbulent suspension rather than due to small-scale currents that produce ripples and dunes on the seabed. However they also noted that the lateral extent of the sediment sheets indicated that the tsunami surges were capable of transporting fine sands over distances greater than 0.75 km despite being associated with bottom shear stresses that were insufficient to disturb or remove the stems of plants rooted in the underlying marsh surfaces. Detailed information from coastal Washington State indicated the former occurrence of a large tsunami that accompanied an episode of coseismic coastal submergence during a large earthquake took place ca. 300 years ago (Atwater and Yamaguchi, 1991). Sedimentary evidence for this tsunami is widespread throughout the Pacific west coast (Clague, 1997). Around 6100 BC, Storegga slides occurred under the water near the edge of Norway’s continental shelf. An area roughly the size of Iceland shifted causing a megatsunami in the North Atlantic Ocean. Harbitz (1992) attempted to develop a numerical model of the second Storegga submarine slide. He noted that the scale of tsunami run-up along the Scottish and Norwegian



53

coastlines very much depended upon the average landslide velocity that was introduced into the model. He also noted that an average slide velocity of 20 m/s resulted in run-up values on to adjacent coastlines of between 1 and 2 m. By contrast a modeled landslide velocity of 50 m/s resulted in run-up values between 5 and 14 m, values significantly in excess of the estimates for adjacent coastlines based on geological data. Atwater and Moore (1992) described stratigraphical evidence from the Puget Sound, Washington, for a paleo-tsunami that flooded coastal areas ca. 1000 years ago. At Cultus Bay a sand sheet between 5 and 15 cm in thickness containing marine foraminifera is enclosed within peat. The deposits typically have a medium grain size of 0.1 mm and exhibit a progressive fining inland. Shi et al. (1995) demonstrated that the Flores Tsunami of December 12, 1992 was associated with the deposition of extensive sheets of sediments up to 1 m thick, and these are continued landward by discontinued sediment accumulations. The highest of these sediment accumulations always occurs below the upper limit of tsunami run-up. 4.6

EARTHQUAKE-TRIGGERED TSUNAMI

In the historical past earthquakes have triggered the occurrence of devastating tsunami. Clague and Bobrowski (1994) described the tidal marshes near Tofino and Ucleuelet Vancouver Island British Columbia salt marshes overlain by sand sheets containing marine foraminifera and vascular plant fossils, demonstrating rapid submergence prior to burial by marine sands. Similar sheets of sand attributed to the 1964 great Alaska earthquake and tsunami have been described by Clague et al. (1994) for Port Alberni, British Columbia. Recent studies of coastal sediments deposited by paleo-tsunamis have shown that tsunami sediments deposition is frequently associated with the deposition of sediment sheets that rise in altitude inland as tapering sediment wedges (Dawson, 1994). Around 1650 BC, at Santorini a Greek volcanic island eruption caused a tsunami, estimated to be between 100 and 150 m high and devastated the island of Crete 75 km away. Santorini is believed to be the cause of the Great Flood recorded in Jewish, Christian, and Islamic historical texts. The violent eruption and explosion of the volcano of Santorini, in the 15th century BC generated a tremendous tsunami, which destroyed most of the coastal Minoan settlements on the Aegean Sea islands acting as the trigger for the decline of the advanced Minoan civilization. A massive tsunami caused by an earthquake along a 1000-mile fault hit the coastal areas of northern California, Oregon, Washington, and British Columbia, on January 26, 1700. The tsunami also caused flooding and damage in Japan. Brian Atwater of the US Geological Survey made many discoveries exposing the history of the land and the coastal peoples of the Northwest. Layers of beach sand enabled him to pinpoint the exact date of the 1700 tsunami. The 1700 Cascadia tsunami can be identified with confidence from a sheet of sand that tapers landward, contains marine fossils, extends kilometers inland from the limit of sand deposition by storm surges, and coincides stratigraphically with evidence for abrupt tectonic subsidence and seismic shaking (Atwater et al., 2005). Tsunami geology, which began with surveys of the 1946 Aleutian tsunami in Hawaii (Shepard et al., 1950) and the 1960 Chile tsunami in Japan (Kitamura et al., 1961), now encompasses a broad range of stratigraphic and geomorphic evidence, and it includes several published comparisons between tsunami and storm deposits. The Sunday earthquake in 1775 at Lisbon, Portugal, that devastated Lisbon sent many people fleeing from churches to the coastlines to avoid falling debris. The tsunami that followed killed tens of thousands of people. In Algarve, Portugal, tsunami deposits were produced during the great Lisbon earthquake of November 1, 1755 AD. At Boca do Rio tsunami deposits occur as a continuous sheet of sediments inland from the coast but farther inland are replaced by


54


discontinuous and eventually sporadic sediment sheets until a point is reached when there was no sedimentary trace of the tsunami despite historical observations that tsunami flooding took place to considerably higher altitudes (Hindson et al., 1996). An earthquake that measured 7.2 on the Richter scale occurred beneath the ocean on the Grand Banks underwater plateaus southeast of Newfoundland in 1929. The tsunami reached heights of over 7 m and hit the southern coast of Newfoundland. On April 1, 1946 an earthquake triggered a tsunami near the Aleutian Islands of Alaska. The magnitude of this earthquake was 7.8. The height of the tsunami is not known but in the Aleutian Islands it had killed 165 people and caused over $26 million in damage. A Pacific-wide tsunami was also created as a result of this earthquake. The tsunami traveled through the Pacific Ocean and struck Hawaii and the French Marquesas Islands. In the Marquesas Islands, the local people knew the dangers of a tsunami and some of the warning signs. Survivors of the 1946 tsunami or “taitoko” as it is called on the islands, recall being warned by their elders to flee for higher ground. Waters ran up into low-lying areas of this small group of islands during this tsunami at a depth of 20 m in the low-lying regions. The largest recorded earthquake of the 20th century occurred on May 22, 1960 off the coast of south-central Chile. It was measured at a magnitude of 9.5 and generated a Pacific-wide tsunami similar to the tsunami of 1946. The death toll in Chile was estimated at 2300 people. In Hilo, Hawaii the destructive waves took the lives of 61 people. The waves also reached Japan, damaging coastlines and the fishing industry. An earthquake that measured 9.2 generated tsunamis and struck Alaska, British Columbia, California, and Pacific Northwest towns in 1964 on Good Friday and hence also called as Good Friday Tsunami. Waves reached a height of nearly 6 m and struck as far away as Crescent City, California. A 7.9 magnitude earthquake occurred off the Pacific coast of Colombia and Ecuador on December 12, 1979. This tsunami killed an estimated 400 people and left 798 wounded. It is a common misconception that tsunamis only occur in oceanic areas. The 1999 tsunami that struck parts of western Turkey originated in the Sea of Marmara at Izmit Bay, part of the Turkish Straits. The earthquake event known as Kocaeli was located on the Northern Anatolian Fault, sending water from the sea towards Turkey. Areas incurring the largest damage were Golcuk, where water run-up reached a height of 4 m. The cities of Degirmendere and Karamursel also experienced heavy damage due to flooding.

4.7

PALEO-TSUNAMI AND STORM SURGES IN INDIAN OCEAN

Tsunamis are a common phenomenon in the Pacific and the Atlantic but they are not quite frequent in the Indian Ocean. In earliest known tsunami occurred in the Bay of Bengal in 1762, caused by an earthquake on Myanmar’s, Arakan Coast. This tsunami event was experienced in multiple regions throughout the world. Tsunami has also been triggered due to debris flow and avalanches in higher latitudinal regions. Though tsunamis cause a havoc of destruction they have also shaped the coastal geomorphology and created an esthetic landscape. REFERENCES Atwater, B.F. and Moore, A.L. (1992). A tsunami about 1000 years ago in Puget Sound, Washington. Science, 241, 1614–1617. Atwater, B.F. and Yamaguchi, D.K. (1991). Sudden, probably co-seismic submergence of Holocene trees and grass in coastal Washington State. Geology, 19, 706–709.



55

Atwater, B.F., Musumi-Rokkaku, S., Satake, K., Tsuji, Y., Ueda, K., and Yamaguchi, D.K. (2005). The orphan tsunami of 1700: Japanese clues to a parent earthquake in North America, U.S. Geol. Surv. Prof. Paper., 1707, 144. Bobrowski, P.T., Clauge, J., Hutchinson, J., and Lopez, G.I. (1999). Earthquake induced land subsidence and sedimentation on the west coast of Canada. In: Proceedings and Abstracts, XV International INQUA Congress, Durban, South Africa, August 3–11, 1999, pp. 25–26. Braitseva, O.A., Ponomareva, V.V., Sulerzhitsky, L.D., Melekestsev, I.V., and Bailey, J. (1997). Holocene key-marker tephra layers in Kamchatka, Russia. Quatern. Res., 47, 125–149. Clague, J.J. (1997). Evidence of large earthquakes at the Cascadia subduction zone. Rev. Geophy., 35, 439–460. Clague, J.J., Bobrowski, P.T., and Hamilton, T.S. (1994). A sand sheet deposited by the 1964 Alaska Tsunami at Port Alberni British Columbia. Estuar. Coast. Shelf Sci., 38, 413–421. Cooke, R.J.S. (1981). Eruptive history of the volcano at Ritter Island. In: R. W. Johnson, (ed.), Cooke-Ravian Volume of Volcanological Papers, Mem. 10, Geological Survey of Papua New Guinea, Port Moresby, pp. 115–123. Darienzo, M.E. and Peterson, C.D. (1990). Episode tectonic subsidence of late Holocene salt marshes, northern Oregon, central Cascadia margin. Tectonics, 9, 1–22. Dawson, A.G. (1994). A geomorphological effects of tsunami run-up and backwash. Geomorphology, 10, 83–94. Deplus, C., Le Friant, A., Boudon, G., Komorowsk, J.C., Villemant, B., Harford, C., Segoufin, J., and Cheminee J.L. (2001). Submarine evidence for large-scale debris avalanches in the Lesser Antilles Arc. Earth Planet. Sci. Lett., 192, 145–157. Harbitz, C.B. (1992). Models simulation of tsunami generated by the Storegga Slide. Mar. Geol., 105, pp. 1–21. Hemphil-Haley, E. (1995). Diatom evidence for earthquake-induced subsidence and tsunami 300 yr ago in southern coastal Washington. Geol. Soc. Am. Bull., 107, 367–378. Hindson, R., Andrade, C., and Dawson, A. (1996). Sedimentary processes associated with the tsunami generated by the 1755 Lisbon earthquake on the Algarve coast, Portugal, Phys. Chem. Earth, 21, 57–63. Hutchinson, I., Guilbault, J.P., Clauge, J.J., and Bobrowski, P.T. (2000). Tsunamis and the tectonic deformation at the northern Cascadia margin: A 3000 year record from Deserted Lake, Vancouver Island, British Columbia, Canada. Holocene, 10, 249–439. Kitamura, N., Kotaka, T., and Kataoka, J. (1961). Ofunato-Shizugawa chiku (region between Ofunato and Shizugawa), In: E. Kon’no (ed.), Geological Observations of the Sanriku Coastal Region Damaged by Tsunami due to the Chile Earthquake in 1960, Contribution Institute of Geology Paleontology, Tohoku University, 52, 28–40. Minoura, K., Nakaya, S., and Uchida, M. (1994). Tsunami deposits in a lacustrine sequence of the Sanriku coast, northeast Japan. Sedimen. Geol., 89(1/2), 25–31. Moore, J.G., Clague, D.A., Holcomb, R.T., Lipman, P.W., Normark, W.R., and Torresan, M.E. (1989). Prodigious submarine landslides on the Hawaiian Ridge. J. Geophy. Res., 94(B12), 465–484. Peters, B., Jaffe, B.E., Peterson, C., Gelfenbaum, G., and Kelsey, H. (2001). An overview of tsunami deposits along the Cascadia margin. Proceedings of the International Tsunami Symposium, pp. 479–490. Schlichting, R.B. (2000). Establishing the inundation distance and overtopping height of paleotsunami from the late-Holocene geologic record at open-coastal wetland sites, central Cascadia margin. MS Thesis, Portland State University, Portland, OR, US, pp. 166. Shepard, F.P., Macdonald, G.A., and Cox, D.C. (1950). The tsunami of April 1, 1946, Bull. Scripps Inst. Oceanogr., 5, 391–528. Shi, S., Dawson, A.G., and Smith, D.E. (1995). Coastal sedimentation associated with the December 12th 1992 Tsunami in Flores, Indonesia. In: K. Satake and K. Imamura. (eds.), Recent Tsunamis, Pure and Applied Geophysics, 144, 525–536. Urgeles, R., Canals, M., Baraza, J., Alonso, B., and Masson, D. (1997). The most recent megalandslides of the Canary Islands: El Golfo debris avalanche and Canary debris flow, west El Hierro Island. J. Geophy. Res., 102(B9), 20305–20323.


CHAPTER 5

Overview and Integration of Part 1


U. Aswathanarayana Mahadevan International Centre for Water Resources Management, Hyderabad, Andhra Pradesh, India

5.1

GEOSTRUCTURAL ENVIRONMENT OF TSUNAMI GENESIS

Raison d’ etre: Part 1 deals with the Geostructural Environment of Tsunami Genesis. It is based on the dictum, “The Past is the key to the Future”. By tracing the geostructural environments in which the tsunamis were generated in the past, and their periodicity, we identify the sites wherefrom and when they could possibly get generated in the future. The vulnerability of a given coastal site to tsunami damage is dependent on the slope and morphology of the coast. In order for an earthquake to generate tsunami, the magnitude should be ≥7.9, the nature of faulting should be either thrust or normal, and the earthquake should be shallow enough to cause vertical uplift in the ocean floor. Paleo-tsunami records are useful for extending the magnitude and frequency record of the tsunamis back in time. Rastogi (Chapter 1) compiled a catalogue of tsunamis that occurred in the Indian Ocean during the period 326 bc–2005 ad. In order to identify possible sites of future great earthquakes, the sites of large megathrust earthquakes (>Mw 7.5) are plotted on the subduction zones, along with information on the rupture zones of the great earthquakes. Thrust type earthquakes occurring along subduction zones that cause vertical movement of ocean floor tend to be tsunamigenic. As compared to average eight tsunamis per year in the Pacific, Indian Ocean has no more than one in 3 years or so. Eighty percent of the tsunamis of the Indian Ocean originate in the Sunda arc covering Java and Sumatra. The seismic gap areas along subduction zones like Andaman–Sumatra and Makran can be assessed as possible future source zones of tsunami generating earthquakes in the Indian Ocean and the repeat periods of great earthquakes can be assessed from past seismicity. Along the Andaman–Sumatra trench convergence rate is 40–50 mm/year, yielding return periods of 150–200 year for great to giant earthquakes of magnitude 8.5 or greater. Major tsunamigenic earthquakes of magnitude 5.0). This implies that the coastal regions have to take note of this new seismic hazard. Hitherto the observed seismicity in the coastal regions of the Stable Continental Region (SCR) is mainly due to the reactivation of weak zones due to the stresses developed as a result of the northward movement of the Indian plate. However there is now a new possibility of reactivation of weak zones of the coastal areas, due to the aftershock, of high amplitude, occurring continuously at the eastern end, i.e., along the Andaman and Nicobar arc. Under these circumstances, it is very essential to carryout geophysical studies in the coastal region in order to identify the land–ocean tectonic lineaments and their correlation with earlier reported seismicity so that seismic zonation maps can be generated for the Coastal regions. According to Chadha et al. (Chapter 3), the entire east coast of India is vulnerable to varying degree of tsunami threat from large earthquakes occurring in the Andaman–Sumatra subduction zone. The three primary conditions for an earthquake to generate a tsunami are: (i) the magnitude should be ≥7.9, (ii) the nature of faulting should be either thrust or normal, and (iii) the earthquake should be shallow enough to cause vertical uplift in the ocean floor. The 26 December 2004 earthquake off the coast of Sumatra fulfills all these three conditions, as the magnitude was M9.3, the faulting was a thrust type, the depth was 30 km or less which deformed the ocean floor by 10–20 m. Although the 28 March 2005 earthquake of M8.7 below the Nias Island in Sumatra, was strong enough, it did not deform the ocean floor. Further, the focus of the earthquake was below the Nias Island and any displacement of ocean water would not have been significant to create large tsunami, even if there was some deformation of the ocean floor. This also brings in the important factor of focusing of energy in a direction perpendicular to the strike of the fault. Similarly, an earthquake of M8.1 which occurred on 24 December 2004, south of Australia, did


Overview and integration of Part 1

59

not generate any tsunami as this earthquake occurred on a strike-slip fault associated with the spreading mid-oceanic ridge. From the Indian point of view, if tsunamis are generated due to the earthquakes occurring on the Andaman–Nicobar section of the subduction zone, which has a north northwest to north–south trend, the impact on the east coast of India will be much severe due to directivity of energy and also lesser distance to the Indian coastline. Conversely, if tsunamis are generated due to earthquakes further south along the Sumatra–Java axis along the Sunda trench, it will not have any damaging effect on the Indian coast, as the strike of the fault in this region changes to west northwest to east–west. On the western side the Indian coast is likely to be affected due to large earthquakes in the Makran subduction zone in southern Pakistan. There are reports of tsunami affecting coastal regions up to Goa on the west coast of India, during the earthquake of 28 November 1945 in Makran subduction zone. In the recent times, there have been some suggestions about the breakup of Indo-Australian plate into two along an east–west nascent boundary developing in the Indian Ocean, but there have been few earthquakes recorded from this region. At present the tsunami potential of this region is unknown. According to Arun Kumar et al. (Chapter 4), paleo-tsunami records are useful not only for extending the magnitude and frequency record of the tsunamis back in time, but also for verification and augmentation of model data and for iteration with model data to ensure realistic inundation scenarios. Rapid industrialization coupled with the population growth in the coastal areas some times makes it difficult to retrieve the evidences of historic tsunamis. Tsunami deposits are typically thin and fine landward and must contain marine and brackish water fossils. They commonly exhibit evidence of rapid deposition, such as grading or massive structure. Tsunami deposits are not uniquely identifiable, and other kinds of deposits share some of their characteristics, but in general will not share all. Storm deposits most closely resemble tsunami deposits, but storm waves will not penetrate the distances of a long wave such as a tsunami. Tsunami deposits will tend to show less contemporaneous reworking than storm deposits. A tsunami deposit is usually identified by the sedimentary context (e.g. deposited on soil associated with coseismic subsidence), larger grain size than surrounding sediments indicating higher-energy depositional conditions, spatial distribution of the deposit, and by ruling out other high-energy depositional modes (e.g. storm surges or floods). Thicker deposits with larger grain sizes indicate faster flows. A deposit is formed by spatial gradients in transport (more coming into an area than leaving it), by change in storage of sediment in suspension in the water column, or by a combination of these processes. The variation (both horizontal and vertical) in grain size in the deposit may be used to constrain the relative contributions of transport gradients and sediment storage in the water column to forming the deposit. Foraminiferal assemblages are the best way to study the inundation caused by the tsunamis. When the sediment is characterized as a tsunami deposit the number of broken shell fragments is much lower than the number of foraminiferal assemblages; particularly the deep-sea forams are in abundance. To differentiate a storm surge from the tsunami deposit foraminiferal analyses are most useful. A storm surge consists of foraminifera, which are characteristic to the beach environment, but a tsunami deposit contains more of deep-sea foraminifers. In a lacustrine environment, plant detritus of diverse sizes and reworked submarine shelf or intertidal material can also be encountered within the sand sheet and or towards the top. Cataloguing and assessing tsunami records are important for long-term tsunami prediction and for tsunami-hazard mapping. Historical records of tsunamis are too short to develop a predictive chronology of events using only historical data. The way to obtain long-term data is to study paleo-tsunami, i.e., to identify, map and date prehistoric and historical tsunami deposits. These deposits provide a proxy record of large earthquakes. Paleo-tsunami sediments can be chronologically dated using radiocarbon, optically stimulated luminescence and thermoluminescence dating methods and these are being carried out for several sites along the east coast of India.



Part 2

Modelling of Tsunami Generation and Propagation


CHAPTER 6

A Review of Classical Concepts on Phase and Amplitude Dispersion: Application to Tsunamis


N. Nirupama Atkinson School of Administrative Studies, York University, Toronto, Canada T.S. Murty and I. Nistor Department of Civil Engineering, University of Ottawa, Ottawa, Canada A.D. Rao Centre for Atmospheric Sciences, Indian Institute of Technology, New Delhi, India

6.1

INTRODUCTION

In the analytical and numerical modelling of tsunami generation and propagation some of the classical concepts, such as, phase (frequency) and amplitude (non-linear effects) dispersion are one of the main considerations. It is beneficial to review here some of the mathematical concepts underlying these important processes. The phase and amplitude dispersions, while both are important in tsunami modelling, play their role at different stages of the tsunami event. The phase dispersion mainly happens during the propagation of the tsunami, whereas, the amplitude dispersion is relevant in the coastal amplification of the tsunami. Even if there is only one wave, when the tsunami is generated, the ocean bathymetry and phase dispersion, among other things, contribute to the separation and spreading of the tsunami into a multi-wave event. The amplitude dispersion is due to the non-linear interaction of the tsunami as it enters shallow water and interacts with the coastal topography. It is generally known (Murty, 1977) that the non-linear effects amplifies the currents several times more than the amplification of the water level. The Indian Ocean Tsunami of 26 December 2004 exhibited both phase and amplitude dispersion effects (Kowalik, 2005a, b; Murty et al., 2005a–e; Murty et al., 2006; Nirupama et al., 2005; Nirupama et al., 2006).

6.2

DISPERSION AND THE URSELL PARAMETER

Amplitude and phase dispersion relations relevant for long gravity waves, and the theory of generation of gravity waves by deformation at the bottom (e.g. earthquake), or deformation at or near the surface (e.g. explosions), will be discussed. Under the assumption that depth is small compared to a horizontal length scale, there are three regions of approximation for the long-wave theory (Chen et al., 1975): (a) linear equations, (b) finite-amplitude equations, and (c) Boussinesq or Kortweg–de Vries (KdV) type equations. Three characteristics lengths determine which equation is most appropriate: water depth, D, wavelength, λ, and wave amplitude, η. 63

64

N. Nirupama et al.

Three non-dimensional parameters can be defined: ε≡

η ε D2 ηλ2 ; µ≡ 2; U ≡ = 3 D λ µ D

(6.1)

U is generally referred to as the “Ursell parameter” and expresses the relative significance of amplitude and phase dispersion. In the linear periodic wave theory (see Lamb, 1945) the frequency, ω, is given by:


ω2 = gk tanh (KD)

(6.2)

where g is gravity, K is wave number, and the phase velocity, C, is given by: C=

ω K

(6.3)

For very long waves, tanh (KD) can be approximated by the leading term in its expansion. Then from equations (6.2) and (6.3): C=

2π2 D2 gD 1 − 3 λ2

(6.4)

where wave number, K, is 2π/λ. From equation (6.4) it can be seen that long waves travel with a speed mainly determined by water depth but subject to a small negative correction proportional to µ. Two wave components with a slightly different value of µ will tend to separate as they progress; then µ is a measure of “frequency dispersion.” To understand the second type of dispersion, consider the formula for the celerity of a solitary wave (see equation (6.39)): ε C∼ (6.5) = gD 1 + 2 √ The celerity is approximately gD but is subject to a small positive correction proportional to the relative amplitude. Thus, ε is a measure of the amplitude dispersion. One can distinguish among the following three regimes of U : ⎧ 1 Amplitude dispersion can be ignored. Linear long-wave theory is valid. ⎪ ⎪ ⎪ ⎪ ⎪ 0(1) Both amplitude and phase dispersions are important. The Boussinesq ⎪ ⎨ equations (to be introduced later) are appropriate. Under certain conditions U these equations reduce to the KdV equations. ⎪ ⎪ ⎪ ⎪ ⎪ 1 Amplitude dispersion dominates. Finite-amplitude, non-linear, long-wave ⎪ ⎩ theory is appropriate. In tsunami studies, both linear and non-linear long-wave equations have been utilized. However, for tsunami travel over the continental shelf, neither the linear nor non-linear cases might be relevant; indeed, one might have to use the intermediate type, e.g. Boussinesq-type equations. LeMéhauté (1969) pointed out that the Ursell parameter is not wholly satisfactory in delineating the different regimes. He agrees that when U 1, the linear small-amplitude wave theory applies.

A review of classical concepts on phase and amplitude dispersion

65

However, for very long waves in shallow water (flood waves, bore, near-shore tsunami) the value of U (supposed to be 1) depends on the interpretation given to λ. (For very long waves, the concept of wavelength loses its meaning because the wavelength of a solitary wave is ∞, but the flow curvature under the crest is that of a cnoidal wave for which a finite wavelength can be defined.) The relative amplitude, η/D, is then more relevant than U for interpreting the importance of non-linear terms.


6.3

MATHEMATICAL DEVELOPMENT OF THE URSELL PARAMETER

Following Broer (1964), the Ursell parameter will be formally developed, and the problem of treatment of interaction of non-linearity (or amplitude dispersion) and dispersion (i.e. phase dispersion) in wave propagation will be discussed. The Boussinesq equation (6.6) approximately describes the unidirectional propagation of finite-amplitude waves on a water layer of uniform depth, when the ratio of depth of wavelength, although small, is not negligible as in the theory of tides. The classical form of this equation is: ∂2 h ∂2 h 3 ∂2 1 3 ∂4 h 2 − gD = (h − D) + g gD 4 ∂t 2 ∂x2 2 ∂x2 3 ∂x

(6.6)

where t is time and x is the horizontal direction of wave propagation. In this equation, the first term on the right is the non-linear term due to finite wave amplitude, and the second term represents the dispersion due to finite depth to wavelength ratio. Here h(x, t) is the local wave height above the horizontal bottom. Assuming irrotational flow, the velocity components, u and w, are given in terms of the velocity potential, (x, z, t), by: u=

∂ ; ∂x

w=

∂ ∂z

(6.7)

The potential, , satisfies Laplace’s equation: ∂2 ∂2 + 2 =0 ∂x2 ∂z

(6.8)

The boundary condition at the bottom is no flow normal to it, i.e. ∂ = 0 for z = 0 ∂z

(6.9)

There are two surface boundary conditions. The kinematic condition is (e.g. Lamb, 1945): ∂h ∂ ∂h ∂ + = ∂t ∂x ∂x ∂z

for z = h(x, t)

The dynamic condition is:

∂ 1 ∂ 2 ∂ 2 gh + = gD + + ∂t 2 ∂x ∂z

(6.10)

for z = h

(6.11)

66

N. Nirupama et al.

Assuming that is analytical in x and z (i.e. no singularities), equations (6.8) and (6.9) are satisfied by writing:


(x, z, t) = φ(x, t) −

z 2 ∂2 φ z 4 ∂4 φ + − ··· 2! ∂x2 4! ∂x4

(6.12)

where φ(x, t) is the potential at the bottom. From equations (6.10) and (6.11) after using equation (6.12), two simultaneous equations for φ(x, t) and η(x, t) are obtained. These differential equations will be of infinite degree in η and infinite order in ∂/∂x. To obtain an equation similar to equation (6.6), one has to truncate equations (6.10) and (6.11). However, before this truncation, it is convenient to work with dimensionless variables. Choose dimensionless variables (denoted by prime) such that: Lt x ≡ Lx ; z = Dz ; t = √ ; φ = φ εL gD gD

(6.13)

Also write h = D(1 + εη )

(6.14)

where ε is the relative wave amplitude defined in equation (6.1) and η (x, t ) is so chosen that its maximum value is unity for some initial or boundary value. This means the dimensionless slope ∂η /∂x is of the order of unity provided L is chosen appropriately. Suppose the dominant wavelength, λ, is chosen for L, and noting the definition of µ from equation (6.1) and from equations (6.10), (6.11), and (6.12), retaining terms of order zero and one only, then: 2

∂η ∂2 φ ∂ φ ∂η ∂φ 1 ∂4 φ + 2 = −ε η 2 + + µ 4 ∂t ∂x ∂x ∂x ∂x 6 ∂x

(6.15)

and η+

2 ∂φ 1 ∂3 φ 1 ∂φ + µ 2 =− ε ∂t 2 ∂x 2 ∂x ∂t

(6.16)

From equations (6.15) and (6.16) the solutions will depend on the ratio ε/µ, the Ursell parameter defined earlier in equation (6.1).

6.4

FREQUENCY AND AMPLITUDE DISPERSION

Lighthill (1958) appears to be the first to coin the words “frequency dispersion” and “amplitude dispersion.” Other authors used the terms “dispersion” to refer to “frequency dispersion” and “non-linear effects” to refer to amplitude dispersion. Frequency dispersion means wave components of different frequencies propagate with different velocities whereas amplitude dispersion refers to the situation where greater values of surface elevation propagate with greater velocities to cause steepening of the waves. Situations when phase and amplitude dispersions tend to balance each other will be discussed.


67

First, consider the case when the terms with ε are ignored in equations (6.15) and (6.16). The equations then become linear and on eliminating η between them, one obtains: ∂2 φ ∂2 φ 1 ∂4 φ 1 ∂3 φ − = − µ 2 µ ∂x2 ∂t 2 6 ∂x4 2 ∂x ∂t

(6.17)

express φ = ei(Kx−ωt)

(6.18)


√ where i = −1, the following dispersion equation is obtained: 1 + 16 µK 2 ω2 1 ∼ = = 1 − µK 2 K2 3 1 + 12 µK 2

(6.19)

To this order, the exact dispersion relation is in the units used so far. (gravity is contained in the non-dimensionalization of t): K √ ω2 = √ tanh (K µ) µ

(6.20)

Next, in equations (6.15) and (6.16) ignore the terms with µ and define: u=

∂φ ∂x

(6.21)

the velocity at the bottom in the x direction. Then equations (6.15) and (6.16) become: ∂η ∂ [(1 + εη)u] = 0 + ∂t ∂x ∂η ∂u ∂u + + εu =0 ∂t ∂t ∂x

(6.22) (6.23)

In these equations there is no restriction on ε because if the expansions leading to equations (6.15) and (6.16) are continued, the terms with ε2 and higher powers occur always with µ, and these terms drop out when terms with µ are ignored. When terms with both ε and µ are ignored in equations (6.15) and (6.16), linear equations without dispersion are obtained. For waves travelling to the right, the solutions is: η = u = η(x − t)

(6.24)

Hence: ∂η ∂η ∂u ∂u + = + =0 ∂x ∂t ∂x ∂t 6.5

(6.25)

REDUCED FORM OF THE BOUSSINESQ EQUATION

In this non-dimensional notation, the Boussinesq equation (6.6) becomes: ∂2 η ∂2 η 3 ∂2 1 ∂4 η − 2 = ε 2 (η)2 + µ 4 2 ∂t ∂x 2 ∂x 3 ∂x

(6.26)

68

N. Nirupama et al.

However, the left side of equation (6.26) can be deduced from equations (6.15) and (6.16) and this gives: 2 2

∂2 η ∂2 η u ∂ ∂2 1 ∂4 η − = ε − (ηµ) − µ ∂t 2 ∂x2 ∂x2 2 ∂x · ∂t 3 ∂x3 ∂t

(6.27)


It is clear that equation (6.27) is not the same as equation (6.26) but will reduce to equation (6.26) provided equations (6.24) and (6.25) are valid. Actually, due to the approximate nature of equations (6.15) and (6.16), all one has to assume instead of equations (6.24) and (6.25) are η − O(ε, µ) and ∂ ∂ + = O(ε, µ) ∂x ∂t

(6.28)

The significance is that solutions of equations (6.15) and (6.16) (where the main part is waves travelling to the right, assuming these exist at least during some time interval) could be found from the simpler equation (6.26) under the present approximation. For waves propagating to the left, the signs in equation (6.28) can be changed; then also equation (6.26) can be obtained from equation (6.27). Thus, provided equation (6.28) holds and assuming equation (6.21) throughout, equations (6.15) and (6.16) become: ∂η ∂u ∂ 1 ∂3 η + = −ε (ηu) + µ 3 ∂t ∂x ∂x 6 ∂x 2 ∂η ∂u ∂ u 1 ∂3 u + = −ε + µ 2 ∂x ∂t ∂x 2 2 ∂x ∂t

(6.29) (6.30)

From equation (6.28) one can write: ∂η ∂η ∂u ∂u + − − =0 ∂t ∂x ∂t ∂x

(6.31)

Take equation (6.29) + equation (6.30) − equation (6.31) and use equation (6.28) for the right side to give: ∂η ∂η 3 ∂ 1 ∂3 η + + ε (η)2 + µ 3 = 0 ∂t ∂x 4 ∂x 6 ∂x

(6.32)

This is the reduced equation (from Boussinesq’s equation) that can be used to understand the interaction between amplitude and phase dispersions.

6.6

CNOIDAL WAVES

Solitary Wave: To examine the properties of the reduced equation following Broer (1964), drop the numerical factors in equation (6.32) and write: ∂η ∂η ∂η ∂3 η + + εη + µ 3 = 0 ∂t ∂x ∂x ∂x

(6.33)


69

This equation is suitable for initial value problems in which: η(x, 0) = F(x)

(6.34)

is given. Both amplitude and phase dispersions will tend to distort the wave forms; however, there might be situations when both effects cancel each other for special wave forms. In this case, the solution is simplified:


η = F(x − at)

(6.35)

where a is the speed of propagation of the waves. From equations (6.33) and (6.35) after introducing t = 0 and integrating with respect to x one gets: 1 ∂2 F (1 − a)F + εF 2 + µ 2 = 0 2 ∂x

(6.36)

Multiply this with ∂F/∂x and integrating again leads to: 2 1 1 1 ∂F (1 − a)F 2 + εF 3 + µ =b 2 6 2 ∂x

(6.37)

where b is a constant of integration. Equation (6.37) can be solved in terms of the elliptic functions. As these are represented by “cn”, the name “cnoidal waves” was coined to refer to solutions of equation (6.37). For b = 0, the simple solution is: F=

p cosh2 (qx)

(6.38)

where 3(a − 1) p≡ ε

and

1 q≡ 2

a−1 µ

This is the solution for the so-called “solitary wave” and the Ursell parameter becomes ε/(3µ/2) and is independent of a and p. The speed of the solitary wave from equation (6.36) is: 1 µ ∂2 η a = 1 + εη + 2 η ∂x2

(6.39)

If the third term is ignored, and it is taken into consideration that equation (6.39) is in nondimensional units, then equation (6.39) reduces to equation (6.5). Before going into some detail of cnoidal waves, solitary waves, the Stokes finite-amplitude waves (to be introduced later), it is worthwhile to indicate the relevance to tsunamis of the various waves and approximations to the theories discussed so far. In deep water, especially in the near field of tsunami generation, the linear theory (phase dispersion alone is relevant) is probably adequate; on the continental shelf both phase and amplitude dispersions will be important, thus, cnoidal waves and solitary waves are relevant. In the very shallow coastal areas (bays, harbours, inlets) the amplitude dispersion dominates.

