Deformation along oblique and lateral ramps in listric normal faults: Insights from experimental models

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1 GEOLOGIC NOTE Deformation along oblique and lateral ramps in listric normal faults: Insights from experimental models Shamik Bose and Shankar Mitra ABSTRACT Listric growth faults in passive margin settings such as the Gulf of Mexico and Niger Delta are commonly characterized by lateral and oblique ramps related to preexisting structural or stratigraphic discontinuities. Clay experiments have been used to model the geometry, orientation, density, and connectivity of secondary faults formed along lateral and oblique ramps. Extension results in the formation of an expanding set of synthetic faults tied to the fixed footwall and a corresponding set of antithetic faults tied to a moving hanging wall. Some of the synthetic fault strands eventually connect to form the master fault, whereas antithetic faults continue to develop, with progressive transfer of slip to newly formed faults. Characteristics such as fault orientation, fault density distribution, and shape, size, and distribution of connected fault clusters vary with (1) ramp offset angles, (2) structural position, and (3) total extension. In map view, secondary antithetic and synthetic faults mimic the geometry of the main fault, but the orientations of secondary faults are approximately 25 33% of the offset angle of the oblique or lateral ramps. Fault densities and connectivities are initially higher along the frontal ramps. With increasing extension, the maximum cluster size of connected faults increases dramatically in the oblique and lateral segments due to the intersection of fault sets of different orientations. These observations regarding fault orientations, densities, and connectivities provide important insights on the AUTHORS Shamik Bose ConocoPhillips School of Geology and Geophysics, University of Oklahoma, Norman, Oklahoma 73019; shamik.bose-1@ou.edu Shamik Bose is a Ph.D. student at the University of Oklahoma. He received his B.Sc. degree from the University of Calcutta (India), an M.Sc. degree from the Indian Institute of Technology, Kharagpur (India), and an M.S. degree from the University of Oklahoma. His research interests include analog modeling of natural structures in the extensional regime, primarily using wet clay and three-dimensional structural modeling. Shankar Mitra ConocoPhillips School of Geology and Geophysics, University of Oklahoma, Norman, Oklahoma 73019; smitra@ou.edu Shankar Mitra holds the Monnett Chair in Energy Resources at the University of Oklahoma. He received his Ph.D. in geology from Johns Hopkins University in His primary interests are in structural interpretation and modeling and their application to hydrocarbon exploration and production. ACKNOWLEDGEMENTS The authors would like to thank AAPG reviewers Don Medwedeff, Sandro Serra, and Hongbin Xiao and AAPG editor Gretchen M. Gillis for their comments and suggestions, which improved the manuscript. We also thank Kajari Ghosh for her help with ARCView GIS and Ze ev Reches for his suggestions regarding clay modeling. H. C. Spinks provided the clay for the experimental modeling. Shamik Bose also acknowledges the Society of Exploration Geophysicists for a scholarship in support of the study. Copyright The American Association of Petroleum Geologists. All rights reserved. Manuscript received September 4, 2008; provisional acceptance October 29, 2008; revised manuscript received November 20, 2008; final acceptance December 8, DOI: / AAPG Bulletin, v. 93, no. 4 (April 2009), pp

