Quantitative Geometry of Thrust and Fold Belt Structures (AAPG Methods in Exploration 6)

Quantitative Geometry of Thrust and Fold Belt Structures Peter B. Jones International Tectonic Consultants (ITC) Ltd. Calgary, Alberta

Published by The American Association of Petroleum Geologists Tulsa, Oklahoma, U.S.A.

Quantitative Geometry of Thrust and Fold Belt Structures Peter B. Jones International Tectonic Consultants (ITC) Ltd. Calgary, Alberta Principles of step-faulting are simulated in computer-synthesized and balanced structural cross sections of faulted and folded terranes. Isolation of geometry from mechanics and chronology allows a review of kinematics and chronology of deformation in layered rocks. Blind faults and duplex structures are geometric consequences of stepfaulting, and are responsible for disparities in crustal shortening between superposed tectonostratigraphic units. These disparities are greatest in fold belts, which overlie belts of blind thrusts. Failure to recognize blind thrusts leads to incorrect estimates of both timing and amount of deformation. Geometric modeling demonstrates the intuitive nature of some widely accepted geologic assumptions. Geometric considerations alone suggest that faults and folds, which can be represented as products of faulting, form in response to a balance between differential tangential and vertical stresses. Where tangential stress provides the driving force, distribution of overburden load appears to control location of thrust ramps. Forward modeling by computer generates balanced cross sections at all stages of growth of a given structure, and shows that purportedly balanced cross sections may include impossible intermediate stages. Forward modeling also reveals geologic questions that must be answered before more sophisticated computer modeling programs can be written.

BIOGRAPHY Following 25 years in petroleum and minerals exploration, Peter Jones founded International Tectonic Consultants Ltd. in 1980 as a geological consulting company specializing in exploration of areas of complex geological structure. Educated in Great Britain and the U.S.A., Dr. Jones has worked on deformed belts in Europe, Asia and the Americas. Author of more than 25 papers on structural geology and tectonics, he has given seminars in structural geology to oil company exploration staffs around the world, and has recently returned from a lecture tour of Chinese universities and research institutes. For the past six years he has been involved in the development of computer techniques for simulating the formation of geological structures.

most hand-balanced cross sections are geometric transforms in which a deformed stage is balanced with respect to an originally undeformed stage. This can be done even Exploration for petroleum requires much data, and the though it may be geometrically impossible to reach the principles with which to interpret them. Because well and deformed state from the undeformed one along the fault seismic data are extremely expensive in fold and thrust belts, paths specified. In contrast, forward modeling by computer application of simple geometric principles can multiply the simulates progressive movement along fault planes, so that effectiveness of geological and geophysical interpretation. each balanced cross section includes within it an infinite Geometry of layered rocks, expressed by maps, cross sec- number of balanced cross sections of intermediate stages. tions, and seismic profiles, is the basis for interpreting the All balancing involves approximations. This follows geological structure. from the fundamental geometric fact that it is not possible Rigorous geometric modeling can simulate many thrust to transform a plane figure with a given area and perimeter and fold belt structures; but even where it cannot, hitherto into another figure with the same area and perimeter withunconsidered factors may be highlighted. For example, the out passing through intermediate stages in which one or impossibility of synthesizing a balanced cross section to fit both parameters must change. Any balanced cross section the data may lead to the recognition of posr-tectonic gravity must involve distortion of one or more of the following: slides within a deformed belt. area, bed length, or fault cutoff. In drawing a balanced As more deep seismic-reflection data become available, cross section, a geologist judges (perhaps unwittingly) the thin-skinned style of deformation is becoming more which distortions to accept. important in interpreting geological structures on all scales. In the models used in this paper, cross-sectional area is In thin-skinned deformation, faults are listric, flattening constant. The computer program uses a grid containing a into a basal decollement. Depending on the scale involved, specified number of cells (usually 150,000), like the squares this base may be anything from an incompetent shale to the on a sheet of graph paper, and maintains that number durbase of the lithosphere. Geometric principles of thin- ing deformation so that the resultant cross section is areally skinned deformation in layered sedimentary rocks are out- balanced. The logic might be called thepack-of-cards logic, lined by Rich (1934), Douglas (1950), Fox (1959), with each card represented by a column of cells (Figure 2a). Dahlstrom (1969a,b; 1970), Bally et al. (1966), Royse et al. Lines representing stratigraphic boundaries are drawn on (1975), Elliott (1976), Boyer and Elliott (1982), Suppe the edge of the pack. Fault planes slice through the pack of (1983), and Laubscher (1985). This paper owes much to cards along or oblique to the bases of layers representing those authors. stratigraphic units. The user specifies the positions of Figure 1 is a sketch cross section through a typical thrust faults, and the amount and sense (compression or extenand fold belt. Structures include folds, thrusts, and listric sion) of movement (Figure 2b). Relative movement occurs normal faults, rooted in a basal decollement or detachment along fault planes and, on a very much smaller scale, zone, and overlain (in some cases) by an upper detachment between adjacent "cards" (which need not be vertical), like zone, all of which can be simulated by the Thrustbelt™ sys- cleavage planes. The pack-of-cards model maintains contem, a computer program for forward modeling of bal- stant vertical thicknesses and cross-sectional area. Stratianced cross sections, developed by Helmut Linsser. Models graphic thicknesses in a dipping sequence are reduced in generated by this program are described by Jones (1982, proportion to the cosine of the dip angle, while the bed 1984), and Jones and Linsser (1984). Charlesworth and length increases inversely with the cosine of the dip angle. Gagnon (1985) describe what appears to be a similar model- The distortion is systematic and can be corrected manually ing program. Most of the illustrations that follow were cre- if required. ated by the Thrustbelt Program. The program incorporates the following geologic criteria: 1. Thrust faults are emplaced in sequence from higher to Balancing Cross Sections by Computer lower, by progressive deformation of an undisturbed footwall (Elliott, 1976). They cut up-section in their direction of movement and may also follow bedding Balancing is an essential process in constructing cross secplanes. Normal faults cut down-section in their directions through folded and faulted terranes. A balanced cross tion of movement, or follow bedding planes. section is not necessarily correct, but an unbalanced one is 2. Faults do not cut earlier faults but may merge with wrong. them and transfer their movement to them. Cross-sectional area and bed length of each stratigraphic These definitions are dependent on the dip of fault planes unit, as well as fault offsets, are adjusted in balancing, so that the deformed structure can be restored back to an relative to bedding, and are independent of the absolute dip assumed undisturbed condition without gain or loss of of the fault planes. Sub-horizontal faults that cut steeply material (cross-sectional area). Offsets of boundaries across dipping strata are often referred to as thrusts, but as Perry a given fault should be consistent in all units. Balancing (1978) shows, they are extensional relative to the strata they does not mean that shortening must be the same at all levels cut. Using the thrust-fault symbol to designate these extenor in all deformed stratigraphic units; indeed one of the con- sional faults on geologic maps causes many problems in clusions of this paper is that equality and synchroneity of structural interpretation. shortening are extremely unlikely. Each computer run generates the entire cross section in a Computer balancing of cross sections does nothing that higher-to-lower sequence of fault emplacement. A lowercannot be done manually using pencil and paper. However, to-higher sequence can be simulated by successive computer