70

N. Nirupama et al.

Both amplitude and phase dispersions will tend to cause a gradual distortion of the waves. The nature of the distortion produced by amplitude and phase dispersions need not be the same. The reduced form of Boussinesq equation (6.33) will be used to examine this problem. Consider a frame of reference that moves with unit speed (in non-dimensional units). For this, define: S =x−t

(6.40)


Then equation (6.33) becomes: ∂η ∂η ∂3 η + εη +µ 3 =0 ∂t ∂S ∂S

(6.41)

The effects of amplitude and phase dispersions will be estimated qualitatively by integrating equation (6.41) with respect to S. However, solutions will be restricted to those where η is either periodic or of the nature of a solitary wave, so that η and its derivatives tend to zero for large |S|. In both cases, the integrated terms can be discarded after integrating by parts. Integration of equation (6.41) gives: d ηdS = 0 (6.42) dt Multiplying equation (6.41) by η, η2 , ηn gives the following relations after integration: d 1 2 η dS = 0 dt 2 d dt

1 3 η dS = −µ 3

∂η ∂S

3

dS

(6.43) (6.44)

and the general relation is: d dt

η

n+1

1 dS = − n(n + 1)(n − 1)µ 2

∂η ∂S

3

ηn−2 dS

(6.45)

Differentiate equation (6.41) with respect to S, multiply by ∂η/∂S and integrate to give: d dt

∂η ∂S

2

dS = −ε

∂η ∂S

3

dS

(6.46)

The integrals on the right sides of equations (6.44)–(6.46) can be considered as expressing the asymmetry of the waves. For waves with steep fronts the integrals will be negative. Thus, these equations show that phase dispersion will tend to heighten the crests and flatten the troughs. Equation (6.46) shows that the amplitude dispersion will increase the averaged square of the slope of the waves. 6.7

SUMMARY

There are two types of dispersion associated with tsunami waves: phase dispersion mainly happens during the propagation of the tsunami over the ocean, while amplitude dispersion occurs due to


71

non-linear interactions in shallow water near the coastline. The Ursell parameter involving the tsunami amplitude, its wavelength, and the water depth determines which type of equations should be used in analytical–numerical modelling of tsunamis. Here the classical concepts on these two types of dispersions as well as cnoidal waves and reduced forms of the Boussinesq equation and their mathematical development are briefly reviewed.


REFERENCES Broer, L.J.F. (1964). On the interaction of nonlinearity and dispersion in wave propagation I. Boussinesq’s equation. Appl. Sci. Res. Sect. B, 2, 273–285. Chen, M., Diroky, D., and Hwang, L.S. (1975). Nearfield Tsunami Behaviour. US National, Science Foundation. By Tetra Tech. Inc., Pasadena, CA. 49 pp. Kowalik, Z., Knight, W., Logan, T., and Whitmore, P. (2005a). Numerical modeling of the global tsunami: Indonesian tsunami of 26 December 2004. Sci. Tsunami Hazards, 23(1), 40–56. Kowalik, Z., Knight, W., Logan, T., and Whitmore, P. (2005b). The tsunami of 26 December 2004: numerical modeling and energy considerations. In: G.A. Papadopoulos and K. Satake (eds.), Proceedings of International Tsunami Symposium. Chania, Greece, 27–29 June, pp. 140–150. Lamb, H. (1945). Hydrodynamics, 6th edn. Dover Publishing, Inc., New York, NY, 738 p. LeMéhauté, B. (1969). On the nonsaturated breaker theory and the wave run-up. In: 8th Conference of Coastal Engineering, American Society Civil Engineering, Mexico City, Mexico, pp. 77–92. Lighthill, M.J. (1958). River Waves, Proceeding 1st Symposium Naval Hydrodynamics, Washington, DC, 1956, US National Research Council, pp. 17–44. Murty, T.S. (1977). Seismic seawaves-tsunamis, Bulletin 198, Fisheries Research Board of Canada, Ottawa, 337 pages (in English and Russisan). Murty, T.S., Nirupama, N., and Rao, A.D. (2005a). Why the earthquakes of 26th December 2004 and the 27th March 2005 differed so drastically in their tsunami-genic potential. Newslett. Voice Pacific, 21(2), 2–4. Murty, T.S., Rao, A.D., and Nirupama, N. (2005b). Inconsistencies in travel times and amplitudes of the 26 December 2004 Tsunami. J. Mar. Med., 7(1), 4–11. Murty, T.S., Nirupama, N., Nistor, I., and Hamdi, S. (2005c). Why the Atlantic generally cannot generate trans-oceanic tsunamis. ISET J. Earthq. Technol., 42(4), 227–236. Murty, T.S., Nirupama, N., Nistor, I., and Hamdi, S. (2005d). Far field characteristics of the Tsunami of 26 December 2004. ISET J. Earthq. Technol., 42(4), 213–217. Murty, T.S., Nirupama, N., Nistor, I. and Rao, A.D. (2005e). Conceptual differences between the Pacific, Atlantic and Arctic tsunami warning systems for Canada. Sci. Tsunami Hazards, 23(3), 39–51. Murty, T.S., Rao, A.D., Nirupama, N., and Nistor, I. (2006). Numerical modelling concepts for the tsunami warning systems. Curr. Sci., 90(8), 1073–1081. Nirupama, N., Murty, T.S., Rao, A.D., and Nistor, I. (2005). Numerical tsunami models for the Indian Ocean countries and states. Indian Ocean Survey, 2(1), 1–14. Nirupama, N., Murty, T.S., Nistor, I., and Rao, A.D. (2006). The energetics of the tsunami of 26 December 2004 in the Indian Ocean: a brief review. Mar. Geod., 29 (1), 39–48.


CHAPTER 7

A Partial Explanation of the Initial Withdrawal of the Ocean during a Tsunami


N. Nirupama Atkinson School of Administrative Studies, York University, Toronto, Canada T.S. Murty Department of Civil Engineering, University of Ottawa, Ottawa, Canada A.D. Rao Centre for Atmospheric Sciences, Indian Institute of Technology, New Delhi, India I. Nistor Department of Civil Engineering, University of Ottawa, Ottawa, Canada

7.1

INTRODUCTION

One of the interesting phenomenon that occur at some locations during tsunami events is the withdrawal of the ocean, before the main tsunami waves arrive at that location, which is generally referred to as the initial withdrawal of the ocean (IWO). However, always IWO neither occurs at the same location for every tsunami nor at every location for the same tsunami. Sometimes IWO leads to tragic circumstances because curious people go to the ocean to watch the ocean bottom, which under normal circumstances is never exposed. While it is not a random occurrence, intuition tells us that the local ocean bathymetry and coastal topography, as well as the tsunami wave characteristics must have something to do with IWO. However, these factors alone may not be able to completely account for IWO. Until now there has been no completely satisfactory explanation for IWO. Here we attempt to provide at least a partial explanation. Tadepalli and Synolakis (1994) suggested that the so-called N-waves, which are waves with a leading depression can account for the IWO process. However, they say that their theory is relevant only if the epicenter of the earthquake is about 100 km from the coastline where the IWO occurs. Hence, it is difficult to envisage whether the N-wave phenomena can account for IWO on far off coast such as Tamil Nadu in India and Sri Lanka since the distances involved are more than an order of magnitude greater than 100 km.

7.2

SOLITARY WAVES AND ROLE OF VISCOSITY IN TSUNAMI PROPAGATION, FORERUNNER

It is well known that solitary waves are single crests propagating over the ocean surface. Single troughs will quickly fill up and are not stable to have equilibrium configurations or waveforms 73


74

N. Nirupama et al.

Figure 7.1. Tide gauge record at Hanasaki, Japan, showing a tsunami forerunner (Nakamura and Watanabe, 1961).

(Murty, 1977). Cherkesov (1966) showed that inclusion of viscosity in the calculations of the form of the free surface produced a depression wave that arrived before the leading wave of the tsunami. Although the effect of viscosity on the main tsunami wave itself is rather small (it might reduce its amplitude by 2% at most), if viscosity is ignored, then there will be no depression wave before the main wave arrives. Tsunami forerunners can occur even before the initial withdrawal (Figure 7.1) and at other times, there are no forerunners at all (Figure 7.2). Nakamura and Watanabe (1961) developed a simple theory to explain the occurrence of the forerunner and showed that, for large angles of incidence, the forerunner cannot be well developed. Also, for a forerunner to be produced, the tsunami period has to be considerably greater than the seiche period of the bay in which the tide gauge is located. Nakamura and Watanabe (1961) explained that the absence of forerunner at the Japanese coast associated with the tsunamis generated by the Kamchatka earthquake of 1957 and Aleutian earthquake of 1946 was due to oblique incidence. They gave the same reason for the absence of the forerunner from the 1960 Chilean tsunami at stations other than Japanese. Munk (1947) treated the problem of increase in the period of waves traveling over large distances and applied his general treatment to tsunamis, and seismic surface waves. Although this work may not properly belong to this section, it was included because Munk’s theory examined, as a by-product, the period of forerunners. The forerunners Munk dealt with were those observed at Pendeen, England, and Woods Hole, MA. Nevertheless, his theory is sufficiently general to be of relevance to the tsunami forerunner problem. He applied his theory to three tsunamis, the Chilean tsunami of November 10, 1922, the Kamchatka tsunami of April 13, 1923, and the Aleutian tsunami of April 1, 1946. He found good agreement between the calculated and observed increase in period of the tsunami during propagation. The results showed that the period of the tsunami increases with the increase of travel distance but decreases with time at a given station.


A partial explanation of the initial withdrawal of the ocean during a tsunami

75

Figure 7.2. Tide gauge records showing tsunami forerunners at some locations on the Pacific coast of Canada for the 1960 Chilean and the 1964 Alaska earthquake tsunamis (Murty, 1977).

Munk’s theory showed that the period of the forerunner is proportional to I , where I is an integral defined below and inversely proportional to the square root of time 2π2 1 I= 3 D 2 dx (7.1) g2 Where g is gravity, D(x) is the depth of the ocean, and x is the direction of tsunami travel. 7.3 THE THEORY OF SPIELVOGEL Spielvogel (1976) showed theoretically that in certain situation, the run-up on a beach was caused by a leading negative wave, followed by a positive wave. Following Speilvogel, we will present his theory here.

76

N. Nirupama et al.

Consider a two-dimensional flow on a sloping beach. Let V *, η*, X *, and t* be velocity, surface elevation, horizontal coordinate, and time (* denotes dimensional quantity). Introduce non-dimensional quantities through: V ∗ ≡ V0 V

x∗ ≡ Lx

η∗ ≡ βLη

T ∗ ≡ Tt

(7.2)

Where L is a typical length, g is gravity, β is the inclination of the beach, and:


T ≡ V0 ≡

L βg

(7.3)

g Lβ

Spielvogel transforms the problem from the x, t plane to the σ, λ plane defined by: V ≡

1 ∂ φ(σ, λ) σ ∂σ

(7.4)

x=

1 ∂ V2 σ2 φ− − 4 ∂λ 2 16

(7.5)

η=

1 ∂ V2 φ− 4 ∂λ 2

(7.6)

t=

λ −V 2

(7.7)

where σ ≥ 0. The significance of this transformation is that σ = 0 gives the instantaneous shoreline and λ = 0 gives the initial time. The momentum equation valid for shallow water in the σ, λ plane becomes:

∂2 ∂2 3 ∂ − − 2 2 ∂λ ∂σ σ ∂σ

V =0

(7.8)

or alternatively 1 ∂ ∂ ∂2 σ − 2φ = 0 σ ∂σ ∂σ ∂λ

(7.9)

The following Jacobian has to be nonzero in the proper domain for transformation back to the x, t plane: Carrier and Greenspan (1958) gave the following solution for (7.9) φ=−

0

∞

1 J0 (τσ) sin (τλ)I (τ)dτ τ

(7.10)

A partial explanation of the initial withdrawal of the ocean during a tsunami

77

with I (τ) =

∞

4σJ1 (στ)(η0 )σ dσ

0

(7.11)

where (η0 )σ = η(σ, 0)

(7.12)


gives the initial shape. The following formulae could be derived from above: η1 (σ, λ) = −

1 4

∞

0

J0 (τσ) cos (τλ)I (τ)dτ

(7.13)

and V (σ, λ) =

0

∞

1 J1 (τσ) sin (τλ)I (τ)dτ σ

(7.14)

Spielvogel assumed run-ups of the form: η˜ (x, 0) = A e16p(x−A)

(7.15)

where A is positive and is the amplitude of run-up and is small enough to satisfy (7.9). Here p is also a positive quantity and is a measure of the width of the run-up and has to satisfy (7.9). To specify the initial condition as a function of σ, invert: σ 2 = 16[A e16p(x−A) − x]

(7.16)

For x(σ). However, instead of this, one can start with the following initial shape: 2

η0 = η(σ, 0) = A e−pσ ,

A>0

(7.17)

η σ2 1 0 = η0 + n 16 16p A

(7.18)

Thus 2

x0 = x(σ, 0) = A e−pσ − which gives: η0 = A e16p(x−η0 )

as the initial condition. The fact that pA is small implies that η0 obeys (7.15) except in a small area near σ = 0. Then: x∼−

σ2 16

η0 ∼ A e−px

(7.19) (7.20)

78

N. Nirupama et al.

and 1

0 < (η0 )x =

1+

e(pσ 2 /16pA)

−H ( jwet + 1))

then ujmwet +1 = ujmwet

If wetting is possible (as stated by the above condition) the velocity from the wet point is extrapolated to the right (dry point), but sea level is calculated through the equation of continuity. The model has been calibrated and tested through a comparison with analytical solutions as well as with laboratory experiments. Initially, a series of comparisons was made against benchmark

102

Z. Kowalik et al.

problems suggested at the Third International Workshop on Long-wave Run-up Models held at Catalina Island in 2004, namely:


1 A wave run-up on uniformly sloping beach. An analytical problem introduced by Carrier et al. (2003). 2 A run-up due to Gaussian shape landslide which initially is located at the shoreline. An analytical solution was proposed by Liu et al. (2003). 3 A maximum run-up on Okushiri Island during tsunami 1993 reproduced in the large wave flume by Matsuyama and Tanaka (2001). In order to further test how the model’s numerical approximation works, a case of a wave running up the beach without friction (which was solved analytically by Carrier and Greenspan, 1958) was also simulated. The solution derived by Thacker (1981) for a two-dimensional oscillation in a parabolic basin was useful in the model testing and in predicting the extent of inundation. A stringent condition on the run-up computations is set by a dam-break problem (Shigematsu et al., 2004), which was also used for testing and validation of the model. Comparison of the model against analytical solutions and testing cases proposed by the International Tsunami Community and against experimental data showed very good agreement. But in some cases, as one would expect a priori, the analytical and numerical solutions converge only when the numerical model uses very fine spatial and temporal stepping (resolution). This situation is described in detail by Horrillo et al. (2005) particularly for a case representing the dam-break problem formulated by Shigematsu et al. (2004). The spatial grid step of numerical computation is 1 (R0 φ = 1.852 km), and it changes with latitude as R0 φ cos φ. Numerical stability requires that this step be smaller than the distance √ T gH . The deepest point in the World Ocean (h 11000 m) is located close to 11◦ N and therefore, the time step of numerical integration is less than 7.9 s. This step was diminished to 2 s as the run-up scheme requires smaller time stepping. The total number of the grid points was close to 200 million, therefore the simple time stepping solution, even on a supercomputer may take several weeks. To reduce the computational time the entire domain was split along meridians into 60 subdomains to apply 60 processors. With this parallelization, 50 h of tsunami propagation was reproduced in 9 h on a CRAY X1. Consideration of a small spatial step is important as the shortperiod waves can be obliterated during large distances of propagation when using large spatial steps. Taking the average depth of the World Ocean as 4000 m, a wave with 10-min period has a wavelength close to 120 km. Such a wave length is discretized by the 1.852 km grid into about 64 mesh lengths. The amplitude of a sinusoidal wave propagating over 10000 km distance will diminish only about 2%, but some shorter dispersive waves will be generated as well (Kowalik, 2003). 10.4 A SIMPLE MODEL OF TSUNAMI GENERATION BY THE BOTTOM DISPLACEMENT The IOT observations indicated strong amplifications of the tsunami in the near-shore regions due to bottom shoaling. Additionally, observations described numerous reflections and long ringing of tsunami oscillations in the coastal regions (Merrifield et al., 2005; Rabinovich, 2005), suggesting either the local resonance or the local trapping of tsunami energy. To elucidate how a tsunami generated by the bottom displacement interacts with the shelf/shelf break bathymetry to generate a complex signal which travels into open ocean domain, we consider a channel of the 1000 km long and 3 km deep connected to the shelf/shelf break domain (see Figure 10.3). We start the computation by considering a tsunami generated by uniform bottom uplift at the source region located between 200 and 400 km (Figure 10.3). In Figure 10.3 a 2 m tsunami wave mirrors the uniform bottom uplift occurring at T = 40 s from the beginning of the uplift process.


Numerical modeling of the Indian Ocean tsunami

Figure 10.3.

103

History of tsunami propagation. Generated by bottom deformation at T = 40 s this tsunami experiences significant transformations and reflections. Black dashed lines denote bathymetry in meters. Numbers for the bathymetry in the figure should be multiplied by 10.

Later, this water elevation separates into two waves of 1m height each traveling in opposite directions (T = 16.7 min). The wave traveling toward the open boundary exits the domain without reflecting (radiation condition), and the wave traveling toward the shelf propagates without change of amplitude. This is because the bottom friction at 3 km depth is negligible (T = 39 min). At T = 57.6 min, the tsunami impinges on the shelf break resulting in the tsunami splitting into two waves (T = 1 h 16 min) due to partial reflection: a backward traveling wave with amplitude of ∼0.5 m, and a forward traveling wave toward the very shallow domain (T = 1 h 27 min). While the wave reflected from the shelf break travels without change of amplitude, the wave on the shelf is amplified and becomes shorter. The maximum amplitude attained is approximately 7.2 m (not shown). Figure 10.3 (T = 3 h) shows the time when the wave reflected from the shelf break left the domain and the wave over the shelf oscillates with an amplitude diminishing toward the open ocean. These trapped and partially leaky oscillations continue for many hours, slowly losing energy due to waves radiating into the open ocean and due to the frictional dissipation at the bottom. This behavior is also described in Figure 10.4, where temporal changes of the sea level are given in proximity to the open boundary. The initial box signal of about 20-min period is followed by the wave reflected from the shelf break and the semi-periodic waves radiated


104

Z. Kowalik et al.

Figure 10.4. Tsunami signal propagating from the generation domain into the open ocean. Initial box signal of 20-min period is followed by the signal reflected from the shelf break and signal radiated from the shelf domain.

back from the shelf/shelf break domain. The open boundary signal which is radiated into the open ocean is therefore the result of superposition of the primary wave and secondary waves. The period of the primary wave is defined by the width of the bottom deformation and the ocean depth (initial wave generated by earthquake), while the periods of the secondary waves are defined by reflection and generation of the new modes of oscillation through an interaction of the tsunami waves with the shelf/shelf break geometry. The evidence for tsunamis transformation and trapping have been presented both, theoretically (Nekrasov, 1970; Abe and Ishii, 1980) and in observations (Loomis, 1966; Yanuma and Tsuji, 1998; Mofjeld et al., 1999). 10.5

SOURCE FUNCTION

The generation mechanism to model the IOT is mainly the static sea floor uplift caused by abrupt slip at the India/Burma plate interface. Permanent, vertical sea floor displacement is computed using the static dislocation formulae from Okada (1985). Inputs to these formulae are fault plane location, depth, strike, dip, slip, length, and width as well as seismic moment and rigidity. The earthquake’s total rupture extent can be estimated by several approaches. Finite fault seismic data inversion is one method, which yielded fault lengths on the order of 350–650 km (e.g. Ji, 2004; Yagi, 2005). Another traditional method to delineate earthquake fault zones is by plotting the aftershocks which occur in the first 24 h following the main shock. The aftershocks are expected to cluster within the slip zone. This approach led to an estimate of 1200 km for the fault length (NEIC, 2004). In this study, the fault extent is constrained by observed tsunami travel times to the northwest, east, and south of the slip zone. Figure 10.5 displays the tsunami arrival time constraints on the fault zone. Tsunami arrival times at Paradip–India (SOI, 2005), Ko Tarutao–Thailand (Iwasaki, 2005), and Cocos Island (Merrifield et al., 2005) tide gauges are plotted in reverse. That is, the observed travel time contour is plotted with the tide gauge location as the origin point. This method indicated a fault zone approximately 1000 km by 200 km. The epicenter location lay on the southern end of the fault zone. To accommodate trench curvature, the fault plane is broken into two segments. Fault parameters for the two segments are listed in Table 10.1. Strike, dip, and slip are based on the definitions from Aki and Richards (1980). Strike is determined by the trench orientation. Dip is taken from the



Figure 10.5.

105

December 26, 2004 Sumatra earthquake uplift as constrained by tsunami travel times.

Table 10.1.

Fault parameters used to generate vertical sea floor movement.

Earthquake parameter

Southern fault segment

Northern fault segment

Strike Dip Slip Length Depth (SW corner) SW corner latitude SW corner longitude Moment Rigidity

335◦ 8◦ 110◦ 300 km 8 km 3.0N 94.4E 3.2 × 1029 dyn cm 4.2 × 1011 dyn cm−2

350◦ 8◦ 90◦ 700 km 8 km 5.6N 93.3E 7.6 × 1029 dyn cm 4.2 × 1011 dyn cm2

Harvard CMT solution (HRV, 2005). The slip for the southern segment is based on the Harvard CMT solution while the slip for the northern segment is set at 90◦ based on observed tsunami first motions on Indian tide gauges (NIO, 2005). Depth is based on the finite fault inversion of Ji (2004). The total moment released (derived by assuming an average slip of 13 m and rigidity of 4.2 × 1011 dyn cm−2 ) in the two segments equals 1.08 × 1030 dyn cm (Mw = 9.3), which is in good agreement with 1.3 × 1030 dyn cm proposed by Stein and Okal (2005) based on normal mode analysis. The 3-D rendering of the source function is shown in Figure 10.6.


106

Z. Kowalik et al.

Figure 10.6. The source function. Maximum uplift is 507 cm and maximum subsidence approximately 474 cm. Coordinates are given in geographical degrees. Point (0,0) is located at 89◦ E and 1◦ N.

The total potential energy related to the bottom deformation given in Figure10.6 which is transferred to the sea level oscillations is calculated as: Ep = 0.5 ∫ ∫ ρgζ 2 R20 cos(φ)δφδλ

(10.10)

Calculation over the area of deformation sets the potential energy to 5.39 × 103 TJ (terra joule). 10.6

IMPORTANT SNAPSHOTS OF IOT DEVELOPMENT

The IOT of December 26, 2004 was quite different from the large scale tsunamis of the Pacific and Atlantic oceans. Post tsunami analysis suggests that boundary reflections significantly influenced tsunami levels in the Indian Ocean (Murty et al., 2006). Reflections from land, focusing and trapping of tsunami energy by the long island chains, and amplification and reorganization of the tsunami signal in the straits between continents all played an essential role in the IOT propagation. Figure 10.7 depicts multiple reflections from the Indian Peninsula and Sri Lanka as a reverse wave traveled back toward Indonesia. The initial reflection occurred about 2 h after the earthquake onset. We will demonstrate later that this reflection sends more energy southward than the initial wave generated by the earthquake. The tsunami interaction with the semi-transparent Maldives islands was different from that with the India and Sri Lanka coasts (Figure 10.8). While propagating toward Africa, the tsunami impinged on the Maldives Island chain. Only a portion of the incoming tsunami energy crossed this chain. Some energy was trapped around the islands and the rest was reflected backwards. As Figure 10.8 depicts, the forward signal is changed through refocusing. An island (or a few islands) splits the tsunami into two parts. These two parts coalesce behind the island, often generating local amplification of the tsunami (see wave front south-west of the Maldives). The trapped signal around the islands tends to interact with the local bathymetry generating quite large amplitudes which are slowly dissipated through bottom friction and radiation into the open ocean. This behavior is similar to the process discussed earlier and demonstrated in Figure 10.4. The role of multiple reflections in the sea level variations during IOT is well depicted by the sea level recorded on the Cocos Island (Figure 10.9). Even though Cocos Island (12◦ 7 S 96◦



107

Figure 10.7.

Distribution of the tsunami amplitude in the Indian Ocean at 2 h 50 min from the tsunami onset. The wave reflected from India and Sri Lanka propagates back to the source region.

Figure 10.8.

Distribution of the tsunami amplitude in the Indian Ocean at hour 4 from the tsunami onset. Along with the reflection shown in Figure 10.7, the reflection from the Maldives also sends energy eastward.

53 E) is not within the field of view of the figures (southern most latitude in Figure 10.8 is 10◦ S), it is close enough to draw valid conclusions on the arrival time of reflected waves. There is very good correspondence between predicted reflections from Sri Lanka and the Maldives and features recorded in the mareogram. The reflected wave from Sri Lanka arrived about 3 h after direct wave and the Maldives reflected wave arrived close to 5 h after the direct wave. Figure 10.10 gives a different perspective on the tsunami. Here, one is looking at the IOT from the African continent toward Indonesia. The time of this snapshot is about 9 h 25 min from the


108

Z. Kowalik et al.

Figure 10.9.

Sea level recorded at Cocos Island on December 26, 2004.

Figure 10.10. A birds-eye view of the IOT at time 9 h 25 min from the tsunami onset, looking from Africa toward India and Indonesia. Trapped tsunamis around continents and islands still display a strong signal.

onset of the earthquake. Although by this time the tsunami has essentially dissipated in the open ocean domain, a strong tsunami signal still persists along the continents and islands demonstrating trapping of tsunami energy by local shelf bathymetry. The IOT in the global ocean displays many interesting features. One of them observed through the animation technique is tsunami transformation when it travels through the narrows between oceans. The passage between Antarctica and Australia/New Zealand plays a noticeable role in tsunami amplification. As the passage is wide on the Indian Ocean side and constrained on the Pacific side, the eastward moving signal is amplified and also reorganized into periodic wave-like structures. A similar reorganization of a quasi-turbulent signal into oscillatory wave pattern can be observed in the passage between South America and Africa for the tsunami propagating from the Southern into the Northern Atlantic (Figure 10.11).



Figure 10.11.

10.7

109

Sea level pattern generated by the IOT of December 26, 2004 at 30 h 40 min from the onset. Tsunami signals in the Northern Atlantic and Southern Pacific have been reorganized into coherent waves after passing through the narrows between Africa and South America, and Australia and Antarctica.

GLOBAL DISTRIBUTION OF MAXIMUM AMPLITUDE

Model computations using the source discussed in Section 4 were made for the first 50 h of propagation by such time the tsunami signal had traveled over the entire World Ocean. During this computation the maximum tsunami amplitude in every grid point was recorded. The plot of maximum amplitude in the proximity of the generation domain is given in Figure 10.12, and the corresponding plot for the World Ocean is given in Figure 10.13. The strong directional signal generated by the elongated source dominated the Indian Ocean domain. The main energy lobe was directed toward Sri Lanka and the secondary lobe pointed toward South Africa, sending a strong signal into the Atlantic Ocean. The computation indicated that the maximum amplitude was 15.5 m in proximity to the fault, 9.3 m at the shore of Thailand, 8.1 m at Sri Lanka, and 3.3 m at the coast of East Africa. This figure also depicts the amplitude enhancement in shallow water and especially in proximity to peninsulas and islands due to energy concentration through the refraction process. The large domain of the Arabian Sea is located in the shadow of the main energy beam. Both computation and observation demonstrated significant increase of the tsunami amplitude up to 1.5 m at the coast of Oman as recorded by the tide gauge in Salalah. This global maximum amplitude distribution (Figure 10.13) shows that the IOT encompassed all over the World Ocean. Although the source directed most of the wave energy towards South Africa, a strong signal was also directed towards the Antarctica. It is obvious that the ocean bathymetry affected the tsunami propagation. For example, tsunamis tended to propagate toward Antarctica along the oceanic ridges, and subsequently continued to transfer higher energy along the South Pacific ridge toward South and Central America. This mode of propagation resulted in the tsunami amplitude increase up to 65 cm along the Pacific coast of South America. A similar mode of energy transfer is observed in the Atlantic, where the Mid-Atlantic ridge channeled the tsunami to produce 30 cm wave amplitude as far north as Nova Scotia. An especially large energy flux was ducted from the South Atlantic Ridge toward Brazil and Argentina. The filaments of energy trapped along the South Pacific ridges are most spectacular as they ducted tsunami


110

Z. Kowalik et al.

Figure 10.12.

Maximum modeled tsunami amplitude in the Indian Ocean.

Figure 10.13.

Maximum modeled tsunami amplitude in World Ocean.



111

energy for many thousands of kilometers. A simple explanation of the energy trapping using the continuity equation leads us to conclude that the amplitude should increase over the ridges due to the relatively shallower depth there. At the same time the role of bottom friction over the 3 km deep ridge is negligible and, therefore, the tsunami can travel long distance without much energy losses. The trapping of this energy is probably related to the long wave trapped along the ridge (Mei, 1989). The cross-ridge trapping length, which is responsible for energy concentration, is approximately defined by the tsunami wavelength. As the IOT carried a wide spectrum of waves with periods from 20 to 50 min, the wavelength for the mid-ocean ridge is in the range of 100–600 km. A simple explanatory model for the long wave trapping may be based on tsunami wave speed over and off the ridge. As the waves over ridge are slower and the waves off ridge are faster, the joint tsunami wave front is curved in such a way that the energy is fluxed toward the ridges (see sea level pattern in Figure 10.11 over the South Pacific ridge). However, the above explanation neglects the influence of the Coriolis force on tsunami propagation. Tsunamis are typically computed without Coriolis force because their periods are much smaller than the inertial period. As propagation proceeds over long distances the compounding effect of Coriolis force may sum up and significantly increase. In Figure 10.14 the residual maximum amplitude is given as the difference between two computed distributions, one with and one without Coriolis force. The difference given in Figure 10.14 shows locations where Coriolis force dominated. The amplitudes are not very large and according to expectation the influence was increasing toward the south since the Coriolis effect increases poleward from equator. Consistent change is observed along the South Pacific Oceanic Ridge. Residuals due to Coriolis force were close to 1 cm and since the total amplitude along this ridge according to Figure 10.13 is approximately 4 cm, we conclude that Coriolis force plays a role in the energy trapping along the oceanic ridges (see also trapping in the South Atlantic). A simple model for energy trapping due to the Coriolis force is a Kelvin wave propagating along the depth discontinuity

Figure 10.14.

Residual maximum amplitude in World Ocean.

112

Z. Kowalik et al.


(Longuet-Higgins, 1969). The across-discontinuity trapping distance is defined by the Rossby radius of deformation (Gill, 1982). This distance is a function of depth and latitude and for ranges of depth 1–4 km and for latitude of 40–60◦ the Rossby radius ranges from 1000–2000 km. As this length is much larger than the tsunami wavelength we can conclude that Coriolis force is less effective in the concentrating tsunami energy along the oceanic ridges. To demonstrate the pattern of the energy trapped over the various bathymetric features we considered the energy flux. In the rectangular system of coordinates, with the x coordinate along E–W direction and y along N–S direction, the u component of velocity along x direction can be combined with the sea level (ζ) to define E–W component of the energy flux vector (Kowalik and Murty, 1993a): Ex = ρgHuζ

(10.11)

Similarly, the N–S component of the energy flux vector is defined (with v, the velocity component along the y direction): Ey = ρgHvζ

(10.12)

Where ρ is the sea water density, g = 9.81 m s−2 is the Earth’s gravity acceleration and H is the ocean depth. The energy flux vector for the progressive wave is always propagating into the same direction as the sea level and velocity and its direction is perpendicular to the wave front. To preserve direction of the energy flux in the progressive wave the velocity and sea level elevation remain in phase (Henry and Foreman, 2001). Energy flux units which are expressed as Joule/(s cm) is an energy flux per unit width and per unit time. To derive the total energy flux the above expressions should be multiplied by the length of a cross-section and integrated over the time period. In Figure 10.15 the energy flux vectors are shown in the south-western part of the Pacific Ocean. The larger tsunami amplitudes are located above the oceanic ridge and the energy flux is directed along the ridge. This small group of higher amplitude waves does not belong to the

Figure 10.15.

Energy flux vectors over the South Pacific ridge at time 26 h 20 min. Colors denote sea level. Dark-brown lines denote the ridge depth – 3000 m depth contour.


113


first tsunami signal to arrive in this region. Its average wavelength was about 1350 km, as the depth of the ridge is close to 3 km the wave period was about 2 h. This is a somewhat long period for a free tsunami wave, but the longer period suggested possible influence of the Coriolis force. The wave pattern also showed that the waves over ridges were slower than the off-ridge waves, suggesting trapping due to refraction and focusing of off-ridge energy toward the ridge. Nonetheless, we cannot exclude the possibility of a resonance interaction of the tsunami wave and ridge bathymetry since Snodgrass et al. (1962) demonstrated the presence of discrete spectra in waves trapped over depth discontinuities. Mei (1989) showed that over a stepped bottom ridge the discrete spectra exist as well. If an incident wave can excite these trapped modes, an amplification of the tsunami signal due to resonance will follow. 10.8 TIME-DEPENDENT PROPAGATION Although the maximum amplitude defines tsunami distribution in the World Ocean, it does not reveal the temporal development of tsunamis. To improve understanding of the large scale temporal processes we used the temporal change of the tsunami energy fluxes passing through various cross-sections. The first cross-section considered is in the Indian Ocean, from 80◦ E to 105◦ E along 10◦ S (see Figure 10.12). The southward directed energy flux shown in Figure 10.16 is responsible for the tsunami signal propagating into the Pacific. The first maximum in this figure has been associated with the direct wave passing through the latitude 10◦ S at 2 h after the initial source motion. The next, even bigger energy influx arrived 2 h later, and is caused by the reflection from Sri Lanka and the east coast of India. The reflection from the Maldives Islands generates a signal which passed the cross-section at about 6.5 h from the initial disturbance. This cross-section is located quite close to the Bay of Bengal and therefore a large portion of the Maldives-reflected signal omitted this route. Since the Bay of Bengal acted as a parabolic mirror, it reflected many signals of smaller amplitude southward. The conclusion from the above experiment is that the reflected signal may send more energy south than the direct signal. With the major maxima in the southward directed signal identified, the task to associate them with the signal propagating into the Pacific Ocean remains. For this purpose an energy flux is considered through the three cross-sections located between Antarctica and the major continents. The cross-section (light shading in Figure 10.17) along the longitude 20◦ E from AS shows the time variation of the energy flux between Indian and Atlantic oceans. This flux remains negative for the entire period of 50 h, thus confirming that the inflow is directed into the Atlantic Ocean.

Figure 10.16.

Southward directed energy flux through the E–W cross-section located in the Indian Ocean along 10◦ S from 80◦ E to 105◦ E.


114

Z. Kowalik et al.

Figure 10.17.

Energy flux through the cross-sections located between Antarctic and major continents. Along 20E fromAntarctica to SouthAfrica (AS) (light shading); along 140◦ E, fromAntarctic to Australia (AA) (dark shading).

On the other hand the energy flow through a cross-section along 140◦ E (dark shading in Figure 10.17) from AA is at all times positive (from the Indian to Pacific oceans). The flux through the cross-section located between South America and Antarctica at 70W, reveals a small in-flow from the Atlantic into the Pacific. Figure 10.17 clearly demonstrates that the magnitude and the time variability of energy fluxes through cross-sections AA and AS are quite different in character. The flux passing AS has a large value and the maximum energy in-flow to the Atlantic is located close to the initial wave front, even though the first arriving signal is not related to the maximum energy. The energy flow into the Atlantic is a result of the source orientation as shown in Figure 10.12. The main energy maximum is slower to arrive than the initial signal because, as Figure 10.13 depicts, the maximum energy directed toward South Africa cross-section is located along the oceanic ridge. Due to smaller depth over this ridge the more energetic signal propagates slower. The energy flow through AA demonstrates that tsunami arrives about 10 h from the onset of the earthquake; it initially has small amplitude which slowly increases in time from 18 to 21 h to achieve a few maxima. To understand the origin of this complicated temporal pattern of energy flux through AA we turn to Figure 10.16 and analyze the southward energy flux from the source area. The first signal arriving at the southern boundary in Figure 10.16 also crosses AA as the initial signal, since the travel time for this signal is close to 10 h. The second signal arriving 2 h later is caused by the reflection from the Sri Lanka and Indian coasts. The maxima in Figure 10.17 occurring from 18 to 21 h are related to the energy flux arriving by the various routes from the Indian Ocean. The arrival time of these signals depends on the depth and on the traveled distance. Therefore, it is useful to notice that the route from the generation domain to South America via passages between Australia and Antarctic is the great circle of a sphere. Signals which travel from the generation area to the section AA through the deep ocean travel faster, in about 10 h, but transfer less energy. The slower signal travels along oceanic ridges and transfers more energy as confirmed in Figure 10.15 by the energy flux vectors. This appears to be only a part of the story. Tracking (through animations) the signal shown in Figure 10.17 backwards (in time), the


115

tsunami which passes between Australia and Antarctica, as depicted in cross-section AA (Figure 10.17), then loses its identity going back into the southern Indian Ocean. The large in-flow of energy shown in Figure 10.17, is related to the reflected signals off the Seychelles, Maldives and Africa, and to a slowly traveling reflection which originated in the Bay of Bengal. To compare the total energy flux entering Pacific and Atlantic oceans over the first 50 h of process, the energy fluxes given in Figure 10.17 have been integrated in time. The total energy flowing into the Pacific Ocean is approximately 75% of the total flow to the Atlantic Ocean.