2 structural geometry and mechanisms of formation of faults as well as the configuration of fault networks for fluid flow in passive margin settings. INTRODUCTION Passive margin settings such as the Gulf of Mexico and the Niger Delta contain listric growth faults and related rollover folds. Extensive research has been conducted on the two-dimensional crosssectional geometries of these fold-fault systems, as well as the mechanism of formation of the hanging-wall rollover geometries and their relationship to the faults. The approach used has included both the use of experimental clay and sand models (Cloos, 1968; McClay and Ellis, 1987; Dula, 1991; Withjack et al., 1995), and related kinematic and geometric models (Groshong, 1989; Dula, 1991; Xiao and Suppe, 1992). This research has enabled the development of models for predicting fold and fault shapes in areas with limited data (Dula, 1991; Xiao and Suppe, 1992). Analog experimental models have been successfully conducted to study listric faults terminating in salt substrates in passive margin settings (Vendeville and Cobbold, 1988; Vendeville and Jackson, 1992a, b; Brun and Fort, 2004; Vendeville, 2005). Several insights regarding these fold-fault systems have been obtained from the experimental models. The models have also enabled a good understanding of the formation of secondary synthetic and antithetic faults and their relationship to the larger structures. With the exception of Cloos (1968) and Serra and Nelson (1988), however, all of the clay experiments used a preexisting listric ramp with a rigid footwall. Although this configuration enables the detailed study of the hanging-wall deformation, it does not provide any information on the development and geometry of the master fault. Maps of growth-fault systems, such as those from the Niger Delta (Doust and Omotsola, 1989) and the Gulf of Mexico, show that the map patterns of these faults are also complex. The faults commonly exhibit lateral or oblique ramps (Figure 1), which form by the linkage of discrete fault segments with progressive lateral fault propagation. The offsets of the original fault segments may be related to preexisting stratigraphic or structural discontinuities, such as facies changes or preexisting faults. A few studies (Cloos, 1968; Braun et al., 1994; Medwedeff and Krantz, 2002) have addressed the map or three-dimensional patterns of the major and secondary faults along listric normal faults. Serra and Nelson (1988) observed variation of secondary fault patterns and half-graben development in convergent transfer zone setups using clay models. The boundary conditions used in these models, however, are more applicable to rift systems. Several studies of oblique extension in rift systems have also been conducted (Withjack and Jamison, 1986; McClay and White, 1995; Clifton and Schlische, 2001; McClay et al., 2002). These studies have addressed the development of oblique and strike-slip faults along oblique rift systems, but the results do not specifically pertain to the nature of deformation along the boundaries between frontal and oblique or lateral ramps in listric faults. An understanding of the deformation associated with lateral and oblique ramps is critical in understanding the geometry and kinematics of growthfault systems. This article presents a study of the deformation associated with lateral and oblique ramps using experimental clay models. The models study the following features associated with the deformation: 1. The geometry and kinematic evolution of hangingwall and footwall structures in cross sectional view along frontal ramps, with particular emphasis on the evolution of secondary synthetic and antithetic faults 2. The map patterns of secondary faults along frontal and lateral or oblique ramps, and their mechanism of propagation and progressive evolution 3. The variation in density and connectivity of the secondary faults along the frontal and lateral oblique segments of the master fault The evolution of faults, map patterns of fault networks, variation of density, and connectivity 432 Geologic Note

3 Bose and Mitra 433 Figure 1. Subsurface map of Niger Delta (modified from Doust and Omotsola, 1989) showing major faults in the basement and listric faults in the sedimentary cover. Several lateral and oblique ramps and fault linkages of different scales are present. Some of these are highlighted by boxes.

