Applied geodesy: global positioning system : networks, particle accelerators, mathematical geodesy

Lecture Notes in Earth Sciences Edited by Somdev Bhattacharji, Gerald M. Friedman, Horst J. Neugebauer and Adolf Seilacher

12 Stuart Turner (Ed.)

Applied Geodesy Global Positioning System - Networks - Particle Accelerators - Mathematical Geodesy

Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo

Editor Stuart Turner LEP Division, CERN CH- 1211 Geneva 23, Switzerland

Originally published as Internal Report under the Title: Proceedings of the CERN Accelerator School of Applied Geodesy for Particle Accelerators, Editor: S. Turner, Geneva 1987 ISBN 3-540-18219-5 Springer-Verlag Berlin Heidelberg New York ISBN 0-38?-18219-5 Springer-Verlag New York Berlin Heidelberg

This work Is subject to copyright. All rights are reserved, whether the whole or part of the material Is ooncerned, specKflcally the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or m other ways, and storage In data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, Jn ~ts version of June 24, 1985, and a copyright fee must always be paid. Violat~ons fall under the prosecution act of the German Copyright Law. © Sprlnger-Verlag Berlin Heidelberg 198"7 Printed in Germany Pnntmg and binding Druckhaus Beltz, Hemsbach/Bergstr 213213140-543210

PREFACE

The CERNAccelerator School (CAS) was founded in 1983 with the aim to preserve and disseminate the knowledge accumulated at CERN (European Organization for Nuclear Research) and elsewhere on part i c l e accelerators and storage rings.

This is being achieved by means of a biennial programme of

basic and advanced courses on general accelerator physics supplemented by specialized and topical courses as well as Workshops. The chapters included in this present volume are taken from one of the specialized courses, Applied Geodesyfor Particle Accelerators, held at CERNin April 1986. When construction of the f i r s t large accelerators started in the 1950's, i t was necessary to use geodetic techniques to ensure precise positioning of the machines' components. Since that time the means employedhave constantly evolved in line with technological progress in general, while a number of specific developments - manyof them achieved at CERN - have enriched the range of available instruments.

These techniques and precision instruments are used for most of the world's accelerators

but can also be applied in other areas of industrial geodesy: surveying of c i v i l engineering works and structures, aeronautics, nautical engineering, astronomical radio-interferometers, metrology of large dimensions, studies of deformation, etc. The ever increasing dimensions of new accelerators dictates the use of the best geodetic methods in the search for the greatest precision, such as distance measurementsto 10-7, riqorous evaluation of the local geoid and millimetric exploitation of the Navstar satellites.

At the same time, the

powerful computer methods now available for solving d i f f i c u l t problems are also applicable at the instrument level where data collection can be automatically checked. Above a l l , measuring methods and calculations and their results can be integrated into data bases where the collection of technical parameters can be e f f i c i e n t l y managed. In order to conserve the logical presentation of the different lectures presented at the CAS school, the chapters presented here have been grouped under four main topics.

The f i r s t and the

fourth deal with spatial and theoretical geodesy, while the second and third are concerned with the work of applied geodesy, especially that carried out at CERN. Readers involved in these subjects will find in the following chapters, i f not the complete answer to their problems, at l e a s t the beginning of solutions to them. J. Gervaise

P.J. Bryant, Head of CAS

M. Mayoud

S. Turner, Editor

Applied GeodesyGroup CERN

LIST OF AUTHORS

BAKER, L.S. BEUTLER, G. BOUCHER. C. BORRE, K. BURKI, B.

8612 Fox Run, Potomak, USA University of Berne, Switzerland Inst. G~ographiqueNational, Salnt-Mand~, France Aalborg University, Aalborg Ost, Denmark Institute for Geodesy & Photogram~etry, ETH Zurich, Switzerland

CAMPBELL, J. CASPARY,W.F.

Geodetlc Inst. University of Bonn, FRG Univ. der BundeswehrMunchen, Neubiberg, FRG

COOSE~%~NS,W. DUFOUR, H.M.

CERN, Geneva, Swltzerland Inst. G~ographiqueNational, Saint-Mand~, France

FISCHER, J.C. HAYOTTE,M.

