Normal Faults and Their Hanging-Wall Deformation: an Experimental Study1

Home , Deformation mechanism, Extensional fault

Normal Faults and Their Hanging-Wall Deformation: An Experimental Study1

Martha Oliver Withjack,2 Quazi T. Islam,3 and Paul R. La Pointe4

ABSTRACT The observed particle paths, displacement distributions, bedding dips, and orientations of the prin- We have used clay models to study the effects of cipal-strain axes in our physical models with and fault shape and displacement distribution on defor- without a basal plastic sheet are compatible with mation patterns in the hanging wall of a master the assumption that homogeneous, inclined simple normal fault. The experimental results show that shear accommodates the hanging-wall deforma- fault shape influences the style of secondary fault- tion. Not all of our modeling observations, however, ing and folding. Mostly antithetic normal faults are consistent with this assumption. Specifically, form above concave-upward fault bends, whereas the observed variability with depth of the distribu- mostly synthetic normal faults form above low- tion and intensity of deformation is incompatible angle fault segments and convex-upward fault with homogeneous, inclined simple shear as the bends. Beds dip toward the master normal fault hanging-wall deformation mechanism. above concave-upward fault bends and away from the master normal fault above low-angle fault segments and convex-upward fault bends. Generally, INTRODUCTION secondary faulting and folding are youngest at fault bends and become progressively older past fault For more than 60 yr, geologists have used physi- bends. cal models to simulate normal faults and their Hanging-wall deformation patterns differ signifi- hanging-wall deformation (Cloos, 1928; Cloos, cantly when a basal plastic sheet imposes a con- 1930; Cloos, 1968; McClay and Ellis, 1987a, b; Ellis stant-magnitude displacement distribution on the and McClay, 1988; McClay, 1989; Islam et al., 1991; master normal fault. In models without a plastic McClay and Scott, 1991; McClay et al., 1992; sheet, numerous secondary normal faults form in Withjack and Islam, 1993). These experimental the hanging wall of the master normal fault. Most studies have guided the structural interpretation of secondary normal faults propagate upward and, field, well, and seismic data. Additionally, they have consequently, have greater displacement at depth. provided data for testing and calibrating geometric In models with a plastic sheet, few visible sec- models of normal faults (Groshong, 1990; Dula, ondary normal faults develop. Most of these faults 1991; White and Yielding, 1991; Kerr and White, propagate downward and, consequently, have less 1992; White, 1992; Xiao and Suppe, 1992). displacement at depth. Hanging-wall folding is Physical models of normal faults differ in terms wider and bedding dips are gentler in models with- of modeling materials (wet clay vs. dry sand) and out a plastic sheet than in identical models with a experimental constraints placed on fault shape, plastic sheet. development, and displacement distribution. In physical models by Cloos (1968), the shape and development of the master normal fault and its dis- Copyright 1995. The American Association of Petroleum Geologists. All placement distribution are unconstrained (Table rights reserved. 1Manuscript received January 11, 1994; revised manuscript received 1). A master normal fault develops in clay or sand August 8, 1994; final acceptance September 7, 1994. above two diverging, overlapping metal sheets and 2Mobil Research and Development Corporation, P.O. Box 65032, Dallas, propagates upward. In physical models by McClay Texas 75265. 3Bureau of Land Management, 411 Briarwood Drive, Suite 404, Jackson, et al. (1992), the shape and development of the Mississippi 39206. master normal fault and its displacement distribu- 4Golder Associates Incorporated, 4104 148th Avenue NE, Redmond, tion are completely constrained (Table 1). A rigid Washington 98052. We thank ARCO Oil and Gas Company and Mobil Research and block and horizontal base act as the footwall of the Development Corporation for their support during the study. We also thank master normal fault, and sand represents the hang- William Brown, Sybil Callaway, Gloria Eisenstadt, Jack Howard, David Klepacki, and Eric Peterson for their careful and thoughtful reviews of the ing-wall strata. During modeling, a plastic sheet manuscript. carries the sand down the sloping surface of the

AAPG Bulletin, V. 79, No. 1 (January 1995), P. 1Ð18. 1 2 Normal Faults and Their Hanging-Wall Deformation

Table 1. Comparison of Modeling Parameters and Results

Modeling Parameters Fault Modeling Fault Fault Displacement Material Shape Development Distribution Modeling Results* Wet clay Unconstrained; Unconstrained; Unconstrained sloping surface sloping surface along sloping of master of master surface; normal fault normal fault constant forms during the forms during the magnitude on experiment experiment flat surface Dry sand