10.9 TRAVEL TIME Tsunami travel time from the source region to the given location is an important parameter in the tsunami prediction and warning. The Indonesian tsunami arrival times have been determined for many locations (Merrifield et al., 2005; Rabinovich, 2005; http://www-sci.pac.dfo mpo.gc.ca/osap/projects/tsunami/tsunamiasiax_e.htm; http://ilikai.soest.hawaii.edu/uhslc/iotd/; http://www.nio.org/jsp/tsunami.jsp). This set of data presents a possibility for the ocean-wide comparison of the data and our model. The first numerical experiment delineates the tsunami arrival time at every grid points for a signal of 0.1 cm amplitude. The computed tsunami travel time chart is depicted in Figure 10.18. The chart shows that even at such small limiting amplitudes the tsunami signal arriving at Alaska and North America did not pass through the Indonesian Straits but rather around Australia and New Zealand. The next numerical experiment computes isolines of arrival time for the tsunami signal of 0.5 cm amplitude (Figure 10.19). In the vast regions of Northern and Central Pacific this figure does not show a consistent arrival time. We may conclude that the main premise used to construct these figures, namely that the first train of tsunami waves is associated with the largest wave, does not hold true. We were able to construct isolines of arrival time in the regions of larger amplitudes, that is in the Indian Ocean, in the South Pacific (especially along the South Pacific ridge) and in the South

Figure 10.18. Travel time (in hours) for the tsunami of 0.1 cm amplitude.


116

Z. Kowalik et al.

Figure 10.19. Travel time (in hours) for the tsunami of 0.5 cm amplitude. Table 10.2.

Observed and calculated travel time.

Station location

Travel time observed

Travel time for 0.1 cm amplitude

Travel time for 5 cm amplitude

Chennai (80◦ .17E, 13◦ .04N) Male (73◦ .52E, 4◦ .18N) Hanimadhoo (73◦ .17E, 6◦ .77N) Diego Garcia (72◦ .40E, 7◦ .28S) Hillarys (115◦ .73E, 31◦ .82S) Salalah (54◦ .00E, 16◦ .93N) Pt. La Rue (55◦ .53E, 4◦ .57S) Lamu (40◦ .90E, 2◦ .27S) Zanzibar (39◦ .18E, 6◦ .15S) Portland (141◦ .60E. 38◦ .33S) Richard’s Bay (32◦ .08E, 28◦ .80S) Port Elizabeth (25◦ .63E, 33◦ .97S) Jackson Bay (168◦ .62E, 43◦ .98S) Arraial de Cabo (42◦ .02W, 22◦ .97S) Arica (70◦ .21W, 18◦ .22S) Char. Amalie (64◦ .55W. 18◦ .20N) San Diego (117◦ .12W, 32◦ .45N) Halifax (63◦ .59W, 44◦ .66N) Atl.City (74◦ .25W, 39◦ .21N) Toffino (125◦ .55W. 49◦ .09N) Adak (176◦ .65W, 51◦ .87N)

2 h 36 min 3 h 25 min 3 h 41 min 3 h 55 min 6 h 41 min 7 h 17 min 7 h 25 min 9 h 9 min 9 h 49 min 10 h 39 min 11 h 13 min 12 h 28 min 18 h 18 min 21 h 56 min 26 h 36 min 28 h 42 min 31 h 25 min 31 h 30 min 31 h 48 min 32 h 1 min 35 h



Atlantic. By checking results of computations at the coastal locations we found that a tsunami of 0.5 cm amplitude arrived at every location in the Pacific Ocean. This wave did not arrive at western North America by refracting around New Zealand; it traveled closer to South America via energy ducts located over South Pacific ridges. This is a long travel time compared to the travel time depicted in Figure 10.18. In Table 10.2 the observed arrival time is compared with the computed arrival time of 0.1–5 cm tsunami amplitude. The observations define travel times uniquely when amplitude of the signal



117

is above the noise level. The mixed signal of meteorological and tsunami origin is difficult to differentiate. We took, somewhat arbitrarily, the amplitude of 5 cm as a signal strong enough to be seen above the meteorological noise. As can be seen from Figures 10.16 and 10.17 in many locations, and as close to the source as New Zealand, the first waves to arrive were quite small and they slowly increased in amplitude. For example, the observed arrival time at Jackson Bay, NZ was 18 h 18 min, while according to the travel time computed by the first perturbation of 0.1cm at this location, the arrival time for the first wave was 12 h 30 min. The stations located in the Northern Pacific showed the largest differences between the calculated and observed travel time. This is caused either by small tsunami signal-to-noise ratio, or by multiple paths between the source and gauge locations. In the latter, especially important is an interaction of the higher energy tsunami signals which travel slowly over the oceanic ridges and the lower energy signals which travel faster over the deep oceanic regions.

10.10

OBSERVATIONS VERSUS COMPUTATIONS

Although the 1-min computational mesh resolves many coastal and bathymetric features, nonetheless it is too large to resolve the local dynamics such as run-up. In Figure 10.20, the sea level at four stations have been chosen from the Indian Ocean area and compared with observations described by Merrifield et al. (2005).

Figure 10.20.

Observations and computations for four stations in the Indian Ocean.


118

Z. Kowalik et al.

Figure 10.21.

Ground track of Jason-I and computed tsunami amplitude at 2:55 UT on December 26, 2004 in the Indian Ocean.

The stations are located on Maldives Island (Male), on the Seychelles Islands (Pt LaRue), on the African coast of Kenya (Lamu), and on the Arabian Peninsula coast of Oman (Salalah). The model reproduces quite well the maximum amplitude and the temporal behavior of the tsunami, indicating that with higher resolution bathymetry an even better comparison can be achieved. As luck would have it, the Jason-I altimetry satellite traversed the Indian Ocean about 2 h after the event origin time. It crossed the equator on a NNE path at 02:55 UTC on December 26, 2004 (Figure 10.21). The non-validated altimetry data was downloaded from the JPL Physical Oceanography web site at ftp://podaac.jpl.nasa.gov/pub/sea_surface_height/jason/j1nrtssha/data/ Altitude is sampled approximately once per second and is corrected for tides. In order to remove any background, the raw data from the “tsunami pass” was corrected by subtracting out an average of 4 “non-tsunami” passes. Jason-I repeats its track about once every ten days, so four repeat paths were averaged to generate the background. The corrected signal, was then smoothed by removing fluctuations with wavelengths shorter than 20 km. The smoothed signal with background removed was compared against the model data. Note that Jason-I was above the tsunami for about 10 min. During this time the tsunami was in motion, so the comparison is made to dynamic model predictions and not against a static snapshot. The model wave heights at the moment of equatorial crossing of Jason-I are shown in Figure 10.21. Jason-I crosses the leading edge wave at a point on the wave front where the amplitude is rapidly increasing toward the NW. The comparison between data and model is therefore sensitive to small variations in source details. The final comparison is shown in Figure 10.22 (upper panel). The leading edge wave location is predicted accurately by the model, even if the amplitude is not. The modeled leading wave with the amplitude similar to the recorded by satellite was in the satellite footprint 15 min earlier (see, Figure 10.21). A closer amplitude/period match was obtained by rotating the source strike counterclockwise slightly, and by reducing the fault width from 200–125 km. The comparison, given in Figure 10.22 (lower panel) shows that the model as driven by the adjusted source function reproduces more accurately the leading wave recorded by Jason-I.


119

Ssh on Jason track 80

Model Jason

60

Ssh (cm)

40 20 0 20

60 20

0

10

10

20

Latitude (deg) Ssh on Jason track 80 Model Jason

60 40 Ssh (cm)


40

20 0

20 40 60 80

100 20

Figure 10.22.

10.11

10

0 Latitude (deg)

10

20

Computed and observed tsunami amplitude along the Jason-I track. Upper panel: source function given in Figure 10.1. Lower panel: source function orientation and width adjusted.

DISCUSSIONS AND CONCLUSIONS

The main purpose of the present chapter was to derive a global picture of the IOT of December 26, 2004 based on a computer model. By comparison to the global observation we have identified major patterns of tsunami propagation. The new physics observed through application of the GTM underscores the importance of using a GTM in tsunami investigations. The IOT of December 26, 2004 was quite different from large scale tsunamis in the Pacific and Atlantic oceans. Post IOT analysis depicted numerous reflections and quite long ringing of the tsunami oscillations in the coastal regions suggesting local resonance and local trapping of tsunami energy. Computed distributions of the maximum amplitude compare well with observations analyzed by Merrifield et al. (2005) and by Rabinovich (2005). The observed and computed temporal variation of the tsunami at gauge stations in the Indian Ocean display quite similar amplitude and variability, although the model resolution of about 2 km still needs to be improved for proper run-up calculations. The comparison against satellite data shows that improvements in the source function are needed. The source location was constrained by tsunami travel times to tide


120

Z. Kowalik et al.

gauge locations and by earthquake parameters computed from seismic data inversions. Further investigation through comparison to the magnitude and location of the satellite signal (Gover, 2005) should also improve the source parameters. As the source function is one of the major building blocks of the tsunami model and, as some new insight on the source function pattern and tsunami generation has been suggested by Lay et al. (2005) and Hirata et al. (2005), it will be important to improve the GTM model using this new information. The model computations reveal peculiarities of tsunami signal when it travels from the source over entire World Ocean. The most interesting is ducting the tsunami energy along oceanic ridges, (Kowalik et al., 2005; Titov et al., 2005), which is so clearly shown in Figures 10.12 and 10.13. To demonstrate the pattern of energy trapping over the ridges, the energy flux function is used. The energy flux vectors show magnification over the South Pacific ridge and their distribution suggest trapping due to refraction and focusing the off-ridge energy toward the ridge. Further investigations of energy fluxes show more complicated temporal and spatial patterns in tsunami propagation. The primary signal traveling toward the Pacific Ocean depicted low energy level, therefore it was not well observed at sea level gauges. The more energetic signal arrived with some delay. The investigation of the energy flux along the South Pacific ridge reveals tsunami of approximately 2 h period. Tracking (through animations) tsunamis passing between Australia and Antarctica we have found that the tsunami moving from west to east is amplified and is also reorganized into periodic wave-like structures. Similar reorganization of the tsunami occurs between South America and Africa for the tsunami propagating from the Southern into the Northern Atlantic.

ACKNOWLEDGEMENTS We wish to express our gratitude to Juan Horrillo, Institute of Marine Science, University of Alaska, Fairbanks for testing our model using VOF approach and offering suggestions on the model improvements. We are grateful to Roger Edberg, Arctic Region Supercomputing Center, for constructing high-quality animations which allowed us to grasp the nature of the global tsunami propagation. We are also indebted to Professor Sathy Naidu, Institute of Marine Science, University of Alaska, Fairbanks, who made comments toward improving manuscript.

REFERENCES Abe, K., and Ishii, H. (1980). Propagation of tsunami on a linear slope between two flat regions. Part II reflection and transmission, J. Phys. Earth, 28, 543–552. Aki, K., and Richards, P.G. (1980). Quantitative Seismology Theory and Methods, Vol. 2. W.H. Freeman and Co., San Francisco, p. 557. Carrier, G.F., and Greenspan, H.P. (1958). Water waves of finite amplitudes on a sloping beach. J. Fluid Mech., 4, 97–109. Carrier, G. F., Wu, T.T., and Yeh, H. (2003). Tsunami run-up and draw-down on a plane beach. J. Fluid Mech., 475, 79–99. Flather, R.A., and Heaps, N.S. (1975). Tidal computations for Morecambe Bay. Geophys. J. Roy. Astr. Soc., 42 489–517. Gill, A.E. (1982). Atmosphere-Ocean Dynamics. Academic Press, New York, p. 662. Goto, C., and Shuto, N. (1983). Numerical simulation of tsunami propagations and run-up. In: (eds.), K. Iida and T. Iwasaki. Tsunamis–Their Science and Engineering, Terrapub, Tokyo, pp. 439–451. Gover, J. (2005). Jason 1 Detects the 26 December 2004 Tsunami. EOS, Trans. AGU, 86, 37–38. Henry, R.F., and Foreman, M.G.G. (2001). A representation of tidal currents based on energy flux. Mar. Geod., 2493, 139–152.



121

Hirata, K., Satake, K., Tanioka, Y., Kuragano, T., Hasegawa, Y., Hayashi, Y., and Hamada, N. (2005). The Indian Ocean tsunami: tsunami source model from satellite altimetry. In: G.A. Papadopoulos and K. Satake, (eds.), Proceedings of the International Tsunami Symposium, Chania, Greece, 2005, pp. 72–76. Horrillo, J.J., Kowalik, Z., and Knight, W. (2005). Full navier-stokes approximation in tsunami investigation. In: G.A. Papadopoulos and K. Satake, (eds.), Proceedings of the International Tsunami Symposium, Chania, Greece, 2005, pp. 77–88. HRV Harvard CMT Catalog (2005). Harvard Seismology: Centroid-Moment Tensor Project, posted at http://www.seismology.harvard.edu/CMTsearch.html Imamura, F. (1996). Review of tsunami simulation with a finite difference method. In: H.Yeah, P. Liu and C. Synolakis (eds.), Long-Wave Runup Models World Scientific, Singapore, pp. 25–42. Iwasaki, S.I. (2005). Posting of Thailand Tide Gauge Data to Tsunami Bulletin Board, also posted at http://www.navy.mi.th/hydro/tsunami.htm Ji, C. (2004). Preliminary Result of the 04/12/26 (Mw 9.0), OFF W COAST of Northern Sumatra Earthquake, posted at http://www.gps.caltech. edu/%7Ejichen/Earthquake/2004/aceh/aceh.html Kowalik, Z. (2003). Basic relations between tsunami calculation and their physics II. Sci. Tsunami Hazards, 21(3), 154–173. Kowalik, Z., and Murty, T.S. (1993a). Numerical Modeling of Ocean Dynamics. World Scientific, Singapore, 481pp. Kowalik, Z., and Murty, T.S. (1993b). Numerical simulation of two-dimensional tsunami runup. Mar. Geod., 16, 87–100. Kowalik, Z., Knight, W., Logan, T., and Whitmore, P. (2005a). Numerical modeling of the global tsunami: indonesian tsunami of 26 December 2004. Sci. Tsunami Hazards, 23(1), 40–56. Kowalik, Z., Knight, W., Logan, T., and Whitmore, P. (2005b). The tsunami of 26 December 2004: numerical modeling and energy considerations. In: G.A. Papadopoulos and K. Satake, Chania, (eds.) Proceedings of the International Tsunami Symposium, Greece, 27–29 June, 2005, pp. 140–150. Lay, T., Kanamori, H., Ammon, C.J., Nettles, M., Ward, S.N., Aster, R.C., Beck, S.L., Bilek, S.L., Brudzinski, M.R., Butler, R., DeShon, H.R., Ekstrom, G., Satake, K., and Sipkin, S. (2005). The Great Sumatra–Andaman Earthquake of 26 December 2004. Science, 308, 1127–1139. Liu, P.L.F., Lynett, P., and Synolakis, C.E. (2003). Analytical solution for forced long waves on a sloping beach. J. Fluid Mech., 478, 101–109. Longuet-Higgins, M.S. (1969). On the transport of mass by time-varying ocean currents. Deep-Sea Res., 16, 431–447. Loomis, H.G. (1966). Spectral analysis of tsunami records from sations in the Hawaiian islands. Bull. Seis. Soc. Amer., 56, 697–713. Lynett, P.J., Wu, T.R., and LIU, P.L.F. (2002). Modeling wave run-up with depth-integrated equations. Coast. Eng., 46(2), 89–107. Mader, C.L. (2004). Numerical Modeling of Water Waves, CRC Press, pp. 274. Matsuyama, M. and Tanaka, H. (2001). An experimental study of the highest run-up height in the 1993 Hokkaido Nansei-oki Earthquake Tsunami. International Tsunami Symposium, Seattle, Washington, USA, pp. 879–889. Mei, C.C. (1989) The Applied Dynamics of Ocean Surface Wave. World Scientific, Singapore, pp. 740. Merrifield, M.A., Firing, Y.L., Aarup, T., Agricole, W., Brundrit, G., Chang-seng, D., Farre, R., Kilonsky, B., Knight, W., Kong, L., Magori, C., Manurung, P., Mccreery, C., Mitchell, W., Pillay, S., Schindele, F., Shillington, F., Testut, L., Wijeratne, E.M.S., Caldwell, P., Jardin, J., Nakahara, S., Porter, F.-Y., and Turetsky, N. (2005). Tide Gauge Observations of the Indian Ocean Tsunami, December 26, 2004, Geophys. Res. Letters, 32, L09603, doi:10.1029/2005GL022610. Mofjeld, H.O., Titov, V.V., Gonzalez, F.I., and Newman, J.C. (1999). Tsunami wave scattering in the north pacific. IUGG 99 Abstracts, Week B, July 26–30, B.1326. Murty, T.S., Rao, A.D. Nirupama, N., and Nistor, I. (2006). Tsunami warning systems for the hyperbolic (Pacific), parabolic (Atlantic) and Eliptic (Indian) oceans. J. Indian Geophys. Union, 10(2), 69–78. NEIC – US National Earthquake Information Center (2004). Magnitude 9.0 off the West Coast of Northern Sumatra. Sunday, December 26, 2004 at 00:58:53 UTC Preliminary Earthquake Report, posted at http://neic.usgs.gov/neis/bulletin/neic_slav_ts.html


122

Z. Kowalik et al.

Nekrasov, A.V. (1970). Transformation of tsunami on the continental shelf. In: W.M. Adams. (eds.) Tsunami in the Pacific Ocean. East-West Center Press, Honolulu, 1970. 337–350. NIO – National Institute of Oceanography of India (2005). 26 December 2004 Tsunami, posted at http://www.nio.org/jsp/tsunami.jsp Okada, Y. (1985). Surface deformation due to shear and tensile faults in a half-space. B. of the Seismol. Soc. Am., 75, 1135–1154. Rabinovich, A.B. (2005). Web Compilation of Tsunami Amplitudes and Arrival Times. http://wwwsci.pac.dfo-mpo.gc. ca/osap/projects/tsunami/tsunamiasia_e.htm Reid, R.O., and Bodine R.O. (1968). Numerical model for storm surges in Galveston Bay. J. Waterway Harbor Div., 94(WWI), 33–57. Shigematsu, T., Liu, P. L.-F., and Oda, K. (2004). Numerical modeling of the initial stage of dam-break waves. J. Hydraul. Res., 42(2), 183–195. Snodgrass, F.E., Munk, W.H., and Miller, G.R. (1962). California’s continental borderland. Part I. Background spectra. J. Mar. Res., 20, 3–30. SOI – Survey of India (2005). Preliminary Report of Tsunami Observations, posted at http://www.surveyofindia.gov.in/tsunami4.htm Stein, S., and Okal, E. (2005). Ultra-Long Period Seismic Moment of the Great December 26, 2004 Sumatra Earthquake and Implications for the Slip Process, posted at http://www.earth.northwestern.edu/people/seth/research/sumatra2. html Thacker, W.C. (1981). Some exact solutions to the nonlinear shallow—water wave equations. J. Fluid Mech., 107, 499–508. Titov, V., Rabinovich, A.B., Mofjeld, H.O., Thomson, R.E., and González, F.I. (2005). The Global Reach of the 26 December 2004 Sumatra Tsunami. Science, 309, 2045–2048. Titov, V.V., and Synolakis, C.E. (1998). Numerical modeling of tidal wave run-up. J. Waterway Port Coast. Ocean Eng., 124(4), 157–171. Yagi, Y. (2005). Preliminary Results of Rupture Process for 2004 off Coast of Northern Sumatra. Giant Earthqauke (ver. 1), posted at http://iisee.kenken.go.jp/staff/yagi/eq/Sumatra2004/Sumatra2004. html Yanuma, T. and Tsuji, Y. (1998). Observation of edge waves trapped on the continental shelf in the vicinity of makurazaki harbor, Kyushu, Japan. J. Oceanog., 54, 9–18.

CHAPTER 11

Modeling Techniques for Understanding the Indian Ocean Tsunami Propagation


V.P. Dimri and K. Srivastava National Geophysical Research Institute, Hyderabad, Andhra Pradesh, India

11.1

INTRODUCTION

The most destructive tsunami experienced by humanity has now been attributed to the great Indian Ocean Tsunami with death toll around 300,000. This earthquake that triggered the tsunami has changed the scientific considerations and the understanding of hazard globally. Researchers are now geared up in quantifying and understanding all different aspects for the evaluation and assessment of this natural hazard as this event has all the observations recorded and documented. The devastating mega thrust earthquake occurred in a tectonically active region where the Indian plate is subducting beneath the Burmese platelet in the Sunda trench. The focal depth has been estimated to be about 30 km and the length of the fault rupture has been inferred to be about 1300 km. Numerous studies have been carried out to constrain the rupture parameters however, one notable study was using far-field GPS observations where an average of 11 m of reverse slip has been estimated for the southern part of the rupture zone whilst it is about 10 m in the northern part (Catherine et al., 2005). The earthquake triggered giant tsunami propagated throughout the Indian Ocean. In the larger oceans such as Pacific reflections of the direct tsunami waves are not significant. However, in Indian Ocean, reflections played a very significant role and Kerala was affected by reflections from the Lakshadweep Islands. The sustained high water level in the Andaman and Nicobar Islands could be also due to the reflection of direct tsunami waves and trapping of wave energy. The location of the earthquake was such that it was land locked more or less from the three sides and instead of tsunami energy being spread to higher northern latitudes, the Bay of Bengal and the Arabian Sea got the brunt of it. Ocean depth gradients that give rise to convergences and divergences of tsunami wave energy (i.e. constructive and destructive interference) were responsible for devastating waves at Sri Lanka. The tsunami traveled and arrived in north of Sumatra within half an hour after the earthquake and a few hours later they arrived in Thailand, Sri Lanka, India and Maldives and after about 10 hours the tsunami reached the east coast of Africa. The tsunami waves arrived at different times at different locations on the Indian coast (Nair et al., 2005). They reached the Andaman and Nicobar Islands after an hour of the earthquake i.e around 07.25 h. They then reached Chennai at 08.45 h, Velankani coast at 09.05 h and in Kanyakumari around 11.45 h. In the west coast near Kayamkulam lagoonal mouth they reached around 12.30 h. Heavy loss of life and property at Nagapattinam (Tamil Nadu) could be because of resonance of tsunami waves with natural frequency of the coast. Subrahmanyam et al. (2005) have shown that the tsunami traveled with great speed across the Bay of Bengal and approached the continental slope and moved along the shoreline and surged through the bathymetric window between Nagapattinam and Cuddalore. They bought out the importance of bathymetry on tsunami amplification along the continental slopes. The wave heights observed at some locations are: along the north west coast of Sumatra 123


124 V.P. Dimri and K. Srivastava is around 10–15 m, whilst in Sri Lanka’s east coast was found to be around 5–10 m, in Andaman Islands it is >5 m and in Thailand, Phuket Island it is 3–5 m. Chadha et al. (2005) measured the tsunami run-up heights from water marks on houses and ocean debris transported on land along the east coast of India and found it to vary from 2.5 m to 5.2 m with the maximum height measured at Nagapattinam. The tsunami of the December 26, 2004 in the Indian perspective has been complied in book edited by Ramasamy and Kumanan (2005). Ramalingeswara Rao (2005) has discussed about the possible reasons for the triggering of the tsunami. Mahadevan et al. (2005) have simulated the tsunami waves using Delft 3D-Flow model which has been developed by WL/Delft Hydraulics of the Netherlands. The effect of tsunami on the ground water flow in coastal zones of Tamil Nadu was studied by Elango and Sivakumar (2005). Solving the ground water flow through porous media under non-equilibrium and anisotropic conditions they showed that the saline water recharges the coastal aquifer and the salinity of the ground water increased by about eight times which was later expected to decrease as the ground water flows towards the sea. 11.2

SOME GREAT AND DESTRUCTIVE TSUNAMIS OF THE WORLD

According to the US National Oceanic and Atmospheric Administration (NOAA) the Pacific is by far the most active tsunami zone; tsunamis have been generated in other bodies of water, including the Caribbean and Mediterranean Seas, and the Indian and Atlantic oceans. Some great and destructive tsunamis of the world have been shown in Table 11.1 using the information from Dudley and Lee (1988), Lander and Patricia (1989), Choi et al. (2003), Yalciner et al. (2005) with details about the magnitude, wave heights and the affected places. 11.3

MATHEMATICAL MODELS

11.3.1 Tsunami magnitude scales The tsunami magnitude scales have been discussed in Satake (2002). The tsunami magnitude scale is expressed as the Imamura-Iida scale m, I is the tsunami intensity. This scale was originally expressed by Idia et al. (1967) as, m = log2 h

(11.1)

where h is the maximum run-up height in m. This scale was later modified by Hatori (1979) to include the far-field data and gave the magnitude as, m=3+

log{(h/0.5)(R/1000)1/2 } √ log 5

where h is in m and R is in km. Tsunami intensity scale is defined by Soloviev (1970) as: √ ¯ i = log2 ( 2h)

(11.2)

(11.3)

Later, Chubarov and Gusiakov (1985) defined the tsunami intensity on the Soloviev-Imamura scale as, I = 3.55Mw − 27.1

(11.4)

where Mw is the moment magnitude of the earthquake. This relation holds good for steep dip-slip or low angle thrust fault mechanism. However for large strike slip faults tend to generate tsunamis of decreasing wave heights.

March 9, 1957; Aleutian

May 2, 1960; Chilean March 28, 1964; Alaska

September 2, 1992; Nicaragua November 27, 1999; Sydney, Australia October 4, 1994; Russia-Kuril Islands, Shikotan November 15, 1994; Phillipines-Mindora October 9, 1995; Mexico-Manzanilo February 2, 1996; Mexico-Manzanilo July 17, 1998; Papua New Guinea November 26, 1999; Vanuatu June 23, 2001; Peru-Southern January 2, 2002; Vanuatu

3

4 5

6 7 8 9 10 11 12 13 14 15

8 7.7 7.8 7.3

November 27, 1945; Makaran Coast, Pakistan December 12, 1992; Indonesia – Flores Island June 2, 1993; Indonesia, Java May 3, 2000; Indonesia – Sulawesi Island

December 26, 2004; Indian Ocean

4 5 6 7

8

9.3

7.9 – 7.7

Indian Ocean earthquakes, volcanic eruption and tsunami 1 December 31, 1881; Car Nicobar 2 August 27, 1883; Karkatau volcanic eruption 3 June 26, 1941; Andaman

7.6 7.1 8.1 7.1 8 7.8 7.0 7.4 8.4 7.4

9.5 8.4

8.3

8.2

November 4, 1952; Kamchatka

2

6

11–11.5 26.2 1–14 6

1 42 Not available

10 – 10 5–8 1–5.7 0.6 10 2–3 3–4.5 3

2–6

4–16

1–15

3.5

Magnitude Wave height of of earthquake tsunami (m) 7.8

Earthquake and tsunami

Affected places

Kutch and Mumbai The islands of the Pacific nation of Vanuatu Indonesia Sulawesi and the neighboring offshore smaller islands in Indonesia From Indonesia in the east, to the coast of Africa, some 7000 km (4000 miles) away

All along east coast of India Indonesia All along east coast of India

Near Unimak Island in Alaska’s Aleutian Island Chain, Hawaiian The coast of Kamchatka Peninsula, the Kuril Islands and other areas of Russia’s Far East South of the Andreanof Islands, in the Aleutian Islands of Alaska The coast of south central Chile Alaska, Vancouver Island (British Columbia), the states of Washington, California and Hawaii, in the USA Nicaragua The islands of the Pacific nation of Vanuatu The islands of the Pacific nation of Vanuatu Mindora, Verde and Baco Island Mexico Mexico Northern coast of Papua New Guinea The islands of the southwest Pacific North of town of Ocona in Southern Peru The islands of the southwest Pacific

Some of the world’s destructive tsunamis of the Pacific and Indian Ocean.

Pacific ocean earthquakes and tsunamis 1 April 1, 1946; Aleutian

S.no.

Table 11.1.


300,000

Heavy loss 690 423 46

Not available 36,000 3000

70 8 11 78 40 12 2182 10 96 10

2300 120

Nil

Nil

165

Death toll

Modeling techniques for understanding the Indian Ocean Tsunami propagation 125

126 V.P. Dimri and K. Srivastava 11.3.2 Tsunami propagation


The non-linear form of long wave equations to describe the tsunami wave propagation is given below. The governing equation are expressed as; ∂η ∂[u(h + η)] ∂[v(h + η)] + + =0 ∂t ∂x ∂y

(11.5)

∂u ∂u ∂u ∂η τx +u +v +g + =0 ∂t ∂x ∂y ∂x ρ

(11.6)

∂v ∂v ∂v ∂η τy +u +v +g + =0 ∂t ∂x ∂y ∂y ρ

(11.7)

where η is the water elevation, u and v are components of the horizontal velocities, τx and τy are the bottom shear stress components, x and y are horizontal coordinates, t is time, h(x,y) is unperturbed depth, g is the gravitational acceleration. Using the total depth D = h + η, the discharge fluxes M and N in x, y directions respectively can be described as; M = u(h + η) = uD;

N = v(h + η) = vD

and

(11.8)

Equations (11.5)–(11.7) can be written in the following form for the discharge fluxes M and N : ∂η ∂M ∂N + + =0 ∂t ∂x ∂y ∂M ∂ + ∂t ∂x ∂N ∂ + ∂t ∂x

M2 D

MN D

+

∂ ∂y

+

∂ ∂y

(11.9)

MN D N2 D

+ gD

+ gD

∂η gn2 + 7/3 M M 2 + N 2 = 0 ∂x D

∂η gn2 + 7/3 N M 2 + N 2 = 0 ∂y D

(11.10) (11.11)

This formulation was used to develop the TSUNAMI-N2 model first by Professor Fumihiko Imamura in Disaster Control Research Center in Tohoku University (Japan). The TSUNAMI-N2 is one of the key tools in studying the propagation and coastal amplification of tsunamis in relation to different initial conditions. It solves equations (11.9)–(11.11) using a leap-frog scheme in finite difference technique for the basins of irregular shape and topography (Yalciner et al., 2003). This program is used to compute the water surface fluctuations and velocities at all locations, even at shallow land regions. However, there are limitations on the grid size (Imamura, 1996). 11.3.3

Discussions and approaches

Using the TSUNAMI-N2 program, the December 26, 2004 earthquake was modeled for wave propagation and the estimated results are shown in Figure 11.1 (Yalciner et al., 2005). The initial wave was simulated using the source parameters of this earthquake (Yalciner et al., 2005) and state of the sea at 5, 30, 60, 120, 180, 240, 300, 360, 420, 480, 600 min in Indian Ocean is shown in Figure 11.1. The observed and modeled run-up distributions along the east coast of India are taken from Yalciner et al. (2005) and are presented in Figure 11.2.

Figure 11.1. The sea state at 5, 30, 60, 120, 180, 240, 300, 360, 420, 480, 600 min in Indian Ocean (Yalciner et al., 2005).


Modeling techniques for understanding the Indian Ocean Tsunami propagation 127


128 V.P. Dimri and K. Srivastava

Figure 11.2. The observed run-up distributions along the east coast of India and comparison with model results (Yalciner et al., 2005).

The wave equations have been extensively used in different fields and analytically have been solved for various initial and boundary conditions (Witham, 1974). Tsunami wave propagation modeling can be projected on to an easier hyperbolic approach for the larger oceans like Pacific and Atlantic, but in the case of Indian Ocean one has to use the more difficult elliptic modeling. This essentially means that the coast line geometry and topography has to be mapped in much greater detail for the Indian Ocean. While modeling refraction (change of velocity from deep to shallow water), reflection and diffraction of the waves the vertical obstacles like sea mount or ridges that obstruct the path needs to be taken into account. Also the boundary conditions for closed domain need to be specified. The advantage of the FEM is precise error control of the approximate solution of the partial differential equation and another advantage is the diversity of possibilities to discretize the numerical domain (2D: quadrilaterals, triangles; 3D: tetrahedral, prisms, pyramids) and to adapt complex geometries. Having obtained a numerical solution for propagation, several simulations can be performed by varying parameters of uneven bathymetry. This can be efficiently done with fractal approach. There is a solution for accurate mapping of topography in terms of Voronoi tessellation, which can generate realistic and uneven fractal surfaces as desired with the help of a few parameters known as Voronoi centers (Dimri and Srivastava, 2005). The placement of these centers decides about the structure of final uneven surfaces and can be used to improve girding and mapping technique for uneven bathymetry. They have generalized the notion of Voronoi tessellation by using Lp distances instead of the least square distances so that Voronoi domains are not necessarily of polygonal shape. Analytically the wave has been solved and used extensively in other branches of science (Witham, 1974). The linear and non-linear partial differential equations are now being solved using the Adomians decomposition method. This is a relatively new method and the solution to the problem is built using a series solution. This method is now being used to solve deterministic, stochastic, linear or non-linear equations in various branches of science and engineering (Adomian, 1994; Wazwaz and Gorguis, 2004). The method has been shown to be systematic, robust,

Modeling techniques for understanding the Indian Ocean Tsunami propagation

129

and sometimes capable of handling large variances in the controlling parameters. The convergence of the decomposition series is very rapid and only a few terms in the series are required for an accurate solution. The forcing function and boundary conditions both have randomness and variability. Thus tsunami fields needs to be characterized by its statistical characteristics such as mean, variances and probability density functions. Theory of stochastic partial differential equations which have been developed extensively in statistical and theoretical physics literature can be used effectively to characterize these effects.


11.4

CONCLUSIONS

There is need to develop high-resolution models for tsunami wave propagation in the Indian Ocean using denser bathymetry and irregular coastal topography by employing fractals and finite element method for obtaining run-up heights as well as inundation regions for different earthquake sources and magnitudes which are likely to occur in the Bay of Bengal, Indian Ocean and Arabian Sea. It would be desirable to develop analytical and numerical models of tsunami propagation for earthquake sources in Andaman and Nicobar and off the coast of Makaran as these have generated tsunamis in the past. Quantifying and understanding of Indian Ocean Tsunami will provide us useful knowledge for better evaluation of the tsunami hazards along the east and west coast of India in order to mitigate the suffering of the population living along these vast coastlines. ACKNOWLEDGEMENT The authors wish to thank Prof. Yalciner, Middle East Technical University, Civil Engineering Department, Ocean Engineering Research Center, Ankara, Turkey, for sharing his modeling results and permitting us to use them. REFERENCES Adomian, G. (1994). Solving Frontier Problems of Physics – the Decomposition Method. Kluwer Academic, Boston. Catherine, J.K., Gahalaut, V.K., and Sahu, V.K. (2005). Constraints on rupture of Dec 26, 2004 Sumatra Earthquake from Far Field GPS Observations. Earth Plan. Sci. Lett., 273, 673–679. Chadha, R.K., Latha, G., Harry, Y., Peterson, C., and Katada, T. (2005). The Tsunami of the Great Sumatra Earthquake of Magnitude 9.0 on 26 Dec 2004, Impact on east coast of India. Curr. Sci., 88(8), 1297–1301. Choi, B.H., Pelinovski, E., Kim, K.O., and Lee, J.S. (2003). Simulation of the Trans Oceanic Tsunami Propagation due to the 1883 Karkatau Volcanic Eruption. Nat. Hazards Earth Syst. Sci., 3, 321–332. Chubarov, L.B., and Gusiakov, V.K. (1985). Tsunamis and earthquake mechanism in the island arc regions. Sci. Tsunami Hazards, 3(1), 3–21. Dimri, V.P. and Srivastava, R.P. (2005). Fractal modeling of complex subsurface geological structures. In: V.P. Dimri (ed.), Fractal Behavior of the Earth System. The Netherlands, Springer, 208p. Dudley, W.C. and Lee, M. (1988). Tsunami! University of Hawaii Press, Honolulu, Hawaii. Elango, L., and Sivakumar, C. (2005). Numerical modeling of effect of tsunami on ground water flow and solute transport. In: S.M. Ramasamy and C.J. Kumanan (eds.), Tsunami: The Indian Context, pp. 221–229, Allied Publishers Ltd, Chennai, India. Lander, J.F. and Lockridge, P.A. (1989). United States Tsunamis. Publication, 41–42. U.S. Department of Commerce. Hatori, T. (1979). Relation between tsunami magnitude and wave energy. Bull. Earthquake Res. Inst. Univ. Tokyo, 54, 531–541. Idia, K., Cox, D.C., and Paras-Carayannis, G. (1967). Preliminary catalog of tsunamis occurring in the Pacific Ocean. Data report No 5, HIG 67-10, University of Hawaii, Honolulu.