CERN, Geneva, Switzerland CERN, Geneva, Switzerland CERN, Geneva, Switzerland National Geodetic Survey, NOAA,Rockville, USA Astronomical Institute, University of Berne, Switzerland CERN, Geneva, Switzerland

GERVAISE, J., GOAD, C.C. GURTNER,G., HUBLIN, M. ILIFFE, J. LASSEUR, C. MAYOUD,M. MORITZ, H. OLSFORS, J. QUESNEL, J.P. TROUCHE,G. UNGUENDOLI,M. WELSCH, W.M. WILSON, E.J.N.

University College London, United Kingdom CERN, Geneva, Swltzerland CERN, Geneva, Switzerland Technical University, Graz, Austrla CERN, Geneva, Switzerland CERN, Geneva, Switzerland CERN, Geneva, Switzerland University of Bologna, Italy. Univ. der BundeswehrM~nchen, Neubiberq, FRG CERN, Geneva, Switzerland

CONTENTS

I.

GLOBALPOSITIONING SYSTEMAND V.L.B.I.

L.S. BAKER GPS Its Development and Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

C. BOUCHER GPS Receiver Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

C.C. GOAD Precise Positioning with the GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

G. BEUTLER GPS Orbit Determination Using the Double Difference Phase Observable

. . . . . . . . . . . .

31

W.M. WELSCH Accuracy Problems when Combining Terrestrial and S a t e l l i t e Observations

..........

47

J o CAMPBELL Very Long Base Interferometry II.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

SURFACEGEODETIC NETWORKSAND UNDERGROUNDGEODESY

J. GERVAISE, J. OLSFORS The LEP T r i l a t e r a t i o n Network

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111

W. GURTNER, B. BURKI Deviation of the Vertical G. BEUTLER Co~Darison between Terrameter and GPS Results - and How to Get There

. . . . . . . . . . . .

125

Geodetic Networks f o r Crustal Movements Studies . . . . . . . . . . . . . . . . . . . . . . .

135

P. BALDI, M. UNGUENDOLI

W.F. CASPARY Gyroscope Technology, Status and Trends

. . . . . . . . . . . . . . . . . . . . . . . . . .

163

J.C. FISCHER, M. HAYOTTE, M. MAYOUD, G. TROUCHE Underground Geodesy . . . . . . . . . . . . . . . . . . . . . . . . . .

.. . . . . . . . . . .

181

III.

APPLIEDGEODESYFOR PARTICLEACCELEPJ~TORS

J. GERVAISE, E.J.N. WILSON High Precision GeodesyApplied to CERNAccelerators . . . . . . . . . . . . . . . . . . . . .

209

J. ILIFFE Three-Dimensional Adjustments in a Local Reference System . . . . . . . . . . . . . . . . . .

247

M. HUBLIN Computer Aided Geodesy (I) LEP Installation Pro F~ ~.~ ~ (normally 3.29) the observation is eliminated and the adjustment is 1 i--~,i, , r e p e a t e d . I t i s p o s s z b l e t o have an i n t e r a c t i v e v e r s i o n o£ t h i s p r o c e d u r e . One can a l s o use an alternative approach based on the minimisation o£ the sum o£ the absolute value of residuals jz), ~which in some situations seems to be more efficient 33 )

146

4 ) The analysis of the network is carried out by considering the absolute and relative error ellipses, distance error, and that o£ the bearings between pairs o£ points. The ellipses can be plotted automatically. 5) Other programs for similarity transformation, for testing the significance of supposed movements, for studying the local strain field etc. are needed. From amongst the various networks installed in Italy to study crustal movement, let us show you as an example the one we set up in the Cassino Area (south of Rome ) in 1984. Starting form the geophysical need to connect three mountainous blocks separated by two supposed Fault zones, the work sequence has been as follows: I

to search, using suitable cartography, for those intervisible points which might be to form a very compact network (within a circle),

used

to mount a field campaign in order to verify the supposed possible connections by means of powerful lamps; to verify the possible routes and transportion needs (special cars, mules, helicopters.. ); to obtain permission from the owners o£ the land; to study the geological and lithological features o£ those places selected in order to choose the foundations o£ the bench-marks (reinforced concrete pillars ); and so on. After that we planned various possible networks on the basis o£ optimisation criteria, taking into account all the information collected during on-the-spot investigations. In this manner we chose the network in Fig. 10 consisting o£ three points on every three blocks. 4) Another field campaign was necessary to construct the pillars, built upon rock foundations, and with a self-centring device on the top. On a geologically stable block we installed two pillars in order to have a base line for the calibration of the instruments before, during and after every measurement campaign. 5 ) During the first measurements campaign we experienced difficulty in measuring some o£ the long sides, and thus decided to add another three points in order to eliminate such long connections. The final network is that shown in Fig. 11 in which the error ellipses are laid out. As you can see the network is characterised by very good homogeneity and isotrophy, which is most important since the direction of the expected movements is not known.