Dry sand Completely Completely Constant constrained: constrained magnitude 45°-, 30°-, and 0°-dipping segments Wet clay Initially Lower Unconstrained constrained: two-thirds along sloping 45°- and initially surface; 0°-dipping constrained constant segments; magnitude on 30°-, 45°–, flat surface and 0°-dipping segments; 45°-, 30°-, and 0°-dipping segments

Wet clay Completely Completely Constant constrained: constrained magnitude 45°-, 30°-, and 0°-dipping

footwall block and along the horizontal base. In surface of the footwall block is either planar or has these models, the rigid footwall block and horizon- a single concave-upward or convex-upward bend. tal base predetermine the shape of the master nor- Our models differ from those of Cloos (1968) in mal fault. The plastic sheet prevents the fault shape that the rigid footwall block and horizontal base from changing during modeling and imposes a define the initial shape of the master normal fault. constant-magnitude displacement distribution on Unlike the models of McClay et al. (1992), the the master normal fault. shape of the master normal fault can change dur- We have conducted our own physical models of ing modeling and the displacement distribution on normal faults to study how fault shape and dis- its sloping surface can vary in all but one of our placement distribution affect hanging-wall defor- experiments. In that experiment, a mylar sheet mation (Table 1). In our models, a rigid block and beneath the clay layer prevents the master normal horizontal base act as the footwall of the master fault from changing during the experiment and normal fault, and a layer of wet, homogeneous clay imposes a constant-magnitude displacement distri- represents the hanging-wall strata. The sloping bution on the master normal fault. Withjack et al. 3

Figure 1—Cross-sectional view of experimental apparatus. An aluminum block (black) and horizontal base (gray) act as the footwall of a master normal fault. Wet clay (white) represents the strata in its hanging wall. As shown on the right, the sloping side of the aluminum block is planar and dips 45° in experiment 1, has an upper 30˚-dipping segment and a lower 45°-dipping segment in experiment 2, and has an upper 45°-dipping segment and a lower 30°-dipping segment in experiments 3 and 4. During the experiments, the middle moveable wall and the attached aluminum sheet move toward the right, away from the aluminum block.

MODELING PROCEDURE mylar sheets move away from the aluminum block. The clay, passively carried by the mylar sheet, The experimental apparatus has a horizontal moves away from the block and down its sloping base and three vertical walls (Figure 1). The outer side. The displacement rate of the moveable wall is walls are stationary, whereas the middle wall can 0.004 cm/s in all experiments. We repeat each move toward either outer wall. An aluminum experiment at least twice to verify the modeling sheet, attached to the moveable wall, covers the results. base. A 5-cm-high aluminum block overlies the To ensure geometric and kinematic similarity sheet and is attached to a fixed wall. The top sur- between physical models and actual rock deforma- face of the block is square, 25 cm wide and long. tion (assuming that inertial forces are negligible The sloping side of the block is planar and dips 45° and that the density of the modeling material and in experiment 1, has an upper 30°-dipping seg- rock are identical), the strength of the modeling ment and a lower 45°-dipping segment in experi- material and the model dimensions must be scaled ment 2, and has an upper 45°-dipping segment and down by the same factor (Hubbert, 1937). The a lower 30°-dipping segment in experiments 3 and cohesive strength of rock is about 105 times greater 4. In experiment 4, a mylar sheet, attached to the than the cohesive strength of the wet clay in the moveable wall, overlies the sloping side of the alu- physical models. The thickness of sedimentary minum block and the aluminum sheet. cover is also about 105 times greater than the clay A 7.5-cm-thick layer of clay directly overlies the thickness in the physical models. Although the cri- aluminum block and aluminum sheet in experi- teria for geometric and kinematic similarity have ments 1, 2, and 3. In experiment 4, a 5-cm-thick been satisfied, we emphasize that the physical layer of clay overlies the mylar sheet. In all experi- models are not exact scale models. Rock may ments, the clay density is 1.6 g/cm3, and its cohe- deform differently than the clay in the models. For sive strength is about 10–4 MPa (Sims, 1993). The example, rock with preexisting inhomogeneities top and sides of the clay layer are free surfaces. (e.g., faults, fractures, bedding) may behave very dif- Circular markings applied to the top and sides of ferently than the homogeneous clay in the models. the clay layer record strain during modeling. During experiments 1, 2, and 3, the moveable wall and the attached aluminum sheet move away from MODELING PARAMETERS the aluminum block. In response, the clay above the aluminum sheet moves away from the block The constraints on fault shape, development, and and down its sloping side. During experiment 4, displacement distribution differ in the four experi- the moveable wall and the attached aluminum and ments. The aluminum block initially constrains 4 Normal Faults and Their Hanging-Wall Deformation

