Numerical modeling of trishear fault propagation folding

Transcription

1 TECTONICS, VOL. 16, NO. 5, PAGES , OCTOBER 1997 Numerical modeling of trishear fault propagation folding Stuart Hardy 1 Institute of Earth Sciences (Jaume Almera), Consejo Superior de Investigaciones Cientificas, Barcelona Mary Ford Geologisches Institut, Eidgenossische Technische Hochschule Zentrum, Zurich Abstract. In contrast to kink band migration modeling methods, bend (or passive) folds, fault propagation folds, detachment folds trishear numerical models produce fault propagation folds with [e.g., Jamison, 1987] although some authors also recognize smooth profiles and rounded hinges. Modeled fold hinges tighten wedge thrust folds in which the fold is formed by the insertion of and converge downward, within a triangular zone of distributed a wedge of material [Medwedeff, 1992]. Fault propagation folds, deformation which is focused on the fault tip. Such features have the subject of this paper, are asymmetrical fold pairs that develop been reported from field studies and are also seen in analogue ahead of propagating faults and which can eventually be cut by models of compressional deformation. However, apart from its their fault. Much research effort has been undertaken to initial application to Laramide folds, little quantitative work has understand the relationship between faulting and folding in been undertaken on trishear fault propagation folding in other external fold and thrust belts, in particular, fault propagation settings. In addition, no study has been undertaken into the folds, using a combination of numerical modeling and field growth strata which might be associated with such structures. observations [e.g., Elliot, 1976; Williams and Chapman, 1983; This paper uses an equivalent velocity description of the Jamison, 1987; Mitra, 1990; Suppe and Medwedeff, 1990; Erslev, geometric model of trishear, together with models of erosion and 1991; Hardy and Poblet, 1995; Ford et al., 1997]. Several recent sedimentation, to investigate trishear fault propagation folding of studies use growth strata associated with fault-related fold both pregrowth and growth strata. The trishear model is structures to investigate fault-fold development [e.g., Suppe et generalized to include a variety of fault propagation to slip ratios al., 1992; Hardy and Poblet, 1995;Storti and Salvini, 1996; Ford and fault propagation from a flat decollement. The modelshow et al., 1997]. The majority of models for fault bend and fault continuous rotation of the forelimb with the characteristic propagation folding are based upon kink band migration [Suppe, development of cumulative wedges within growth strata. When I983; Suppe and Medwedeff, 1990], which predicts uniform bed total slip on a structure is high, the model predicts overturned dips and homogeneous deformation in fold limbs. However, pregrowth and growth strata. During the initial stages of several observationsuggesthat kink band kinematics may not deformation, beds in the forelimb thicken but later thin when they be applicable in all cases of fault propagation folding. This paper become steep or overturned. The effect of variations in fault investigates and develops the trishear model for fault-propagation propagation to slip ratios on two-dimensional finite strain in the folding, introduced by Erslev [1991]. In this model, folds models is assessed by the use of initially circular strain markers. develop progressively in a triangular zone of distributed High fault propagation to slip (p/s) ratios lead to narrow zones of deformation which opens away from the fault tip. The folds, high finite strain, while lower p/s ratios lead to more ductile which have smooth profiles and rounded hinges, tighten and deformation and broader zones of high strain. In all cases, converge downward toward the fault tip. The trishear zone hanging wall anticlines and footwall synclines originate as early develops ahead of the propagating fault tip which eventually cuts ductile folds which are later cut by the propagating fault. through the trishear fold pair. Although the main topic of this Modeled structures are compared with natural examples. paper, the tdshear model is not dedicated to reverse faulting but can also be applied to normal and strike-slip faults. Nor does trishear have to be accommodated by folding; instead it could develop as a zone of fracturing [e.g., McGrath and Davison, Introduction 1995]. The model satisfactorily replicates several important In external zones of orogenic belts compression is observations made in both nature and experiment which are accommodated principally by folding and thrusting. The incompatible with kink band migration models and in many ways complex interaction between these two processes produces a wide replicates a specific type of distributedeformation (the ductile range of geometrical relationships. Thrust-related folds are bead) that previous authors have suggested accompanies fault-tip usefully classified into three main geometrical categories: fault propagation [e.g., Elliot,!976; Williams and Chapman, 1983; Fisher and Coward 1982; Cooper and Trayner 1986; Johnson, 1995]. First, trishear can replicate field observations of tnow at Department of Geosciences, Princeton University, asymmetrical fold pairs verging in the direction of thrusting Princeton, New Jersey. comprising a footwall syncline and a hanging wall anticline with highest strains in the forelimb and a thrust (or zone of thrusts) Copyright 1997 by the American Geophysical Union. cutting through the common limb with a smooth trajectory and high cutoff angles [e.g., Williams and Chapman, 1983; Butler, Paper number 97TC ; Gidon, 1988; Fisher and Coward, 1982]. Second, many /97/97TC natural thrust-related folds display limbs in which beds are not 841

2 842 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING uniform in dip and where deformation is characteristically heterogeneous and complex. This is particularly so in the steep forelimbs of asymmetrical fold pairs where local tectonic thickening and thinning are commonly observed [e.g., Pfiffner, 1990; Alonso and Teixell, 1992; Erslev and Rogers, 1993]. Instead of layer parallel slip as predicted by kink band migration type models, foreland-vergent shear is commonly reported in steep or overturned fold limbs [e.g., Alonso and Teixell, 1992; Vergds et al., 1996]. Third, as demonstrated by Erslev [1991] and Erslev and Rogers [ 1993], the trishear model can be applied to areas involving competent, massive lithologies (e.g., crystalline basement of the Laramide uplifts). It can also be applied to poorly layered lithologies common in many fold and thrust belts such as the massive conglomerates of foreland basins [e.g., Ford et al., 1997]. Such lithologies cannot be expected to deform by kink band migration. Fourth, growth strata in many foreland fold and thrust belts display variations in dip and thickness across fault-related folds that are interpreted to indicate progressive rotation of fold limbs [e.g., Riba, 1976; Nichols, 1987; Pocovi et al., 1990; DeCelles et al., 1991; Tailing et al., 1995]. However, in kink band models limb dips are attained instantaneously and do not change through time [Suppe et al., 1992]. Fifth, analogue (Figure 1) and numerical models for both extensional and compressional faulting indicate that broadly triangular zones of distributed deformation develop in front of propagating fault tips [Withjack et al., 1990; Saltzer and Pollard, 1992; Mitra and Islam, 1994, Storti and McClay, 1995]. Analogue models show that within these zones the primary mechanism of deformation is slip on a series of minor faults and (a)! distributed strain expressed by folding of beds. Beds within these shear zones rotate and steepen until the propagating fault breaks through the structure. The trishear model has been applied so far only to Lararnide basement uplifts [Erslev, 1991; Erslev and Rogers, 1993]. In this paper we investigate the applicability of the model to fault propagation folds in general by introducing fault propagation from a flat decollement, a variety of ratios between fault propagation rate and fault