130 V.P. Dimri and K. Srivastava Imamura, F. (1996). Review of tsunami simulation with a finite difference method. In: H. Yeh, P. Liu, and C. Synolakis (eds.), Long-Wave Runup Models. World Scientific (ISBN 981-02-2909-7), Singapore, pp. 25–42. Mahadevan, R., Chandramohan, P., and Van Holland, G. (2005). Hydrodynamics of Tsunamis. In: S.M. Ramasamy and C.J. Kumanan (eds.), Tsunami: The Indian Context, pp. 69–77. Nair, M.M., Nagarajan, K., Srinivasan, R., and Kanishkan B. (2005). Indian Ocean Tsunami 2004 – An Indian Perspective. In: S.M. Ramasamy and C.J. Kumanan (eds.), Tsunami: The Indian Context, pp. 99–109, Allied Publishers Ltd, Chennai, India. Ramasamy, S.M. and Kumanan, C.J. (2005). Tsunami: The Indian Context. Allied Publishers Ltd, Chennai, India. Ramalingeswara Rao, B. (2005). Tsunami Triggering Mechanism on Indian Coast with Reference to 26 Dec 2004. In: S.M. Ramasamy and C.J. Kumanan (eds.), Tsunami: The Indian Context, pp. 43–50, Allied Publishers Ltd, Chennai, India. Satake, K. (2002). Tsunamis. In: International handbook of Earthquake and Engineering and Seismology, Vol. 81(A). Academic Press, New York, pp. 437–451. Soloviev, S.L. (1970). Recurrence of Tsunamis in the Pacific. In: W.M. Adams (ed.), Tsunamis in the Pacific Ocean. Honolulu, East-West Center Press, pp. 149–164. Subrahmanyam, C.S., Girish, R., and Gahalaut V. (2005). Continental slope characteristics along the tsunami affected areas of eastern offshore of India and Sri Lanka. J. Geol. Soc. India., 65, 778–780. Wazwaz, A.M. and Gorguis, A. (2004). Exact solutions of heat-like and wave-like equations with variable coefficients (with). Appl. Math. Comput., 149(1), 15–29. Witham, G.B. (1974). Linear and Non Linear Waves. Wiley-Interscience, New York. Yalciner, A.C., Pelinovsky, E., Synolakis, C., and Okal, E. (2003). In: A.C. Yalçıner, E. Pelinovsky, C. Synolakis, E. Okal (eds.), NATO SCIENCE SERIES Submarine Landslides and Tsunamis. Kluwer Publishers, The Netherlands, 329p. Yalciner, A.C., Karakus, H., Ozer, C., and Ozyurt, G. (2005). Short course on “Understanding the generation, propagation near and far field impacts of Tsunamis and planning strategies to prepare for future events”, Kuala Lumpur.

CHAPTER 12


Validation of Tsunami Beach Run-up Height Predictive Model Based on Work–Energy Theorem G. Muraleedharan and A.D. Rao Centre for Atmospheric Sciences, Indian Institute of Technology Delhi, New Delhi, India T.S. Murty Department of Civil Engineering, University of Ottawa, Ottawa, Canada M. Sinha Centre for Atmospheric Sciences, Indian Institute of Technology Delhi, New Delhi, India

12.1

INTRODUCTION

Natural hazards have always been a challenge to the modelers and tsunamis are in the top list. Even though there are many numerical models for understanding the propagation of tsunamis such as MOST (Method Of Splitting Tsunamis) its behavior in the coastal waters is highly complicated. Hence prediction of a destructive tsunami is highly difficult. It is to be noted that it is not the prediction of a tsunami event but the run-up heights on beaches is more important. The same tsunami will behave in a very different way due to the bottom topography and greater momentum of the terminal speed. A tsunami which is harmless in one coastal location will be very destructive in another location. Hence a clear estimation of the beach run-up heights at each and every coastal locations which are vulnerable to tsunami attacks is highly recommended. The importance of the predictive models developed (Muraleedharan et al., 2006) based on work–energy theorem for estimating the time required by the tsunami to travel from 1 m depth to 0 m depth and thereby the beach run-up heights is to be seen from this point of view. 12.2

MATERIALS AND METHODS

The run-up heights and the maximum inundation distance along a few coasts of Indian Ocean due to 26 December 2004 Indian Ocean Tsunami are mainly considered in this work. A few historical information provided by National Geophysical Data Centre (NGDC) of tsunamis that had occurred along the coasts of Indonesia is also considered in this study (Figure 12.1 and Table 12.1). The scientists of Andaman and Nicobar Centre for Ocean Science and Technology (ANCOST) of National Institute of Ocean Technology (NIOT) Chennai, conducted run-up measurements of the 26 December 2004 Indian Ocean Tsunami from 18 January to 5 February 2005 (Figure 12.2). Elevations at clearly visible sea water mark on building/structures were taken as the run-up levels for measurements. Table 12.2 gives the details of the measured run-up levels, which 131


132

G. Muraleedharan et al.

Figure 12.1. Table 12.1.

Map of Indonesia (www.worldatlas.com). Maximum water height and maximum inundation distance along the coasts of Indonesia during historical tsunamis.

Tsunami source date

Run-up location

Year

Month

Day

Country

Name

1992 1992 1994 1994 1994

12 12 6 6 6

12 12 2 2 2

Indonesia Indonesia Indonesia Indonesia Indonesia

Flores Riangkroko Lampon Pancer Rajekwesi

Latitude (S)

Longitude (E)

Maximum water height

−8.500 −8.150 −8.620 −8.589 −8.560

121.000 122.800 114.090 114.005 113.940

25.00 26.20 11.00 9.50 7.00

Maximum inundation distance 300.00 600.00 1000.00 300.00 100.00

have been corrected to mean sea level (approximately 0.8 m added to Mean Sea Level (MSL) to accommodate the land subsidence occurred during earthquake). Beach profiles for some coastal locations of the Andaman and Nicobar Islands are given in Figure 12.3(a)–(d). The significant beach angle (θs – average of 1/3 highest slopes (angles) on land) is suggested for a complicated beach profile. Details of beach run-up heights and sea water inundation inland of north Chennai coast due to Boxing Day tsunami are provided by Department of Ocean Development (Table 12.3). Another study area (Figure 12.4) is the southern and western part of the Tamil Nadu State, India (8◦ 04 to 8◦ 17 N:77◦ 32 to 77◦ 54 E). It is bounded by Indian Ocean in the south, Arabian Sea in the west and Bay of Bengal in the east but the main part of the coast is in the Arabian Sea. The study area is marked with marine terrace, sand dunes, beaches, mangroves, uplands, etc. The continental shelf along the study area extends far away from the shoreline (Chandrasekar et al., 2006). The run-up level of sea water due to 26 December 2004 Indian Ocean Tsunami in this area is given in Table 12.4.


Validation of tsunami beach run-up height

Figure 12.2. Andaman and Nicobar Group of Islands (map by ANCOST, NIOT, Chennai). Table 12.2.

Location Flores Riangkroko Lampon Pancer Rajekwesi

Predicted time (t) required to travel from 1 m depth to 0 m depth and tsunami height (Hs ) near coastlines of Indonesia. Maximum water height (m)

Maximum inundation distance (m)

Beach slope (tan θ)

t (s) (assumed θ = θ1 )

Predicted tsunami height (Hs ) (m)

25.00 26.20 11.00 9.50 7.00

300.00 600.00 1000.00 300.00 100.00

0.0836 0.0437 0.011 0.0317 0.0702

9.43 18.77 81.10 26.41 11.36

10.12 10.19 03.93 03.62 02.80

133

134

G. Muraleedharan et al. Transect near Malacca (Car Nicobar) 8 7

Elevation (m)

6

Maximum Water Level Observed during Tsunami

5 4 3


2 Beach

1 0 0

200

400

600

(a)

1000

1200

1400

Distance (m) Profile of coastal land and run-up levels at Campbell Bay (Great Nicobar)

3.5

Maximum Water Level Observed during Tsunami

3 Elevation (m)

800

2.5 2 1.5 1 0.5 0

50

0.5

100

150

200

250

300

Distance (m)

(b)

Elevation (m)

Transect near Hut Bay (Little Andaman)

(c)

Figure 12.3.

12 11 10 9 8 7 6 5 4 3 2 1 0

Maximum Water Level Observed during Tsunami Crop land Fishing village

0

200

400

600

800

1000

1200

1400

1600

Distance (m)

(a)–(d) Real shore profiles of a few Andaman and Nicobar Group of Islands (by ANCOST, NIOT, Chennai).

Validation of tsunami beach run-up height

135

Transect near Chidiyatopu Maximum Water Level observed during Tsunami 5 Elevation (m)

4 3 2 1


0 10

10

30

Figure 12.3.

50

70

90

110

130

150

Distance (m)

(d)

(Continued).

Table 12.3.

Maximum run-up level distance up to which seawater inundated inland during boxing day tsunami in Andaman and Nicobar Islands.

Location South Andaman (Port Blair) JNRM College, Aberdeen Bamboo Flat New Wandoor Wandoor Chidiyatopu Chouldari Sippighat (Creek) North Andaman Diglipur Rangat Little Andaman Hut Bay Car Nicobar Malacca Air base Great Nicobar Campell Bay (central) Campell Bay (south)

Maximum run-up level (m)

Distance up to which seawater inundated inland (m)

2.9 3.5 3.7 3.9 4.5 2.0 2.0

130 250 215 215 130 250 2000

1.5 1.5

100 200

5.0

1200

7.0 7.0

1000 1100

3.0 6.0

300 50

A few historical tsunami events in the Pacific and Atlantic oceans provided by the NGDC is also considered in this study (Table 12.5). This study is the validation of the expression derived from the work–energy theorem for estimation of beach run-up heights and the time required to travel from 1 m depth to 0 m depth by tsunamis (Muraleedharan et al., 2006) given below as: Hr =

g Hs t tan θ d1

(12.1)

136

G. Muraleedharan et al. 8°30

r a barani R.

Index Map

Namb iya rR

R.

Se

a

P a la l yar R.

Panniy ar

Inayam Colachel Midalam Vaniakudy Mandakadu Kadiapattinam Muttom Rajakkamangalam Pallam

Kuttapuli

Manakudy

n


A r a bia

Study Area

R. an m

Taingapatnam Tamilnadu

Investigated Beach

77°00

Vattakottai Lakshmipuram Chinnamuttom Kanyakumari Cape Camorin

Indian Ocean

Navaladi

Idhinthakarai

Scale – 1:20,000 l

V a lliy ar R.

Ha nu

Ovari Perumanal

.

Th

ami

Tamilnadu

N

ga

India

Be B a y of

n

8°00

77°30

Figure 12.4.

Location map of the study area of the Tamil Nadu coasts (www.sthjournal.org/241/ chand.pdf ).

Table 12.4.

Predicted tsunami travel time (t) from 1 m depth to 0 m depth and tsunami height (Hs ) near coastline of Andaman and Nicobar Islands.

Location South Andaman (Port Blair) JNRM College, Aberdeen Bamboo Flat New Wandoor Wandoor Chidiyatopu Chouldari Sippighat (Creek) North Andaman Diglipur Rangat Little Andaman Hut Bay Car Nicobar Malacca Air base Great Nicobar Campell Bay (central) Campell Bay (south)


Distance up to which seawater inundated inland (m)


t (s) (assumed as θ = θ 1 )

Predicted tsunami height (Hs ) near coastline (m)

2.9 3.5 3.7 3.9 4.5 2.0 2.0

130 250 215 215 130 250 2000

0.02 0.01 0.02 0.02 0.03 0.008 0.001

38.31 62.79 50.44 47.70 24.03 113.68 1031.61

1.08 1.27 1.36 1.44 1.73 0.70 0.62

1.5 1.5

100 200

0.02 0.008

58.36 121.75

0.55 0.52

5.0

1200

0.004

227.12

1.69

7.0 7.0

1000 1100

0.007 0.006

130.98 144.93

2.44 2.42

3.0 6.0

300 50

0.01 0.12

89.72 6.38

1.07 2.48

Validation of tsunami beach run-up height Table 12.5.

Few examples in Andaman and Nicobar Islands to show the improvement in tsunami height (Hs ) predictions when different slopes on land (Figure 12.3(a)–(d)) are considered. Distance up to Beach slope – Predicted Maximum which seawater | tan θ s | t (s) tsunami height run-up inundated (significant beach (off shore (Hs ) near level (m) inland (m) angle – θs ) slope θ1 ) coastline (m)

Location


137

South Andaman (Port Blair) Chidiyatopu

4.9

130

Little Andaman Hut Bay

5.0

Car Nicobar Malacca Great Nicobar Campell Bay (central)

0.74 (θs = 36.5◦ )

0.65 (θ1 = 46◦ )

3.25

1200

0.02 (θs = −1.17◦ )

42.08 (θ1 = 1.2◦ ) assumed

1.86

6.8

1000

0.167 (θs = 9.5◦ )

4.28 (θ1 = 10◦ )

3.03

3.0

300

1.96 (θs = 63◦ )

0.33 (θ1 = 63◦ )

1.48

where g is acceleration due to gravity, Hr is beach run-up height by the tsunami, d1 (>0) is water depth (= 1 m), Hs is tsunami height at 0 m depth and t is time required by the tsunami wave to travel from d1 m (here it is equal to 1 m) to 0 m depth which is functionally related with offshore angle θ1 (Muraleedharan et al., 2006) as: t = 0.6791(tan θ1 )−1.0606

(12.2)

tan θ = beach slope (= average of 1/3 highest slopes on land for a complicated beach configuration). If the beach profile is not known, then the beach angle (θ) is calculated as: θ = sin−1(maximum water height/maximum inundation distance)

(12.3)

The offshore slope (tan θ1 ) is considered to be the same as beach slope (tan θ) for unknown offshore slopes. Tsunami heights near coastlines are estimated for various coastal locations along the rim of the Indian Ocean using expression (12.1) as:

Hs =

12.3

Hr

d1 g

t tan θ

RESULTS AND DISCUSSIONS

The tsunami travel time from 1 m depth to 0 m depth (t) and tsunami height (Hs ) near coastlines for a few coastal locations along the rim of the Indian Ocean are predicted. Since the horizontal distance from 1 m depth to 0 m depth will be more for small offshore slopes compared to large offshore slopes, the time required by the wave to travel from 1 m depth to 0 m depth will be more

138

G. Muraleedharan et al. Table 12.6.

Run-up level of sea water during 26 December 2004 Indian Ocean Tsunami at selected locations along Tamil Nadu coasts.

Location


Distance of seawater inundation inland (m)

3.9 2.8 1.8 1.4 3.5

750 200 190 45 80


Nagapattinam (Light House transect) Chennai (Besant Nagar) Chennai (Kattupalli) Chennai (Kalanji) Sathan Kuppam

Table 12.7.

Prediction of travel time (t) from 1 m depth to 0 m depth and tsunami height near coastline for Tamil Nadu coasts for 26 December 2004 Indian Ocean Tsunami.

Location Nagapattinam (Light House transect) Chennai (Besant Nagar) Chennai (Kattupalli) Chennai (Kalanji) Sathan Kuppam


Distance of seawater inundation inland (m)


t (s) (assumed as θ = θ1 )

Predicted tsunami height (Hs ) near coastline (m)

3.9

750

0.0052

179.56

1.33

2.8 1.8 1.4 3.5

200 190 45 80

0.0140 0.0095 0.0311 0.0438

62.79 95.03 26.91 18.74

1.02 0.64 0.53 1.36

in the first case. Muraleedharan et al. (2006) have shown using equation (12.1) that it is true for the numerical experiment conducted by Marchuk and Anisimov in 2001 for run-up height estimations for different beach angles. Also tsunami run-up heights will be more for small beach slopes than for large beach slopes (Marchuk and Anisimov, 2001). Another important phenomena is that a tsunami wave height near coastline can have a run-up height more than double its height due to bottom topography and greater momentum of the terminal velocity. These findings are reaffirming here for real shore profiles. The time required to travel from 1 m depth to 0 m depth (t) and the tsunami height at 0 m depth (Hs ) are predicted for the historical tsunami events (Table 12.1) for the Indonesian coasts and are given in Table 12.6. Similar predictions are carried out for the 26 December 2004 Indian Ocean Tsunami for the most affected Andaman and Nicobar Group of Islands and for Tamil Nadu coasts (Tables 12.7–12.10). Real shore profiles for a few coasts in Andaman and Nicobar Islands are given in Figure 12.3(a)–(d). Significant beach angles are computed and time (t) and tsunami heights (Hs ) are predicted (Table 12.8). Nearshore tsunami heights are predicted for historical tsunami events in the Pacific and Atlantic oceans (Table 12.11). It is very interesting to see that in all these studies the time (t) is more for small offshore slopes (here the offshore slopes are considered to be equal to the respective beach slopes) compared to large offshore slopes and small tsunami heights can have large run-up heights for small beach slopes.

Validation of tsunami beach run-up height Table 12.8.

Inundation distance extent along the study area.


Location

Longitude (E)

Latitude (N)

Elevation (m)

Inundation distance (m)

77.49 77.45 77.39 77.37 77.34 77.34 77.34 77.33 77.29 77.25 77.22 77.19 77.18 77.16 77.15 77.14 77.12 77.09 77.1

8.17 8.14 8.09 8.08 8.07 8.07 8.06 8.04 8.05 8.05 8.06 8.07 8.08 8.09 8.1 8.11 8.12 8.13 8.14

19 18 17 16 15 16 17 21 09 14 16 11 14 16 12 16 17 15 14

150 175 200 200 300 250 350 300 600 400 150 200 100 100 750 100 300 130 200

Ovari Idinthakarai Perumanal Navaladi Vattakottai Lakshmipuram Chinna muttam Kanyakumari Keelamanakudi Pallam Rajakkamangalam Muttom Kadiapatanam Mandakadu Colachel Vaniakudy Midalam Enayam Taingapatnam

Table 12.9.

Predicted time (t) required to travel from 1 m depth to 0 m depth and tsunami height (Hs ) near coastline for 26 December 2004 Indian Ocean Tsunami.

Location Ovari Idinthakarai Perumanal Navaladi Vattakottai Lakshmipuram Chinna muttam Kanyakumari Keelamanakudi Pallam Rajakkamangalam Muttom Kadiapatanam Mandakadu Colachel Vaniakudy Midalam Enayam Taingapatnam

Elevation (m)

Inundation distance (m)



19 18 17 16 15 16 17 21 09 14 16 11 14 16 12 16 17 15 14

150 175 200 200 300 250 350 300 600 400 150 200 100 100 750 100 300 130 200

0.1277 0.1034 0.085 0.0803 0.0500 0.0641 0.0486 0.0702 0.0150 0.0350 0.1073 0.0551 0.14 0.16 0.0160 0.16 0.0567 0.1162 0.07

6.02 7.53 9.24 9.85 16.26 12.50 16.77 11.36 58.36 23.75 7.24 14.69 5.41 4.68 54.50 4.68 14.23 6.66 11.36

Predicted tsunami height (Hs ) near coastline (m) 7.89 6.97 6.88 6.46 5.88 6.37 6.65 8.41 3.28 5.37 6.57 4.34 5.84 6.73 4.39 6.73 6.72 6.19 5.61

139

Month

2 2 11

11 11 11 3 1 9 10 10 12 4 3 11 11 9 9 4 9 9 6

1835 1835 1867

1867 1867 1867 1868 1878 1899 1918 1918 1944 1946 1964 1969 1975 1985 1985 1991 1992 1994 2001

18 18 18 17 20 10 11 11 7 1 28 22 29 19 21 22 2 19 23

20 20 18

Day

USA USA USA USA Japan USA USA Russia USA Mexico Mexico Costa Rica Nicaragua Papua New Guinea Peru

Chile Chile Saint Vincent and the Grenadines USA Territory British Virgin Islands USA

Country

Virgin Islands: Frederiksted Tortola Island: Road Town Puerto Rico: Arroyo Bequia Island: Admiralty Bay Waialua, Oahu, HI Yakutat Bay, West Shore, AK Puerto Rico: Caja De Muertos Puerto Rico: Punta Borinquen Temma Pakala Point, HI Klawock, AK Ok’khovaya River Punaluu Bay, Hawaii, HI Playa Azul Zihuatanejo Cahuito-Puerto Viejo Masachapa Simpson Harbour, New Britain Camana

Maule River Talcahuano Bequia Island: Admiralty Bay

Location

Historical tsunami events and run-up levels in the Pacific and Atlantic oceans.

Year

Table 12.10.

−64.883 −64.616 −66.050 −61.250 −139.840 −66.533 −67.169 135.933 −133.083 162.800 −155.500 −102.350 −101.550 −82.770 −86.520 152.170 −72.720

59.730 17.867 18.484 33.633 55.550 57.000 19.140 17.980 17.650 9.650 11.780 −4.210 −16.630

−72.417 −73.130 −61.250

Longitude

17.717 18.414 17.983 13.000

−35.317 −36.740 13.280

Latitude


7.60 1.50 0.90 0.90 3.00 9.00 1.50 4.50 5.00 10.00 4.60 15.00 7.60 2.50 2.50 2.00 6.00 1.20 8.00

3.50 9.00 1.80


76.00 9.00 40.00 21.00 150.00 500.00 15.00 100.00 200.00 227.00 15.20 500.00 137.00 150.00 200.00 300.00 100.00 200.00 1000.00

140.00 4000.00 146.00

Maximum inundation distance

140 G. Muraleedharan et al.

USA USA USA USA Japan USA USA Russia USA Mexico Mexico Costa Rica Nicaragua Papua New Guinea Peru

Chile Chile Saint Vincent and the Grenadines USA Territory British Virgin Islands USA

1835 1835 1867

1867 1867 1867 1868 1878 1899 1918 1918 1944 1946 1964 1969 1975 1985 1985 1991 1992 1994 2001

Country

Virgin Islands: Frederiksted Tortola Island: Road Town Puerto Rico: Arroyo Bequia Island: Admiralty Bay Waialua, Oahu, HI Yakutat Bay, West Shore, AK Puerto Rico: Caja De Muertos Puerto Rico: Punta Borinquen Temma Pakala Point, HI Klawock, AK Ok’khovaya River Punaluu Bay, Hawaii, HI Playa Azul Zihuatanejo Cahuito-Puerto Viejo Masachapa Simpson Harbour, New Britain Camana

Maule River Talcahuano Bequia Island: Admiralty Bay

Location

7.60 1.50 0.90 0.90 3.00 9.00 1.50 4.50 5.00 10.00 4.60 15.00 7.60 2.50 2.50 2.00 6.00 1.20 8.00

3.50 9.00 1.80


76.00 9.00 40.00 21.00 150.00 500.00 15.00 100.00 200.00 227.00 15.20 500.00 137.00 150.00 200.00 300.00 100.00 200.00 1000.00

140.00 4000.00 146.00

Maximum inundation distance

0.1005 0.1690 0.0225 0.0429 0.0200 0.0180 0.1005 0.0450 0.0250 0.0441 0.3175 0.0300 0.0556 0.0167 0.0125 0.007 0.06 0.006 0.008

0.0250 0.00225 0.0123


7.76 4.47 37.96 19.15 43.01 48.10 7.76 18.18 33.94 18.60 2.29 27.97 14.56 52.19 70.82 137.93 13.39 154.24 113.68

34.01 436.59 71.86


3.11 0.63 0.34 0.35 1.11 3.32 0.61 1.75 1.88 3.89 2.02 5.70 3.00 0.92 0.90 0.69 2.38 0.41 2.81

1.32 2.92 0.65

Predicted tsunami height at 0 m depth (m)

Predicted tsunami travel time (t) from 1 m depth to 0 m depth near coastlines and tsunami heights (Hs ) of historical tsunamis of Pacific and Atlantic oceans.

Year

Table 12.11.


Validation of tsunami beach run-up height 141

142

G. Muraleedharan et al.

12.4

CONCLUSION


The predictive model for tsunami beach run-up heights based on work–energy theorem is validated for various tsunami events including the 26 December 2004 Indian Ocean Tsunami along the coasts of the rim of the Indian Ocean. The predicted tsunami heights for known beach run-up heights and distance to which seawater inundated inland (beach run-up) are reasonably good. The predicted heights are agreeing the logic that they can have a run-up height of more than double its height due to bottom topography and greater momentum of the terminal speed. This beach run-up height model is a guide to the public to what height to move from MSL in the event of a tsunami warning for safety. REFERENCES Department of Ocean Development (2005). Preliminary Assessment of Impact of Tsunami in selected coastal areas of India, Integrated Coastal and Marine Area Management Project Directorate, Chennai, India. Marchuk, A.G. and Anisimov, A.A. (2001). A method for numerical modeling of tsunami run-up on the coast of an arbitrary profile. ITS Proceedings, Session 7, No.7–27, 933–940. Muraleedharan, G., Sinha, M., Rao, A.D., and Murty, T.S. (2006). Statistical simulation of the Boxing Day tsunami of the Indian Ocean and a predictive equation for beach run-up heights based on work–energy theorem. Mar. Geod., Special issues on Tsunamis, Part I, 29(3), 223–231. Chandrasekar, N., Saravanan, S., Immanuel, J.L., Rajamanickam, M., and Rajamanickam, G.V. (2006). Classification of tsunami hazard along the southern coast of India: an initiative to safeguard the coastal environment from similar debacle. Sci. Tsunami Hazards, 24(1), 3–23.

CHAPTER 13

Normal Modes and Tsunami Coastal Effects


N. Nirupama Emergency Management, Atkinson School of Administrative Studies, York University, Toronto, Canada T.S. Murty Department of Civil Engineering, University of Ottawa, Ottawa, Canada A.D. Rao Centre for Atmospheric Sciences, Indian Institute of Technology, New Delhi, India I. Nistor Department of Civil Engineering, University of Ottawa, Ottawa, Canada

13.1

INTRODUCTION

In a tsunami event, the most important aspects happen at the coastline, mainly because it is here that loss of life and damage occurs due to land inundation. The so-called normal modes are free oscillations of the coastal gulfs, bays, estuaries, inlets, lagoons and backwaters, and all these play an important role in determining the coastal behavior of the tsunami. Here we will briefly review some of the classical concepts of the normal mode dynamics, following Murty (1977), and Kowalik and Murty (1993). The role of the normal modes in tsunami coastal effects is evident from Kowalik (2005a,b), Murty et al. (2005a–c), Murty et al. (2006a–c), Nirupama et al. (2005) and Nirupama et al. (2006). Any water body (either completely closed or partially open) undergoes natural or free oscillations, which are referred to as normal modes. Several different physical phenomena can set a water body into oscillation (i.e. excite its normal modes). The frequencies of the fundamental normal mode and its higher harmonics can be determined solely from knowledge of the geometry of the water body and the water depths. The question of normal modes was first discussed in connection with tidal theories (LaPlace, 1775, 1776; Hough, 1898). 13.2

OSCILLATIONS OF THE FIRST CLASS AND OSCILLATIONS OF THE SECOND CLASS

Consider an artificial situation in which a thin layer of water covers the Earth’s surface entirely. We ask the question how this water can move freely, subject to gravity and the earth’s rotation. Hough (1898) showed that free motion can occur in either of two ways. Oscillations of the first class (OFC) are essentially gravity waves whose periods are modified by Earth’s rotation. However, OFC can exist even if the Earth does not rotate. Oscillations of the second class (OSC) owe their very existence to Earth’s rotation and have periods greater than 24 h. If the earth’s 143


144

N. Nirupama et al.

rotation tends to zero, OSC will lose their periodicity and will degenerate into steady currents. One manifestation of OSC is the so-called Rossby wave. If σ is frequency of oscillation and ω is the frequency of rotation, then OFC are those for which σ → σ0 ( = 0) as ω → 0 and OSC are those for which σ → O(ω) as ω → 0. Bjerknes et al. (1934) distinguished between these two types of oscillation by means of the ratio σ/2ω. Gravity modes (OFC) are those for which σ/2ω ≥ 1. Elastoid-inertia modes (OSC) are those for which σ/2ω ≤ 1. For the gravity modes, gravity appears in the frequency equation. In the case of the rotational (elastoid-inertia) modes, the frequency for a given mode is a function mainly of the ratio of the depth of the liquid to the radius of the container and gravity does not play an important role in the frequency equation. Here this discussion is restricted to gravity modes. In the mathematical analysis this restriction is imposed by introducing the approximations of the shallow water theory called the quasi-static approximation (Bjerknes et al., 1934). This means that in the vertical direction, equilibrium exists not only before the motion but also during the motion, with vertical accelerations of the liquid being considered negligible compared to that of gravity. In studying tidal motions on a rotating earth, Kelvin (1879) considered a shallow layer of water in a circular flat-bottomed cylinder and assumed the quasi-static approximation to the pressure field. Kelvin considered small rotations and neglected the curvature of the free surface due to rotation. If σ is the frequency of the rotating mode, σ0 is the frequency of the non-rotating mode and ω is the rotation frequency, then the result obtained is: σ 2 = σ0 + 4ω2 This result shows that the rotation increases the frequency and thus increases the restoring tendency of the system when disturbed. However, if the curvature of the free surface is taken into account, this is not always true, especially for the higher modes. Since one of the manifestations of normal modes in water bodies is in the form of seiches, we will start with a discussion of this phenomenon, following mainly Wilson (1972).

13.3 THE PHENOMENA OF COASTAL SEICHES Probably the first scientific study of seiches was that of Forel (1892), Chrystal (1905), Proudman (1953), Defant (1961), Wilson (1972) and Miles (1974). Merian (1828) gave a theory for free oscillations of water in a rectangular basin of length L and uniform depth h, the period T being given by: 2L T =√ gH

(13.1)

where g is gravity. Forel (1892) applied this formula to seiches in lakes. For real lakes with variable depth, he chose an average value of H to replace the variable depths. Lagrange (1781) showed that the velocity of c of a long wave is given by: c ∼ gH (13.2) From equations (13.1) and (13.2): T =

2L λ = c c

(13.3)

where λ is the wavelength of the oscillation (assuming it is in the form of a wave). Thus, the length of the wave is twice that of the water body (or basin). Forel explained this apparent paradox


Normal modes and tsunami coastal effects

145

as being due to the superposition of two long waves whose length is twice that of the basin and traveling in opposite directions. In the following, an attempt will be made to visualize a seiche as a special type of standing wave. For this, consider two progressive waves traveling in opposite directions in water of uniform depth. At every quarter period, the crests and troughs are either in phase or out of phase. At halfwavelength intervals (x = λ/4, 3λ/4, 5λ/4, …) surface elevation is continuously zero with time. Such points are called nodes and the points that intermediate to these are the antinodes. This type of standing wave can also result if a progressive wave is reflected (without dissipation) at a vertical wall. Then, there will be an antinode of amplitude 2A (A being the amplitude of the progressive wave) at the wall and a first node at x = λ/4 from the wall. A seiche is a special case of a standing wave that would result from interposing a second vertical barrier at any of the points x = λ/2, 3λ/2, 2λ, … The standing wave or seiche exists due to repeated reflections (assuming no dissipation) from the two vertical walls, where it would have its antinodes. On the other hand, if the second vertical barrier were inserted at any point other than a multiple of λ/2, the standing wave would become an irregular motion of the water surface. Thus, one can think of a seiche as a standing wave that is commensurate with the basin length L. The seiche is uninodal for L = λ/2, binodal for L = λ, trinodal for L = 3λ/2, …. n-nodal for L = nλ/2. Hence, from equation (13.3), the period Tn of the nth mode of oscillation in a rectangular basin of length L and uniform depth H is: 2L Tn = √ n gH

(13.4)

Here n = 1, 2, 3, … For an open bay of rectangular geometry (length L) and uniform depth H , the period is given by: 4L Tn = √ n gH

(13.5)

Here n = 1, 3, 5, … This is a generalization of the Merian formula and is valid for a onedimensional oscillation (no transverse motions). Note that at the nodes the motion is purely horizontal and at the antinodes it is purely vertical. The higher nodal (binodal, trinodal, etc.) seiches that may occur simultaneously with the fundamental mode (i.e., uninodal oscillation) are higher harmonics of the fundamental. From equation (13.4) Tn 1 1 1 = 1, , , . . . , , n = 1, 2, . . . , n T1 2 3 n However, for irregular water bodies with variable depth (unlike in the case of a narrow rectangular basin of uniform depth), such a simple relation as above need not exist. Another point worth remembering is that neither the use of an average depth H nor a better version of this, as done by du Boys (see Defant, 1961): 2 Tn ∼ n

0

L

dx [gh(x)]1/2

improves the Merian formula significantly.