4 and change in structural relief of the top surface of the clay provide us with important insights on the location of traps, the degree of complexity in the compartmentalization of a reservoir, and the possible fluid-migration pathways. Both sand and clay models provide scaled models for large-scale extensional structures, and the merits of using both materials have been discussed in detail in many of the articles discussed above. Clay was used in the present study because it forms discrete faults whose parameters ( length, orientation, density, and displacement) can be measured. The main disadvantage of using clay is that it does not enable the study of growth sediments, which represent an important part of listric fault systems. However, because the main purpose of the present study was to analyze the geometry and evolution of secondary faults, this factor does not negatively impact the experimental results. EXPERIMENTAL APPROACH The experiments were conducted using an apparatus in which a clay layer was deformed by progressively moving a plate attached to a backstop away from a stationary plate attached to a second backstop. The rate of extension was controlled by two motors and kept constant at 0.4 mm/min (0.039 in./min) for all experiments. The analog material used to model the sedimentary units was a layer of wet clay with a thickness of about 8 cm (3.1 in.) and a density of 1.6 to 1.65 g/cm 3. Deformation at the master fault was simulated using two separate setups: a flat base-plate setup and a rigid footwall setup (Figure 2). The flat baseplate setup consisted of two thin metal plates, attached to each of the backstops, with the stationary plate overlying the moving plate. The relative motion between the plates resulted in the master normal fault propagating upward from the detachment (moving plate) at its contact with the fixed plate. This experimental setup does not use a preexisting ramp geometry and enables the study of the progressive development of the master fault. In the rigid footwall setup, the stationary plate was attached to a predefined ramp dipping at 30 overlying a moving plate containing the clay layer. Motion of the clay layer away from the rigid stationary ramp resulted in the formation of a rollover structure in the hanging wall of the fault. This setup was used to study the deformation in the hanging wall of the fault associated with a well-defined master fault. Three sides of the clay cake were free surfaces, and the clay remained attached to the moveable base plate as it was pulled away from the fixed base plate. The fault surfaces were the only frictional surfaces within the clay cake. These boundary conditions remained constant throughout the length of the experiment. For each setup, two sets of experiments were conducted, the first with a lateral (90 ) offset in the position of the footwall ramp and the second with a 30 offset along an oblique ramp (Figure 2). The lateral ramp and oblique ramp geometries were produced using lateral or oblique offsets in the footwall plate for the flat base-plate experiments. For the rigid footwall setup, the fixed footwall ramps were designed to contain the lateral and oblique ramps. The top of the clay layer was studied during the incremental deformation, and the development of secondary faults was mapped in detail at finite steps in the deformation process. In addition, cross sectional views of the frontal ramp segment were also studied to enable a correlation between observations in the cross sectional and map views. In the following sections, the results of the experiments for the flat base-plate experiments will be discussed in detail. The similarities and differences in the rigid footwall experiments will then be briefly discussed. CROSS-SECTIONAL GEOMETRY AND EVOLUTION The fault growth of both the master fault and the secondary synthetic and antithetic faults is best understood in the flat base-plate experiments. Therefore, our discussions will focus primarily on the results of these experiments. Significant differences in results for the rigid footwall experiments will then be described. 434 Geologic Note

5 Figure 2. Experimental setup with configuration of base plates and rigid footwall blocks used to generate listric faults in the overlying clay. Arrows indicate the direction of motion of the moveable base plate (gray). (a) Average dimensions of lateral ramp setups. (b) Average dimensions of oblique ramp setups. (c) Flat base-plate lateral setup with 90 offset in the frontal edge of the overlying fixed base plate. (d) Flat base-plate oblique ramp setup with 30 offset in the frontal edge of overlying fixed base plate. (e) Rigid footwall lateral ramp setup with 90 offset in the aluminum block. (f) Rigid footwall oblique ramp setup with 30 offset in the aluminum block. Initial extension results in the formation of a symmetric graben bounded by a curved primary synthetic fault system (PS) and a conjugate antithetic fault system (PA) forming immediately above the fault. During the development of both the primary synthetic and antithetic faults, deformation is Bose and Mitra 435