slip rate, variation of the trishear apex angle, and strain markers. We simultaneously investigate the geometry of growth strata generated by this model by combining it with models of erosion, transport, and sedimentation. We incorporate growth strata into nearly all model runs as they help to highlighthe differences between model runs, both in its progressive development and in the final geometry, and are themselves comparable to natural examples. Therefore the features produced in pregrowth and growth strata can e considered separately in each model. Typical pregrowth and growth stratal architectures are generated by the trishear fault propagation folding model for a variety of conditions and are compared with some natural examples. Two-dimensional strain within the trishear zone is trackeduring modeling using initially circular strain markers. Mathematical Modeling of Tectonics and Sedimentation The mathematical models discussed in this paper have been developed using the general tectonosedimentary forward modeling equation of Waltham [1992], which has been successfully used to model tectonics and sedimentation in a wide variety of environments: carbonate platforms [Bosence et al., 1994], deltas [Hardy and Waltham, 1992; Hardy et al., 1994], domino fault blocks [Waltham et al., 1992; Hardy, 1993], fault bend and fault propagation folds [Hardy and Poblet, 1995] and detachment folds [Hardy and Poblet, 1994]. The modeling approach is based upon the concepthat the height of a geological surface can be modified in four ways: (1) material can be added to, or removed from, the surface; (2) material can be moved from one part of the surface to another; (3) the surface can be moved; and (4) the surface can be deformed. The first two of these mechanisms are sedimentary, while the second two are tectonic. Waltham [1992] derived the following partial differential equation for use in modeling tectonics and sedimentation in two dimensions: 3h/3t = [ p - 3F/3x ] + [ v - u.3hl3x ] (1) Sedimentary processes Tectonic processes (b) (d) where: h is the height of a geological surface at a fixed horizontal Figure 1. Examples of distributed deformation associated with fault tips observed in analogue models: (a) and (b) deformation location, t is time, p is a source term, F is the sediment flux, xis a horizontal coordinate, v is the vertical velocity (uplift positive, associated with two extensional faults of different dips, (modified subsidence negative), and u is the horizontal velocity (left to right fr6m Withjack et al. [1990], 1990, reprinted by permission of positive, right to left negative). the American Association of Petroleum Geologists) and (c) and (d) sequential evolution of an experiment (from the inversion experiments of Mitra and Islam [ 1994]) (, 1994, redrawn with Equation (1) combines sedimentary and tectonic processes in an Eulerian coordinate system, that is, a fixed coordinate system which does not move as a result of flow or tectonic deformation. kind permission of Elsevier Science- NL, Sara Burgerhartstrat The strength of this approach is that it allows tectonics and 25, 1055, KV Amsterdam, Netherlands). The shaded zones are the zones of deformation indicated by the authors. sedimentation to be combined formulation ensuring that they are modeled as simultaneous in a single mathematical

3 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING 843 Ul:S Vl=O s2cøse Hanging wall e = 0 v2.s2sine _. _... Footwall Un=O Vn=O Figure 2. Schematic diagram illustrating the trishear fault propagation model used in this paper. Velocity vectors within the hanging wall and shear zone and sectors of equal velocity vector are illustrated schematically. The symmetric shear zone has an apical angle of 27. rather than sequential processes [Waltham, 1992; Waltham and Hardy, 1995]. Mathematical modeling of both tectonics and sedimentation is, constructions that the original model involved. Here we present a simpler Eulerian velocity description of trishear. In the triangular shear zone, slip is assumed to vary linearly from a however, only required for the topmost surface in any geological finite value to 0 from the top to the bottom of the shear zone setting. Therefore, in the mathematical models discussed in this along any fault-normal tie line (Figure 2). Therefore sectors of paper the top surface is modeled using an Eulerian scheme equal slip are separated by straight lines which converge on the (Equation (1)), whereas the deformation of buried surfaces is apex of the shear zone (or are parallel in the case of a tabular modeled using a Lagrangian scheme [cf. Contreras and Surer, simple shear zone). Thus, for a given sector both the magnitude!990]. Importantly, this allows overturned fold limbs to develop of slip and the boundaries of the sector are known. Erslev which is not possible using a simple Eulerian scheme and also [1991] showed that in order to conserve area within a symmetric avoids problems of numerical diffusion and dispersion associated trishear zone there must be a component of displacement toward with Eulerian schemes [Fletcher, 1991 ]. The relationship of the Eulerian and Lagrangian descriptions of deformation is fully discussed by Waltham and Hardy [ 1995]. As with any application of (1) to the modeling of tectonics and sedimentation, two distinct steps must be undertaken: (1) the specification of the horizontal and vertical velocities which result from a given deformation mechanism and (2) the specification of the footwall within the shear zone. The problem is then to find the correct direction of the velocity vector given the slip distribution throughout the shear zone in order to maintain area. Waltham and Hardy [1995] derived the block contact condition for just such problems in which velocities on one side of a specified boundary are known but those on the other side are not: the models of sedimentation applicable to the geological setting under consideration. Vl - ulaf/ax = v2 - u23fiax (2) where v] and u] are the velocities on the left-hand side of the Trishear Fault Propagation Folding boundary f and v 2 and u2 are the velocities on the right-hand side. Thus, within any sector, velocities are constant and the Here the geometric model of trishear fault propagation continuity condition is respected, and between sectors velocities folding described by Erslev [1991] and Erslev and Rogers are compatible. Applying this technique to trishear, Vl and Ul [1993] is used to provide the horizontal and vertical velocities in are known for the hanging wall block (as they are specified), and (1). Trishear distributed shear in a triangular (in profile) shear we wish to find v2 andu2 in a sector across the boundary of the zone, one apex of which is located at the tip of a propagating shear zone. Therefore Vl, u I and f are known, and v 2 and u 2 are fault. In the original model [Erslev, 1991] the shear zone was given by fixed with respect to either the footwall or hanging wall of the fault. Since trishear was first introduced, it has only been used v2 = -s2sin( (3) infrequently and has not received the attention that it perhaps merits. This is par.tly due to the complicated trigonometric u2 = s2cos(o) (4)