(13.6)


146

N. Nirupama et al.

13.4

SEICHE AS A COMBINATION OF FREE AND FORCED OSCILLATIONS

Next, the concept of regarding seiches as a combination of free and forced oscillations will be developed. Any natural system, when displaced from its equilibrium position, will try to regain its equilibrium position (due to a restoring force) and will exhibit free oscillations once the disturbing force is removed. The nature of these oscillations depends on the system alone, the influence of the disturbing force being restricted to setting the initial amplitude of the oscillation. After some time, the free oscillations will gradually dissipate. In a water body or basin, the seiche is a type of free oscillation of the water, the restoring force being gravity. However, in nature the seiches could be of a forced nature because the disturbing force, instead of being instantaneous, can act over some period of time. The equation of motion for a linear vibrating mass spring system subject to a displacement X due to a disturbing force F(t), in the canonical form is: F(t) X¨ + 2βX˙ + ω2 X = m

(13.7)

where β is a non-dimensional damping coefficient, m is the mass of the vibrating body, ω is the angular frequency and mω2 is a spring constant for the restoring force. The solution of equation (13.7) can be visualized as the combination of a free and forced part of a transient and steady-state part. To obtain the solution for the free oscillation, put F(t) = 0. Then: X0 = e−βωt [a sin(γt) + b cos(γt)]

(13.8)

where a and b are amplitudes of the motion determined by the initial conditions. The natural frequency γ of the system is: γ = ω(1 − β2 )1/2

(13.9)

and the natural period T is given by: T =

2π γ

(13.10)

The frictional damping, which is given by β, makes the free oscillations decay at a rate such that the amplitude decreases in one cycle by e−δ where δ is the logarithmic decrement and is given by: δ = βωT

13.5

(13.11)

CONTRIBUTION FROM THE FORCED SOLUTION

For the forced solution, one must use equation (13.7) in complete form and take a periodic disturbing force as follows: F(t) = F cos(σt + ε) m

(13.12)


147

where ε is an arbitrary phase angle. Then the forced solution is: Xf =

Fµ cos(σt + ε − α) ω2

(13.13)

where:


σ 2 2

µ=

1−

tan σ =

2β(σ/ω) 1 − (σ/ω)2

ω

σ 2 + 2β ω

−1/2 (13.14)

(13.15)

Here, µ is the dynamic amplification of the oscillation and α is a phase angle by which the forced oscillation lags the disturbing force. Thus, the total solution is: X = X0 + Xf

(13.16)

Here, X0 decays with time whereas Xf persists as long as the disturbing force is applied. One can deduce that: µ=

Xmax Xmax = (F/ω)2 Xi

(13.17)

where Xi is the amplitude of the input displacement. Ordinarily, µ and α are shown as ordinates versus σ/ω as abscissa. If the damping coefficient β < 12 , then from equation (13.9), the natural frequency γ of the system is approximately given by ω. Hence, the ratio σ/ω in equations (13.14) and (13.15) is effectively the ratio of the forced to the natural frequency. The dynamic amplification µ approaches its peak value when σ/ω ∼ 1. When this happens, resonance occurs and the amplitude of motion will be several times greater than the amplitude of the disturbing force. For small frequency ratios σ/ω 1, the magnification is small, µ ∼ 1 and the motion follows the excitation (i.e., α → 0). For σ/ω 1, the resulting motion is much smaller than that of the exciting force. Then, µ → 0 and the motion tends to become out of phase (i.e., α → 180◦ ). Hence, the degree of resonance is determined by the damping factor 2β. Miles and Munk (1961) defined the degree of resonance through the factor Q, which is the maximum value of the dynamic amplification µ. From equation (13.14), if σ/ω ∼ 1 (as occurs at resonance): µmax ≡ Q ≡

1 2β

(13.18)

In the frequency range (1 − β) < σ/ω < (1 + β), if damping factor 2β is small, the power amplification µ2 has a value greater than Q2 /2. Hence, the frequency band width (over which the power amplification exceeds half its maximum value Q2 ) is 1/Q. Thus, the sharper is the resonance, the narrower will be the spectral energy peak. This can be quantitatively expressed by stating that near resonance: Q2 σ 2 2 ∼ 1 + 4Q 1 − µ2 ω

(13.19)

148

N. Nirupama et al.

The following results can be easily deduced from the above relations. For low Q conditions (i.e., heavy dissipation), a large rate of absorption of energy from the disturbing force to the oscillating system is necessary whereas for high Q (small damping) only a small energy absorption rate is sufficient for resonance. Miles and Munk (1961) showed that for a water body with a rather regular topography, low damping prevails. Hence, the response is of the high Q type. Hence, a relatively small amount of energy (e.g., from atmospheric pressure gradients) at the correct damping is heavy and a low Q situation prevails.


13.6 THEORETICAL ASPECTS OF FREE AND FORCED SEICHES Next, some theoretical aspects of free and forced seiches will be considered. With reference to a Cartesian coordinate system (x, y), let Mx and My be the components of the transport, ζ is the water level deviation from its equilibrium position, H be the water depth, Pa be the atmospheric pressure, τxs and τys be the wind stress components and r be the bottom friction coefficient. Omitting the Coriolis term and assuming that ∂y∂ = 0, and v = 0: ∂M ∂ζ + rM + g(H + ζ) = Fs(x, t) ∂t ∂x

(13.20)

where subscript x on M is omitted. The external force is given by: Fs(x, t) =

rxs H + ζ ∂Pa + ρ ρ ∂x

(13.21)

The continuity equation is: ∂ζ ∂M + =0 ∂t ∂x

(13.22)

Equation (13.20) and continuity equation can be transformed into two hyperbolic equations in the dependent variables M and ζ:

∂2 ζ ∂ζ ∂ ∂ζ ∂Fs + r − g (H + ζ) =− 2 ∂t ∂t ∂x ∂x ∂x

(13.23a)

∂2 M ∂Fs ∂M ∂2 M +r − g(H + ζ) 2 = ∂t ∂t ∂x ∂t

(13.23b)

The solutions of equation (13.23) with the right-hand sides set to zero give the solutions for the free oscillation, whereas the solutions for the complete equations are the forced oscillations. In a rectangular basin of length L and uniform depth H , in which a free oscillation is generated by equating the disturbing force Fs to zero, equations (13.22) and (13.23) give: 2 ∂2 ζ ∂ζ 2∂ ζ + r =0 − c ∂t 2 ∂t ∂x2

(13.24)

∂2 M ∂M ∂2 M +r − c2 2 = 0 2 ∂t ∂t ∂x

(13.25)


149

Since these equations have the same form in ζ and M , one can use the method of separation of variables to solve them: ζ (or M ) = X (x)T (t)

(13.26)

The solution can be shown to be: ζ (or M ) = e−rt/2 [A cos(kx) + B sin(kx)][C cos(γt) + D sin(γt)]

(13.27)


where the angular frequency γ of the free oscillation is given by:

k γ =ω 1− 2ω

1/2

(13.28)

The wave number k and the angular frequency ω are related through: ω = kc

(13.29)

in which either k or ω must be determined. To determine the constants of integration A, B, C, D, the following boundary conditions must be used. At the ends of the basin, x = 0, L transport M must be zero for all time. Thus, M (x = 0) = 0

and

M (x = L) = 0

(13.30)

From the continuity equation and taking a as the amplitude of free oscillation, ζ ∼ ae−rt/2 cos (kx) cos(γt + ε) M∼

(13.31)

aγ −rt/2 sin(kx) sin(γt + ε) e k

The wave number k can be determined from the second equation of (13.30) to give kL = nπ

n = 1, 2, 3, . . .

(13.32)

Then γ and ω can be determined from equations (13.28) and (13.29). Since equation (13.31) represents a standing wave whose amplitude is a at t = 0 and decays exponentially with time, this oscillation is similar to the mechanical system discussed earlier. Thus, r = 2βω

(13.33)

In real applications, the disturbing force should be explicitly introduced. In the case of tsunamis, this disturbing external force could be the tsunami amplitude in shallow water that could excite edge waves. 13.7

SUMMARY

The normal modes are free oscillations of coastal water bodies, which play an important role in the coastal behavior of tsunamis. Not only these oscillations contribute to the transformation of the tsunami waves in the coastal region, but also they play a very dominant role in the secondary undulation that persists in the coastal water bodies up to several days after the main tsunami

150

N. Nirupama et al.

activity has died down. Here we briefly reviewed some classical concepts of these normal modes and coastal seiches in terms of the so-called OFC and OSC.


REFERENCES Bjerknes, V., Bjerknes, J., Solberg, H., and Bergeron, T. (1934). Hydrodynamic Physique, Vol. II, Cap XI. Les Presses Universitatires de France, Paris, pp. 457–491. Chrystal, G. (1905). On the Hydrodynamical theory of Seiches (with bibliography on seiches). Trans. Roy. Soc. Edin., 41(3), 599–649. Defant, A. (1961). Physical Oceanography. Pergamon Press, NY, 598 pp. Forel, F.A. (1892). Le Leman (collected papers). Two Volumes, Rouge, Lausanne, Switzerland. Hough, S.S. (1898). On the application of harmonic analysis to the dynamical theory of tides, Part II, On the general integration of Laplace’s dynamical equations. Philos. Trans. Roy. Soc. A, 191, 138–185. Kelvin, Lord W. (1879). On gravitational oscillations of rotating water. Proc. Roy. Soc. Edin., 10, 92–109, Papers, 4, 141–148. Kowalik, Z. and Murty, T.S. (1993). Numerical Modeling of Ocean Dynamics World Scientific Publishers, Singapore, 481 pp. Kowalik, Z., Knight, W., Logan, T., and Whitmore, P. (2005a). Numerical modeling of the global tsunami: Indonesian tsunami of 26 December 2004. Sci. Tsunami Hazards, 23(1), 40–56. Kowalik, Z., Knight, W., Logan, T., and Whitmore, P. (2005b). TheTsunami of 26 December 2004: numerical modeling and energy considerations. In: G.A. Papadopoulos and K. Satake (eds.), Proceedings of the International Tsunami Symposium, Chania, Greece, June 27–29, pp. 140–150. Lagrange, J.L. (1781). Memoire sur la Théorie du Mouvement des Fluides. Nouv. Mem. Acad. R. Berli, Qeuvres 4. LaPlace, P.S. (1775, 1776). Reserches sur plusiers points du systeme du monde. Mem. Acad. Roy. Sci., 88, 75–182; 89, 177–267. Merian, J.R. (1828). Uber die Bewegung. Tropfbarer Flussigkeiten in Gebässen (Basle). Miles, J.W. (1974). Harbor seiching. Ann. Rev. Fluid Mech., 6, 17–35. Miles, J.W. and Munk, W.H. (1961). Harbor paradox. J. Waterway, Harbors Coast. Eng. Div., Proc. ASCE, 87, 111–130. Murty, T.S., Rao, A.D., and Nirupama, N. (2005a). Inconsistencies in travel times and amplitudes of the 26 December 2004 Tsunami. J. Mar. Med., 7(1), 4–11. Murty, T.S., Nirupama, N., Nistor, I., and Rao, A.D. (2005b). Conceptual differences between the Pacific, Atlantic and Arctic tsunami warning systems for Canada. Sci. Tsunami Hazards, 23(3), 39–51. Murty, T.S., Nirupama, N., and Rao, A.D. (2005c). Why the earthquakes of 26th December 2004 and the 27th March 2005 differed so drastically in their tsunami-genic Potential. Newslett. Voice Pac., 21(2), 2–4. Murty, T.S., Nirupama, N., Nistor, I., and Hamdi, S. (2006a). Far field characteristics of the tsunami of 26 December 2004. ISET J. Earthq. Techno., 42(4), 213–217. Murty, T.S., Nirupama, N., Nistor I., and Hamdi, S. (2006b). Why the Atlantic generally cannot generate trans-oceanic tsunamis. ISET J. Earthq. Technol., 42(4), 227–236. Murty, T.S., Rao, A.D., Nirupama, N., and Nistor, I. (2006c). Numerical modelling concepts for the tsunami warning systems. Curr. Sci. 90(8), 1073–1081. Nirupama, N., Murty, T.S., Rao, A.D., and Nistor, I. (2005). Numerical Tsunami Models for the Indian Ocean Countries and States, Indian Ocean Survey, 2(1), 1–14. Nirupama, N., Murty, T.S., Nistor, I., and Rao, A.D. (2006). The energetics of the tsunami of 26 December 2004 in the Indian Ocean: a brief review. Mar. Geod., 29(1), 39–48. Proudman, J. (1953). Dynamical Oceanography. London, Methuen, J. Willey, 409 pp. Wilson, B.W. (1972). Seiches. Adv. Hydrosci., 8, 1–94.

CHAPTER 14


Helmholtz Mode and K–S–P Waves: Application to Tsunamis N. Nirupama Emergency Management, Atkinson School of Administrative Studies, York University, Toronto, Canada T.S. Murty and I. Nistor Department of Civil Engineering, University of Ottawa, Ottawa, Canada A.D. Rao Centre for Atmospheric Sciences, Indian Institute of Technology, New Delhi, India

14.1

INTRODUCTION

During the Indian Ocean Tsunami of 26 December 2004, high water levels persisted in certain harbors (for example in the state of Kerala in India) in the Indian Ocean, even after the main tsunami was dissipated. For a detailed analysis of various aspects of this tsunami, see Murty et al. (2005a–c), Murty et al. (2006a–c), Nirupama et al. (2005) and Nirupama et al. (2006). The reason for this persistence is the so-called Helmholtz mode of resonance, in which the long gravity wave energy of the tsunami enters a wide harbor through a narrow entrance channel. The energy, once entered the harbor cannot easily get out of the harbor because each successive reflection from the harbor walls only leak out a small amount of energy. Another type of wave motion, referred to as K–S–P (Kelvin–Sverdrup–Poincaré) waves are generally invoked to account for the coastal behavior of long gravity waves, such as, tides, storm surges, and tsunamis. Specifically, the role of these waves is to explain the propagation near the coastlines of tides and tsunamis and the variation of their amplitudes from the coast in an offshore direction. Here we will explore some of the classical concepts about these waves as well as the Helmholtz mode, following Kowalik and Murty (1993).

14.2

HELMHOLTZ MODE – ACOUSTIC ANALOGY

Following mechanical and acoustical analogy, the so-called Helmholtz mode will be defined and then a hydrodynamic explanation invoked. With reference to Figure 14.1, the equation of motion for the mechanical system shown can be written as (Raichlen, 1966): M x¨ + c˙x + kx = F0 cos(ωf t)

(14.1)

where M is the mass of the oscillating body, c is a linear damping coefficient, k is a spring constant, ωf is a (circular) forcing frequency, and dots denote differentiation with respect to t. 151

N. Nirupama et al.


152

Figure 14.1.

Resonance characteristics of a system with a single degree of freedom (Raichlen, 1966).

The following steady-state solution can be assumed: x = X cos(ωf t − φ)

(14.2)

where X is the maximum displacement and φ is a phase angle between the input and output functions. The parameters X and φ can be made non-dimensional as follows: X = Xst

1

2 2 1/2 ωf ωf 2 1 − ωn + 2ζ ωn

tan φ =

2ζωf /ωn 1 − (ωf /ωn )2

(14.3)

(14.4)

where F0 k 1/2 k ωn ≡ M c ζ≡ 2M ωn

Xxt ≡

(14.5)

Figure 14.1 represents graphically equations (14.3) and (14.4). First, consider the behavior of X /Xxt . For the case of small frictional dissipation, when the frequency is approximately equal to the undamped natural frequency of the system, the forcing function Xst is greatly amplified. As the damping ζ gets bigger, the difference between the resonant frequency and ωn increases.

Helmholtz mode and K–S–P waves: application to tsunamis

153

For low values of the frequency ratio, the amplitudes of the input and the output are approximately equal. However, for frequencies considerably above the resonant frequency, the response decreases substantially and the maximum displacement of the mass approaches zero. If the damping is zero, equation (14.3) gives infinite amplitude at resonance. However, this result, which is obtained from the linear theory, must be modified at great amplitudes to include the influence of the non-linear effects.


14.3

DEGREES OF FREEDOM AND DEPENDENCY OF PHASE ANGLE ON FORCING FREQUENCY

Next, consider the behavior of the phase angle with respect to the forcing frequency. For low values of the frequency ratio, the forcing function is mainly in phase with the output displacement, and at higher values they are 180◦ out of phase. At resonance, the phase angle becomes 90◦ and hence, the Force F0 cos(ωf t) is in phase with the velocity x¨ . Thus, when the mass is going through its zero displacement position, a maximum force is impressed upon the system. The number of degrees of freedom of a system is the number of independent coordinates that are required to describe the motion of the system. Raichlen (1966) cited the vibration of a clamped circular membrane as an example of a system possessing infinite degrees of freedom, whereas the spring–mass–dashpot system considered here is an example of a system with a single degree of freedom. In acoustics, an example of a single degree of freedom system is the so-called Helmholtz resonator, which consists of a cavity of volume V connected to a tube of length l and area of cross-section A. The equation of motion for this system is: M x¨ + ra x˙ +

x = P cos(ωf t) B

(14.6)

where x is the volume displacement, c is the wave velocity, ra is the radiation loss coefficient, and: M≡

ρl A

B≡

V ρc2

(14.7)

The natural frequency of the Helmholtz resonator is given by: ωn ≡ c

A lV

(14.8)

Since equations (14.6) and (14.1) are similar, it can be seen that when the frequency is equal to ωn , the ratio of the volume displacement to the applied pressure will be ∞, when ra is zero. Also, the ratio of the volume displacement to the applied pressure varies, as shown in Figure 14.1. 14.4

HELMHOLTZ MODE IN THE CONTEXT OF HYDRODYNAMICS

Next, consider the Helmholtz mode in the context of hydrodynamics. Miles (1971) used the term “Helmholtz mode”, Platzman (1972) used “co-oscillating mode”, and Lee and Raichlen (1972)


154

N. Nirupama et al.

referred to it as the “pumping mode”. Basically, Helmholtz resonance represents the balance between the kinetic energy of water flowing in through a narrow connecting channel and the potential energy from the rise in the mean water level within the harbor (Freeman et al., 1974). It is an additional gravitational mode of a substantially longer period than the fundamental free oscillation, as can be seen below. To conceptualize the Helmholtz mode, Platzman (1972) presented the following argument. Suppose that at the mouth of a rectangular bay an adjustable barrier exists and that this barrier is gradually moved from the two sides of the bay to the center, completely closing off the bay. The open modes with periods initially of the form 2T /(2n − 1), n = 1, 2, 3, . . . , will be transformed continuously into the closed mode periods of T /n, n = 0, 1, 2, . . . . It is obvious that the fundamental mode for the open bay transforms into the zeroth mode the closed basin, and as the barrier closes, this period approaches ∞. For small openings, the period of the Helmholtz mode is less than ∞ but greater than the period for a completely open bay. Platzman (1972) showed that rotation changes the period of the Helmholtz mode by, at most, 3%. The classic theory for the Helmholtz mode can be applied only to a single channel harbor. Freeman et al. (1974) extended this to a harbor (or basin) with multiple channels for openings. The dissipative forces (due to the eddy viscosity of the fluid and to the energy radiated from the mouth) are ignored. These forces affect the amplification factor at resonance and will shift the resonant frequency slightly. The solution developed by Freeman et al. (1974) for the frequency ω0 is: n g Si 1/2 ω0 = A i=1 Li

rad/s

(14.9)

where g is gravity, A is the surface area of the harbor, Si is the cross-sectional area of the ith channel, and Li is the length of the ith channel. Miles and Munk (1961) introduced the so-called harbor paradox in which they showed that narrowing of a harbor mouth (relative to the other dimensions) diminishes the protection from seiching. For a quantitative estimation of this in terms of the sharpness or Q at resonance, the reader is referred to their paper. Miles and Lee (1975) used equivalent electric circuit analysis to study this problem. Garrett (1970) showed that the harbor paradox, as originally postulated by Miles and Munk (1961), only holds for the Helmholtz mode.

14.5

KELVIN WAVES, SVERDRUP WAVES, AND POINCARÉ WAVES

There are classes of normal mode solutions with special properties that have been referred to as Kelvin waves, Sverdrup waves, and Poincaré waves. These wave types have been frequently invoked to explain the tidal phenomena in water bodies. For an excellent review on this topic, see Platzman (1971). Other relevant works are Defant (1961), Proudman (1953), Voyt (1974), and LeBlond and Mysak (1978). Simons (1980) has given a rather concise summary, and this discussion will essentially follow his line of argument. Earlier, the gravitational and rotational modes were introduced, also referred to as oscillations of the first class (OFC) and oscillations of the second class (OSC). It was also pointed out that OFC are motions with large divergence whereas OSC are essentially non-divergent. For introducing the concepts of different types of wave motion mentioned here, discussion begins with the linearized version of the vertically integrated equations, and these will be applied to a


155

rectangular basin of uniform depth:


∂U ∂ζ − fV = −c2 ∂t ∂x ∂V ∂ζ + fU = −c2 ∂t ∂y ∂ζ ∂U ∂V + + =0 ∂t ∂x ∂y

(14.10)

where U and V are the x and y components of the volume transport, ζ is the deviation of the water level from its equilibrium position, f is the Coriolis parameter, and c2 = gH where H is the uniform water depth. Assuming a time factor eiσt where σ is the frequency, and eliminating U and V from equation (14.10) gives the wave equation: (σ 2 − f 2 )ζ + c2 ∇ 2 ζ = 0

(14.11)

The boundary condition of zero normal transport to a boundary can be stated as: f

∂ζ ∂ζ + iσ =0 ∂S ∂n

(14.12)

where S and n are the coordinates along and perpendicular, respectively, to the wall. Equation (14.11) can be satisfied by: exp[i(kx + ly)] where the frequency σ is given by: σ 2 = f 2 + c2 (k 2 + l 2 )

(14.13)

For the non-rotating case, equation (14.12) is easily satisfied by standing waves with wave numbers k = mπ/L and l = nπ/B, where m and n are the integers and L and B are the length and breadth of the basin, respectively. However, in the rotating case, because of the compacted nature of the boundary condition (14.12), it is difficult to determine the normal modes. However, even in the rotating case, for an infinitely long channel, there are some elementary wave solutions that do not satisfy the boundary conditions. In equation (14.10), if V = 0, then the solutions to the resulting equations are: ζ = ζ0 e−fy/c eik(x−ct) U =−

c2 ∂ζ f ∂y

(14.14)

V =0 The wave speed is the same for the non-rotating and the rotating cases, but in the latter, the wave amplitude decreases exponentially from right to left for an observer looking in the direction of wave propagation. The rate of decrease of the amplitude from right to left is proportional to c/f , the Rossby radius of deformation. These waves are known as Kelvin waves. Another elementary

156

N. Nirupama et al.

solution can be obtained by setting ∂/∂x and ∂/∂y to zero. This will result in inertial oscillations with the frequency f (note that ζ is zero for these and there is only horizontal motion). If only the gradients in one horizontal direction are ignored, e.g., ∂/∂x = 0, then the solutions are: ζ = ζ0 ei(ly−σt)


σ = f 2 + c2 l 2

(14.15)

These waves are referred to as Sverdrup waves and have horizontal crests. For a straight coast parallel to the x axis, two Sverdrup waves traveling in opposite directions may be combined to form a standing wave that satisfies the boundary condition (14.12). Thus standing Sverdrup waves with wave numbers l = nπ/β are the normal modes of an infinitely long rotating channel. The more general solutions of equation (14.11) are known as Poincaré waves. Pairs of progressive Poincaré waves can be combined into standing waves that display cellular patterns. For an infinite channel, in analogy with Sverdrup waves, Poincaré waves can be made to satisfy the boundary conditions by properly choosing the transverse wave numbers. At a transverse barrier in the channel, none of these waves could be made to satisfy the boundary condition (14.12). Hence, the analytical determination of the normal modes of a rotating rectangular bay is more difficult, and it is convenient to resort to numerical techniques. 14.6

SUMMARY

In certain tsunami events, it is known that the water levels in certain harbors persists for a long time even after the main tsunami waves have dissipated. The reason for this is the so-called Helmholtz resonance in which the long gravity wave energy of the tsunami enters the wide harbor through a narrow entrance channel, but cannot leave the harbor easily. Successive reflections of this energy from the harbor walls provide only a slow leak to outside the harbor region. The propagation of the tsunami (and tides) along coastlines and the variations of their amplitudes perpendicular to the coastlines can be explained through the so-called K–S–P waves. Here some of the classical concepts on the Helmholtz mode as well as the K–S–P waves have been briefly reviewed. REFERENCES Defant, A. (1961). Physical Oceanography. Pergamon Press, New York, 598 pp. Freeman, N.G., Hamblin, P.F., and Murty, T.S. (1974). Helmholtz resonance in harbours of the great lakes, Proceedings of 17th Conference on Great Lakes Research International Association, Great Lakes Res. Proc. 15, 399–411. Garrett, C.J.R. (1970). Bottomless harbors. J. Fluid Mech., 43, 433–449. Kowalik, Z. and Murty, T.S. (1993). Numerical Modeling of Ocean Dynamics. World Scientific Publishers, Singapore, 481 pp. LeBlond, P.H. and Mysak, L.A. (1978). Waves in the Ocean. Elsevier Oceanographic Series 20, Amsterdam, 602 pp. Lee, J.J. and F. Raichlen (1972). Oscillations in harbours with connected basins, J. Waterway, harbours and coastal engineering division, Proceedings of the ASCE, 98, 311–332. Miles, J.W. (1971). Resonant response of harbors: an equivalent circuit analysis. J. Fluid Mech., 46, 241–265. Miles, J.W. and Lee, Y.K. (1975). Helmholtz resonance of harbors. J. Fluid Mech., 67, 445–464. Miles, J.W. and Munk, W.H. (1961). Harbor Paradox. J. Waterway, Harbors Coast. Eng. Div., Proc. ASCE, 87, 111–130.



157

Murty, T.S., Nirupama, N., and Rao, A.D. (2005a). Why the earthquakes of 26th December 2004 and the 27th March 2005 differed so drastically in their tsunami-genic potential, Newsletter. Voice of the Pacific, 21(2), 2–4. Murty, T.S., Rao, A.D., and Nirupama, N. (2005b). Inconsistencies in travel times and amplitudes of the 26 December 2004 tsunami. J. Mar. Medi., 7(1), 4–11. Murty, T.S., Nirupama, N., Nistor, I., and Rao, A.D. (2005c). Conceptual differences between the Pacific, Atlantic and Arctic tsunami warning systems for Canada. Sci. Tsunami Hazards, 23(3), 39–51. Murty, T.S., Nirupama, N., Nistor, I., and Hamdi, S. (2006a). Far field characteristics of the tsunami of 26 December 2004. ISET J. Earthq. Technol., 42(4), 213–217. Murty, T.S., Nirupama, N., Nistor, I., and Hamdi, S. (2006b). Why the Atlantic generally cannot generate trans-oceanic tsunamis. ISET J. Earthq. Technol., 42(4), 227–236. Murty, T.S., Rao, A.D., Nirupama, N., and Nistor, I. (2006c). Numerical modelling concepts for the tsunami warning systems. Curr. Sci. 90(8), 1073–1081. Nirupama, N., Murty, T.S., Rao, A.D., and Nistor, I. (2005). Numerical tsunami models for the Indian Ocean countries and states, Indian Ocean Survey, 2(1), 1–14. Nirupama, N., Murty, T.S., Nistor, I., and Rao, A.D. (2006). The energetics of the tsunami of 26 December 2004 in the Indian Ocean: a brief review. Mar. Geod., 29(1), 39–48. Platzman, G.W. (1971). Ocean tides and related waves, 239–291. In: W.H. Reid (ed.), Mathematical Problems in the Geophysical Sciences. AMS, Providence, Rhode Island. Platzman, G.W. (1972). Two-dimensional free oscillations in natural basins. J. Phys. Oceanogr., 2(2), 117–138. Proudman, J. (1953). Dynamical Oceanography. Methuen, J. Willey, London, 409 pp. Raichlen, F. (1966). Long period oscillations in basins of arbitrary shapes. In: Coastal Engineering Speciality Conf., Santa Barbara, CA, USA, 1965, ASCE, Part I. pp. 115–145. Simons, T.J. (1980). Circulation models of lakes and inland areas. Can. Bull. Fish. Aquat. Sci., Bull., 203, Ottawa, 146 pp. Voyt, S.S. (1974). Long waves and tides. In: P.S. Lineykin (ed.), ITOGI. Summaries of Scientific Progress. Oceanology, 2. G.K. Hall and Co., Boston, pp. 33–51.


CHAPTER 15

Numerical Models for the Indian Ocean Tsunami of 26 December 2004: A Brief Review


P. Chittibabu Baird & Associates, Ottawa, Canada T.S. Murty Department of Civil Engineering, University of Ottawa, Ottawa, Canada

15.1

INTRODUCTION

The devastating tsunami of 26 December 2004 in the Indian Ocean prompted many numerical modeling groups around the world to either develop or adapt their existing models to simulate this event. Following the Indian Ocean Tsunami of 26 December 2004, several numerical models for this tsunami, either were posted on the world wide web and or appeared in the literature. This is an attempt to summarize briefly the parameters and important results of these models. The order in which we arranged the review, has no particular significance, except to suggest that, that was the order in which we found them. Our cut-off date for this review is 1 November 2005, in the sense that any models that appeared after this date were not included this review. It is also quite probable that, there were some other models that appeared in the literature, but some how escaped our attention. Finally it should be pointed out that all these models mainly dealt with the tsunami generation and propagation aspects, and whatever results were included on the inundation aspects, are mostly from simple runup algorithms, rather than from exhaustive and detailed coastal inundation models. This is not a critical review of the models; it is a brief presentation of relevant information about the models for this tsunami event. The following models will be reviewed: 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Tsunami N2 Method of Splitting Tsunami Model TOAST Model Delft Model Italy Model E.C.J.R.C Model University of Frankfurt, Geophysical Institute Model NIO – India Model DCRC – TOHOKU Model AIST (SATAKE) Model Wakayama National College Model Model of Shunichi Koshimura Baird Model Kowalik et al. Model.

159

160

P. Chittibabu and T.S. Murty


15.2 TSUNAMI N2 MODEL The software for the TSUNAMI N2 model originally was developed by Fumihiko Imamura in Tohoku University, Japan and later modifications were done further development carried at Middle East Technical University by Ahmet Cevdet Yalçiner (2005) and his group and in the University of Southern California by Costas Synolakis. It is an outcome of IOC (Inter Governmental Oceanographic Commission of UNESCO) Tsunami Inundation Modeling Experiment (TIME) project. The generation and propagation of December 2004 Indian Ocean Tsunami was carried out using this model. Table 15.1. lists the fault parameters, based upon which the initial tsunami wave generation was simulated. The model also computed the maximum tsunami amplitudes and travel times to various locations, which are presented in Figure 15.1. Table 15.1. The fault data used to compute the tsunami source for simulation. Epicenter eastern coordinate Epicenter northern coordinate Fault length Fault width Strike angle Dip angle Slip angle Displacement Focal depth Maximum +ve amplitude at tsunami source Maximum −ve amplitude at tsunami source

93.13◦ N 03.70◦ E 443 km 170 km 329◦ 8◦ 110◦ 30 25 km +10.7 m −6.6 m

Figure 15.1. Tsunami travel times in hours (annotation “s” does not stand for second) Yalciner (2005).

Numerical models for the Indian Ocean Tsunami 2004


15.3

161

MOST MODEL

This model was developed at the Pacific Marine Environmental Laboratory (PMEL) of National Oceanic and Atmospheric Administration (NOAA) in Seattle, USA. Details of the model are described by Titov and Synolakis (1995, 1996), Titov and Gonzalez (1997) and Titov (2005). The MOST model simulates all three stages of the tsunami namely generation, propagation and runup. The generation process is based upon the elastic deformation theory (Gusiakov, 1978; Okada, 1985), which assumes an incompressible liquid layer on an underlying elastic half space, to characterize the ocean and the earth’s crust. The elastic fault plane model contains a formula for static sea floor displacement to compute the initial conditions required for further simulations of tsunami propagation and coastal inundation. Since tsunamis propagate over long distances, earth’s curvature must be taken into account. Hence the momentum and continuity equations are written in spherical polar coordinates (Murty, 1984). The other parameters that should be included are Coriolis force and dispersion. Because tsunami waves with different frequencies propagate with slightly different speeds, the shape of the wave changes due to dispersion. However, explicit inclusion of the dispersion terms makes the equations too complex. As a simple alternative, Shuto (1991) suggested that physical dispersion can be simulated through numerical dispersion, which is present in finite difference algorithms. The most model makes use of non-linear shallow water equations in spherical polar coordinates (Murty, 1984) and uses numerical dispersion and equations are solved using splitting method. Model simulation results are presented in Figures 15.2–15.4. Figure 15.2 shows amplitude and tsunami travel times for global ocean and Figure 15.3 shows same for Indian Ocean region. Figure 15.4 compares the observed and computed travel times. As can be seen, the agreement is good. Figure 15.5 shows the arrival time of first wave in the Indian Ocean and Figure 15.6 shows the observed versus model wave arrival time.

Figure 15.2.

Maximum wave amplitude for the Global Ocean.


162


Figure 15.3. Arrival time of first wave of the tsunami for the Global Ocean.

Figure 15.4.

Maximum tsunami wave height (cm) in the Indian Ocean.

15.4 TOAST MODEL This model was combination of different models developed under Advance Ocean State Forecast activity at MOG/SAC (Agarwal et al., 2005). The model is originally designed for ocean general circulation and also for the prediction of tides and storm surge coupled with a cyclone prediction model. Flexible grids in the model also allows to simulate coastal inundation due to storm surges. TOAST’s ocean general circulation model has separate barotropic and baroclinic modes of energy propagation. On 26 December 2004, Indian Ocean Tsunami was simulated by adapting this model



Figure 15.5. Arrival time of first wave in the Indian Ocean.

Figure 15.6.

Observed versus model wave arrival times.

163


164


Figure 15.7.

Computed and observed inundation in Banda Aceh Indonesia from http://www.wldelft. nl/cons/area/ehy/flood/tsunami.html.

for tsunami generation and propagation. For tsunami generation elastic plate movement model was used. Agarwal et al. assumed the intensity of the quake as 9.0 Ritcher scale and also compared the simulation results with Jason altimeter pass in the central Bay of Bengal at 0256 UTC. According to them the model is working well and results are encouraging. 15.5

DELFT HYDRAULICS MODEL

There are two versions – a three-dimensional (3D) and a two-dimensional (2D). These models are mainly applied for simulation of tides and storm surges. In the 3D version, the vertical grid follows sigma coordinates and in the 2D version, a curvilinear boundary fitted grid is used. For the tsunami version, the computation started an initial disturbance of 650 km in length along the coast of Banda Aceh, Sumatra, Indonesia. The maximum tsunami amplitude in the open ocean is about 1 m. The computed tsunami travel times are some what less than the observed travel times. According to Delft, a high-resolution nested model of Aceh is applied to simulate the flooding. For the flooding simulations the “flood” scheme, which was recently incorporated in the Delft 3D system, has been applied. Figure 15.7 shows the computed flooded area in the coastal region of Banda Aceh. The satellite picture taken by IKONOS satellite show that the model has reproduced the flooded areas extremely well.

Numerical models for the Indian Ocean Tsunami 2004 15.6

165

ITALY MODEL


This model belongs to the Istituto Nazionale Geofisica e Vulcanologia. It is a 2D shallow water code in a finite difference frame work and used the Okada (1985) equations for the fault (slip amplitude of 20 m and dip angle of 15) plane model for tsunami generation with rupture dimensions of 700 km length and 100 km in width. The simulation produced some interesting results with the 2 min by 2 min grid. Seven hours of propagation took about 6 h of CPU time (on a laptop with a 1.7 GHz processor). The initial disturbance towards Thailand is depression or the trough of a wave. A tsunami wave reflected from the east coast of Sri Lanka returns towards the epi central area. The computed travel time of the tsunami to Maldives is slightly greater than the observed travel time. 15.7

EUROPEAN COMMISSION JOINT RESEARCH CENTRE MODEL

This is a simple model (Annunziato and Best, 2005) and was used to compute the travel times of the tsunami under the shallow water approximation. The grid used was based upon the ETOPO5 ocean bathymetry with a 5-min grid resolution. The main objective of this model is to predict travel times quickly so that early warnings for tsunami risk can be provided in the Earthquake alert system of GDAS. Diffraction and hydro dynamics are not included in the model. 15.8

UNIVERSITY OF FRANKFURT/MAIN, GEOPHYSICAL INSTITUTE MODEL

It is a non-linear shallow water model (Babeyko and Sobolev, 2005) in spherical coordinates with coriolis and bottom friction terms included. It is an explicit finite difference model with a grid size of 2 min for the coarse model and 30-arc seconds for a fine grid model. The time steps for these two models are 2 and 1 s respectively. Six hour simulation time is used. The ocean bathymetry used is ETOPO2. The authors, Babeyko and Sobolev remark that the model results degrade in the near shore region. According to authors, initial sea bottom displacement is calculated following Okada’s (1985) analytical solution for the surface deformation caused by deep planar fault of arbitrary size and orientation. In this scenario the fault zone follows the plate boundary between Indian and Sunda plates and is composed of 6 planar Okada’s segments with the following parameters. The rupture starts at time = 0 at the epicenter and moves northwards along the plate boundary with velocity Vr. As rupture moves along a segment, the slip at this segment linearly increases from zero up to its maximal value (here – 15 m). The total slip at a segment is being decomposed into vertical and horizontal parts depending on the segment orientation relative to the convergence direction of the Indian and Sunda plates (thick black arrow). Accordingly, the vertical bottom displacement, which is responsible for the tsunami generation, varies among the segments and is minimal at the northern segment. Current model of the seismic source corresponds to the total seismic moment of 1.2 × 1030 dyncm. 15.9

NIO MODEL

The tidal model of Unnikrishnan et al. (Proc. Ind. Acad. Sci. (Earth Planet. Sci.), volume 108, pp. 155–177, 1999) was adapted to simulate this tsunami by an initial water level elevation of 25 m along an arc encompassing the epicenter (which was at 3.4◦ N, 95.7◦ E) and the Andaman Nicobar Islands. The ETOPO5 bathymetry that was used provided a resolution of 5 min of arc,

166



Table 15.2.