6 accommodated by the formation of a narrow zone of secondary faults (SA and SS), which are conjugate to the primary fault systems and typically have shallower dips (Figure 3a). Continuing extension results in the formation of a more asymmetric half graben and associated rollover structure with different geometries and kinematic evolution histories of the synthetic and antithetic fault systems (Figure 3b d). Some of the primary synthetic faults ultimately coalesce to form the master synthetic fault, whereas the formation of antithetic faults involves the progressive transfer of slip to newly formed active faults. The synthetic faults are tied to the stationary footwall and develop as a narrow band along the initial contact between the stationary and moving plates. Several of the synthetic fault strands coalesce to form a single master fault, which increases in dip up section. The blocks between the individual fault strands form fault-bounded horses and are eventually smeared out along the master fault (Figure 4). Once a through-going master fault has developed, most of the movement is concentrated on this fault and the formation of additional synthetic faults is restricted. The formation of the primary synthetic faults is initially related to a drape of the units above an upwardly propagating fault zone. After the master fault has propagated through the entire section, additional faulting is related primarily to synthetic shear associated with frictional resistance to movement on the master fault. In the final stage, the secondary synthetic faults form a narrow band extending from the footwall to the hanging wall of the master fault. The antithetic fault system that is tied to the moving hanging wall shows a slightly different behavior. In the early stage, the formation of antithetic faults is related to symmetric graben development (Figure 3a), and the density and geometry of antithetic faults are very similar to the synthetic faults. Secondary antithetic and synthetic faults also form between the main antithetic faults. However, with the progressive evolution of an asymmetric graben, the formation of antithetic faults is related to the formation of the rollover structures. During this later stage, the antithetic faults are formed primarily at important bends in the master fault. With increasing extension, each antithetic fault moves away from the base of the ramp, and a new fault forms in its place so that the hanging wall consists of a number of evenly spaced faults. MAP PATTERNS Lateral Ramp Fault Geometry and Evolution The progressive evolution of fault patterns in map view was analyzed by studying the top view of the experimental model in a series of incremental steps. Initial extension results in the formation of a band of short synthetic faults above the contact between the footwall and hanging-wall plates and an associated band of antithetic faults. Both sets of secondary faults are parallel to the trend of the frontal ramp. The two bands of faults are offset along the change in position of the base of the footwall ramps. Initially, no faults are formed in the lateral ramp segment (Figure 5). Increasing extension results in an increase in the width of the band of faults. The individual faults propagate laterally and eventually link up with adjacent faults. The faults exhibit small jogs or hooked patterns along the zones of linkage (Figure 6). Because of the offset of the main fault along the lateral ramp, the antithetic faults from one zone overlap with synthetic faults of the other zone. In general, the extent of overlap will depend on the amount of offset of the two fault segments. Oblique faults initiate and propagate through the lateral ramp segment and occur in a distinct enechelon pattern. Beyond a certain amount of extension, strain is focused on a single master fault on each side of the lateral ramp. Along the frontal ramp, few additional synthetic faults develop beyond this stage, and the restored map width of the synthetic faulted zone shows a relatively constant band of faults. The antithetic faults, however, continue to develop with progressive shearing of the hanging wall. In the lateral ramp zone, the oblique synthetic and antithetic fault segments continue to propagate, and 436 Geologic Note

7 Bose and Mitra 437 Figure 3. Series of photographs of the sectional view showing the sequential development of antithetic and synthetic faults changing the overall geometry of the clay cake from a symmetrical graben (a) to an asymmetrical half graben (d). (a) Sectional view at 0.4-cm (0.15-in.) extension. PS and PA = primary synthetic and antithetic faults; SS and SA = secondary synthetic and antithetic faults. (b) Sectional view at 0.7-cm (0.27-in.) extension. (c) Sectional view at 1-cm (0.39-in.) extension. (d) Sectional view at 1.4-cm (0.55-in.) extension. Note the coalescence of synthetic faults to form the major listric normal fault and the continued development of antithetic faults to accommodate the hanging-wall rollover.

8 Figure 4. Sequence of photographs a f, displaying the development of the master synthetic fault by linkage of individual segments of secondary normal faults. 438 Geologic Note

9 Figure 5. Series of diagrams displaying the map traces of faults at extensions of (a) 1.9, (b) 2.3, (c) 3.3, and (d) 4.8 cm (0.74, 0.9, 1.29, and 1.88 in.) for the lateral ramp experiment. The rose diagrams show the orientations of antithetic and synthetic faults at the frontal and lateral ramps. The mean direction of faults in the frontal ramp zone is 0 and in the lateral ramp zone is 31.5 (synthetic) and 30 (antithetic). as a result of the interference of these faults with the faults on the frontal ramp, the faults show a characteristic jogged pattern (Figure 5c, d). The intersection of the fault sets also results in rhombic blocks bounded by faults with two different orientations (Figure 5d). Structural relief also changes from the frontal ramp to the lateral ramp. Rollover folds form in the hanging-wall blocks adjacent to the frontal ramps, and local structural highs develop on the crests of the folds. Because the slip along the frontal ramp decreases toward the lateral ramp, a structural high forms above the lateral ramp. This provides us with an important insight on the development of possible structural traps in these settings. Fault Orientations The secondary faults along the frontal ramp are oriented perpendicular to the direction of extension, whereas along the lateral ramp zone, the mean direction of synthetic faults is 31.5 and that of the antithetic faults is 30 with reference to the strike of the frontal ramp. These values are approximately 25 33% of the base-plate offset angle Bose and Mitra 439

10 440 Geologic Note Figure 6. Series of map-view photographs showing fault linkage along (a) the frontal ramp and (b) the intersection of the frontal and lateral ramps. (a) Arrows show locations where parallel fault strands on the frontal ramp overlap and coalesce by hooking to form larger faults. (b) Arrows show locations where faults with different orientations intersect or merge to form curved faults at the frontal-lateral ramp intersection.