4 844 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING Position along tie line Figure 3. Graph of direction (0) of velocity vector calculated along a fault-normal tie line through a trishear zone with a half apical angle 7 of 2 ø. The tie line has an arbitrary length of 100 units measured from the base of the shear zone. where $2 is the known slip in the sector on the fight-hand side of the boundary and 0 is the direction of the unknown velocity vector. By substitution is then a simple matter to solve (2) for the unknown direction, 0, of the velocity vector. This procedure can be repeated downward along a given tie line in order to derive the distribution of 0. As all tie lines have the same distribution of slip and all points of equal slip lie along equivalent sectors, this 0 distribution applies throughouthe entire shear zone. Knowing 0 and s (the slip) along a tie line allows one to derive the complete velocity field. An analysis of a trishear zone using this technique is shown in Figure 3, where the number of sectors is arbitrarily large, that is, slip varies linearly, and the velocities are everywhere compatible with the boundary conditions. It can be seen that theta varies linearly from 0 to ¾ (the half apical angle of the shear zone) along a tie line from top to bottom of the shear zone. Along a given tie line, slip magnitude is equal to that of the hanging wall block at the top of the shear zone and is equal to zero at its base; similarly, the slip vector is parallel to the fault at the top of the shear zone but parallel to the boundary of the shear zone at the bottom. This velocity description of deformation can be shown to give identical results to the geometric method of Erslev [1991] and in the case of a tabular shear zone is equivalent to simple shear. Thus, to the fight of the shear zone (or fault), material is static, to the left material is moving but is internally undeformed, and within the shear zone material moves with a velocity dependent upon its position relative to the shear zone boundaries. Knowing the position of a point on a bed (surface) within the shear zone allows the determination of the slip vector which is easily decomposed to give the horizontal and vertical velocities. In the modeling presented here all calculations are done in a norm al coordinate frame (i.e., the shear zone dips with the fault) in ord er that both tectonics and sedimentation can be modeled [cf. Erslev, 1991]. The calculated velocities are then used to model the deformation of the layers under consideration. Erosion, Transport, and Sedimentation A velocity description of deformation in an Eulerian coordinate frame allows the combination of tectonics and sedimentation [Waltham, 1992; Waltham and Hardy,!995]. Both regional (fluvial or marine) sedimentation and local erosion, transport, and sedimentation are modeled in this paper. To model the evolving sediment geometries in this system, a base level must first be defined, which is the datum below which sediments may be deposited. Here base level is independent of deformation and may rise or fall during a model run in order to create or destroy accommodation space. Having defined a base level, models of erosion, transport, and sedimentation are included in the modeling scheme. First, a background sedimentation rate is introduced, which is considered to represent nonlocally derived material such as fine. siliciclastics. This additional sediment input can be regarded, on this scale, as approximately constant across the fold and may thus be simulated by introducing a constant value for p in (1). This sediment will be deposited everywhere across the model at a given rate, except where the fold is uplifted above the specified base level. In addition to any background sedimentation the evolving fold will generate a structural high (a subaerial ridge or submarine high) which may lead to local erosion and sedimentation. To account for this, a simple model of sediment transport can be built into (1) using the diffusion equation in which the sediment flux, F, is assumed to be proportional to slope and directed down the slope, that is, F = -or amax (5) where os is the diffusion coefficient. This leads to the diffusion equation 3F/3x = -a 32 h/3x 2 (6) provided os is assumed constant. A full discussion of the use of the diffusion model is given by Flemings and Jordan [1989], The value of the diffusion coefficient is very difficult to assess because published estimates vary from 9 x 10 '4 m2/a for add fault scarps [Colman and Watson, 1983] to 5.6 x 105 m2/a for a prograding delta [Kenyon and Turcotte, 1985]. It appears to depend on a variety of factorsuch as climate, lithology, and scale [Kooi and Beaumont, 1994]. Assuming that fault-related

5 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING 845 folds lie somewhere between these extreme suggests an intermediate value of approximately 1 m2/a might be appropriate. The values used in the examples presented in this paper are close to unity and have been chosen because they illustrate well the distinctive features caused by the interaction of tectonics and sedimentation in this setting. It should be noted that many coarse-grained alluvial deposits are localized at the mouths of deep canyons, which means thathe diffusion coefficient chosen is approprate for a canyon cutting across a structure, and average out of plane profiles would require much lower diffusion coefficients. (a) Footwall fixed t 1 krn Pregrowth and Growth Strata Associated With Trishear Fault Propagation Folding The modeling method described above will now be applied to a reverse or thrust fault as might typically be expected in the external part of a foreland fold and thrust belt. The modeled thrust fault dips 40 ø and has a 20 ø shear zone apex angle. A slip rate, parallel to the fault, of 1 m/ka will be used together with a total run time of 1 Ma. Growth strata are displayed at intervals of 200 ka. For a variety of conditions the stratal architectures predicted when the triangular shear zone is fixed with respect to either the footwall (i.e., fault does not propagate) or the hanging wall (i.e., fault propagates at the slip rate [cf. Erslev, 1991]) will be assessed. (a) Footwall fixed I Figure 5. Growth strata associated with trishear fault propagation folding: (a) footwall-fixed shear zone and (b) hanging wall-fixed shear zone. Base level rise and sedimentation rate were both 0.5 m/ka, together with a diffusion coefficient of 3.0 m2/a. All other parameters were the same as in Figure 4. There is no vertical exaggeration. I T J... Growth strata._] In the first example (Figure 4) a base level rise of 1.0 m/ka '/"',-" ß "' '... Pregrowth' ' has been included in the model run, together with a st rat a sedimentation rate of 1.0 rn&a, resulting in sediment always "filling to the top" [cf. Suppe et al., 1992; Hardy and Poblet, 1995]. Several features of note are seen in these models. First, I I in the case of footwall-fixed trishear (Figure 4a), pregrowth strata are moderately to steeply dipping, whereas hanging wallfixed trishear (Figure 4b) results in greater deformation of (b) Hanging wall fixed pregrowth strata, resulting in the lowest pregrowth strata being steep to overturned. In the higher growth strata the fold pair is more open with a greater wavelength in the footwall-fixed model (Figure 4a). This increased deformation in lower strata is caused by the forward propagation of the fault tip and therefore of the shear zone, which results in the upward migration of the area of st rat a most intense deformation within the triangle (as seen in Figures 5 and 6). Second, growth strata developed during both footwalland hanging wall-fixed trishearecord the progressive rotation of the forelimb and relative uplift of the anticline. All growth strata I I thin toward the anticlinal hinge, resulting in a cumulative wedge structure, and dips decrease upward through the common limb. These features are commonly observed in growth strata [e.g., Figure 4. Growth stratassociated with trishear fault propagation Anadon et al., 1986]. folding: (a) footwall-fixed shear zone and (b) hanging wall-fixed shear zone. A slip rate of 1 m/ka was imposed during a total run Note that when the trishear zone is footwall fixed, the upper boundary of the trishear zone and the anticlinal axial plane are time of 1 Ma, with growth strata recorded at intervals of 200 ka. not coincident. This is because the trishear (kinematic) Base level rise and sedimentation rate were both 1 rn/ka. There is no vertical exaggeration. boundary is static and hanging wall material progressively enters the shear zone and is deformed. The opposite is true in the case