3.2

Alt£metric networks

A series of high-precision levelling c&mpaigns is the most fruitful method o£ investigating vertical crustal movements; using this technique it is possible to examine in detail and with great accuracy displacements extending over even the largest areas. Vertical control networks should be planned bearing in mind a considerable number of parameters, such as the area affected by deformation, the characteristics o£ the displacement and its supposed magnitude and velocity, the type and location o£ the bench marks and their density, the possible level routes and the degree of accuracy expected, also taking into account the high cost of such measurements. It is not possible here to give a detailed examination o£ all the problems associated with precise levelling, such as instrumentation, operation methods, refraction, magnetism, rod calibration, bench-mark stability and so on. We will only emphasise the fact that interest in this technique has increased to such an extent that entire conferences are dedicated to it, many interesting suggestions and ideas are given in their proceedings 34,35,36) . As far as accuracy is concerned, we have no problems in the detection o£ coseismic deformations, large scale subsidence or bradeisism. However, we

147

N

o,.,,

E~,'I Fig.

10

8 k,,,.

o '!' ~' c,..

Scheme of the trilateration network o£ Cassino and comparison between the error ellipses obtained in the First c~npain and the expected ones (dashed lines)

N

5 I

Icm, Fig. 11 Scheme of a modified network in Cassino

10 km. I

148

encounter some difficulties in other cases, such as pre-seismic or post-seismic deformations, or with a slow subsidence or uplift where the small degree o£ movement concerns a large area. Amongst the various souses o£ error we shall consider the following two in particular: refraction, and movement occuring during the measurement phase. Regarding refraction, the greatest limiting factor for lines in hilly areas, there are essentially two ways in which it may be taken into account: the first is based on the well-known Kukkumaki 's formula R = -10-6 A (5~----) (~h (~t L = length of sight in metres 6 h = difference in level in metres ~t = difference in temperature in degrees at two hights, normally 0,5 m and 2.5 m. A

1190 c c z 2- z 1

1

I~7T

, C+1 C+1 ~zI - z2 ) -z 0 (z I - z 2)I

where Z is the height o£ the instruments, ~ and Z 2 6L~e the sight heights, and C is a 0 coefficient the value of which is normally assumed to be equal to - I/3. The second way is based upon the creation of atria)sphericmodels which provide a means o£ adjusting the measurements using one temperature and general data regarding insolation, wind, etc. Different techniques can be applied to check on any possible movellents taking place during the measuring campaign, or to obtain a periodic indication of whether or not it is necessary to repeat the measurements over the entire network. One o£ these is based on the continous recording of tilt components by tiltmeter; another method we have used extensively is based on the use of double levels at night 37). This technique makes it possible to ascertain with accuracy, and within a few hours, the difference in height between points at almost the same height, but located at a considerable distance (3-6 km) from each another. By way o£ example we have set out the closing error o£ a control triangle used in various campaigns. ~

I

97___7

1978

1980

-0,9

1,4

It must be remembered that the length of the precise levelling lines necessary to join the three points is over 20 km, with routes characterised by average differences in height o£ 50 mlbn. Having an idea o£ the movements occuring during the measurement period, it is possible for one to take them into account during the data processing phase 38 ). Neverthless, we think that the best method is to limit the entire network's measurement period to as short a time as possible. This can be achieved by contracting small areas of the network to a variety o£ companies working simultaneously. The need to employ several firms is typical o£ levelling networks, and this fact should be taken into account when preparing the specifications for the contracting finns concerning instrumentation, rod calibration, observation procedures, refraction, tolerances for a single section, for a line, for a loop etc. 39) In addition we must emphasise that when all the blocks, already analysed separately, are put together, other errors arise; it by no means being a simple matter to complete a serious data analysis or the adjustment o£ a whole network consisting of hundreds or thousands of measured sections. As an example of this kind o£ work we present in Table I a flow diagram o£ the program prepared in my institute by Prof. Barbarella.