11 Figure 7. Plots of length (centimeters) versus orientation (degrees) of synthetic and antithetic faults at extensions of 1.9, 2.3, 3.3, and 4.8 cm (0.74, 0.9, 1.29, and 1.88 in.) (lateral ramp experiment). An increase in the spread of orientations and lengths is noticeable as extension progresses. Bose and Mitra 441

12 Figure 8. Density maps of faults at (a) 1.9-, (b) 2.3-, (c) 3.3-, and (d) 4.8-cm (0.74-, 0.9-, 1.29-, and 1.88-in.) extensions, calculated using a search radius of 1 cm (0.39 in.) for a cell size of 0.01 cm (0.003 in.) (lateral ramp experiment). Scale units are in centimeters per square centimeter (cm/cm 2 ). of 90. Although the mean directions of the synthetic and antithetic faults are unchanged through the entire experiment, the range in the orientation of the faults increases with extension. A plot of the length of the faults versus orientation displays the fact that both the length and range of orientation of the faults increase with increasing extension (Figure 7). The reasons for this increase are the late formation of oblique faults in the lateral fault segment and the rotation of preexisting faults along the junction of the frontal and lateral ramps. Fault Density and Connectivity Densities of faults were measured using the total length of faults of all orientations within a unit area. 442 Geologic Note

13 Figure 9. Connectivity cluster maps of faults at extensions of (a) 1.9, (b) 2.3, (c) 3.3, and (d) 4.8 cm (0.74, 0.9, 1.29, and 1.88 in.) (lateral ramp experiment). Shaded regions indicate connected network of faults. Initial stages show connectivity clusters in the frontal ramps. At later extensions, rhombic clusters form along the intersections of the frontal and lateral ramps. The densities are estimated in ARC GIS, using the summed lengths of faults within a circle with a 1-cm (0.39-in.) radius, throughout the grid. The temporal variations in fault density are illustrated in Figure 8. The fault density is initially highest in isolated pods along the frontal ramps. Almost Bose and Mitra 443