INTRODUCTION

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Figure 1. Typical thrust belt, showing thrust and listric normal faults, duplex structures, underthrust foreland margin. All these structures can be created by the forward modeling program described in the text. runs in which each new fault is added behind the preceding one. This is common operational practice. Because each fault is deformed by its successor, it is easier to model the last-formed fault first. Folding of layered rocks involves a mixture of concentric, similar, and kink-band styles. The pack-of-cards model generates quasi-similar folds in which flanks thin and bed lengths extend. This is a workable approximation in most cases and is systematic and reproducible. According to W. B. Perry (personal communication, October, 1983), "The idealized concentric fold with a constant radius of curvature (to an inflection point) is almost never present." There are many questions to be resolved with regard to geometry and kinematics before more sophisticated modeling becomes feasible.

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THRUST FAULTS Effects of Spacing of Incipient Thrust Faults Relative to Their Displacements The profile in Figure 3b is typical of many thrust belts. The surface geology features an irregular spacing and local concentration of faults, which a geologist might interpret as evidence for an underlying zone of weakness or basement buttress. However, the irregular thrust spacing in this model is due entirely to varied slipping of a uniformly spaced set of incipient thrusts (3a). While basement warping and faulting may have a significant influence in localized thrust ramping (Wiltscho and Eastman, 1983), basement warping and faulting may not be applicable to this style of thrusting, which involves large numbers of faults having no immediate connection with basement. In areas such as the southern Alberta foothills, where this structural style predominates (Ollerenshaw, 1978), it seems more likely that thrust ramping in the sedimentary cover is ultimately controlled by the distribution of overburden in the hanging wall sequence (Royse et al., 1975). This overburden may govern the distribution of high fluid pressure at the base of the overthrust mass (Gretener, 1972). Controlling ramp location by differential overburden loading is a feature of thrust emplacement at the bases of deltas and submarine fans (Evamy et al., 1978). Differential loading in those environments is caused by sedimentation (Mandl and Crans, 1981), and is

Figure 2. (a) Undisturbed section with incipient fault represented by "pack of cards" 1000 cards long, with stratigraphic units drawn on edge of pack, sliced along line of fault, (b) After displacement of upper part of pack along fault plane. Thicknesses of tilted beds in hanging wall are reduced in proportion to the cosine of their angle of dip. This model is also described as a vertical shear model. Oblique shear can be simulated by tilting the model.

unrelated to the underlying section. Although a more competent section may be involved in thrust and fold belt deformation, differential loading because of faulting is potentially much greater. Displacement Transfer (En Echelon Faults) Closely spaced incipient thrusts interact with each other. Figure 4 is a set of cross sections parallel to each other along the strike of a thrust belt. Aggregate slip is the same in all profiles and slip is progressively transferred from fault A to fault B in successive profiles along strike. In Profile 1, thrust A moves to create a ramp anticline. Along strike, as fault B develops and A dies out, the ramp anticline and the culmination of the surface structure reach maximum amplitude in Profile 4 where both A and B are only partly developed. At that stage, thrust A has a slip equal to the spacing between it and thrust B, measured along a bedding plane. This causes the leading edge of a given stratigraphic unit in

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