Fault parameters as used in the DCRC model.

Fault-1

Fault-2

Fault-3

• 95.75◦ E, 2.5◦ N • (Strike, dip, slip) = (329, 15, 110) • (L,W) = (330 km, 150 km) • Dislocation = 11 m • Depth = 7.0 km



which is approximately 9 km (5 min) and the simulation carried out for 10 h, by which the tsunami spread more or less across the Indian Ocean. Refer to http://www.nio.org/jsp/tsunami.jsp 15.10

DCRC (DISASTER CONTROL RESEARCH CENTER, TOHOKU UNIVERSITY, JAPAN) TOHOKU MODEL

The model used ETOPO2 ocean bathymetry in computational domain of 30◦ N to 30◦ S and 60◦ E to 120◦ E. The fault zone was treated as made up of three different parts with the fallowing fault plane parameters as shown in Table 15.2. The simulated tsunami at Banda Aceh (Indonesia), Galle (Sri Lanka) and Chennai (India) are shown in Figure 15.8. 15.11 ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY (AIST) MODEL SATAKE (2005) It was assumed that the aftershock area represents the tsunami source and a fault of 1200 km in length was used for the simulation. The tsunami reached Phuket (Thailand) and Sri Lanka in about 2 h and the coast of Africa in 8 to 11 h. East of the epicenter, the tsunami started as a receding wave, whereas as to the west, the initial tsunami wave form was a crest. 15.12 WAKAYAMA NATIONAL COLLEGE OF TECHNOLOGY MODEL Simulation of the tsunami model was done using a linear shallow water model in spherical polar coordinates with a grid size of 2 min arc by Nobuaki Koike (2005) Department of Civil and Environmental Engineering. Tsunami generation was modeled by moving a basic fault model (Yamanaka, 2004). The directivity of the tsunami energy can be seen clearly in Figure 15.9. 15.13

KOSHIMURA MODEL (2005)

Numerical modeling of tsunami was performed using TUNAMI, code of the Disaster Control Research Center, Tohoku University by Koshimura of Disaster Reduction and Human Renovation Inst., Japan. The model is based on the linear shallow water theory of spherical co-ordinate system. Seismic deformation modeling is based on the theory of Okada (1985). The computational grid size is approximately 2 and 5 min. Following model cases are mainly based on the revised CMT solution by Harvard University. Initial model parameters were given in Table 15.3.

Numerical models for the Indian Ocean Tsunami 2004 9.00

[m]

167

Banda Aceh

6.00 3.00 0.00 3.00 6.00 9.00


0 3.00

100

200

300

400

[min]

[m] Galle

2.00 1.00 0.00 1.00 2.00 3.00 0

100

200

300

[m]

3.00

400

[min]

Madras

2.00 1.00 0.00 1.00 2.00 3.00 0

100

200

300

400

[min]

Figure 15.8. Tsunami amplitudes at Banda Aceh (Indonesia), Galle (Sri Lanka), Madras (now Chennai, India).

Model-6 1st. segment (Southern part) • • • •

(Strike, dip, slip) = (329, 15, 90) (L,W) = (500 km, 150 km) Dislocation = 11 m Depth = 10 km

2nd. segment (Northern part) • • • •

(Strike, dip, slip) = (345, 15, 90) (L,W) = (400 km, 150 km) Dislocation = 11 m Depth = 10 km


168


Figure 15.9.

Maximum water elevation. Table 15.3.

Model parameters.

Governing equation Numerical scheme Spatial grid size Temporal grid size Computational domain Bathymetry data

15.14

Linear shallow water equations in spherical co-ordinate system Leap-frog FDM 2 min/5 min 5 s/10 s 2-min grid: (15N, 70E)–(15S, 120E) 5-min grid: (25N, 20E)–(75S, 120E) 2-min grid: Sandwell-Smith sea floor topography 5-min grid: NOAA ETOPO 5

BAIRD MODEL

Numerical modeling of the tsunami in the Indian Ocean was done by Baird and Associates (Ottawa, Canada) using Danish Hydraulic Institute’s M21 Hydrodynamic flow module. It is a 2D shallow water model for free-surface flows. This model was extensively used to simulate hydraulic and environmental phenomena in lakes, estuaries, bays, coastal areas and seas. The hydrodynamic module is basic model in the flow model and is used to simulate water level variations and flows driven by wind, tide and other forcings. The model includes bottom shear stress, wind shear stress, barometric pressure gradients, Coriolis force, dispersion sources and sinks, evaporation, flooding and drying. A preliminary simulation of Indian Ocean Tsunami is carried out using a rectangular grid (with 15 km resolution) covering entire Indian Ocean. Three



Figure 15.10.

169

Grids used in the model.

fine grids as shown in Figure 15.10 (with resolution of 5, 1 and 500 m) nested within the main grid to resolve the tsunami propagation around Southern India, Sri Lanka and Indonesia coasts. ETOPO2 ocean bathymetry as well as hydrographic charts were used for the grid generation. Initial sea surface elevation is based on the data provided by USGS. Figure 15.11 show computed maximum surface elevations. 15.15

KOWALIK ET AL. MODEL

Kowalik et al. (2005) developed a comprehensive model for this tsunami and we reproduced below from their paper, their abstract (which summarizes the work) their source function (Table 15.4) and their table comparing computed and observed travel times (Table 15.5). A new model for the global tsunami computation is constructed. It includes a high order of approximation for the spatial derivatives. The boundary condition at the shore line is controlled by the total depth and can be set either to runup or to the zero normal velocity. This model, with spatial resolution of 1 min, is applied to the tsunami of 26 December 2004 in the World Ocean from 80_S to 69_N. Because the computational domain includes close to 200 million grid points, a parallel version of the code was developed and run on a supercomputer. The high spatial resolution of 1 min produces very small numerical dispersion even when tsunamis wave travel over large distances. Model results for the Indonesian tsunami show that the tsunami traveled to every location of the World Ocean. In the Indian Ocean the tsunami properties are related to the source function (i.e., to the magnitude of the bottom displacement and directional properties of the source). In the Southern Ocean surrounding Antarctica, in the Pacific, and especially in the


170


Figure 15.11.

Computed maximum water elevation in the Indian Ocean.

Table 15.4.

Fault parameters used to generate vertical sea floor movement.

Earthquake parameter Strike Dip Slip Length Depth (SW corner) Moment Rigidity

Southern fault segment

Northern fault segment

335 8 110 300 km 8 km 3.2 × 1029 dyn/cm 4.2 × 1011 dyn/cm2

350 8 90 700 km 8 km 7.6 × 1029 dyn/cm 4.2 × 1011 dyn/cm2

Atlantic, tsunami waves propagate over large distances by energy ducting over oceanic ridges. Tsunami energy is concentrated by long wave trapping over the oceanic ridges. Our computations show the Coriolis force plays a noticeable but secondary role in the trapping. Travel times obtained from computations as arrival of the first significant wave show a clear and consistent pattern only in the region of the high amplitude and in the simply connected domains. The tsunami traveled from Indonesia, around New Zealand, and into the Pacific Ocean. The path through the deep ocean to North America carried miniscule energy, while the stronger signal traveled a much longer distance via South Pacific ridges. The time difference between first signal and later signal strong enough to be recorded at North Pacific locations was several hours. The generation mechanism for the Indian Ocean Tsunami is mainly the static sea floor uplift caused by abrupt slip at the India/Burma plate interface. Permanent, vertical sea floor displacement is computed using the static dislocation formulae from Okada (1985). Inputs to these formulae are fault plane location, depth, strike, dip, slip, length and width as well as seismic moment and rigidity. The earthquake’s total rupture extent can be estimated by several approaches.



Table 15.5.

171

Observed and calculated travel time.

Station location

Travel time observed

Travel time for 0.1 cm amplitude

Travel time for 5 cm amplitude

Chennai (80.17E, 13.04N) Male (73.52E, 4.18N) Hanimadhoo (73.17E, 6.77N) Diego Garcia (72.40E, 7.28S) Hillarys (115.73E, 31.82S) Salalah (54.00E, 16.93N) Pt. La Rue (55.53E, 4.57S) Lamu (40.90E, 2.27S) Zanzibar (39.18E, 6.15S) Portland (141.60E, 38.33S) Richard’s Bay (32.08E, 28.80S) Port Elizabeth (25.63E, 33.97S) Jackson (168.62E, 43.98S) Arraial de Cabo (42.02W, 22.97S) Arica (70.21W, 18.22S) Char. Amalie (64.55W, 18.20N) San Diego (117.12W, 32.45N) Halifax (63.59W, 44.66N) Atl.City (74.25W, 74.25W,39.21N) Toffino (125.55W, 49.09N) Adak (176.65W, 51.87N)




Finite fault seismic data inversion is one method which yield fault lengths on the order of 350– 650 km (e.g. Ji, 2004; Yagi, 2005). Another traditional method to delineate earthquake fault zones is plotting the aftershocks which occur in the first 24 h following the main shock. The aftershocks are expected to clusterwithin the slip zone. This approach leads to an estimate of 1200 km for the fault length (NEIC, 2004). In this study, the fault extent is constrained by observed tsunami travel times to the northwest, east and south of the slip zone. Figure 15.3 displays the tsunami arrival time constraints on the fault zone. Tsunami arrival times at Paradip–India (SOI, 2005), Ko Tarutao–Thailand (Iwasaki, 2005) and Cocos Island (Merrifield et al., 2005) tide gauges are plotted in reverse. That is, the observed travel time contour is plotted with the tide gage location as the origin point. This method indicates a fault zone approximately 1000 km by 200 km. The epicenter location lies on the southern end of the fault zone. To accommodate trench curvature, the fault plane is broken into two segments. Fault parameters for the two segments are listed in Table 15.1. Strike, dip and slip are based on the definitions from Aki and Richards (1980). Strike is determined by the trench orientation. Dip is taken from the Harvard CMT solution (HRV, 2005). The slip for the southern segment is based on the Harvard CMT solution while slip for the northern segment is set at 90_based on observed tsunami first motions on Indian tide gages (NIO, 2005). Depth is based on the finite fault inversion of Ji (2004). The total moment release (derived by assuming an average slip of 13 m and rigidity of 4.2 × 1011 dyn/cm2 ) in the two segments equals 1.08 × 1030 dyn/cm (Mw = 9.3) which is in good agreement to 1.3 × 1030 dyn/cm proposed by Stein and Okal (2005) based on normal mode analysis. 15.16

CONCLUSIONS

The numerical models simulating the generation and propagation of the tsunami of 26 December 2004, in the Indian Ocean, that were posted in the Internet were briefly reviewed here. The cut-off

172


date for this review was 1 November 2005. The order in which models were reviewed here has no particular significance, other than it is the order, which we found the models. It should be noted that this review is only meant to provide information about the models posted on the web sites and no attempt was made to compare and contrast these models. Finally, it quite possible that there were several other models, that some how escaped our attention.


REFERENCES Agarwal, K., Vijay, N., Agarwal and Kumar, R. (2005). Simulations of the 26 December 2004 Indian Ocean Tsunami using a multi-purpose ocean disaster simulation and prediction model. Curr. Sci., 88(3). Aki, K. and Richards, P.G. (1980). Quantitative Seismology Theory and Methods Volume 2, W.H. Freeman and Co., New York, 557pp. Annunziato, A. and Best, C. (2005). E.C. JRC Tsunami Propagation Model. Posted at http://tsunami.jrc.it/model/ Babeyko, A. and Sobolev, S. (2005). A Numerical Simulation of the Indian Ocean Tsunami 26 December 2004. Posted http://www.gfzpotsdam. de/news/recent/archive/20041226/TsunamiModelling/content.html DCRC Model http://www.tsunami.civil.tohoku.ac.jp/hokusai2/topics/04sumatra/index. html Delft3D simulation package of WL. Delft Hydraulics (2005). Posted at http://www.wldelft.nl/gen/news/ tsunami/ NIO, Goa, Tsunami Simulation (2005). Posted at http://www.nio.org/jsp/tsunami.jsp Gusiakov, V.K. (1978). Static Displacement on the Surface of an Elastic Space. Ill-Posed Problems of Mathematical Physics and Interpretation of Geophysical Data, Novosibirsk, VC SOAN SSSR, 23–51 (in Russian). Italy Model (2005). Posted at http://www.ingv. it/%7eroma/reti/rms/terremoti/estero/indonesia/indonesia. htm Iwasaki, S.I. (2005). Posting of Thailand tide Gage Data to Tsunami Bulletin Board, also posted at http://www.navy.mi.th/hydro/tsunami.htm Ji, C. (2004). Preliminary Result of the 04/12/26 (Mw 9.0), Off West Coast of Northern Sumatra Earthquake, posted at http://www.gps.caltech.edu/%7Ejichen/Earthquake/2004/aceh/aceh.html Koike Nobuaki (2005). Preliminary Report of Numerical Computation of Tsunamis Generated by the December 26, 2004 Off Sumatra Island Earthquake, Indonesia. Posted at http://www.wakayama.nct.ac.jp/gakkasyoukai/kan/staff/koike/sumatra.html Kowalik, Z., Knight, W. Logan, T. and Whitmore, P. (2005). Numerical modeling of the global tsunami: Indonesian Tsunami of 26 December 2004. Sci. Tsunami Hazards, 23(1), 40–56. Koshimura, S. (2005). DRI Preliminary Tsunami Modeling Report, Modeling a tsunami Generated by the December 26, 2004 Earthquake off the West Coast of Northern Sumatra, Indonesia. Posted at http://www.dri.ne.jp/koshimuras/sumatra/ Merrifield, M.A., Firing, Y.L., Brundrit, G., Farre, R., Kilonsky, B., Knight, W. and Kong L. (2005). Preliminary Report of Tsunami Observations, Survey of India, posted at http://www.surveyofindia.gov.in/tsunami4.htm Murty, T.S. (1984). Storm Surges – Meteorological Ocean Tides, Bulletin No. 212, Fisheries Research Board, Canada, Ottawa, 897pp. Okada, Y. (1985). Surface deformation due to shear and tensile faults in a half-space. Bull. Seismol Soc. Am., 75, 1135–1154. Satake Kenji. (2005). Posted at http://staff.aist.go.jp/kenji.satake/animation.gif Shuto, N. (1991). Numerical Simulation of Tsunamis, In: E. Bernard, (ed.) Tsunami Hazard, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 171–191. Titov, V.V. (2005). Tsunami Event – 26 December 2004. Posted at http://www.pmel.noaa.gov/tsunami/indo_ 1204.html Titov, V.V. and Gonzalez, F.I. (1997). Implementation and Testing of the Method of Splitting Tsunami (Most) Model Noaa Technical Memorandum ERL PMEL-112 . Titov, V.V. and Synolakis, C.E. (1996). Numerical modeling of 3-D long wave runup using VTCS-3. In: P. Liu, H. Yeh, and C. Synolakis (eds.), Long Wave Runup Models, World Scientific Publishing Co. Pte. Ltd., Singapore, pp. 242–248.


173


Titov, V.V. and Synolakis, C.E. (1995). Modeling of breaking and nonbreaking long wave evolution and runup using VTCS-2. J. Waterways Ports Coast. Ocean Eng., 121(6), 308–316. Yagi, Y. (2005). Preliminary Results of Rupture Process for 2004 off coast of Northern Sumatra Giant Earthquake (ver. 1), posted at http://iisee.kenken.go.jp/staff/yagi/eq/Sumatra2004/Sumatra2004.html Yalciner A.C., Taymaz, T., Kuran, U., Pelinovsky, E. and Zaitsev. A. (2005). The Model Studies on December 26, 2004 Indian Ocean Tsunami, Posted at http://yalciner.ce.metu.edu.tr/sumatra/ Yamanaka (2004). Posted at http://www.eri.u.tokyo.ac.jp/sanchu/Seismo_Note/2004/EIC161.html


CHAPTER 16

The Cauchy–Poisson Problem: Application to Tsunami Generation and Propagation


N. Nirupama Atkinson School of Administrative Studies, York University, Toronto, Canada T.S. Murty and I. Nistor Department of Civil Engineering, University of Ottawa, Ottawa, Canada A.D. Rao Centre for Atmospheric Sciences, Indian Institute of Technology, New Delhi, India

16.1

INTRODUCTION

The classical Cauchy–Poisson (C–P) problem is the initial value problem for surface waves. The classical C–P problem as described by Lamb (1945) deals with one-dimensional standing waves in an ocean of infinite depth. Although the classical problem is hardly suitable for tsunami studies, it is simple and can be used to introduce certain concepts. Two different initial states are considered: initial elevation of the free surface with no motion, and a horizontal surface with an initial distribution of surface impulse. The classical C–P problem deals with only a symmetric source of tsunami generation. We will also consider asymmetric sources which are more common for real tsunami generation events. Other factors we will consider include sloping nature of the ocean bottom in the area of tsunami generation as well as the effect of viscosity of the fluid on tsunami generation. The Indian Ocean Tsunami of 26 December 2004 afforded an opportunity to test the validity of the classical C–P problem, with an initial surface elevation as well as an initial impulse. This tsunami has been studied in detail by (Kowalik et al., 2005a,b; Murty et al., 2005a–c; Murty et al., 2006a–c; Nirupama et al., 2005; Nirupama et al., 2006).

16.2

MOTION STARTING WITH INITIAL EVALUATION

First consider initial evaluation. Taking the origin at the undisturbed level of the surface, the water level, η, and the velocity potential, φ, can be written for simple harmonic standing waves: η = cos(ωt) cos(kx) φ=

(16.1)

g sin(ωt)φ kz e cos(kx) ω

(16.2)

where ω2 = gk

(16.3) 175

176

N. Nirupama et al.

The initial state is given by: η = f (x), φ0 = 0

(16.4)


The Fourier double integral representation is: ∞ 1 ∞ f (x) = dk f (α) cos k(x − α) dα π 0 −∞ From equations (16.1)–(16.5) ∞ 1 ∞ η= cos(ωt) dk f (α) cos k(x − α) dα π 0 −∞ g φ= π

∞

0

sin(ωt) kz e dk ω

∞

−∞

f (α) cos k(x − α) dα

(16.5)

(16.6) (16.7)

Lamb assumed that the initially elevated region is small in extent and is confined to the immediate vicinity of the origin, so that f (α) is nonzero for infinitesimal values of α. Lamb expressed φ and η in a series as well as in another form involving Fresnel’s integrals. 16.3

MOTION STARTING WITH INITIAL IMPULSE

For initial impulse, the initial conditions are: ρφ0 = f (x)

(16.8)

η=0 A similar procedure was followed as above. For large gt 2 /4x, the following expressions hold approximately. For initial elevation: 2 2 g 1/2 t 2 gt gt η = 3/2 1/2 3/2 cos + sin 2 π x 4x 4x

(16.9)

and for initial impulse: η=

2 2 g 1/2 t 2 gt gt cos − sin 5/2 1/2 5/2 2 π ρx 4x 4x

(16.10)

One drawback of these solutions is that as the origin is approached the wavelength decreases monotonically, whereas the wave height increases asymptotically. 16.4

KELVIN’S METHOD OF STATIONARY PHASE AND AIRY INTEGRAL

Kelvin (1877) suggested that the C–P problem can be studied by more simple methods than were adopted by Cauchy and Poisson.

The Cauchy–Poisson problem: application to tsunami generation and propagation

177

Consider the integral:


a

b

φ(x) eif (x) dx

and assume that f (x) varies much more rapidly than in a periodic manner. Kelvin’s method uses the fact that the various elements of the integral will for the most part cancel by annulling interference except in the neighborhood of x, if any, for which f (x) is stationary. For details on Kelvin’s method of stationary phase see Jeffreys and Jeffreys (1946) and Stoker (1957). Consider one-dimensional propagation of a disturbance due to an initial elevation over the water surface. Following Jeffreys and Jeffreys, represent the disturbance as: f (x) =

∞

0

f (K) cos(Kx − ωt) dK

(16.11)

Then at point x0 , at time t0 , the disturbance can be asymptotically represented by Kelvin’s method of stationary phase as: f (x0 , t0 ) ≈

fK0 π 1/2 cos K0 x − ωt ∓ dC 4 1 πt dKg 2

(16.12)

Here the subscript 0 signifies that the function has to be evaluated for the wave number, K0 . Also Cg is the group velocity and the ∓ sign should be taken when dCg /dK is positive or negative. However, equation (16.12) is not valid in the following cases: (a) when the√ group velocity is stationary or (b) at the head of a wave train where the long-wave formula (C = gD) holds. In these situations the method of stationary phase should be carried out to a higher approximation. Then the disturbance could be expressed, instead in equation (16.11), in terms of the Airy integral given by: 1 Ai (α) = π

0

∞

3 t cos + αt dt 3

(16.13)

where α is some variable. If one approximates 1 tanh(KD) ∼ KD − (KD)3 6

(16.14)

The group velocity of tsunami waves arriving at any point is: Cg =

1 gD 1 − K 2 D2 2

(16.15)

Let the initial form of the surface be such that: η = 1 in√the region L < x < L and η = 0 elsewhere. If α is identified with the phase velocity of a long wave, gD, the asymptotic form of η near x = αt is: η∼L

2 αtD2

1/3

Ai

2(x − αt)3 αtD2

1/3 (16.16)

178

N. Nirupama et al.


The form of the Airy function is such that it increases monotonically to a maximum and then oscillates with decreasing amplitude. For positive α, Ai (α) can be expressed in terms of the Bessel functions of imaginary argument, whereas for negative α, it can be expressed in terms of the Bessel function, J . Based on the behavior of Ai (α), one can deduce that at any given point after the passage of the head of the wave train succeeding waves must be of the form of a dispersive wave train. The following asymptotic form is valid for η after the initial few oscillations.

1/12 2 1/3 αtD2 1 2 1/2 π 2 3/2 η=L ×sin + (αt − x) (16.17) αtD2 π1/2 (αt − x)1/4 2 3 αtD2 4

16.5

C–P PROBLEM WITH ASYMMETRIC SOURCE

Braddock and Van Den Driessche (1971) developed a theory for the C–P problem when the source is asymmetric with reference to the axis (of a cylindrical polar coordinate system) with the origin placed at the bottom. The ocean bottom is assumed to move with the velocity F(x, y, t) = X (x)Y (y)T (t)

(16.18)

Although this separation of variables is somewhat simplistic, some generality is achieved by expanding X (x), Y (y), T (t), in series of orthogonal functions. This type of bottom motion is more general than in the theory of Kajiura. 2 x X (x) = αn Hm (s) exp − for −∞ < x < ∞ 2 m=0 2 ∞ y Y (y) = βn Hn (y) exp − for −∞ < y < ∞ 2 n=0 2 ∞ t T (t) = γp Lp (t) exp − for 0 < t < ∞ 2 p=0 ∞

(16.19)

Here Hm (x) is the Hermite polynomial of degree, m, and Lp (t) is the Laguerre polynomial of degree, p. The coefficients αm , βn , and γp can be written as follows: 2 ∞ 1 x αm = m √ X (x) exp − Hm (x) dx 2 2 m! π −∞ 2 ∞ 1 y βn = n √ Y (y) exp − Hn (y) dy 2 2 n! π −∞ 1 ∞ t γp = T (t)Lp (t) exp − dt p! −∞ 2

(16.20)

Because of the presence of factors 2m , m!, n!, p! in the denominators of equation (16.20), the coefficients of αm , βn , γp decrease rapidly as m, n, p increase. Hence, in practice only a few terms will be necessary.

The Cauchy–Poisson problem: application to tsunami generation and propagation

179

It is possible that the source area for a tsunami could be very close to the shore such as a shallow submarine earthquake or an underwater nuclear explosion. In this case, the effect of the sloping nature of the bottom on the tsunami generated has to be taken into account. Slatkin (1971) used a three-dimensional model to study this problem. The origin of a Cartesian coordinate system, x, y, z, is taken at the equilibrium position of the free surface with the Z-axis pointing upward. Then the bottom is given by Z = −D(x, y, t) and the free surface perturbation is η(x, y, t). In the linear shallow-water theory for the nonrotating case, the wave equation is (see Lamb, 1945):


g {∇(D∇η)} −

∂2 η ∂2 D = − ∂t 2 ∂t 2

(16.21)

where ∇ is the gradient operator. Let the bottom profile be specified as: D(x, y, t) = D0 (y) + D1 (x, y, t)

(16.22)

where D1 4 15 >15 >15 >10 >15 >15 ND ND 15 15 9 1.7 (Continued)

194

I. Nistor et al.

Table 17.2.

(Continued) Physical location

Location (tide gauge)


Medan East

Survey point Kuala Ruteri Belawan port Ferry port

Sumatra (local time = UTC +7) Lhokseumawe Lhokseumawe Sibolga (fishery port) Sibolga (fishery port) Sibolga (passenger port) Sibolga (tide gauge) South of Sibolga Pasarsorkam Barus Sigli Sigli Sigli Sigli Thailand (local time = UTC +7) Ranong Kuraburi Ta Phao Noi Krabi Kantrang Ta Ru Tao Tummarang Tummarang Yacht Mercator Karon Beach (South part) Karon Beach (Central part) Karon Beach (North part) Moodong Canal (Chalong Bay) Phalai village (Chalong Bay) Makham Bay (North, Pier) Sire village (Siray Is.) Khao Lak Khao Lak Chalong Bay Pier Leam Him Bang Rong Pier Phi Phi Don (North coast) Phi Phi Don (South coast) Phi Phi Don South–North Patong Beach Patong Beach Patong Beach Patong Beach Patong Beach Patong Beach

Latitude Longitude

Arrival time Wave in UCT run-up (m)

ND 3.784 3.787

ND 98.715 98.705

ND ND ND

5.249 5.235 1.718 1.719 1.729 1.729 1.664 1.871 2.008 5.387 5.388 5.388 5.388

96.913 97.060 98.797 98.795 98.785 98.785 98.826 98.565 98.403 95.964 95.963 95.962 95.962

1:40 1:40 1:40 1:40 1:40 1:40 1:40 1:40 1:40 1:40 1:40 1:40 1:40

2.9 1.7 1.6 1.63 1.5 2.6 1.5 1.0 1.7 4.4 4.0 3.5 3.1

9.967 9.133 7.667 8.167 8.667 6.083 6.083 6.083 7.750 7.829 7.842 7.821 7.842 7.839 7.870 7.873 8.637 8.637 7.819 7.943 8.047 7.739 7.748 7.738 7.884 7.888 7.888 7.887 7.887 7.894

98.583 98.083 98.033 99.200 99.867 100.000 100.000 100.000 98.280 98.298 98.297 98.298 98.375 98.373 98.417 98.425 98.251 98.253 98.403 98.401 98.419 98.777 98.772 98.773 98.292 98.296 98.296 98.296 98.296 98.299

4:38 4:10 3:20 4:20 5:50 4:00 6:10 6:10 2:38 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00

1.00 3.2 1.45 2.1 3.0 1.8 1.6 ND ND 4.04 4.49 ND 3.15 2.75 1.39 2.67 8.8 9.6 3.62 0.72 1.29 5.84 4.58 ND 5.09 4.88 5.44 5.33 5.28 5.48 (Continued)

A review and listing of 26 December 2004 tsunami Table 17.2.




195

Survey point

Latitude

Longitude

Patong Beach Patong Beach Patong Beach Kamala Beach Kamala Beach

7.892 7.904 7.904 7.947 7.947

98.298 98.301 98.301 98.283 98.282

Bang Thao Beach

8.002

98.296

Nai Yang Beach

8.087

98.300

8.636

98.249

8.635

98.250

8.637 8.637 8.638 8.640 8.640

98.251 98.251 98.253 98.250 98.250

8.640 8.640 8.661 8.661

98.250 98.250 98.249 98.250

8.683

98.244

8.683

98.244

8.742

98.255

8.726 8.734 8.729

98.232 98.225 98.226

8.184

98.291

8.197 8.272

98.300 98.280

Khao Lak

Arrival time in UCT

Wave run-up (m)

3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00

5.02 4.79 4.90 4.85 5.29 4.47 3.41 4.04 3.76 4.41 3.95 4.05 4.07 8.76 9.34 9.5 9.45 9.28 8.67 8.71 ND ND 9.91 9.56 8.35 9.46 9.35 9.71 7.38 ND 8.27 8.30 7.99 8.59 10.62 8.50 8.17 6.46 6.06 6.11 6.24 4.48 6.30 8.86 4.83 3.32 3.11 4.05 (Continued)

196

I. Nistor et al.

Table 17.2.




Latitude

Longitude

Arrival time in UCT

Kata Noi Beach Rawai Beach Frendship Beach Hotel (Rawai Rest Area) Kamala Beach Ban Na Tai Tap Lam Navy Base Ban Kao Lak

8.304 7.803 7.772 7.796

98.275 98.303 98.328 98.340

3:00 3:00 3:00 3:00 3:00

4.30 4.28 3.88 2.43 2.35

7.950 8.293 8.570 8.611

98.280 98.273 98.224 98.238

3:00 3:00 3:00 3:00

Ban Niang Beach

8.675

98.242

3:00

Ban Niang Beach Ban Niang Beach Ban Niang Beach Laem Pakarang

8.671 8.700 8.700 8.736

98.243 98.240 98.240 98.222

3:00 3:00 3:00 3:00

Ban Nam Kem Ta pou Noi Ta pou Noi Ta pou Noi Chalong Ban na Tai Rai Dan Nai Rai Ban Thung Wa Thai Muang Thai Muang, visitor center Thai Muang, Natural Conservation Park Ban Laem Po Ban Bang Phng Ban Num Kim Ban Ma Kap Ban Nok Na Ban Pak Ko Ko Koh Kao port Ban Nam Kim Ban Nam Kim Ban Nam Kim Ban Nam Kim Ko Yao Ban Pak Chok Ban Thung Dap Ban Ao Luk Tum Ko Yao, fishing village

8.864 7.834 7.834 7.834 7.821 8.274 8.297 8.310 8.378 8.399 8.436 8.484

98.274 98.422 98.421 98.421 98.345 98.278 98.272 98.273 98.255 98.265 98.238 98.228

3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00

5.40 4.3, 5.1 3.80 7.80 8.5, 8.6, 9.5, 8.8 7.60 5.8, 6.2 7.9 7.1, 8.7, 9.3,(14.6, 15.5) ND 3 6.40 2.53 4.70 1.70 3.90 4.801 6.77 5.29 6.78 6.07 6.25 5.19

8.573 8.812 8.857 8.923 8.999 8.882 8.872 8.860 8.860 8.858 8.857 9.222 9.160 9.028 9.203 9.222

98.225 98.266 98.269 98.258 98.257 98.270 98.275 98.275 98.279 98.279 98.268 98.375 98.271 98.257 98.272 98.375

3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00

ND 13.085 ND 6.0345 12.61 6.391 3.72 4.08 ND ND 15.77 ND 6.632 19.572 8.617 0.982

Survey point

Wave run-up (m)

(Continued)

A review and listing of 26 December 2004 tsunami Table 17.2.




197

Survey point

Krabri Tide Station, National Park Office Krabri Tide Station, National Park Office Krabri Tide Station, National Park Office Ban Ko Dam Ban Tam Nang Ban Pak Nam Ban Pak Nam Ban Pak Nam Ban Pak Nam Ban Pak Nam fishering port Ban Pak Nam port Had Sai Dam (Ban La Ong) Ka Yu Harbor (Ban La Ong) Ka Yu Harbor (Ban La Ong) Ban Ao Khoei Hat Praphat Ban Thale Nok Ban Thale Nok Ramson Ramson Ramson Ban Chang Hak Ban Nam Kim Ban Nam Kim Khao Lak Malaysia (local time = UTC +8) Sungai Batu, Penang Is. Sungai Batu, Penang Is. Pasir Panjang Penang Is. Muara Sungai Pulau Betong, Penang Is. Muara Sungai Pulau Betong, Penang Is. Penang Is. Penang Is. Tanjung Bungah, Penang Is. Miami Beach, Penang Is. Gurney Drive, Penang Is. Mainland Kampung Tepi Sungai Kampung Paya Kampung Paya Sungai Chenang (Langkawi) Pelangi Beach Hotel Resort (Langkawi)

Latitude

Longitude

Arrival time in UCT

Wave run-up (m)

9.225

98.377

3:00

ND

9.225

98.377

3:00

2.43

9.225

98.377

3:00

ND

9.277 8.993 9.951 9.951 9.951 9.951 9.946 9.979 9.744 9.781 9.781 9.299 9.376 9.460 9.460 9.602 9.602 9.602 9.669 8.853 8.859 8.631

98.386 98.412 98.596 98.596 98.596 98.596 98.598 98.601 98.552 98.554 98.554 98.384 98.401 98.437 98.437 98.470 98.470 98.469 98.559 98.272 98.272 98.258

3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00 3:00

1.136 0.70 2.02 2.86 ND 1.16 1.66 1.67 3.727 1.979 −0.321 9.213 4.974 6.77 6.206 4.8 4.91 1.075 1.06 5.779 6.379 ND

5.280 5.283 5.295 5.306

100.239 100.236 100.183 100.192

5:15 5:15 5:15 5:15

1.5 1.5 2.2 ∼3.0

5.280

100.239

5:15

∼3.0

5.326 5.338 5.467 5.476 5.439 5.575 5.580 5.611 5.599 6.304 6.301

100.196 100.195 100.277 100.266 100.308 100.338 100.338 100.341 100.341 99.721 99.720

5:15 5:15 5:15 5:15 5:15 5:15 5:15 5:15 5:15 4:15 4:15

∼2.0 ∼3.0 ∼2.5 ∼3.0 ∼2.5 ωg , there is no ambiguity in the two types of modes. However, centered at about 120 km in the atmosphere there is an anomalous zone in which ωg > ωa . This anomalous zone is probably important for ground-level detection of surface-gravity waves excited by atmospheric nuclear explosions. Tolstoy and Pan (1970) showed that simple models involving two to four layers in the atmosphere, can be used to determine the propagation and dispersion of the lowest two to three gravity modes of the atmospheric wave guide. Two important facts brought out by this paper are: these


230 T.S. Murty et al. simple models could explain the long-period portion of the 300 m/s group velocity plateaus in terms of coupling effects of the internal gravity wave guide. Tolstoy and Pan cautioned that, as this result is obtained from an atmospheric model with two incompressible layers, the 300 m/s value is somewhat fortuitously related to the velocity of sound in the air. Also, surface gravity-wave modes of the atmosphere are better understood by this approach. Another concept introduced pertains to the top boundary condition in the atmosphere. For example, Pfeffer and Zarichny (1962), Press and Harkrider (1962), and Harkrider and Wells (1968) used a free-surface condition, at several heights arbitrarily, to compute surface modes of the atmosphere, but did not explain the logic of this. Tolstoy (1967) showed that it is indeed impossible to justify the use of a free-surface boundary condition, and thereby make the selection of H , the effective atmospheric wave height, less arbitrary. For this he used the concept of vacuum, i.e., at height where the mean free path, , of the neutral gas molecules exceeds the wavelength, L, of the disturbance, the medium is considered to be vacuum. Hence, for heights where L, the usual continuum equations apply. Then the effective free surface of the atmosphere is at height, z = H , where = L. This means the effective height of the atmosphere depends on the wavelength of the disturbance. However, the region, Z = h, at which L is not infinitesimal, but is a transitional layer of thickness, d (say). In this transitional layer, strictly speaking, Boltzmann’s equations must be applied. For d L, the layer mainly behaves as a region with large viscosity and strongly attenuates waves with periods less than 10 min. Another consideration is that (at the heights relevant here) because of large ionization, hydromagnetic interactions could occur. However, Dungey (1954), Fejer (1960), and Hines (1955) showed that these interactions are effective only for periods greater than or equal to 3 h. Hence, it can be assumed that the atmosphere acts as a window for surface-gravity waves, with periods between 10 and 200 min. 20.4 TOLSTOY AND PAN’S MATHEMATICAL MODEL: THE CONCEPTS The simple mathematical model of Tolstoy and Pan (1970) for wavelengths L > 300 km will now be discussed, with particular attention to aspects of the propagation directly relevant to recent observations with microbarographs. They showed motions with 600 m/s and energy concentrated around the 15-min period. The logic behind using a simple model is given by Tolstoy and Pan (1970, p. 35): “Since in the present study we are interested chiefly in internal and surface gravity modes with periods >10 min and wavelengths >200 km, a small number of layers provides adequate approximations for discussing the propagation properties of atmospheric waves. One must remember that the frequency–wave number relationship and the group velocity may be written as quotients of two quadratic forms in the wave amplitudes (Boit, 1957). These are stationary with respect to variations of the amplitude, so that in most calculations relatively large errors in the amplitude distribution of the displacement field can be tolerated, without appreciably affecting the eigenvalue and propagations velocity calculations. Thus, even though amplitude of the vertical displacement predicted by an oversimplified model may be in error, the characteristic curve calculations can be quite accurate. We have limited ourselves to calculations on two and four-layer models, illustrating the effects of compressibility, of the upper boundary condition, of the earth’s rotation, and of layering upon the propagation of long periods. Within the limitations imposed by the small number of layers, we have used models that represent fits to the Vaisala frequency, the density, and sound velocity functions in the earth’s atmosphere.”