14 no faults develop initially in the lateral segments. With increasing extension, the band of high densities extends through the lateral ramp zone, but the highest densities are located in the frontal ramp segments. From the perspective of understanding fluid flow along faults and their sealing properties, a factor that is more important than the fault density is the nature of fault connectivity. Fault connectivity can be best represented through cluster analysis, an approach based on percolation theory, which has primarily been applied to study the connectivity of rock fractures (Stauffer, 1985; Bebbington et al., 1990; Berkowitz, 1995). Twodimensional mapping of clusters of connected faults provides a qualitative estimate of the spatial distribution of connected fault networks. In these maps (Figure 9), the shaded patches indicate areas that constitute a single connected network. The size of the connectivity clusters increases with progressive extension. In the early stages of extension, the development of connected networks is limited because most faults are short and approximately parallel to each other. With increasing extension, the secondary synthetic and the antithetic faults are connected along the frontal ramps by the overlap and hooking of fault segments (Figure 6); however, the lateral ramp segments show relatively low connectivity. When the magnitude of extension is significant enough to result in well-developed synthetic and antithetic faults along the lateral ramp segments, a significant increase in connectivity is observed, particularly along the intersections of the frontal and lateral ramps. These zones are marked by intersections of faults of different orientations resulting in wide clusters consisting of rhombic fault intersections. Oblique Ramp The oblique ramp experiments were conducted using oblique ramp segments at an angle of 30 to the frontal ramps. Fault Geometry and Evolution The development of faults follows a similar pattern to that in the lateral ramp experiment. The faults begin to form in the frontal ramp zones with a small amount of extension and later in the oblique ramp zone as en echelon faults. However, initiation of faults in the oblique ramp zone occurs at an earlier stage in the experiment than in the lateral ramp experiment. Initial stages of fault growth are dominated by lateral segment linkage and by development of new faults (Cartwright et al., 1996). After a certain amount of extension, development of new synthetic faults ceases, and all displacement occurs along the preexisting faults. Antithetic faults continue to develop throughout the experiment. In contrast to the lateral ramp experiment, the synthetic and antithetic faults form distinct zones, and there is no overlap of these zones. The variation of structural relief is more subtle than that observed in the lateral ramp experiment. Fault Orientations Secondary faults in the frontal ramp zone are oriented perpendicular to the direction of extension. In the oblique ramp zone, the mean orientation of synthetic faults is 8.25 and that of the antithetic faults is 3.75 with reference to the strike of the frontal ramp (Figure 10). The orientations of the synthetic faults are again approximately 25 33% of the ramp offset angle of 30. A plot of the orientation of faults versus their lengths (Figure 11) shows that although there is an increase in the length of the faults resulting from growth by segment linkage, the range of orientation remains relatively small throughout the length of the experiment. The reason for this difference with the lateral ramp experiment is the smaller variation in angle of faults between the frontal and oblique ramps. Fault Density and Connectivity In the early stages, fault densities for both synthetic and antithetic faults are higher along the frontal ramps than along the oblique ramps; however, the variation in density is much smaller than in the lateral ramp experiment (Figure 12). With progressive deformation, the densities increase in both frontal and oblique ramp zones until two wide bands of relatively uniform densities develop separated by a zone with almost no faults. In the very final stages, 444 Geologic Note

15 Figure 10. Series of diagrams displaying map traces of faults at extensions of (a) 1.6, (b) 2.6, (c) 3.4, and (d) 5.1 cm (0.62, 1, 1.33, and 2 in.) for the oblique ramp experiment. Rose plots show orientations of antithetic and synthetic faults at the frontal and oblique ramps. The mean direction of faults in the frontal ramp zone is 0 and in the oblique ramp zone is 8.25 (synthetic) and 3.75 (antithetic). the average density actually drops; this is attributed to the localization of slip on a few key faults. As in the previous experiment, connected fault networks originate along the frontal ramps and increase in size with progressive extension (Figure 13). However, the clusters develop earlier than in the lateral ramp segment because of earlier fault propagation and linkage through the oblique ramp segment. With increasing extension, both the synthetic and antithetic fault zones form a uniform distribution of clusters through the faulted zone. The connected network of faults forms rhombic patterns in the oblique ramp segment; however, the variation in fault orientations making up the rhombic clusters is less than in the case of lateral ramps. RIGID RAMP EXPERIMENTS Rigid footwall experiments were conducted for both lateral and oblique ramp cases using the apparatus shown in Figure 2. The primary purpose of these experiments was to study the controls of ramps of a known geometry on the development and patterns of secondary faults in both cross sectional and map views. The overall results of these Bose and Mitra 445

16 Figure 11. Plots of length (centimeters) versus orientation (degree) of synthetic and antithetic faults at extensions of 1.6, 2.6, 3.4, and 5.1 cm (0.62, 1, 1.33, and 2 in.) (oblique ramp experiment). No significant increase in spread of orientation data with progressive extension is noticeable. 446 Geologic Note

17 Figure 12. Density maps of faults at (a) 1.6-, (b) 2.6-, (c) 3.4-, and (d) 5.1-cm (0.62-, 1-, 1.33-, and 2-in.) extensions, calculated using a search radius of 1 cm (0.39 in.) for a cell size of 0.01 cm (0.003 in.) (oblique ramp experiment). Scale units are in centimeters per square centimeters (cm/cm 2 ). Bose and Mitra 447