6 846 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING /erosion (a).footwall fixe d, P b) Hanging wall fixed erosion t I base level base I level I structure and a contrasting thickening of growth strataway from the steep limb of the structure. The sedimentary hiatus and unconformity at the steepest part of the structure are a result of the diffusion model in which sediment is eroded from this region. In the above models there is overturning of some of the pregrowth strata but none in the growth strata. Vertical or overturned beds are a common feature of growth strata seen in natural structures [e.g., Nichols, 1987; Anadon et al, 1986], and the following model runs will attempto model this situation. In order to create vertical or overturned growth strata, the structure needs to evolve further and take up more slip. This will be done by increasing the run time of the examples given in Figure 5 from 1.0 to 1.6 Ma. The results are shown in Figure 7. In Figure 7a the case of footwall-fixed trishear, the growth strata immediately adjacent to the fold limb are now subvertical, whereas for the case of hanging wall-fixed trishear (Figure 7b), the oldest growth strata are overturned and thinned near the fold limb and show a continuous progression to shallowly dipping younger growth strata. Note that the fall line has migrated over the uplifting structure so that the younger growth strata onlap an older erosion surface to produce a progressive unconformity. Ramp-Flat Geometries and Variable Figure 6. Growth strat associated with trishear fault propagation Fault Propagation to Slip Ratios folding: (a) footwall-fixed shear zone and (b) hanging wall-fixed As an illustration of how the trishear model can be used to shear zone. Base level rise was 1.0 m/ka, and sedimentation rate study more general fault-fold interaction, a fault with a trishear was 0.25 m/ka, together with a diffusion coefficient of 3.0 m2/a. zone at its tip propagating up from a flat decollement will be All other parameters were the same as in Figure 4. There is no vertical exaggeration. (a) Footwall fixed fall line of hanging wall-fixed trishear where the lower boundary is sweeping upward through the rock mass. In the second example (Figure 5) a lower base level rise of 0.5 m/ka has been included in the model run, together with a sedimentation rate of 0.5 m/ka. This simulates a situation in which the anticlinal crest is emergent and forms a topographic high against which sediments bank up [cf. Burbank and Verges, 1994]. Also included is a diffusion coefficient of 3.0 m2/a which simulates moderate local erosion of the uplifting structure. Figure 5a shows the results when the shear zone is fixed to the footwall, and Figure 5b shows the results when it is fixed to the hanging wall. The fold geometries developed in pregrowth strata are identical to those of Figure 4, but there is now erosion of the uplifting region and a pinching out of growth strata agains the uplifting and rotating limb of the structure. No growth anticline develops under these conditions. Once more, deformation within pregrowth and growth strata is more marked in the case of hanging wall-fixed trishear. In the third example (Figure 6) a base level rise of 1.0 m/ka has been included in the model run, together with a sedimentation rate of 0.25 m/ka, which simulates the situation in which a structure is fully submarine but forms a bathymetric high. Also included is a diffusion coefficient of 3.0 m2/a which simulates moderate local erosion in the area of the steep limb of the structure. Figure 6a shows the results when the shear zone is fixed to the footwall, and Figure 6b shows the results when it is fixed to the hanging wall. The models show a marked thinning of growth strata adjacento the uplifting and rotating limb of the (b) Hanging wall fixed fall line Figure 7. Growth strata associated with trishear fault propagauon folding: (a) footwall-fixed shear zone and (b) hanging wall-fixed shear zone. Total run time was increased to 1.6 Ma; otherwise, all parameters were the same as in Figure 5. There is no vertical exaggeration

7 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING 847 (a) (c) (d) 2 km Figure 8. A combined ramp-trishear, fault propagation fold. The slip rate on the fault was 1.0 rnyka, with the ramp dipping at 30 ø. The hanging wall-fixed shear zone had an apex angle of (a) 5 ø, (b) 10 ø, (c) 15 ø, and (d) 20 ø. Growth strata were recorded at intervals of 200 ka; total run time is 1 Ma.. Base level rise and sedimentation rate were both 0.55 m/ka. modeled (i.e., with ramp-flat geometry). Fault bend folding occurs on the backlimb [Suppe, 1983; Suppe et al., 1992] as the the hanging wall moves up the ramp while a trishear fault propagation fold pair develops above the propagating thrust. The dip of the ramp controls the dip of the backlimb. The fault tip propagates (at the slip rate) up from the d6collement with the triangular shear zone attached to its tip. Such a configuration with a variety of different apex angles is shown in Figure 8. When apex angles are low (5 ø to 10 ø) a strongly asymmetric fault propagation fold pair is formed with a steep, narrow, anticlinal forelimb. In contrast, when the apex angle is higher (15 ø to 20 ø) the structure which forms has a long forelimb (growth fold wavelength is greater), and the overall anticline has a more symmetric shape. The progressive evolution of a structure with a 10 ø apex angle is illustrated in Figure 9 (with associated growth strata). The development of the structure is shown after 0.4, 0.8, and 1.2 Ma in order to illustrate some important features. In form the fold evolves from a broadly symmetric structure to a more typical asymmetric fault propagation fold, with an overturning forelimb which will eventually become the site of fault breakthrough [Suppe and Medwedeff, 1990]. Importantly, one can observe that the forelimb rotates continuously through time, with beds initially thickening but, with continued rotation and overturning, later thinning quite markedly in the forelimb. These results are remarkably similar to those reported from sandbox analogue models by Storti et al. [1994] and Storti and McClay [1995] and to the finite element models of fault propagation folding presented by Braun and Sambridge [1994]. In the earlier trishear models presented here and by Erslev [1991] the ratio of fault propagation to slip (p/s ratio) is either 0 (footwall fixed) or 1 (hanging wall fixed). These are, however, only two possible configurations that may occur in nature [Williams and Chapman, 1983; MeNaught and Mitra, 1993] where a fault may propagate faster than its slip giving p/s ratios greater than 1. Indeed, a p/s ratio of 2 is an inherent feature of the fixed axial surface kink band fault propagation models of Suppe and Medwedeff[1990]. In their study of a dislocation model applied to natural fault propagation folds, Williams and Chapman [ 1983] report p/s ratios of 2 and higher. The effects of variable p/s ratios in the trishear model will now be considered. We place no mechanical significance upon this ratio and assume that rates of fault-slip to fault-tip propagation are not directly dependent upon each other. Figure 10 shows the results of a similar model to that in Figure 9c but with p/s ratios of 0, 1, 2, and 4. These results illustrate that the degree of folding (or shear strain) accommodated in the trishear zone ahead of the fault is controlled by the p/s ratio. A p/s ratio of 0 represents one extreme end-member where a very high strain can accumulate ahead of a nonpropagating fault. Withp/s ratios greater than 1, folds are cut increasingly early in their development by the propagating fault. The fault cuts through the common limb of the fold pair leading to the development of characteristic hanging wall anticlines and footwall synclines. Thus, as the p/s increases, the degree of folding ahead of the propagating fault decreases and the zone of deformation narrows. In this model, once the fault cuts through fold development ceases. Hanging wall anticlines and footwall synclines are commonly observed in association with thusts in nature [cf. Williams and Chapman, 1983; Alonso and Teixell, 1992; Mitra, 1990]. In the numerical 0.4 Ma (a) 0.8 Ma (c) Figure 9. Progressivevolution of a combined ramp-trishear, fault propagation fold. The slip rate on the fault was 1.0 m/ka, with the ramp dipping at 30 ø and a hanging wall-fixed shear zone having an apex angle of 10 ø. Growth strata were recorded at intervals of 200 ka. Base level rise and sedimentation rate were both 0.55 m/ka. Results are displayed after (a) 0.4, (b) 0.8, and (c) 1.2 Ma.