Tolstoy and Pan’s model allows interpretation of recent observations by microbarographs. Tolstoy and Herron (1970) also gave a new interpretation of the traveling disturbances in the ionosphere due to nuclear explosions. This is possible because in the moderately long-period range of 10–30 min there is considerable separation between the velocities of surface- and internal gravity waves.


Detection of signals from earthquake and tsunamis in the ionosphere

231

The main difficulty appears to be in the magnitude of the pressure signal. Harkrider and Wells (1968) showed that the observed pressure amplitudes from peak to trough of 10–100 µb would require unrealistically large vertical displacements of the atmosphere above 100 km. Other calculations with simple models essentially confirm their result. Tolstoy and Pan (1970) attributed this to ignoring the anomalous zone between 110 and 200 km, and ignoring the influence of the winds at high altitudes. When these are taken into account the difficulty disappears. That is, the vertical displacements of the atmosphere above 100 km need not be ridiculously large to be consistent with ground-level pressure amplitudes in the range of 10–200 µb. Next Tolstoy and Pan considered the question of the attenuation of the surface-gravity waves and showed that generally the attenuation is small for periods greater than 10 min for the modes m = 0 and 1. Liu andYeh (1971) studied the excitation of acoustic-gravity waves in an isothermal nonrotating atmosphere; because their model is highly idealized it is not included here. Yeh and Liu (1972) gave a good review of the propagation of waves in the ionosphere. 20.5

SIMILARITIES BETWEEN EARTHQUAKE (AND TSUNAMI) SIGNALS AND ACOUSTIC-GRAVITY WAVES FROM ATMOSPHERIC NUCLEAR EXPLOSIONS

Ionization is the phenomenon when ion pairs of separated electrons and positive ions are formed in the ionosphere. There are mainly three regions in the ionosphere – D, E, and F regions. In the daytime, and especially in summer, the F-layer splits in two, F1 and F2 . The electron density is a maximum in each region. However, the electron density increases generally with altitude, i.e. it is greater for the F region than for the E region, which has greater electron density than the D region. In the lower part of the atmosphere, i.e. below 48.3–56.3 km, the air is dense and the probability of collisions between free electrons and atmospheric atoms and molecules is great. Because of this, electrons are rapidly attached to the neutral particles and ionization cannot be produced. Even if it is produced, it is destroyed immediately because, on the average, the life of a free electron in this part of the atmosphere is less than a microsecond. In the ionosphere, electrons and ions are produced by interaction of solar radiation with atoms and molecules of the atmospheric constituents. They are destroyed by combining either with neutral particles or positive ions. Of the two destructive processes, the former dominates at higher levels where electron density is greater. The effect of a nuclear explosion on atmospheric ionization is mainly because of an increase in electron density in the surrounding region. The added electrons can effect all electromagnetic communication, either by attenuating the signal or by changing its direction of propagation through refraction. Donn and Shaw (1967) studied the atmospheric nuclear tests conducted by the USA and USSR during 1952–1962 and, based on the data recorded by a global network of stations maintained by the Lamont Geological Observatory of Columbia University, they arrived at interesting conclusions about pressure waves due to those explosions. In fact, effects of the high-yield atmospheric nuclear explosions are comparable to those of the enormous Krakatoa eruption of 1883 and the impact of the Siberian meteor in 1908, when pressure waves in the atmosphere traveled round the globe more than once, with appreciable amplitudes. Donn and Shaw used the data from sensitive microbarographs at 15 recording stations, and acquired 208 records of 45 nuclear explosions. The dispersion relations of the acoustic-gravity waves in the atmosphere were used to analyze the records and the authors concluded that: “The initial spherical wave at the source, which is modified into a cylindrical wave by the layered structure of the atmosphere, is composed of broad spectrum of pressure waves whose frequencies,

232 T.S. Murty et al.


which propagate away at about the speed of sound in air, range from audible sound to about 0.002 cps. At distances of a thousand or more kilometers, the spectrum becomes considerably narrowed, with the highest frequency detectable being about 0.03 cps (30 s in period). It is more convenient to refer to period rather than frequency for these infrasonic waves. Such waves are also referred to as acousticgravity waves, since their propagation characteristics are controlled by both gravity and the acoustic properties of the atmosphere”. “Because the atmosphere is a dispersive medium for the long waves within this period range (30– 500 s), the initial impulsive because dispersed into a train of the temperature and wind stratification of the atmosphere along the propagation path.”

Daniels et al. (1960) studied vertically traveling shock waves in the ionosphere caused by nuclear explosions at the surface of the earth. They interpreted the distortions in ionosphere recordings as the result of retarded sound waves. Daniels and Harris (1961) reinterpreted the record (because the velocity of the shock wave was 115 m/s) as an ordinary hydrodynamic shock wave. They also mentioned that the pressure amplitude of this upward traveling shock wave was large enough to be detected by acoustic methods at ground level. Webb and Daniels (1964) reported ionospheric oscillations following the Soviet atmospheric nuclear test of 1 November 1962. They measured the rotations of the polarization plane of the radio waves during their travel through the ionosphere, and this parameter was proportional to the electron density. They used a 151-MC/S transmitter at Fort Monmouth, NJ, to reflect signals from the moon. The signals were received at the University of Illinois at Danville, between 11:00 and 18:00 CST on 1 November 1962. Thus the signals traveled twice through the ionosphere. From newspaper and other reports it was known that the Soviet Union had conducted a nuclear test in the atmosphere a few hours earlier. The record at Danville showed an oscillation with 30-min period, larger than the period recorded by the ground-level microbarographs. Webb and Daniels attributed the oscillations to acoustic waves in the atmosphere caused by the explosion. These acoustic waves are expected by the theory to have a group velocity of about 730 m/s, but the authors were unable to check this from the oscillations that may have started before the record began. Long-period ionosphere oscillations have been known to continue for several hours following a nuclear explosion (Daniels and Harris, 1958). Tolstoy and Herron (1970) studied the atmospheric gravity waves excited by nuclear explosions during 1967–1968. The data used were from the large aperture, i.e. a 250 km × 200 km array of 6–12 low-frequency microbarographs with period pass-band 1–60 min, in the New York–New Jersey area. The spectra of these gravity waves showed peaks at 15-min periods and the average group velocity was approximately 600 m/s. The authors deduced that these were indeed atmosphere surface-gravity waves, based on the agreement of the dispersion and attenuation of the recorded waves with expected theoretical relations. Tolstoy and Herron (1970, p. 59) concluded that the 600 m/s, 15-min period arrivals were probably surface-gravity waves traveling along what is effectively the top of the atmosphere. The height, H , of this “effective free surface” depends on the wavelength, L, as it corresponds approximately to the region where the mean free path, , of air molecules is of the order of L (indeed, the condition explicitly applied in making calculations is 2π /L = 1). They thought that a number of published ionosphere observations of fast traveling disturbances generated by US and USSR thermonuclear tests in the early 1960s could probably be explained in a similar way. It appears that reported ionospheric disturbances with horizontal group velocities ≥500 m/s are surface-gravity waves, whereas, lower velocities correspond to internal gravity waves (Hines, 1967). Acoustic modes of propagations (Wickersham, 1966) are possible for spectral components with periods shorter than 10 min. Earlier the problem of the pressure amplitude of atmospheric gravity waves was mentioned. To be consistent with the pressure amplitudes at the ground, it appeared at the outset that

Detection of signals from earthquake and tsunamis in the ionosphere

233

unrealistically large vertical displacements of the atmosphere above 100 km altitude would be needed. Later the problem was explained as neglect of an anomalous zone. Tolstoy and Herron (1970, p. 60) proposed that:


“As much oversimplified one-layer model of the atmosphere (Tolstoy, 1967) can be displacement at these heights, a result which would be quite adequate where it is not for the fact that a more realistic two-layer model decreases this estimate to 0.2 µb or less. Proper inclusion of the effects of a layer between altitudes of 110 and 150 km, in which the acoustic cut-off frequency of the medium is lower than the Vaisala frequency, might eliminate the discrepancy; the problem is discussed in more detail elsewhere (Tolstoy and Pan, 1970).”

Hines (1967) clarified some confusion that arose in connection with the ionospheric disturbances caused by the Soviet upper atmospheric nuclear test over Novaya Zemlaya on 30 October 1962. Obayashi (1962, 1963) attributed these perturbations in the F-layer critical frequency to atmospheric surface-gravity waves with periods in excess of 10 min. Wickersham (1966) differed and proposed that the ionospheric disturbances were due to fully ducted acoustic-gravity waves in the atmosphere. Hines showed that Wickersham’s interpretations is not well founded and Obayashi’s original interpretation is correct.

20.6

SUMMARY

There was considerable work done in the 1950s and 1960s on the possible detection of atmospheric pressure signals in the ionosphere, generated from earthquakes and tsunamis. The linkage is, possible amplification of the signal through acoustic- and internal gravity wave spectrum. However, after the initial burst of earlier research, there was not much work done on this topic. After the Indian Ocean Tsunami of 26 December 2004, there is a renewed interest in this topic at present. REFERENCES Daniels, F.B. and Harris, A.K. (1958). Note on vertically traveling shock waves in the ionosphere. J. Geophys. Res., 66, 3964. Danniels, F.B., Bauer, F.J. and Harris, A.K. (1960). Vertically travelling short waves in the ionosphere, J. Geophy. Res., 65, 1848–1850. Danniels, F. and Harris, A.K. (1961). Note on vertically short waves in the ionosphere, J. Geophy. Res., 66, 3964. Donn, W.L. and Shaw, D.M. (1967). Exploring the atmosphere with nuclear explosions. Rev. Geophys., 5, 53–82. Dungey, J.W. (1954). The propagation of alfven waves through the ionosphere. Pennsylvania State University Ionosphere Research Laboratory Science Report, 57, 19p. Fejer, J.A. (1960). Hydromagnetic wave propagation in the ionosphere. J. Atmos. Terr. Phys., 18, 135–146. Harkrider, D.G. (1964). Theoretical and observed acoustic-gravity waves from explosive sources in the atmosphere. J. Geophys. Res., 69, 5295–5321. Harkrider, D.G. and Wells, F.J. (1968). The excitation and dispersion of the atmospheric surface wave. Proceedings of the Symposium Acoustic-Gravity Wave, Boulder, CO, pp. 299–313. Hines, C.O. (1955). Hydromagnetic resonance in ionospheric waves. J. Atmos. Terr. Phys., 7, 14–27. Hines, C.O. (1960). Internal atmospheric gravity waves at ionospheric heights. Can J. Phys., 38, 1441–1481. Hines, C.O. (1967). On the nature of traveling ionospheric disturbances launched by low altitude nuclear explosions. J. Geophys. Res., 72, 1877–1882. Liu, C.H. and Yeh, K.C. (1971). Excitation of acoustic-gravity waves in tan isothermal atmosphere. Tellus, 23, 150–163. Obayashi, T. (1962). Wide-spread ionospheric disturbances due to nuclear explosions during October 1961. Jpn. Ionosphere Space Res. Rep., 16, 334–340.


234 T.S. Murty et al. Obayashi, T. (1963). Upper atmospheric disturbances due to high altitude nuclear explosions. Planet Space Sci., 10, 47–63. Pfeffer, R.L. and Zarichny, J. (1962). Acoustic-gravity wave propagation from nuclear explosions in the earth’s atmosphere. J. Atmos. Sci., 19, 256–263. Press, F. and Harkrider, D. (1962). Propagation of acoustic-gravity waves in the atmosphere. J. Geophys. Res., 67, 3889–3908. Tolstoy, I. (1967). Long period gravity waves in the atmosphere. J. Geophys. Res., 72, 4605–4622. Tolstoy, I. and Pan, P. (1970). Simplified atmospheric models and the properties of long-period internal and surface gravity waves. J. Atmos. Sci., 27, 31–50. Tolstoy, I. and Herron, T.J. (1970). Atmospheric surface gravity waves from nuclear explosions. J. Atmos. Sci., 27, 55–61. Webb, H.D. and Daniels, F.B. (1964). Ionospheric oscillations following a nuclear explosion. J. Geophys. Res., 69, 545–546. Weston, V.H. and VanHulsteyn, D.B. (1962). The effects of winds on the gravity waves. Can. J. Phys., 40, 797–804. Wickersham, A.F., Jr. (1966). Identification of acoustic-gravity wave modes from ionospheric range time observations. J. Geophys. Res., 71, 4551–4555. Yeh, K.C. and Liu, C.H. (1972). Propagation and application of waves in the ionosphere. Rev. Geophys. Space Phys., 10, 631–709.

CHAPTER 21


Seismo-electromagnetic Precursors Registered by DEMETER Satellite A.K. Gwal Space Science Laboratory, Department of Physics, Barkatullah University, Bhopal, India S. Sarkar LPCE/CNRS, Orleans, France S. Bhattacharya Space Science Laboratory, Department of Physics, Barkatullah University, Bhopal, India M. Parrot LPCE/CNRS, Orleans, France

21.1

INTRODUCTION

Disturbances in the ionosphere linked with seismic activity have been studied from a long time. Many results have been published on satellite observation of electromagnetic and ionospheric perturbations apparently associated with seismic activity (Parrot et al., 1993; Gokhberg et al., 1995; Hayakawa, 1997; Liperovsky et al., 2000). Probably the first results on local plasma density and temperature variations measured onboard AE-C and ISIS-2 satellites were published by Gokhberg et al. (1983). Boskova et al. (1993, 1994) had observed the changes in ion composition before earthquakes over the earthquake preparation zone. Afonin et al. (1999) analyzed a large database of plasma densities recorded in the 3000 orbits of Intercosmos-24. They reported a reliable correlation between the global distribution of seismic activity and ion density variations in the ionosphere, as measured by the normalized standard deviation (NSD) and the relative-normal standard deviation (RNSD). The statistical studies of Afonin et al. (2000) based on Cosmos-900 data and the results of Pulinets and Legenka (2003) had shown the existence of large-scale irregularities in the ionosphere several days or hours before strong earthquakes. Furthermore, significant contributions in the past have reflected on detection of ULF/ELF/VLF emissions at the time of earthquakes by low altitude satellites. Investigation of data by Intercosmos-24 satellite has revealed strong ELF/VLF perturbations associated with earthquakes (Molchanov et al., 1993). Parrot (1994) has performed statistical study of ELF/VLF emissions connected to electric and magnetic field by AUREOL 3 satellite and found increase in the emissions during earthquakes. In spite of several results published, the database collected is not sufficient to reveal the nature of ionospheric earthquake precursors. It is essentially incomplete because only isolated ionospheric effects of individual seismic events have been detected until recently. Also, all these effects have been observed as an additional output of experiments aimed at study of other phenomena, 235


236 A.K. Gwal et al. mainly solar-terrestrial events. Today we cannot be certain if we have regular manifestations of lithosphere–ionosphere coupling or some accidental coincidences of seismic and ionospheric activities occurred (Parrot, 1999). The only way to proceed in the right direction is to carry out high sensitive regular satellite observations in the ionosphere over seismically active and quiet regions supported by ground operations. This will allow to create a sufficient database for statistical study of the seismo-ionospheric effects. It is with this aim that the French microsatellite DEMETER was launched on June 29, 2004 and one of its main scientific objective is to detect anomalous variations of the ionospheric parameters, which could be related to seismic activity. If it can be shown that such perturbations are real and systematic they could be considered as short-term precursors, occurring between a few hours and a few days before the earthquake. Up to now, DEMETER is the only satellite which has the capability to survey on a vast scale the Earth’s electromagnetic environment in the ionosphere. The database which will be built up during this mission will allow us to perform statistical analysis, which will be helpful in reliable detection of ionosphere-earthquake precursors. Some interesting cases of ionospheric irregularities over seismic regions prior to seismic activity identified by the DEMETER records are presented in this chapter. Additionally, some important results of ULF/ELF electric field perturbations found prior to seismic activities have also been presented to emphasize on the correlation of electromagnetic emissions with earthquakes. 21.2 THE DEMETER SATELLITE The French microsatellite DEMETER has been launched on June 29, 2004. The main scientific objective of this mission is to study the ionospheric perturbations, which are linked to seismic activity. The orbit of DEMETER is polar, circular with an altitude of 710 km. There are several sensors onboard DEMETER to survey the ionosphere. The Langmuir Probe Instrument ISL is designed to measure the electron density of plasma (in the range 102 −5.106 particles/cm3 ), electron temperature (in the range ±5 V). An energetic particle analyzer IDP gives the electron energy flux. An ion spectrometer IAP experiment measures the ion composition, density and temperature. A search coil magnetometer IMSC measures the three components of magnetic field in the frequency range from a few Hz up to 20 KHz. A set of four electric sensors ICE to perform a continuous survey of the DC and AC electric fields over a wide frequency range from ULF to HF. Details about these experiments can be found in Berthelier et al. (2006a, b), Lebreton et al. (2006), Parrot et al. (2006) and Sauvaud et al. (2006). DEMETER has two scientific modes of operation: (i) the survey mode collecting averaged data all round the earth (ii) the burst mode collecting data with a bit rate of 1.7 Mb/s above seismic regions. Data and plots are available through a web server dedicated to this mission (http://demeter.cnrs-orleans.fr). Different types of data and the associated products are available on this web server. For data selection we have used the quicklook (QL) images available on the web server. These images give a quick presentation of the data over one half-orbit. All the scientific experiments are presented in a portrait image (format postscript). The standard quicklook image is made from the quick view (QV) experiment frames plus a 14th frame containing earthquake events and with an addition information on the orbital parameters. To get an overview of the science DEMETER payload results we used the QL images. To identify the seismo ionospheric precursors we used the Level 2 data available on the DEMETER web server. Level 2 data processing corresponds to high-resolution plots of the calibrated data, which are obtained from Level 1. The Level 2 image is created by the user itself on the data server, which gives facilities to personalize the output image. To search for earthquakes close to the orbit of DEMETER we have used the web server. We have reduced the DEMETER orbits relative to the earthquake information. Earthquakes selected were greater than 5 in magnitude. Depth was taken up to 1000 km.The distance between the satellite and the epicenter was taken to be 900 km. The time interval between the time of quake

Seismo-electromagnetic precursors registered by DEMETER satellite

237

and data was taken to be 10 days. All these parameters can be changed by the user in the web server. All data files and plots are organized by half-orbits. After selecting the seismic events the QL images were checked for any seismo ionospheric variation. If some variation was found we plotted the Level 2 image. In these images we found good correlation of ionospheric perturbations with the seismic events.


21.3

EVENTS

We discuss here a series of earthquakes that occurred in the Sumatra region of Indonesia. The main shock of the Sumatra earthquake (2.07◦ N, 97.01◦ E) occurred at 16:09:36 UT on March 28, 2005 with M = 8.7. It was followed by aftershocks. The time and location of these earthquakes is given in Table 21.1. Figure 21.1 presents the orbit of DEMETER above Indonesia on March 23, Table 21.1. Time, locations, depth and region of the earthquakes that occurred in the Sumatra region (from the web server http://www.iris.edu/seismon). Date 28-03-2005 28-03-2005 28-03-2005 28-03-2005 29-03-2005 29-03-2005 30-03-2005 30-03-2005 31-03-2005

Epicenter (Latitude, Longitude)

Time (UT)

Depth (km)

M

Region

2.07◦ N, 97.01◦ E 1.33◦ N, 97.39◦ E 0.95◦ N, 97.8◦ E 2.73◦ N, 95.96◦ E 2.61◦ N, 96.54◦ E 2.14◦ N, 96.62◦ E 1.92◦ N, 96.95◦ E 3.01◦ N, 95.37◦ E 1.80◦ N, 97.08◦ E

16:09:36 16:38:43 17:59:47 18:48:52 05:16:29 05:25:25 10:20:22 16:19:41 07:23:55

30 30 30 30 30 30 27.9 22 29

8.7 6.0 5.3 5.5 5.9 5.3 5.4 6.4 5.8

Sumatra Sumatra Sumatra Sumatra Sumatra Sumatra Sumatra Sumatra Sumatra

Demeter March 23, 2005 95

10

97

99

101

103

105

6

2

2

Figure 21.1. Track of DEMETER orbit on March 23, 2005 when the satellite was above the Sumatra region. Stars indicate the epicenters of the earthquakes.


238 A.K. Gwal et al.

Figure 21.2.

From top to bottom the panels successively show the electron density, electron temperature, spectrogram of an electric component between 0 and 2 kHz and earthquakes seen by DEMETER along the orbit. The data are presented as a function of the universal time (UT), The local time (LT), geographic latitude and longitude values are also given.

2005. The corresponding data recorded by DEMETER along this orbit is shown in Figure 21.2. The first panel shows the variation of electron density recorded by the Langmuir Probe Instrument. Second panel gives the electron temperature. Ion density of the O+ ion is shown in the third panel and the spectrogram of electric component up to 2 kHz is shown in the fourth panel. The last panel indicates the satellite closest approach of past and future earthquake epicenters that are within 2000 km from the DEMETER orbit. The Y -axis represents the distances D between the epicenter and the satellite from 750 up to 2000 km. The symbols are filled green square for post seismic events, filled red triangle for pre-seismic events and filled blue circle for earthquakes occurring during the half-orbit. The color scale on the right represents the time interval



Figure 21.3.

239

Spectrogram of ELF electric waveform above the latitude in which earthquake occurred obtained using Level 1 burst mode data for the orbit shown in Figure 21.1.

between the earthquakes and the DEMETER orbit with a color gradation from >30 days up to a [0–6 h] interval. The empty symbols have a similar description except that they are related to the conjugate points of the epicenters. The symbol sizes correspond to the earthquakes of magnitude [5–6], [6–7] and [7–]. Simultaneous disturbances are recorded by three instruments at this time. Rapid fluctuations in electron density (maximum up to 17%) are observed with similar fluctuations in O+ density (maximum up to 60%) near to the epicenters. Fluctuations in the electron temperature were also observed. Electrostatic turbulence was observed in the spectrogram of electric component up to 2 kHz at the same time. As this data was recorded during burst mode it was possible to perform a detailed analysis. We have analyzed the electric field for the same event in ULF/ELF range shown in Figure 21.3. Rapid variations are found in ULF/ELF starting around 15:27:50 h UT (1–60 Hz). Enhancement in the magnitude however is observed around 40–50 Hz. The magnitude of signal intensity on logarithmic scale rises to as high as 3.50 (µV2 m−2 Hz−1 ) around 15:29:00 h UT just above the epicenter. To confirm that the perturbations are associated with the corresponding earthquakes, we have taken the magnetic index Kp for that day (Figure 21.4) and found that the corresponding 3-h Kp values were one suggesting quiet geomagnetic activity. On March 26, 2005 we have another orbit of DEMETER above Sumatra (Figure 21.5). Data recorded along this orbit is shown in Figure 21.6. Electron density increase (∼14% from the unperturbed state) was accompanied with increase of main ion constituent O+ (∼25% from the unperturbed state) near to the epicenters. The three hourly Kp indices shown in Figure 21.7 indicate low and moderate geomagnetic activity.

240 A.K. Gwal et al. 23-03-2005

2.5 2

Kp

1.5 1


0.5 0

0 to 3

3 to 6

6 to 9

9 to 12 12 to 15 15 to 18 18 to 21 21 to 24 Time (hrs) UT

Figure 21.4. Three hourly Kp values for March 23, 2005. Demeter March 26, 2005 90

6

92

94

96

98

100

2

2

6

Figure 21.5. Track of DEMETER orbit on March 26, 2005 when the satellite was close to the Sumatra region.

For comparison, data related to another earthquake occurring in the same area but with a lower magnitude has been studied. These earthquakes occurred in the Indonesian region with maximum magnitude equal to 5.5 at 1.32◦ N, 97.20◦ E. Table 21.2 gives the position and time of these earthquakes. Figure 21.8 shows the ground track of DEMETER satellite on July 6, 2005. Figure 21.9 shows the spectrogram of electric field component up to 400 Hz. We have analyzed the electric field data (shown in Figure 21.10) for the lower frequency band comprising ULF/ELF range as this data was recorded during burst mode. Significant perturbations were observed in the ELF range

241



Figure 21.6.

Data recorded by DEMETER along the orbit shown in Figure 21.5. The top panel shows the electron density, the middle panel shows the ion density and the bottom panel gives the earthquakes “seen” by the satellite. At the bottom, UT, LT, geographic latitude and longitude values are indicated.

(140–220 Hz). It is evident from the spectrogram that perturbations were exhibited at around 15:25:52 h UT and lasted for a few seconds. The magnitude on logarithmic scale was observed to be around 2.2 (µV2 m−2 Hz−1 ). We also find the corresponding day was a geomagnetically quiet day as the 3-h Kp values were less than equal to 1 (shown in Figure 21.11).


Kp

242 A.K. Gwal et al. 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

23-03-2005

0 to 3

3 to 6

6 to 9

9 to 12 12 to 15 15 to18 18 to 21 21 to 24 Time (hrs) UT

Figure 21.7. Three hourly Kp values for March 26, 2005.

Table 21.2. Time, locations, depth and region of the earthquakes that occurred in the Indonesian region (from the web server http://www.iris.edu/seismon). Date July 8, 2005 July 11, 2005 July 11, 2005

Epicenter

Time (UT)

Magnitude

Depth (km)

Region

1.23◦ N, 97.20◦ E 1.32◦ N, 97.20◦ E 2.64◦ N, 94.33◦ E

21:28:23 14:36:10 01:07:55

5.0 5.5 5.0

30 23 30

Indonesia Indonesia Indonesia

Demeter July 6, 2005 96

100

104

4

0

4

Figure 21.8. Track of DEMETER orbit on July 6, 2005 when the satellite was above the Indonesian region. Stars indicate the epicenters of the earthquakes.

243



Figure 21.9. The top panel gives the spectrogram of an electric component between 0 and 400 Hz and the bottom panel gives the earthquake information. At the bottom, UT, LT, geographic latitude and longitude values are indicated.

Figure 21.10.

Spectrogram of ULF/ELF electric waveform above the latitude in which earthquake occurred obtained using Level 1 burst mode data for the orbit shown in Figure 21.8.

1.2

Kp values for 06-07-2005

1 0.8 Kp Unit


244 A.K. Gwal et al.

0.6 0.4 0.2 0 0 to 3

3 to 6

6 to 9

9 to 12 12 to 15 15 to 18 18 to 21 21 to 24 Time ( UT)

Figure 21.11. Three hourly Kp values for July 6, 2005.



21.4

245

DISCUSSION

This chapter presents interesting cases in which ionospheric perturbations were observed before earthquake. These perturbations were recorded by the ISL Langmuir Probe experiment, IAP the Thermal Plasma Analyzer experiment and ICE the electric field experiment onboard the DEMETER satellite. From the insitu measurements of electron and ion density and ULF/ELF electric field changes, the variation of these parameters have been illustrated before earthquake. For the Sumatra earthquakes increase in electron concentration was observed close to the epicenter. Gokhberg et al. (1995) had demonstrated the penetration of seismic electric field into the ionosphere. This electric field leads to the formation of irregularities in the ionosphere and thereby affecting the electron density distribution in the ionosphere (Pulinets, 1998a). The electron concentration variations were found to be accompanied with variations in the main ion constituent O+ and fluctuations of the electron temperature. This is in agreement with previous events reported by Pulinets (1998b). Even small changes of ionospheric electric field can substantially modify the concentration of O+ at heights of the F2 layer maximum before earthquakes (Pulinets and Boyarchuk, 2004). They have reported several examples in which modification of the O+ ion was found above the region of the anticipated earthquake. ULF/ELF emissions are typically observed as bursts above the earthquake epicenters. These emissions may start several days before the earthquake (Pulinets and Boyarchuk, 2004). In both cases studied these emissions were observed several days before the event. 21.5

CONCLUSION

In this chapter we have shown interesting examples of variation of plasma parameters recorded when the satellite was flying over the region of anticipated earthquakes. The electric field perturbations associated with seismic events in the ULF/ELF range have also been presented. These examples have been automatically selected by a tool of the DEMETER mission center (Lagoutte et al., 2006) which sorts out satellite orbits at a selected distance to epicenters of earthquakes with magnitude larger than 6. One of the most intriguing and promising results of local plasma parameter measurements is the change in electron and ion composition before earthquakes over the earthquake preparation zone. In all cases presented in this chapter the variation of these parameters were observed close to the location of epicenters. More importantly these variations observed are of precursor type. The geophysical conditions during our period of observation have been also considered as these ionospheric parameters also show variation with solar and geomagnetic activity of the Earth. They were relatively quiet. ACKNOWLEDGEMENT The authors would like to thank J.J. Berthelier and J.P. Lebreton for the use of the DEMETER data, and to acknowledge the Indo French Centre for the Promotion of Advanced Research (IFCPAR), New Delhi for providing financial support for this research. The Kp values were provided by the International Service of Geomagnetic Indices from the web server http://www.cetp.ipsl.fr/∼isgi/. REFERENCES Afonin, V.V., Molchanov, O.A., Kodama, T., Hayakawa, M., and Akentieva, O.A. (1999). Statistical study of ionosphere plasma response seismic activity: search for reliable result from satellite observations. In: M. HayaKawa (ed.), Atmospheric and Ionospheric Electromagnetic Phenomena Associated with Earthquakes, Terra Scientific Publishing Company, Tokyo, pp. 597–618.


246 A.K. Gwal et al. Afonin, V.V., Akentieva, O.A., Molchanov O.A., and Hayakawa, M. (2000). Statistical Study of equatorial anomaly from high apogee satellite APEX and low apogee satellite COSMOS-900, International Workshop on Seismo-Electromagnetics, Programme and Abstracts, NASDA, 19–22 Sep 2000. Berthelier, J.J., Godefroy, M., Leblanc, F., Malingre, M., Menvielle, M., Lagoutte, D., Brochot, J.Y., Colin, F., Elie, F., Legendre, C., Zamora, P., Benoist, D., Chapuis, Y., and Artru, J., (2006a). ICE, the electric field experiment on DEMETER, Planet Space Science, 54, 456–471. Berthelier, J.J., Godefroy, M., Leblanc, F., Seran, E., Peschard, D., Gilbert, P., and Artru, J., (2006b). IAP, the thermal plasma analyzer on DEMETER, Planetary Space Science, 54, 487–501. Boskova, J., Smilauer, J., Jiricek, F., and Triska, P. (1993). Is the ion composition of outer ionosphere related to seismic activity. J. Atmos. Terr. phys., 55(13), 1689–1695. Boskova, J., Smilauer, J., Triska, P., and Kudela, K. (1994). Anomalous behaviour of plasma parameters as observed by the intercosmos 24 satellite prior to the iranian earthquake of 20 June, 1990. Studia Geoph. Geod., 38, 213. Gokhberg, M.B., Morgounov, V.A., and Pokhotelov, O.A. (1995). Earthquake Prediction, SeismoElectromagnetic Phenomena. Gordon and Breach, Russia. Hayakawa, M. (1997). Electromagnetic precursors of earthquakes: review of recent activities. Rev. Radio Science, 1993–1995, Oxford University Press, 807–818. Lagoutte, D., Brochot, J.Y., de Carvalho, D., Elie, F., Harivelo, F., Hobara, Y., Madrias, L., Parrot, M., Pincon, J.L., Berthelier, J.J., Peschard, D., Seran, E., Gangloff, M., Sauvaud, J.A., Lebreton, J.P., Stverak, S., Travnicek, P., Grygorczuk, J., Slominski, J., Wronowski, R., Barbier, S., Bernard, P., Gaboriaud, A., and Wallut, J.M., (2006). The DEMETER science mission centre, Planetary Space Science, 54, 428–440. Lebreton, J.P., Stverak, S., Travnicek, P., Maksimovic, M., Klinge, D., Merikallio, S., Lagoutte, D., Poirer, B., Kozacek, Z., and Salaquarda, M. (2006). The ISL Langmuir Probe experiment and its data processing onboard DEMETER: scientific objectives, description and first results, Planetary Space Science, 54, 472–486. Liperovsky, V.A., Pokhotelov, O.A., Liperovskaya, E.V., Parrot, M., Meister, C.V., and Alimov, O.A. (2000). Modification of sporadic E-layers caused by seismic activity. Surv Geophys, 21, 449–486. Molchanov, O.A., Mazhaeva, O.A., Goliavin, A.N., and Hayakawa, M. (1993). Observation by the Intercosmos-24 satellite of ELF/VLF electromagnetic emissions associated with earthquakes. Ann. Geophys., 11, 431–440. Parrot, M. (1994). Statistical study of ELF/VLF emissions recorded by a low altitude satellite during seismic events. J. Geophy. Res., 99(23), 339–347. Parrot, M. (1999). Statistical studies with satellite observations of seismogenic effects. In: M. Hayakawa (ed.), Atmospheric and Ionospheric Phenomena Associated with Earthquakes, TERRAPUB, Tokyo, 685–695. Parrot, M., Achache, J., Berthelier, J.J., Blanc, E., Deschamps, A., Lefeuvre, F., Menvielle, M., Planet, J.L., Tarits, P., and Villain, J.P. (1993). High-frequency seismo-electromagnetic effects. Phys. Earth Planet. Interiors, 77, 65–83. Parrot, M., Beonoist, D., Berthelier, J.J., Blecki, J., Chapuis, Y., Colin, F, Elie, F., Fergeau, P., Lagoutte, D., Lefeuvre, F., Legendre, C., Leveque, M., Pincon, J.L., Poirier, B., Seran, H.C., and Zamora, P. (2006). The magnetic field experiment IMSC and its data processing onboard DEMETER: scientific objectives, description and first results, Planetary Space Science, 54, 441–455. Pulinets, S.A. (1998a). Strong earthquakes prediction possibility with the help of topside sounding from satellites. Adv. Space Res., 21(3), 455–458 Pulinets, S.A. (1998b). Seismic Activity as a Source of the Ionospheric Variability. Adv. Space Res., 22(6), 903–906. Pulinets, S.A. and Legen’ka, A.D. (2003). Spatial-temporal characteristics of large scale disturbances of electron density observed in the ionospheric F-region before strong earthquakes. Cosmic Res., 41(3), 221–229. Pulinets, S.A. and Boyarchuk, K.A. (2004). Ionospheric Precursors of Earthquakes, Springer Verlag Publication, Heidelberg. Pulinets, S.A., Legen’ka, A.D., Gaivoronskaya, T.V., and Dupuev, V.Kh. (2003). Main phenomenological features of ionospheric precursors of strong earthquakes. J. Atmos. Sol. Terr. Phys., 63, 1337–1347. Sauvaud, J.A., Moreau, T., Maggiolo, R., Treilhou, J.P., Jacquey, C., Cros, A., Coutelier, J., Rouzaud, J., Penou, E., Gangloff, M., (2006). High energy electron detection onboard DEMETER: the IDP spectrometer, description and first results on the inner belt, Planetary Space Science, 54, 502–511.