149

Table I Flow diagram for network adjustment

"I

I

Field Data

1

Handling of baba (Code number, coordinates ) r . . . . . . . . . . .

ICorrection Or . . . . . .

L o£

t" . . . . . . . . .

[Search !eri'ors

,,

I,

4

Automatic set up o£ condition equations ; Adjustment ;

using

griph

I I

theory '

,.

Itio[

"- ----'I

data

L- . . . . . . . . . . . . .

j

,~

Anal;sis o£ closing errors

[

Are they acceptable?

I

L

yes IStorage of. lllf.or-!

Imation of" the bench-marks o£

[.4~--

Ithe liiles

i

U- ......

-~uM_ap of. the net]

Search of independent loops[

', - I

I . . . . . .

~

"i .....

I

! I'elneasuremeut

--'

•. . . . . .

_J

1

I

,.

;.*.....,

heights using graphs

Alternatively

Computatioll of pseudoobservations :diFFerences in height a.d weight of. the lines

I

Adjustment of. quasi-

]

[

iF-Rejectio,,

or

~--~, remeasuremeut I !o£ some l i n e s t L .... l .....

-1 1

I I

J

] observatious by parametric me thod

t

m- 1

I t e r a t i v e data S | l O O p i n g Or

It°bust identi{ £ication

Adjusted h e i g h t s and m . s . e , o£ nodal p o i n t s

Computation o£ h e i g h t s and m.s.e, o£ all the benclrmarks I . . . . . . . . r- . . . . . . . . . . . .

"I

IPrevious heights ~ Lo£ bench-mar~s .]

i

T

Computation o£ the differences I and automatic design Of [

--[ [contour

lines o£ equal movements[

One can also apply other statistical tests For the study o£ error behaviour in order to obtain information about trends due to systemlatic errors. The tests are baser] on the random variable

150

m~

iJ.

ij

R.. mJ

in which is the discrepancy between the direct and reverse measurements of the relative height of two consecutive bench-marks, and R is the distance between them. The method is based on tests concerning each line, and cumulative tests regarding the entire network, preferably using non-parametric tests because of their generality. Many tests can be used, such as, for example: randcmness tests, nonnality tests, the Wilcoxon test, the Person P. Test, the Kurskal Walis Test, the Bertlett Test 40). At the end of this short dscription o£ altimetric networks we must briefly make one or two conments concerning gravity. Gravity remeasurements may to some extent be used as a substitute for a levelling survey. The accuracy obtainable is less satisfactory, but costs are lower and the method is quicker. Simultaneous monitoring of elevation and gravity change D~ovides us with further e±ements for the interpretation of the phenomenon in question 41) For example, generally speaking the gravity variation corresponding to a vertical displacement caused by an acct~nulating stress field in a seismic area, can be expressed as a sum o£ the free air and Bauguer effects, plus the gravity contribution made by the subsequent density change in relation to the volumetric strain 42) With the use of m_~ern ~crogravimeters, (e.g.: la Coste-Romberg rood.D), standard errors smaller than 5.1(7~ m/sec may be obtained 43 [. Improvements in accuracy depend mainly on the el Jr/nation of effects caused by earth tides, tidal loading, atmospheric mass movements, and so on.

Fig,12

Scheme of the altimetric network in Bologna (Italy)

151

As an example of an altimetric net we shall show you the one set up in the Bologna area, (our home city), where over the last ten years we have had a differential subsidence velocity of at least about 11 on/year, causing many problems regarding the stability o£ buildings, and water management. The network planned in my institute by Prof. Pieri and Dr. Russo was conceived in order to give diF£erent levels o£ information. In Fact it consists o£ a large network, (460 km 2 ), in which the bench-marks are spaced from between I to 0.5 km along the lines, and the distance between the nodal points ranges from 7 to 3 kin, the density increasing towards the town; (areas I ,2 and 3 o£ Fig. 12). Another network, (Fig. 13), covers the old town, with the bench-marks spaced at intervals o£ 0.25 km. along the lines, and with a distance between nodal points o£ about 0.5 kin. Finally there are some local networks set up £or the purpose of studying the movement of buildings or monuments, often in conjunction ~