8 848 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING (a) p/s = 0 thinning, however, such layers only give information one dimension, that is, with respect to the layer boundaries. No information is given on internal layer deformation. Therefore, in order to better understand the character and spatial variation in deformation, particularly within the forelimbs of the numerical models, a series of initially circular strain markers have been included model runs. These markers undergo identical deformation to the horizontal layers, giving a two-dimensional picture of the resultant strain. Figure 12 shows the results of models with strain markers run at p/s ratios of 1, 2, 3, and 4. What is clear from these models is that when fault propagation to slip ratios are low (below 2), then the deformation in the forelimb of the structure, especially at deeper levels, is intense (extreme stretching and flattening of markers). In contrast, when the p/s ratio is greater than 2, the deformation the forelimb experiences before being cut by the propagating fault is relatively low. Deformation is restricted to a (c) p/s = 2 > narrow zone immediately adjacent to the fault plane. The higher 2 km the p/s ratio is, the narrower this deformed zone is. It is thus interesting to speculate that if the trishear mechanism operates in nature, the degree of development of a footwall syncline and hanging wall anticline is dependant largely on the p/s rati of the thrust. If these folds are absent or poorly developed, this could (d) p/s = 4 imply thathe p?s ratio of the fault was high, generally greater than 2. Thus a throughgoing fault with little or no folding could Figure 10. The effect of vailation in propagation to slip (p/s) be interpreted to have had an extremely high fault propagation to ratio on the development of a trishear fault propagation fold. The slip ratio leading to a very restricted zone of precursor slip rate on the fault was 1.0 m/ka, with the ramp dipping at 30 ø deformation adjacent to the fault plane (see Figure 12d). and a hanging wall-fixed shear zone having an apex angle of 10 ø. Growth strata were recorded at intervals of 200 ka; total mn time Comparison With Natural Examples of is 1 Ma. Base level rise and sedimentation rate were both 0.55 Nongrowth Fault Propagation Folds m/ka. Shown are (a) p/s equal to 0, (b) p/s equal to 1, (c) p/s equal to 2, and (d) p/s equal to 4. The applicability of the trishear model to natural fold-thrust geometries is now discussed. Natural examples of nongrowth fault propagation folds at different scales (Figure 13) are here compared to the nongrowth geometries generated by the adapted models presented here, these features are nothe result of "drag" against the fault plane [Berger and Johnson, 1980] but are the result of early ductile deformation ahead of the faul tip being later cut by the fault. The growth stratal geometries for p/s ratios of 0 and I have trishear model presented above. The first two examples are fault propagation folds associated with Vailscan thrusting in Upper Carboniferous coal measures at Broad Haven on the Pembrokeshire coast, west Wales. These structures are analyzed in some detail by Williams and Chapman already been discussed (Figures 4 to 7). Figures 10c and 10d suggesthat with even higher p/s ratios the forelimb of the growth fold pair becomes narrower and steeper so that at high p/s ratios evidence of growth may be hard to detect. A particular geometry of growth strata observed commonly in nature, the growth triangle or upward convergence of the axial planes of the fold pair, can be generated by the trishear model using higher p/s ratios and a reduced base level [e.g., Ford et al., 1997]. An example, generated by a p/s ratio of 2, is illustrated in Figure 11. What can be seen here is a subhorizontal anticlinal axial plane and a curved synclinal axial plane (concave up) within the growth strata, together with marked thinning of strata toward the anticline. The two axial planes converge upward but do not actually meet at a point. In the preceding examples, model results have displayed useful information on the amount of thickening and thinning Figure 11. Detail of growth strata on the forelimb of a trishear experienced in pregrowth and growth strata during deformation. fault propagation fold with a p/s ratio of 2 (Figure 10c). Growth One could, in principle, display many more horizons in order to strata were recorded at intervals of 200 ka; total run time is 1 Ma. better understand the spatial distribution of thickening or Base level rise and sedimentation rate were both 0.55 m/ka.

9 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING 849 (a) ooo (b) 00000,0ooooooooooo ooooooooooooo( ooo , ooooooooooo ooooo ooooooo ooo o 0 ) , I (c) ( ( 000( 0000( I ( ooooooooooooooo )oooooooooooooo Iooooooooo( oooooo oooooooooooooo )ooooooooooo )ooo Figure 12. Example of strains developed in the hanging walls and footwalls of thrusts due to different p/s ratios illustrated by the deformation of initially circular strain markers. The model parameters are identical to those of Figure 10. The strain markers have an initial radius of 50 m. Shown are (a) p/s equal to 1, (b) p/s equal to 2, (c) p/s equal to 3, and (d) p/s equal to 4. [1983], who, using a dislocation model, derived a p/s ratiof 2 for the first structure (Figure 13a). Similar fold forms are predicted by our models when p/s ratios are around 2 (see Figure 10c). In the first example (Figure 13a), thrust displacement dies out upward into an overfold, with considerable thickening of strata in the forelimb, which extends a distance in front of the fault tip. Notable in this example is the'manner in which the overfold opens outward and upward. The second example is a complex structure where the main thrust, labeled X in Figure 13b, can be clearly seen to be associated with both a hanging wall anticline and a footwall syncline. The thrust cuts approximately midway along the shared limb of these folds. Williams and Chapman [1983] derive ap/s ratio of 9.0 for this example and suggesthat, with rapid fault-propagation, the production of an overfold is restricted. Many of the features seen in this fold are similar to those predicted by our modified trishear model. Displacement-distance graphs [Williams and Chapman, 1983; Chapman and Williams, 1985] can be produced for trishear models with variable p/s ratios and compared to measurements on real fold-thrust structures in order to derive their p/s values. Results for the two structures described above are similar to those derived by Williams and Chapman using their dislocation model. The third example (Figure 13c) comes from the Chartreuse fold and thrust belt of the external western Alps. Here major thrusts cut through the forelimbs of kilometric scale west verging asymmetrical fold pairs [Gidon, 1988; Butler, 1992], leaving a footwall syncline and a hanging wall anticline. The forelimbs record complex strain histories [Butler, 1992] and in places have become overturned and stretched. Gidon [1988] suggests that displacement on the main thrusts dies out upward and concludes that the folds were well developed before the thrusts cut through. The fourth example is the famous Turner Valley structure of