CHAPTER 22


Web-Enabled and Real-Time Reporting: Cellular Based Instrumentation for Coastal Sea Level and Surge Monitoring A. Joseph and R.G. Prabhudesai National Institute of Oceanography, Dona Paula, Goa, India

22.1

INTRODUCTION

The 26 December 2004 monster tsunami that struck many South Asian countries, and the severe destruction and devastation wrought by that, have drawn attention to the urgent need for a versatile disaster warning system for the Indian Ocean rim countries. Presence of a network of sealevel gauges spread all along the coasts, with capability for providing real-time information on sea-level elevation and its trend, would provide the requisite data to the disaster management agencies for dissemination of disaster alert warnings to the coastal communities. Immediate alert and related information bulletins disseminated to appropriate local and central disaster management cells and the people by public communication channels such as commercial radio, television, and marine radio system available in almost all these countries, would save many lives. Unfortunately, such a network was not in place during the 26 December 2004 tsunami disaster. This lacuna, together with frequent storms that hit many coastal locations, suggests the urgent need for immediate deployment of a network of real-time integrated sea level and surface meteorological data communication systems (Joseph and Prabhudesai, 2005) for the benefit of the coastal communities, beach tourism agencies, and the local administrators. Given the popularity of Internet on a global scale, providing such state-of-the-art accessibility to sea-level data would mean that the current coastal sea-level scenario can be viewed in real-time from almost any part of the world. If Internet access to the sea-level web site is made available to television channels, then real-time visualization of the coastal sea level (e.g., during anomalous and disastrous state of the coastal seas) and its trend from the previous day to the present instant can be examined by everyone including the common people who are known to make good use of television when anything particularly important happens in any part of the world. Providing Internet accessibility to the sea-level gauge web site at other media centres such as radio stations and the press would also serve an equally important role in the quick dissemination of the current anomalous sealevel scenario to the navigators, and the travelling communities. Such a network would provide useful information also to the mariners sailing in the coastal waters. Moreover, the information obtained would be of great value to the scientific community. 22.2

EXISTING SYSTEMS

Various types of sea-level gauges have been developed over the years (Joseph, 1999). These include tide staff, float-driven gauge, pressure gauge, acoustic gauges, and most recently radar gauge. 247


248 A. Joseph and R.G. Prabhudesai It has been feasible to deploy seafloor-mounted tsunami detection sensors in the Pacific Ocean rim regions with the support of instrumented deepwater moored buoys in the vicinity of seafloor spreading centres. The primary sensors are seismic probes imbedded in the seafloor at varying depths (Hoffman, 1997). High precision pressure sensors that are located on the seafloor are also providing important data on the propagation of tsunamis in deep water (Filloux, 1982; Baba et al., 2004). In moored buoy systems, acoustic modems attached to the moorings transmit eventdetection data (i.e., seismic and bottom pressure data) to a module attached to a surface buoy. This surface module, in turn, relays the data to several land-based disaster warning centres via satellite transmission network. The tsunami buoy systems are aimed at quickly confirming the existence of potentially destructive tsunamis and reducing the incidence of false alarms. It is expected that a series of instrumented deep ocean buoys might provide the much needed and reliable early warning. Where the source motion is known, computer simulations have been found to agree quite accurately with observations (Van Dorn, 1982).

22.3

ENHANCEMENT OF EXISTING COASTAL SYSTEMS FOR TSUNAMI AND STORM-SURGE DETECTION

Tsunami is a special type of long wave (solitary wave) that is generated in the sea following a large scale impulsive disturbance (e.g., earthquake). In contrast, storm surge is a localized disturbance of sea level resulting from the action of a cyclone. Tsunamis and storm surges are the two natural calamities that have hit many Indian Ocean rim countries; and taken heavy toll of lives; and inflicted colossal damage to properties. Underwater earthquakes (seaquakes), which are the most potent cause for tsunamis, have been monitored successfully in limited areas of certain countries (e.g., California, south west Iceland) based on noticeable increase in the background seismic activities (Hoffman, 1997). However, with the present scientific knowledge and technology those are available even with the most advanced nations, reliability of seaquake prediction for warning purposes is considered to be rather poor. Although offshore instrumented buoys are important devices and can be used for detection of both tsunami and storm-surge events far away from land, they are expensive and might pose logistical challenges. Thus, a network of coastal-based systems that provides real-time or nearreal-time sea level and surface meteorological information can be implemented as an alternate system that complements the deep ocean moored system. A suitable network for real-time monitoring of storm surge and running of operational stormsurge models for predictive purposes must consist of real-time transmitting sea level and surface meteorological monitoring systems. A great advantage of storm-surge model is its usefulness in predicting the anticipated flooding at selected locations. The storm-surge model that is established on a geographical information system (GIS) platform would allow a realistic assessment of the impact of elevated/depressed sea levels on the regions covered by the storm-surge model. The prediction will enable the local administrators/planners to issue periodic warning of maximum likely flooding at a given location in a given coastal/estuarine region for a specific meteorological event. Subsequent to the 26 December 2004 tsunami episode, there appears to be a consensus in the Indian Ocean rim countries on the urgent need for establishment of a disaster warning system. A network capable of real-time reporting of integrated sea level and surface meteorological events from coastal sea-level gauges and weather stations is an important ingredient to complement the deep ocean systems that are currently contemplated for providing timely alerts. Such a network would provide a sufficiently large real-time database for running predictive models for stormsurge forecasting if ancillary database on the bathymetry and topography of the region of interest are available. The real-time database so obtained can also be used for real-time validation of the storm-surge model. Based on the above discussions, it would be desirable to go for development

Web-enabled and real-time reporting: instrumentation and monitoring

249

and deployment of a network of web-enabled wireless-transmitting real-time reporting integrated coastal sea level and surface meteorological monitoring systems incorporating the state-of-the-art wireless technology.


22.4

DATA COMMUNICATION OPTIONS

Storm surge or tsunami warning systems would require the data to be reported to the authorities in a very short time. The Intergovernmental Oceanographic Commission (IOC) of UNESCO has recommended that for the Indian Ocean Tsunami warning system, data have to be reported within 5 min of being recorded at the gauge and would need to be made available on the Global Telecommunications System (GTS). There are various communication technologies that could be utilized for real-time reporting of sea-level data. A variety of real-time communication options are being used at present, and newer options are being examined. These include wired telephone connection, VHF/UHF transceivers, satellite transmit terminals, and cellular connectivity. In the past, the method of data communication depended largely on the distance over which the data had to be transmitted. Thus, for short links (e.g., harbour operations), a VHF/UHF radio link was often convenient. However, communication via VHF/UHF transceivers is limited by line-of-sight distance between transceivers and normally offer only point-to-point data transfer. Ideally, nationwide and even global scale links are necessary for storm surge/tsunami warning communication network systems. For countrywide links, Subscriber Trunk Dialling (STD) or dedicated telephone lines of the Public Switched Telephone Network (PSTN) have been successfully used (e.g., tide gauge network of Proudman Oceanographic Laboratory (POL), UK). However, wired telephone connections can be severely susceptible to loss of connectivity during natural disasters such as storm surges, primarily because of telephone line breakage under the force of storm-winds (e.g., uprooted trees and broken branches). Satellite communication via platform transmit terminals (PTT) has wider coverage and, therefore, allows data reception from offshore platforms. For the last decade or more, sea-level installations in a few countries have used satellite systems (ARGOS, GOES, ORBCOMM, IRIDIUM, METEOSAT, GMS, and INMARSAT) for data reporting. Nevertheless, data transfer speeds of many satellite-based communication systems are limited to 9600 baud or less. Many satellites (e.g., GOES, INSAT) permit data transfer only at predefined time-slots, thereby inhibiting continuous data access. To ensure that data transmission by the sea-level gauges takes place at these precise time-slots, the gauge electronics should have its clock derived from a common “time source”. This requirement has necessitated incorporation of GPS receivers with each data collection platform (DCP). A network of geostationary satellites comprising GOES (USA), METEOSAT (Europe), and GMS (Japan) offer overlapping longitudinal coverage and appreciable latitude coverage (75◦ ). However, the size of data that can be transmitted to a satellite during the specified time-slot is limited to 649 bytes. Another option is a network of satellite mobile telecommunications known as IRIDIUM, which is designed to enable data reporting regardless of the user’s location on land or at sea. Subscribers can use their Iridium modem to communicate with any other telephone anywhere in the world. The recently introduced Regional Broadband Global Area Network (RBGAN) by INMARSAT provides reliable and high-speed data communication and data file transfers at broadband speed. This network is expected to provide full world coverage in the near future. RBGAN is based on Internet Protocol (IP) and GPRS technology, which offers reliable and cost-effective access to the Internet. For the INMARSAT, there is a permanent connection with a static IP address, just like broadband but with a maximum speed of 144 kbit/s. Using the new INMARSAT RBGAN data terminal, it is thus possible to share a 144 kbit/s broadband connection, achieving more than double the transfer speed of current terrestrial GPRS mobile

250 A. Joseph and R.G. Prabhudesai networks. Because the service is based on IP packet technology, users only pay for the amount of data they send and receive, and not for the amount of time spent online. This enables them to stay “always connected” to the Internet. Perhaps, the biggest advantage of RBGAN over fixed-line broadband is its independence from local telephone infrastructure. This would mean that the communication network can be expected to continue operating during extreme weather conditions and the resulting storm-surge events.


22.4.1

Cellular modem

While satellite communication is relatively expensive, proliferation of wirelesses networking infrastructure and ubiquity of cellular phones have together made cellular communication affordable. Low initial and recurring costs are an important advantage of cellular data communication. Various services exist for data communication: for example, Short Message Service (SMS), Data Call, and General Packet Radio Service (GPRS). SMS is a common method of sending text messages of up to 140 bytes between cellular devices. This mode of transmission is probably the easiest to implement when the data size is small. However, the recurring cost can be substantial if data needs to be reported frequently. Further, keeping track of lost SMS can easily override its simplicity. Data Call (similar in operation to the conventional STD call) is another alternative, which can also turn out to be expensive if data has to be frequently reported. Both SMS and Data Call services would require modems on the remote reporting device as well as on the receiving end. This adds to the hardware cost as well as software overheads on the receiving end to check the data integrity for transmission errors. The main benefit of cellular connectivity with GPRS technology is that it utilizes the radio resources only when there is data to send. In addition, GPRS offers improved quality of data services as measured in terms of reliability, response time, and features that are supported. Another advantage of GPRS over other data communication services is that it provides an “always on” communication channel without incurring time-based costs. That is, there is no difference in costs whether data is collected once a minute or once a day. Further, GPRS data transmission speeds are of the order of 3 to 4 times that of the traditional cellular data connection. The GPRS allows data rates of 115 k bit/s. Also, GPRS enables a constant TCP/IP connection with the Internet so that data can be easily uploaded. Since data can be posted on the Internet server, there is neither a need for a modem on the receiving side nor the requirement to have special software at the server-side to collect data from the remote site. 22.5

INITIATIVES AFTER THE INDIAN OCEAN TSUNAMI OF 26 DECEMBER 2004

At present, the Pacific Tsunami Warning Centre (PTWC) provides sea level and related information from the University of Hawaii Sea Level Centre for basin-wide tsunami warning to the Pacific Ocean rim countries. Prior to the 26 December 2004 Indian Ocean Tsunami, networks of daily or weekly reporting sea-level gauges have been in existence only in a very few countries. For example, UK had a network which reported sea-level data via land phone on interrogation from the Tide Gauge Directorate at POL. Subsequently, the UK network has been expanded to provide capability for real-time reporting and Internet-accessibility to sea-level data. POL has developed instrumentation that can take the output from a range of sensors, including radar and pressure types. The data are collected by a small Linux-embedded processor and sent back to base by e-mail or by Secure Copy Protocol (SCP). Broadband enabled test sites using a radar sensor connected to an embedded Linux system have been installed at Liverpool and Holyhead in the UK. One-min data values are available every 5 min in the form of an e-mail message. The resulting data are displayed on the NTSLF web pages. Chile established a network, which



251

transmits sea-level data via satellite (Fierro, 2005). Before December 2004, real-time reporting and Internet-accessible sea-level gauges were operational in USA, UK, and Hong Kong. The devastations brought by the 26 December 2004 Indian Ocean Tsunami proved to be an eye-opener internationally. Consequently, IOC of UNESCO established a Technical Committee, with 11 members covering India (Antony Joseph), Kenya (Charles Magori), South Africa (Ruth Farre), Australia (Bill Mitchell), Spain (Begona Perez and Lopez Maldonaldo), Norway (Daniel Hareide), France (Guy Woppelman), UK (Peter Foden), Chile (Juan Fierro), and USA (Bernie Kilonsky) to provide advice and recommendations concerning technical aspects of sea-level observations such as station configuration, data transmission, quality control and data processing, calibration and maintenance of sensors and stations, testing and evaluation of equipment, etc. Many of the Indian Ocean rim countries have plans to put in place networks of instrumented platforms for warning purposes in future. For example, the Government of India has taken initiative for an early warning system (Gupta, 2005) and decided to establish a network by September 2007, which would report sea-level data using India’s own satellite INSAT. In the meantime, the National Institute of Oceanography (NIO) of India conceived a substantially costeffective system for monitoring of sea level and other surface meteorological events (Joseph and Prabhudesai, 2005), and quickly developed and deployed a cellular-based real-time reporting and Internet-accessible coastal sea-level gauge. This system is functional at Mandovi estuary, Goa (India) since 24 September 2005 (Prabhudesai et al., 2006). This system would complement the national efforts towards the development of early warning systems for disaster management. The real-time reporting system developed at NIO is simple and cost-effective, and it can also be deployed in dams, reservoirs, and at any other water sources for water resource management. Deployment of this system would help in equitable sharing and distribution of the scarce water resources with much transparency, and would permit avoidance of many inter-state and international water related disputes which plague many states and countries at present. 22.6

SYSTEM DEVELOPED AT NIO, INDIA

Based on extensive experience in the use of pressure sensors for sea-level measurements in India (Joseph et al., 2006) andAfrica (Joseph et al., 2006), NIO in India quickly designed and developed a sea-level gauge incorporating temperature-compensated piezo-resistive semiconductor pressure transducer from Honeywell, having adequate features and performance (Vijay Kumar et al., 2005). The data is normally sampled at 2 Hz and can be averaged over duration of 15 s to 15-min interval in conformity with the revised requirements of Global Sea Level Observing System (GLOSS) to detect tsunami and storm-surge events. In the past, data recording at intervals less than 15 min was difficult in practice because of memory capacity limitations. However, this limitation has been overcome in the present design by incorporating multimedia cards, with storage capacity ranging from 128 to 1000 megabytes. Additionally, real-time/near-real-time data access capability is also implemented for effective operational applications during anomalous sea-level conditions such as those occurring during storm surges and tsunami episodes. The sea-unit of the gauge is mounted within a cylindrical protective housing, which in turn is rigidly held within the vertical legs and the interconnecting triangular collar of the mechanical structure used for mounting the entire gauge. Figure 22.1(a) shows the top portion of the gauge’s mounting structure, where battery, electronics, solar panel, and cellular modem are mounted. The pressure sensor and the logger are continuously powered on, and their electrical current consumption is 30 and 15 mA respectively. The cellular modem consumes 15 and 250 mA during standby and data transmission modes, respectively. Figure 22.1(b) illustrates the installation of the gauge at Verem Jetty in Mandovi estuary, Goa, India.


252 A. Joseph and R.G. Prabhudesai

(a)

(b)

Figure 22.1.

22.6.1

(a) Top portion of the gauge’s mounting structure, where battery, electronics, solar panel, and cellular modem are fixed (after Prabhudesai et al., 2006). and (b) Illustration of NIO sealevel gauge installed at Verem Jetty, Mandovi estuary, Goa, India (after Prabhudesai et al., 2006).

Sea-level measurement

The methodology employed in the NIO sea-level gauge is to detect the hydrostatic pressure, and to estimate the water column height over the pressure transducer from knowledge of the effective depth-mean water density.


253

An absolute pressure transducer senses the total pressure (i.e., atmospheric pressure + pressure exerted by the water column above the transducer). The total pressure, P(total) , over the pressure inlet, at depth d below the water surface is given by the relationship: P(total) = Pa + Pw

(22.1)

where Pa is the atmospheric pressure and Pw is the pressure exerted by the overlying water column on the transducer. The following well-known relation enables estimation of sea-level elevation:


Pw = (ρ × g × d)

(22.2)

In this relation, ρ is the effective depth-mean density of the overlying column of water, g is the acceleration due to earth’s gravity, and d is the depth of the pressure transducer below the sea surface. Thus, the value of d is estimated. In general, because of the complexities associated with effective density of suspended-sediment-laden shallow water bodies (Joseph et al., 1999, 2004), it is advisable to use alternate sensing methods in heavily suspended-sediment-laden water bodies (e.g., Hooghly estuary in India).

22.6.2

Cellular-based system

In India, practically all the populated areas are networked to cellular-transmitting stations and, therefore, the required dataset can be made available online for real-time or near real-time applications such as warning and predictive model-running applications. The monitored information and forecast can then be disseminated to the coastal communities and the general public through a variety of electronic media. Figure 22.2 illustrates implementation of cellular-based real-time coastal sea-level data reporting utilizing GPRS technology. The GPRS modem with built-in TCP/IP stack incorporated in the present design frees the host controller, which is responsible for acquisition of data from sealevel gauge, from communication overload. These modems need only a few simple commands to upload data on a remote File Transfer Protocol (FTP) server. Data communication is always initiated by the sea-level gauge. After communication link is established, a bidirectional data transfer is possible between Internet server and the sea-level gauge. This is because GPRS Gateway Support Node (GGSN) uses Dynamic Host Configuration Protocol (DHCP) to assign private IP addresses to cellular devices. This IP address is invisible to the Internet network. Although GPRS is termed as an “always on” network, if there is no data exchanged beyond predefined timeout periods, the connection is dropped and a new IP address is assigned to the cellular modem. Because of this scheme, the IP address of the cellular modem can change frequently. One obvious benefit of such a connection mechanism from the security point of view is that risk of attack from hackers and third party is reduced. The software consists of two main components, namely; (i) embedded system software for data acquisition and communication with Internet server, and (ii) web server-based user-interface to visualize the received sea-level data. In the present application, 5-min averaged sensor output data is logged by the embedded system at 5-min interval. Subsequently, all the data logged from the previous day to the current time is uploaded to the Internet server that is located at NIO, Goa, India. The data received at the Internet server is stored in its back-end database, and simultaneously presented in graphical format, together with the predicted fair-weather sea-level and the residual. The residual, which is the measured sea level minus predicted fair-weather sea level, provides a clear indication and a quantitative estimate of the anomalous behaviour of sealevel oscillation. The driving force for such anomalous behaviour could be atmospheric forcing (storm) or geophysical (tsunami).


254 A. Joseph and R.G. Prabhudesai

Figure 22.2.

Schematic diagram illustrating implementation of realtime coastal sea-level data reception utilizing GPRS technology (after Prabhudesai et al., 2006).

Figure 22.3 shows display of predicted fair-weather sea-level, observed real-time sea levels, and residuals from Verem jetty (Mandovi estuary), Goa, India. The scale of real-time display is dynamically adjusted based on the maximum elevation observed. 22.6.3

Communication performance evaluation

In order to examine the performance of data upload from the sea-level gauge to the Internet server, 100 kilobytes of test data were uploaded continuously for 24 h using standard FTP. Figure 22.4 shows the distribution of time taken (throughput) for successive FTP uploads during the above experiment. The minimum and maximum transfer times were in the range 1.29–7.1 min for uplink (average time was 2.06 min). Data was transferred between sea-level gauge and the FTP server using Airtel GPRS service. On an average, 97.47% of data transfer attempts was found to be successful. 22.7

CONCLUSIONS

Because of the international attention bestowed on the December 26 episode, IOC of UNESCO established a Technical Committee to discuss and provide advice on various technical aspects of monitoring systems. In this effort, the already available expertise within the GLOSS community has been considered to be an asset. An obvious advantage that accompanies real-time or nearreal-time data reporting is the possibility to identify instrumental malfunctions, if any, and to

Figure 22.3.

255

Display of predicted fair-weather sea-level, observed real-time sea levels, and residuals from Verem jetty (Mandovi estuary), Goa, India (after Prabhudesai et al., 2006).

10 8 Upload time (mins)



6 4 2 0

0

4

8

12

16

20

24

Time (hours)

Figure 22.4.

FTP up-load time during a period of 24 h for a 100 kb test data (after Prabhudesai et al., 2006).


256 A. Joseph and R.G. Prabhudesai initiate remedial measures more rapidly. This permits remote diagnostics and might also provide the ability to re-program the system remotely. The general notion among the experts is that in addition to the conventional manner of averaging and sampling sequence, high-frequency motions such as waves and swells also need to be measured together with pertinent meteorological parameters such as barometric pressure. Such a scheme would cater to the optimal utilization of the future systems for operational applications in the events of both tsunamis and storm surges. These views are consistent with those espoused by Joseph and Prabhudesai (2005) in the Indian Ocean context. With the current advancement in communication technologies, various options are now available for real-time or near-real-time reporting of data for various operational and predictive applications. Technologies of data reporting via satellites have undergone a sea change recently in terms of frequency of reportage, data size, recurring costs, and so forth. Broadband technology has been identified to be one that can be optimally used for real-time reporting of data because of its many inherent advantages such as continuous two-way connection allowing high-speed data file transfer and near-real-time data reporting. It has been shown that an alternate and complementary cost-effective methodology for realtime reporting of data is cellular-based GPRS technology, which has been recently implemented by the NIO in India for real-time reporting of coastal sea-level data (Prabhudesai et al., 2006). In this system, by using the existing cellular phone network, continuous real-time updates of coastal sea-level elevations are realized on a web server. While satellite communication is expensive, wirelesses networking infrastructure and ubiquity of cellular phones have together made cellular communication affordable. Low initial and recurring costs are an important advantage of GPRS cellular communication. This methodology will soon be extended for real-time reporting of integrated coastal sea level and surface meteorological data as well to cater to effective monitoring and evaluation of trends of storm surge, which plague many nations in the Indian Ocean rim region. This development provides an excellent platform for real-time monitoring of coastal sea level and surface meteorological data; thus providing the requisite input for efficient implementation of any alert and warning mechanism in the event of oceanogenic hazards such as storm surge and tsunami. Considering the popularity of Internet on a global scale, providing such state-of-the-art accessibility to sea-level gauges would mean that the present coastal sea-level scenario can be viewed in real-time by anyone from any part of the world. Providing Internet accessibility to the sealevel gauge web site at other media centres such as television channels, radio stations, and the print media would serve an important role in the quick dissemination of the current anomalous sea-level scenario to the coastal communities, navigators, and the general public. Moreover, the information obtained would be of great value to the national and international scientific community. At the backdrop of the disastrous 26 December 2004 tsunami that caught us unaware, deployment and maintenance of a network of cost-effective monitoring system is an important step forward for the entire Indian Ocean rim regions. REFERENCES Baba, T., Hirata, K., and Kaneda, Y. (2004). Tsunami magnitudes determined from ocean-bottom pressure gauge data around Japan. Geophys. Res. Lett., 31, L08303. Fierro, J. (2005). Chilean Sea Level Network. IOC Manual on Sea Level Measurement and Interpretation, 4: An Update to 2005, pp. 111–114. Filloux, J.H. (1982). Tsunami recorded on the open ocean floor. Geophys. Res. Lett., 9, 25–28. Gupta, H. (2005). Mega-tsunami of 26 December 2004: Indian initiative for early warning system and mitigation of oceanogenic hazards. Episodes, 28, 1–4. Hoffman, C. (1997). Checking on seaquake. Sea Technol., 38(8), 74.



257

Joseph, A. (1999). Modern techniques of sea level measurement. Encyclopedia of Microcomputers, Vol. 23. Marcel Dekker, Inc., New York, pp. 319–344. Joseph, A., Desa, E., Smith, D., Peshwe, V.B., Vijaykumar, and Desa, J.A.E. (1999). Evaluation of pressure transducers under turbid natural waters. J. Atmos. and Oceanic Technol., 16(8), 1150–1155. Joseph, A., Desa, E., Vijaykumar, Desa, E.S., Prabhudesai, R.G., and Prabhudesai, S. (2004). Pressure gauge experiments in India. In: S. Holgate and T. Aarup (eds.), Workshop Report No. 193, Intergovernmental Oceanographic Commission of UNESCO, pp. 22–37. Joseph, A. and Prabhudesai, R.G. (2005). Need of a disaster alert system for India through a network of real time monitoring of sea level and other meteorological events. Curr. Sci., 89, 864–869. Joseph, A., Mehra, P., Joseph, O., and Nkebi, E.K. (2006). Pressure Gauge Based GLOSS Sea Level Station at Takoradi Harbour (Ghana, West Africa) – Experiences over a Year. IOC Manual on Sea Level Measurement and Interpretation, 4: An Update to 2005, pp. 108–110. Joseph, A., Odametey, J. T., Nkebi, E. K., Pereira, A., Prabhudesai, R. G., Mehra, P., Rabinovich, A. B., Vijaykumar, Prabhudesai, S., and Woodworth, P. L. (2006). The 26 December 2004 Sumatra Tsunami Recorded on the Coast of West Africa, African J. Mar. Sci (under revision). Prabhudesai, R.G., Joseph, A., Agarvadekar, Y., Dabholkar, N., Mehra, P., Gouveia, A., Tengali, S., Vijaykumar, and Parab, A. (2006). Development and implementation of cellular-based real-time reporting and internet accessible coastal sea level gauge – A vital tool for monitoring storm Surge and tsunami. Curr. Sci., 90(10), 1413–1418. Van Dorn, W.G. (1982). Tsunami. McGraw-Hill Encyclopedia of Science and Technology, Vol. 14, pp. 140–142. Vijay Kumar, Joseph, A., Prabhudesai, R.G., Prabhudesai, S., Nagvekar, S., and Damodaran V. (2005). Performance evaluation of honeywell silicon piezoresistive pressure transducers for oceanographic and limnological measurements. J. Atmos. Oceanic Technol., 22(12), 1933–1939.


CHAPTER 23

Methodologies for Tsunami Detection


T.S. Murty Department of Civil Engineering, University of Ottawa, Ottawa, Canada N. Nirupama Atkinson School of Administrative Studies, York University, Toronto, Canada A.D. Rao Centre for Atmospheric Sciences, Indian Institute of Technology, New Delhi, India I. Nistor Department of Civil Engineering, University of Ottawa, Canada

23.1

INTRODUCTION

Traditionally, tsunami detection has completely depended on a coastal tide gauge network. In recent years pressure sensors at the ocean bottom in the Pacific have been providing some additional valuable data in real time. Some other possible detection methods of the tsunamigenic earthquake and tsunami signals in the troposphere, as well as in the ionosphere are also being considered. The observation that certain animals are able to detect and react to earthquake and tsunami signals, is gaining some credibility in recent times. If this ability of animals could be exploited, it will provide some additional guidance in real-time tsunami prediction. The Pacific tsunami warning system came into existence in the late 1940s. Following the disastrous Aleutian Earthquake Tsunami of 1 April 1946, the Pacific Tsunami Warning Center (PTWC) was established in Ewa beach on Oahu Island of Hawaii, USA. At present there are 27 member countries in this system which is administered by the Intergovernmental Oceanographic Commission (IOC) of UNESCO in Paris, since 1965. During the Alaska earthquake tsunami of 28 March 1964, tsunami warnings from PTWC did not reach Alaska in an efficient manner. For this reason, the Alaska Tsunami Warning Center (ATWC) was established in Palmer, Alaska in 1967. Because tsunami occurrence is rare in the Atlantic and Indian oceans, as compared to the Pacific Ocean, until now, there have been no tsunami early warning systems for these two oceans. However, following the disastrous tsunami in the Indian Ocean on 26 December 2004, tsunami warning systems are being established, not only for the Atlantic and Indian oceans, but also for several marginal seas, such as the Caribbean Sea, the Mediterranean Sea, the East China Sea, etc. At present, because of very low population density, there is no particular priority for a tsunami early warning systems for the Arctic Ocean. 259



23.2 TRADITIONAL METHOD OF TSUNAMI DETECTION THROUGH TIDE GAUGES Since its inception in the late 1940s, the Pacific tsunami warning system has relied almost completely on a tide gauge network (Figure 23.1) for detection of trans-oceanic or ocean wide tsunamis. However, there are certain exceptions. In northern Japan, sometimes, the time interval between the occurrence of the earthquake and the arrival of the tsunami on the nearest coastline is at most a few minutes. In such situations, there is no time to wait for a confirmation of the existence of the tsunami through recording on a tide gauge. Hence, there is no real alternative, but to issue a tsunami warning, just based on the occurrence of the earthquake itself. Needless to say, this could lead to false alarms in some instances, which cannot be easily avoided. For ocean-wide tsunamis, usually there is at least some time available before a warning has to be issued, assuming that no warning will be issued unless and until the existence of a significant tsunami is confirmed at least at one tide gauge. Of course, the drawback is that, the people living on the coast near the tide gauge (which usually is the gauge closest to the epicenter of the earthquake) would have no warning at all, unless they hear about the earthquake (and possibility of a tsunami) through the news media. The strength of the traditional method is its robustness, i.e. the tide gauges will always record tsunami as long as the gauge can withstand the onslaught of the advancing tsunami. The weakness of the traditional technique, lies in the fact that in some instances, it may be too late to provide any warning, since the tsunami has already approached the coast and is recorded on coastal tide gauges.

Figure 23.1.

Sea level gauge network for the PTWS (McCreery, 2005).

Methodologies for tsunami detection


23.3

261

REMOTELY REPORTING TSUNAMI RUN-UP DETECTORS

Recently the PTWC has installed eight Remotely Reporting Tsunami Run-up Detectors (RRTRD) on the likely tsunami affected areas in Hawaii. Figure 23.2 (McCreery, 2005) shows a typical gauge and its operational links. These tsunami run-up detectors will trigger and send a message to PTWC within seconds of their being flooded by an advancing tsunami. This is definitive way of confirming that there is water on the land where the detector is located. These sensors are 2.1 to 4.4 m above the mean sea level and are located some 18 to 119 m from the shoreline, where, in the past, significant runups have been observed. These detectors are outside the normal surface runup and are not sensitive to rain or moisture, other than to a flood. According to McCreery (2005), these detectors which are based on home security alarm technology and cell phones communication, cost about one thousand US dollars each, are easy to install and maintain. The disadvantage of these detectors is that, they simply establish whether there is a tsunami or not, but cannot give a precise value of the tsunami amplitude, such as one can record on a tide gauge.

23.4

DART SYSTEMS AND THE DEEP WATER SIGNATURE OF A TSUNAMI

One of the serious problems facing numerical modelers of tsunami generation and propagation is the fact that, the rupture parameters of tsunami-genic earthquakes are difficult to obtain in real 160°

22°

159°

155°

156°

157°

158°

Hanalei Kauai Nawiliwili

22° Haleiwa Waianae

PTWC

21°

Oahu Mokuoloe Makapuu KPA Molokai Honolulu Kahului Lanai Maui

21°

Lahaina Hawaii

20°

SEA LEVEL INSTRUMENTATION

160°

– PTWC GAUGE (REAL TIME) – LARC GAUGE (DIAL UP) – NOS GAUGE (HOURLY / DIAL UP / TRIGGERED) – RUNUP DETECTOR (TRIGGERED)

159°

158°

157°

20°

HIL Honokohau KPHO Kapoho

HKH

19°

LPH

Kawaihae

MIL HPO

156°

Figure 23.2. Tsunami run-up detectors used by the PTWC (McCreery, 2005).

19°

155°

GMT



Figure 23.3.

DART systems that were in operation for the Pacific Ocean (Bernard, 2005).

time, which is needed as input of the computer models. Barring this information, the next best piece of information is the deep water signature of the tsunami. Several attempts have been made (Murty, 1977) in the past, to deduce the deep water signature from coastal tide gauge records. These attempts were largely unsuccessful, mainly because of nonlinearity and the contaminations of coastal tide gauge records by local resonances in inlets, bays and gulfs. The inverse problem of obtaining deep water signature from coastal records is a mathematically ill-posed problem, and hence has no unique solution. To get around this difficulty, the Pacific Marine Environmental Laboratory (PMEL) of National Oceanic and Atmospheric Administration (NOAA), USA has installed six DART (Deep-Ocean Assessment and Reporting of Tsunamis) systems in the Pacific Ocean (Figure 23.3; Bernard, 2005). These are basically pressure gauge sensors on the deep ocean floor that can measure and detect the tsunami as it is racing across the deep ocean. Three tsunami meters have been installed offshore of the Alaska–Aleutian trench, two offshore of Washington and Oregon states, and one in the equilateral Pacific far offshore of Ecuador. Chile installed one tsunami meter off its coastline at latitude 20◦ S. Each instrument package consists of a sea floor pressure sensor, in acoustic contact with an anchored Buoy (Figure 23.4) that transmits the ocean bottom data to a Geostationary Operational Environmental Satellite (GOES), from which the data is sent to the tsunami warning centers (Bernard, 2005). Data from these tsunami meters, free of the coastal effects, provide accurate forecasts of tsunamis by assimilating real-time tsunami meter data into nested numerical models (Titov et al., 2005). The value of these tsunami meters to date has been summarized by Gonzalez et al. (2005) and shown in Table 23.1.


Methodologies for tsunami detection

263

Figure 23.4. The DART system as deployed in the ocean (Bernard, 2005).

Gower (2006) provided most recent information on these DART Systems. According to him, there are now a total of 11 systems and he mentions that they detected the tsunami of 26 December 2004 in the Indian Ocean.

23.5

DEEP WATER SIGNATURE OF A TSUNAMI

Reid and Knowles (1970) and Knowles and Reid (1970) are probably the first to use the terminology “inverse tsunami problem” to mean the determination of the deepwater signature of a

264 T.S. Murty et al. Table 23.1.

Use of the data from DART systems in tsunami warning (Gonzalez et al., 2005).


Date – magnitude, time (UTC), location

Tsunameter records

11 July 2000 – 6.5 M, 01:33, ∼70 km southwest of Kodiak, AK

No tsunameters were triggered.

10 January 2001 – 6.9 M, 16:03, ∼110 km southwest of Kodiak, AK

Seismic wave induced 3.2 cm signal that triggered tsunameter D157 at 16:11. Subsequent record was tsunami-free. Seismic waves induced signals that triggered three tsunameter stations. Subsequent records were tsunami-free. Seismic waves induced signals that triggered all six tsunameter stations. Subsequent records were tsunami-free. No tsunameter were triggered.

5 May 2002 – 6.5 M, 05:37, ∼160 km southwest of Sand Point, AK 3 November 2002 – 7.9 M, 22:13, ∼145 km south of Fair Banks, AK 23 June 2003 – 7.1 M, 12:13, Near rat Island, Aleutian Islands

17 November 2003 – 7.5 M, 06:43, ∼90 km southwest of Amchitka, AK

Seismic waves induced signals that triggered three tsunameter stations. Subsequent records registered maximum deep ocean tsunami amplitudes of 2 cm, 0.5 cm, and

The Indian Ocean Tsunami

The Indian Ocean Tsunami of 2004

The Indian Ocean Tsunami of 2004 (Great Historic Disasters)

Tsunami Science Four Years After the 2004 Indian Ocean Tsunami, Part I: Modelling and Hazard Assessment

Tsunami Science Four Years After the 2004 Indian Ocean Tsunami: Part I: Modelling and Hazard Assessment (Pageoph Topical Volumes)