Figure 2—Line drawings from photographs of experiment 1 showing deformation after (a) 0 cm, (b) 2 cm, (c) 4 cm, and (d) 6 cm of displacement of the moveable wall. Gray areas with dashed boundaries define the deformed clay. Bold black lines are faults that were active since the preceding drawing. Thin black lines are inactive faults. Rectangles are locations of close-up photographs in Figure 3.

the shape of the master normal fault in experi- MODELING RESULTS ments 1, 2, and 3. The shape of the master normal fault, however, can change during modeling. For Experiment 1 example, an upward-propagating splay fault can cut through the clay layer during the experiments, During the early stages of experiment 1, the mas- bypassing the master normal fault and becoming ter normal fault propagates upward from the top the new master normal fault. In experiment 4, the edge of the aluminum block to the top surface of mylar sheet prevents the shape of the master nor- the clay layer. As the experiment progresses, two mal fault from changing during modeling. In deformation zones develop (Figures 2b; 3a, b). One experiments 1, 2, and 3, the magnitude of dis- zone forms above the 45°-dipping segment of the placement can vary along the sloping surface of master normal fault (Figure 3b). The folded clay the master normal fault. In experiment 4 with the within this zone dips gently away from the master mylar sheet, the magnitude of displacement is normal fault. Faulting consists predominantly of constant along the surface of the master normal steeply dipping synthetic normal faults that propa- fault. gate upward from the surface of the master normal Withjack et al. 5

Figure 3—Close-up photographs of experiment 1 after 2 cm of displacement of the moveable wall. Locations are shown in Figure 2b. (a) Deformation zone extending upward from the fault bend separating the 45°-dipping 1 cm and flat segments of the master normal fault (i. e., the bottom edge of the aluminum block). (b) Deformation zone above the 45°-dipping segment of the master normal fault.

fault. This deformation zone becomes inactive during the early stages of the experiment. The second deformation zone extends upward from the fault bend separating the 45°-dipping and flat segments of the master normal fault (i. e., the bottom edge of the aluminum block) (Figure 3a). The deformation zone widens upward and dips steeply toward the master normal fault. The folded clay within the zone dips gently toward the master normal fault. Faulting within the zone consists of synthetic and antithetic normal faults with similar dips relative to bedding. Folding, however, has rotated the faults, decreasing the dip of the synthetic normal faults and increasing the dip of the antithetic normal faults (Figure 3a). Generally, the antithetic normal faults have greater displacements than the synthetic normal faults. Most antithetic normal faults form near the base of the clay layer and propagate upward. Consequently, their displacements decrease upward. As the experiment progresses, the faulted and folded clay within the second deformation zone moves past the fault bend (Figure 2c). The defor- a mation zone becomes inactive, and a new deformation zone emanating from the fault bend replaces it. Fold and fault patterns within the new zone are 1 cm similar to those within the old zone, except that antithetic normal faults are more steeply dipping and synthetic normal faults are more gently dipping. Throughout the experiment, deformation zones move past the fault bend and become inactive, and new deformation zones emanating from the fault bend replace them. The location of the active deformation zone, anchored to the fault bend, remains stationary relative to the footwall of the master normal fault during the experiment. After 6 cm of displacement of the moveable wall, the hanging-wall deformation consists of a wide monocline cut by numerous antithetic and synthetic normal faults (Figure 2d). The folded clay has thinned and lengthened. Generally, antithetic normal faults are youngest near the fault bend and oldest far from the fault bend. Most of the synthetic normal faults near the fault bend, however, formed during the early stages of the experiment.

Experiment 2 b During the early stages of experiment 2, secondary faulting and folding occur within two 6 Normal Faults and Their Hanging-Wall Deformation

Figure 4—Line drawings from photographs of experiment 2 showing deformation after (a) 0 cm, (b) 2 cm, (c) 4 cm, and (d) 6 cm of displacement of the moveable wall. Gray areas with dashed boundaries define the deformed clay. Bold black lines are faults that were active since the preceding drawing. Thin black lines are inactive faults. Rectangles are locations of close-up photographs in Figure 5.