the external Canadian Rockie Mountains [Gallup, 1951 ]. As many authors have pointed out [e.g., Dahlstrom, 1977], displacement on the thrust diminishes rapidly upward, and the zone of folding opens upward (i.e., the axial planes converge downward). Dahlstrom [1977] recognized that the fault was propagating up in a growing fold so that at each stratigraphic level folding was followed by faulting. Chapman and Williams [1985] present a model for the progressive development of the Turner Valley structure as a fault propagation fold. They argue that fault propagation was rapid in this structure, yet their displacement-distance graph (Figure 2) suggests a p/s ratio of only 1.3. As pointed out above, the trishear model can also be applied to extensional and strike-slip fault systems. For example,.at Tejerina in the Cantabrian Zone of NW Spain an E-W trending strike-slip fault has cut through the shared limb of a vertically plunging fold pair (Figure 13e) [Alonso and Teixel 1992]. The thickness of strata is constant across the straight northern limb of the fold pair and changes only around the hinge and in the shared limb (forelimb) in the hanging wall. In the forelimb, strata curve and thin toward the fault, indicating a marked increase of deformation toward the fault in the hanging wall. This deformation is also recorded by the presence of pebbles pitted by pressure solution, small fractures, and veins. Elsewhere in the fold pair deformation is limited. Displacement on the fault dies out upsection where a more open fold is present. This structure seems to be consistent with a model in which a propagating fault is cutting a more ductile fold pair developing at its fault tip. The fold form opens away from the fault tip, very similar to a trishear zone of distributed deformation. In a second Pyrenean example of fault propagation folding, this time thrust related, Alonso and Teixell [1992] note that no fold has developed in a sandstone unit in the hanging wall, indicating a high p/s ratio (equivalent to their low s/p ratio), whereas a

10 850 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING (c) -' '-'f' ESE Lo. Berriasian Lip. (d)... ;,Tit honian ' \' ' 500m n'e" '"""N ' nti;' Urgo Oxfordian ' '"' /o. Kimmeridgian (e) N,, 500 m ['--1 Calcareous conglomerates r--! Shales I---] Quart z conglomerat es Figure 13. Five natural examples of nongrowth fault propagation folds: (a) fault propagation fold at Broad Haven, Pembrokeshire [after Williams and Chapman, 1983] (, 1983, reprinted with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington OX5 1GB, UK), (b) fault propagation fold at Broad Haven, Pembrokeshire [after Williams and Chapman, 1983] (, 1983, reprinted with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington OX5 1GB, UK), (c) syntheti cross section through the western Chartreuse thrust and the Fourvoirie anticline on the northern side of the gorges de Guiers Morts, western Chartreuse fold and thrust belt, external French Alps [modified after Gidon, 1988], (d) the Rocky Mountain Turner Valley structure [modified after DaMstrom, 1977], and (e) the Tejerina fault propagation fold in the Cantabrian Zone of Spain [after Alonso and Teixell, 1992, Figure 4]. hanging wall anticline is well developed in the overlying Comparison With Natural Examples of Growth carbonates, indicating a lower p/s ratio. Thus p/s ratio can vary Strata in Fault Propagation Folds along a single fault as it cuts through different lithologies. This feature has not yet been incorporated into the trishear model. The growth stratal geometries generated by the trishear model Comparison with these natural examples of fault propagation on the forelimb of fault propagation folds are here compared folds indicates that trishear fault propagation folding with p/s with some natural examples (Figure 14). Although difficulto ratios of 2 or greatereproduces fold-fault geometries and strains image on steep forelimbs, growth strata are recognized in young commonly seen in nature (see Figure 12). or active fold and thrust belts throughout the world [e.g., Ribr

11 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING 851 (a) N S b) Sierra de Valle F rt il,- -0 W Basement r '-- z- ' /: "'-' '-. '/, ¾ ;;' '.'; ;/ ;---: ' 2.' f... ;"'?(' ,,L:''';.--.-'%'_.:"' [- - -,,, , ? [. '..::.'.'ft +.,+,+ +*' +':, ; ,.! km t i :- -: !-[._q tt+tt i-- Figure 14. Three natural examples of growth strata associated with fault propagation folds: (a) a frontal fold in the external Sierras, central southern Pyrenees [modified after DePaor and Anastasio, 1987]; (b) line drawing of a seismic line across the westward verging Sierra de Valle F6rtil basement uplift, in the Precordilleran thrust belt of Argentina, showing the cumulative wedge on the forelimb (simplified from Zapata and Allmendinger [1996]), (c) N-S profile through the Sant Lloren de Morunys growth fold pair, northern margin of the Ebro Basin, SE Pyrenees [modified after Ford et al., 1997] (, 1997, reprinted with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington OX5 1GB, UK). 1976; Anadon et al., 1986; Nichols, 1987; DeCelles et al., 1991; Erslev, 1991; Colombo and Vdrges, 1992; DeCelles, 1994; Narr and Suppe, 1994; Hungerbuhler et al., 1995; Wickham, 1995; Zapatand Allmendinger, 1996). Figure 14 shows three examples of growth stratal geometries that have been generated during fault-related folding. All these examples clearly show thinning of the syntectonic strata toward the anticline and decreasing bed dips upsection the common limb. In the first example (Figure 14a), from the external Sierras of the Spanish Pyrenees [DePaor and Anastasio, 1987], Tertiary continental growth strata record the progressive rotation of the common limb in a fault-related fold. Minor structures complicate All the strata (alluvial conglomerates) in this structure record growth by gradual rotation of the fold limb. Ford et al. [1997] argue that the fold developed ahead of a propagating fault at depth. Unusually, the growth anticlinal closure has been preserved here. The anticlinal axial plane comprises en echelon segments which give an overall subhorizontal dip while the synclinal axial plane is concave up, so that two axial planes converge upward. A more westerly profile shows that the two axial planes do not eventually meet at a point but become parallel in the uppermost beds [Ford et al., 1997]. The fold pair is comparable in its geometry to the trishear model of Figure 11; however, the history of this fold is somewhat more complex in the growth geometries. Figure 14b shows a very similar but that through time the rate of sedimentation increased with respect larger geometry from the Precordillera thrust belt of Argentina, to tectonic uplift, so that the anticline was progressively recording progressive rotative offiap due to accelerated uplift of overlapped. In the adapted trishear model presented in this paper, the Sierra de Valle F6rtil thrust plate [Zapata and Allmendinger, slip rate and sediment flux can be varied for each time interval, 1996]. In both of thesexamples anticlinal crest has been allowing such structures to be modeled [Ford et al., 1997]. uplifted and eroded as the forelmb has rotated. Figure 14b can be compared to the trishear model of Figure 7, while in Figure 14a Discussion similar wedging the lower units was followed by growth onlap of theroded anticlinal crest. Following the original work of Erslev [ 1991 ], this paper shows A cross section through the growth fold pair of Sant Lloren that trishear provides a viable and important analytical tool for de Morunys on the northern margin of the Tertiary Ebro foreland the prediction and modeling of fault propagation folding. In basin, SE Pyrenees, is shown in Figure 14c [Ford et al., 1997]. homogeneoustratigraphic sequences it may be used to model the