18 Figure 13. Connectivity cluster maps of faults at extensions of (a) 1.6, (b) 2.6, (c) 3.4, and (d) 5.1 cm (0.62, 1, 1.33, and 2 in.) (oblique ramp experiment). Shaded regions indicate connected network of faults. experiments were similar to those in the flat baseplate experiments. The key differences and their significance are outlined below. In the cross sectional view, the primary difference is that the early stage of symmetric half-graben development is absent, along with the symmetrically 448 Geologic Note

19 Bose and Mitra 449 Figure 14. Series of photographs showing the development of a rollover structure and related synthetic and antithetic faults in the rigid footwall experiment. The main antithetic faults form in a progressively widening zone between the active axial surface (dashed line) and passive axial surface (solid line). A secondary set of synthetic and antithetic faults form a small symmetric graben at the top of the rigid ramp.

20 distributed synthetic and antithetic faults. Instead, the structure develops an early asymmetric half graben. The first faults to form are synthetic and are related to synthetic shear or drape along the preexisting fault. With progressive deformation, the formation of new synthetic faults stops. Antithetic faults are related entirely to the formation of the asymmetric rollover (Figure 14) and form between the synthetic active and passive axial surfaces (see also Xiao and Suppe, 1989). Map-view fault configurations are mostly similar to the flat base experiments. The primary differences are that the synthetic faults form and also mature early, resulting in a narrow but well-defined fault zone immediately adjacent to the fault. Antithetic faults, however, form later and are distributed over a wider zone. The fault orientations show similar patterns, with a larger dispersion of orientationsinthelateralrampexperimentthaninthe oblique ramp experiment. The differences in the evolution, distribution, and orientation of the secondary faults are also manifested in the density and connectivity. The synthetic faults form a narrow zone with high densities and connectivities, whereas the antithetic faults show lower densities and connectivities. The fault clusters are marked by more linear patterns along the frontal ramps and more rhombic patterns at the junction between the frontal and lateral or oblique ramps. CONCLUSIONS The results of experimental modeling provide insights on the evolution of listric growth faults and the nature of secondary faulting along oblique and lateral ramps. The cross sectional geometry of structures along a listric growth fault develops in two distinct phases. Early deformation results in the formation of a symmetric graben with symmetrically distributed synthetic and antithetic faults and related lowerorder faults. Increasing extension results in the coalescence of some of the synthetic faults to form a major listric normal fault. Once the major fault has formed, the structure is transformed into a half graben with the formation of an asymmetric rollover structure. During this phase, the formation of new synthetic faults is limited to accommodate synthetic shear because of movement on the major fault. Antithetic faults continue to develop and accommodate the deformation of the hanging wall to form an asymmetric rollover, and are therefore distributed over a broad zone. Early formation of a major normal fault, as modeled by the rigid ramp experiments, results in an earlier transformation to the asymmetric rollover geometry and the formation of the secondary synthetic and antithetic faults. Map views of the developing structures show the evolution of antithetic and synthetic faults, and also their change in orientation along lateral or oblique ramps. Secondary faults initiate at the frontal ramps and develop at a later stage on the lateral or oblique ramps. With progressive deformation, the fault lengths and densities increase by lateral and radial propagation and the linking of adjacent faults. With increasing extension, two parallel bands form, one consisting of synthetic faults and the other of antithetic faults. After the formation of the major listric normal faults, the growth of synthetic faults is limited, whereas, the antithetic faults continue to propagate. Along the lateral and oblique ramps, the secondary faults form at angles of 25 33% of the major lateral or oblique fault angle. Therefore, the range of orientations of secondary faults for lateral ramps is greater than those for oblique ramps. Fault connectivity clusters first form with elongate shapes along the frontal ramps in the early stages of the experiment. As extension progresses, larger clusters appear at the frontal ramps, and in the late stage, they develop at the intersections of the frontal and oblique or lateral ramps. The shape of the clusters is elongated at the frontal ramps because the clusters are made up of subparallel faults, whereas along the intersections of lateral or oblique ramps, more rhombic patterns result from a greater variation in the orientations. The experimental models can be used to obtain a better understanding of the geometry of structures and faults in listric fault provinces such as the Gulf of Mexico and the Niger Delta. The experiments provide predictive models of fault patterns and orientations and their spatial distribution 450 Geologic Note

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