12 852 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING way in which deformation is distributed in front of a propagating fixed to the fault tip. Within the shear zone, faultip. It can also be used to study the development of growth structures above propagating thrusts in foreland environments. vectors were variable with displacement magnitude toward the hangingwall. Outside the shear zone, Rotational growth strata are very common in foreland fold vectors were parallel to the fault plane. Within the shear zone and thrust belts. Whereas these structures can be explained by the primary mechanism of deformation waslip on a series of complex fault bend or fault propagation fold geometries [e.g., minor faults andistributed strain associated with folding of Suppetal., 1997; Zapata and Allmendinger, 1996], simple beds. These shear zones existed until the structures forelimb rotation associated with trishear fault propagation whereafter a distinct fault broke through the structure. Saltzer folding is an alternativexplanation. Overturning of growth and Pollard [1992], using a distinct element method, als0 strata is a natural consequence of trishear fault propagation folding when a structure takes up a large amount of slip. Such predicted such features to occur in overburden during extensional reactivation of basement normal faults. vertical or overturned growth stratare commonly observed in Finally, the production of footwall synclines and hanging wall natural examples (e.g., Figure 14c). It is difficulto imagine, or anticlines is an inherent property of the model presented here. model, growth strata associated with fault propagation folds These features are the expression of folding associated with the which grow self-similarly with an overturned forelimb; in such ductile deformation ahead of the fault tip and are later cut by the cases the conclusion must be drawn that the forelimb rotated propagating fault. They do not represent drag against the fault, through time. Forelimb rotation is also observed in finite although in field examples this interpretation is sometimes made element and analogue models of compressional deformation [Berger and Johnson, 1980]. The degree of development of these where material properties are close to those of natural rocks folds is dependent upon the relationship between fault slip and [Braun and Sambridge, 1984; Mitra and Islam, 1994; Storti et fault propagation. In nature such variations in p/s ratio can be al., 1994; Storti and McClay, 1995; Withjack etal., 1990]. related to lithology, depth in the crust, strain rate, or Upward convergence of the axial planes in a growth fold pair combinations thereof. For example, stronger lithologies lead to can be reproduced by trishear. Thus convergence alone cannot higher p/s ratios. In the trishear model, folding ends once the be used as diagnostic of a kink band migration mechanism of fault cuts through; in nature, however, folding may continue after fold development; the axial planes must additionally be shown to this point in the structure's evolution, indicating that active meet upward at a point. buckling may well be an additional process of variable Although trishear reproduces the broad geometric importance that is ongoing before, during, and after trishear. This relationships of basement, cover, and growth strata, it does not concept is supported by the observation that the backlimbs of predict the detailed patterns of deformation observed at the many growth anticlines contain cumulative wedges recording decimetric scale but rather predicts the broader configuration and rotation of this limb. At present this cannot be reproduced by location of structural and stratigraphic features. It predicts the trishear (e.g., Figure 10). bulk deformation patterns which may be accommodated at a smaller scale by a combination of fault-parallel shear, layer- Conclusions parallel slip, folding, and small-scale faulting. Such features have recently been reported from damage zones in front of thrust Erslev's [1991] original trishear model has been adapted to faultips by McGrath and Davison [1995]. These damage zones allow propagation from a flat decollement, variable fault widen away from the fault tip in an irregular, but broadly propagation to slip ratios, the modeling of growth strata, and triangular, manner. Within the damage zone shear strain analysis of strain across the structure. The models show increases toward the fault tip. In the example of McGrath and continuous rotation of the forelimb and the characteristic Davison [1995], deformation within the triangular zone is development of cumulative wedges within growth strata. When accommodated by folding and minor thrusting. Progressive total slip on a structure is high, the model predicts overturned rotation of fold limbs is indicated by both bedding and calcite- pregrowth and growth strata. During the initial stages of filled fractures. The appearance of large-scale "ductile" deformation, beds in the forelimb thicken but later thin when deformation in fault-related folds is also reported by Pfiffner beds become steep or overturned. High propagation to slip ratios [1990] as being achieved in the Jura Mountains at the smaller lead to the development of smooth fold profiles and detached scale by brittle processes such as bedding parallel extension, footwall synclines and hanging wall anticlines very similar to thrusting, and pinch and swell structures. Similar complex those observed in natural examples. Although not the only rotational strain histories (mainly involving faulting, local mechanism of fault-related folding, trishear appears to be a viable cleavage development, and small-scale folding) have been mechanism for linking distinct faulting at depth with more reported for the limbs of asymmetrical fault-related folds in the distributedeformation (minor faulting and/or folding)in Chartreuse fold and thrust belt of the external French Alps by stratigraphically higher units. Gidon [1988] and Butler [1992] (Figure 13c). Insights into the manner in which this distributed deformation Acknowledgments. S.H. acknowledges the receipt of a Royal Society may be accommodated are also available from analogue European Science Exchange Postdoctoral Fellowship., for which he is modeling studies. Triangular zones of distributedeformation very grateful. M.F. acknowledges the financial support of the BuMesamt above distinct faults have been described in analogue modeling ftir Bildung und Wissenschaft of Switzerland, the Geologisches Institute studies by Mitra and Islam [1994], and such zones of at ETH Ztirich, and the Swiss National Science Foundation. Comments deformation have also bee noted in extensional models by by Rick Allmendinger, Peter DeCelles, and an anonymous reviewer improved an earlier version of the manuscript. This work b, as benefited Withjack et al. [1990] (Figure 1). During modeling studies of greatly from discussions with Dave Waltham, Josep Poblet, Ken McCiay, both extension and compression they noted that deformation in Fabrizio Storti, Jaume Verg6s, Craig Docherty, Conxita Tabemer, Xavi stratigraphically higher units was distributed in a triangular zone Berastagui, Ed Williams, Martin Casey, and many other colleagues. displacement increasing displacement steepened,

13 HARDY AND FORD: TRISHEAR FAULT PROPAGATION FOLDING 853 References Alonso, J.L., and A. Teixell, Forelimb deformation in some natural examples of fault-propagation folds, in Thrust Tectonics, edited by K.R. McClay, pp , Chapman and Hall, New York, Anadon, P., L. Cabrera, M. Colombo, M. Marzo, and O. Riba, Syntectonic intraformational unconformiti6s in alluvial fan deposits, eastern Ebro Basin margin (NE Spain), Foreland Basins, edited by P.A. Allen and P. Homewood, Spec. Publ. Int. Assoc. Sedimentol., 8, , Berger, P., and A.M. Johnson, First order analysis of deformation on a thrust sheet moving over a ramp, Tectonophysics, 70, 9- synorogenic sedimentationand kinematic history of the Sevier thrust belt, northeast Utah and southwest Wyoming, Geol. Soc. Am. Bull., 106,32-56, DeCelles, P.G., M.B. Gray, K.D. Ridgway, R.B. Cole, P. Srivastava, N. Pequera, and D.A. Pivnik, Kinematic history of a foreland uplift from Paleocene synorogenic conglomerate, Beartooth Range, Wyoming and Montana, Geol. Soc. Am. Bull., 103, , DePaor, D. G. and D. J. Anastasio, The Spanish external Sierra: A case history in geometries associated with fault-bend and fault-propagation folding, Mar. Pet. Geol., 12, , Hardy, S., and D. Waltham, Computer modelling of tectonics, eustacy, and sedimentation using the Macintosh, Geobyte, 7, 42-52, Hardy, S., C. Dart, and D. Waltham, Computer modelling of the influence of tectonics upon sequence architecture of coarsegrained fan-deltas, Mar. Pet. Geol., 11, , Hungerbuhler, D., M. Steinmann, W. Winkler, D. Seward, A. Eguez, F. Heller, and M. Ford, An integrated study of fill and deformation in the Andean intermontaine the advance and retreat of mountains, Nat. Geogra. Res., 3 (2), , , Bosence, D.W.J., L. Pomar, D. Waltham, and T. Lankester, Computer modelling a Miocene carbonate platform, Mallorca, Spain, AAPG Bull., 78, , Braun, J., and M. Sambridge, Dynamic Lagrangian Remeshing (DLR): A new Elliot, D., The energy balance and deformation mechanisms of thrust sheets. Philos. Trans. Ro. Soc. London, Ser. A, 283, Erslev, E.A., Trishear fault-propagation folding, Geology, 19, , Erslev, E.A., and J.L. Rogers, Basement-cover basin of Nabon (Late Miocene), southern Ecuador, Sediment. Geol., 96, , Jamison, J.W., Geometrical analysis of fold development in overthrust terranes, J. Struct. Geol., 9, , algorithm for solving large strain geometry of Laramide fault-propagation Johnson, A.M., Orientations of faults deformation problems and its application to fault-propagation folding, Earth Planet. Sci. Lett., 124, , Burbank, D.W., and J. Verg6s, Reconstruction of topography and related depositional systems during active thrusting, J. Geophys. Res., 99, 20,281-20,297, Batler, R.W.H., Structural evolution of the western Chartreuse fold and thrust system, folds, in Laramide Basement Deformation in the Rocky Mountain Foreland of the Western United States, edited by C.J. Schmidt, R.B. Chase, and E.A. Erslev, Spec. Pap. Geol. Soc. Amer. 280, , Fisher, M.W., and M.P. Coward, Strains and folds within thrust sheets: An analysis of the Heilam sheet, northwest Scotland, determined by premonitory shear zones, Tectonophysics, 247, , Kenyon, P.M., and D.L. Turcotte, Morphology of a delta prograding by bulk sediment transport, Geol. Soc. Am. Bull,, 96, , Kooi, H., and C. Beaumont, Escarpment evolution on high-elevation rifted margins: Insights from a surface process model that NW French Subalpine Chains, in Thrust Tectonophysics, 88, , combines diffusion, advection, and Tectonics, edited by K. R. McClay, Chapman and Hall, New York, pp , Chapman, T.J., and G.D. Williams, Strains developed in the hangingwalls of thrusts Flemings, P.B., and T.E. Jordan, A synthetic stratigraphic model of foreland basin development, J. Geophys. Res., 94, , Fletcher, C.A.J., Computational Techniques reaction, J. Geophys. Res., 99, 12,191-12,209, McGrath, A.G., and I. Davison, Damage zone geometry around fault tips, J. Struct. Geol., 17, , due to their slip/propagation rate: A for Fluid Dynamics, vol. 1, Fundamentals McNaught, M.A., and G. Mitra, A kinematic dislocation model: Reply, J. Struct. Geol., and General Techniques, 2nd ed., Springermodel for the origin of footwall synclines, 7, , Verlag, New York, J. Struct. Geol., 15, , Colman, S.M., and K. Watson, Ages estimated Ford, M., E.A. Williams, A. Artoni, J. Verg6s, Medwedeff, D. A., Geometry and kinematics from a diffusion equation model for scarp and S. Hardy, Progressivevolution of a of an active, lateraliy propagating wedge degradation, Science, 221, , fault-related fold pair from growth strata thrust, Wheeler Ridge, California, in Colombo, F., and J. Vergds, Geometria del geometries, Sant Lloren9 de Morunys, SE Structural Geology of Fold and Thrust margen S.E. de la Cuenca del Ebro: Pyrenees, J. Struct. Geol., 19, , Discordancias progresivas en el Grupo Belts, (edited by S. Mitra and G.W Fisher), Baltimore, Md., Johns Hopkins Univ. Scala Dei, Serra de La Llena, (Tarragona), Gallup, W. D., Geology of Turner Valley oil Press, pp. 3-28, Acta Geol. Hisp., 27, 33-53, and gas field, Alberta, Canada, AAPG Bull., Contreras, J., and M. Surer, Kinematic 35, , Mitra, S., Fault-propagation folds: Geometry, modelling of cross-section deformation Gidon, M., L'anatomie des zones de kinematic evolution and hydrocarbon traps, sequences by computer simulation, J. chevauchement du massif de la Chartreuse AAPG Bull., 74, , Geophys. Res., 95, 21,913-21,929, (Chaine subalpineseptentrionales, Is re, Mitra, S., and Q.T. Islam, Experimental (clay) Cooper, M.A., and P.M. Trayner, Thrust France), Geol. Alpine, 64, 27-48, models of inversion structures, surface geometry: implications for thrust- Hardy, S., Numerical modelling of the Tectonophysics, 230, , belt evolution and section-balancing techniques. J. Struct. Geol., 8, , response to variable stretching rate of a domino fault block system, Mar. Pet. Geol., 10, , Narr, W., and J. Suppe, Kinematics of basement-involved compressive structures, Am. J. Sci., 294, , Dahlstrom, C.D.A., Structural geology in the Hardy, S., and J. Poblet, Geometric and Nichols, G.J., Syntectonic alluvial fan eastern margin of the Canadian Rocky numerical model of progressive limb sedimentation, southern Pyrenees, Geol. Mountains, in Guidebook 29th Annual rotation in detachment folds, Geology, 22, Mag., 124, , Field Conference, Wyoming Geol. Assoc., , Pfiffner, O.A., Kinematics and intrabed~strain Jackson, pp , Hardy, S., and J. Poblet, The velocity in mesoscopically folded limestone layers: DeCel!es, P.G, Late Cretaceous-Paleocene description of deformation, 2, sediment Examples from the Jura and Helvetic Zone