upward-widening deformation zones (Figures 4b; faults. The synthetic normal faults propagate 5a, b). As in experiment 1, one deformation zone upward from the fault bend separating the 30°- and extends upward from the fault bend separating the 45°-dipping segments. Eventually, one synthetic 45°-dipping and flat segments of the master normal normal fault propagates through the entire clay fault (Figure 5a). A second deformation zone layer, bypassing the 30°-dipping segment of the extends upward from the fault bend separating the master normal fault (Figure 4c). This through-going 30°- and 45°-dipping segments of the master nor- synthetic normal fault becomes the new master mal fault (Figure 5b). The folded clay within this normal fault. deformation zone dips away from the master nor- During the later stages of experiment 2, defor- mal fault. Faulting consists of steeply dipping syn- mation patterns are similar to those in experiment thetic normal faults and moderately dipping anti- 1. The folded and faulted clay moves past the fault thetic normal faults. Folding has rotated the faults, bend separating the 45°-dipping and flat segments increasing the dip of the synthetic normal faults of the master normal fault. Deformation zones and decreasing the dip of the antithetic normal become inactive, and new deformation zones ema- faults. Generally, the synthetic normal faults have nating from the fault bend replace them (Figure 4c, greater displacements than the antithetic normal d). After 6 cm of displacement of the moveable Withjack et al. 7

Figure 5—Close-up photographs of 1 cm experiment 2 after 2 cm of displacement of the moveable wall. Locations are shown in Figure 4b. (a) Deforma- tion zone extending upward from the fault bend separating the 45°-dipping and flat segments of the master normal fault. (b) Deformation zone extending upward from the fault bend separating the 30°- and 45°-dipping segments of the master normal fault.

1 cm wall, the hanging-wall deformation consists of a wide monocline cut by numerous antithetic and synthetic normal faults. As in experiment 1, antithetic faults are generally youngest near the footwall block and oldest far from the footwall block. Most of the synthetic normal faults near the footwall block, however, formed during the early stages of the experiment.

Experiment 3 During the early stages of experiment 3, the master normal fault propagates upward from the top edge of the aluminum block to the clay surface. As the experiment progresses, secondary faulting and folding occur within two upward-widening deformation zones (Figure 6b). One deformation zone extends upward from the fault bend separating the 30°-dipping and flat segments of the master normal fault. A second deformation zone forms above the sloping footwall of the master normal fault (Figure 7). The folded clay within this zone b dips gently away from the master normal fault. Antithetic normal faults propagate upward from the fault bend separating the 45°- and 30°-dipping 8 Normal Faults and Their Hanging-Wall Deformation

Figure 6—Line drawings from photographs of experiment 3 showing deformation after (a) 0 cm, (b) 2 cm, (c) 4 cm, and (d) 6 cm of displacement of the moveable wall. Gray areas with dashed boundaries define the deformed clay. Bold black lines are faults that were active since the preceding drawing. Thin black lines are inactive faults. Rectangle is location of close-up photograph in Figure 7.

segments of the master normal fault, and synthetic faulted and rotated to gentler dips (Figure 6d). normal faults propagate upward from the 30°-dip- After 6 cm of displacement of the moveable wall, ping segment of the master normal fault. Some syn- the hanging-wall deformation consists of a wide thetic normal faults cut the antithetic normal monocline cut by numerous antithetic and synthet- faults. ic normal faults (Figure 6d). As in experiments 1 As the experiment progresses, the folded and and 2, antithetic faults are generally youngest near faulted clay within each deformation zone moves fault bends and oldest far from fault bends. Many of past the corresponding fault bend. The original the synthetic normal faults near the fault bend sep- deformation zones become inactive, and new arating the 30°-dipping and flat segments of the deformation zones emanating from the same fault master normal fault, however, developed during bends replace them (Figure 6c). This process con- the early stages of the experiment. tinues throughout the experiment. The synthetic normal faults associated with the 30°-dipping segment of the master normal fault remain active until Experiment 4 they move past the fault bend separating the 30°- dipping and flat segments of the master normal During the early stages of experiment 4 with the fault. As they move past this fault bend, they are mylar sheet, folding occurs in two steeply dipping Withjack et al. 9

after 6 cm of displacement of the moveable wall. In experiments 1, 2, and 3, the displacement magnitude varies along the sloping surface of the master normal fault. Points originally near the top of the footwall block move about 4 cm along the surface of the master normal fault; points originally near the middle of the footwall block move about 5 cm; and points originally near the bottom of the footwall block move about 6 cm along the surface 1 cm of the master normal fault. In experiment 4 with the mylar sheet, the displacement magnitude is constant, 6 cm, along the entire surface of the master normal fault.

Fold Shapes The hanging-wall folds in experiments 1, 2, and 3 have similarities and differences (Figure 10a, b, c). During the early stages of the three experiments, the folds are synclinal. Near the master normal fault, the folded clay dips away from the fault. Far from the master normal fault, the folded clay dips 15 to 20° toward the fault. The folds become monoclinal during the later stages of the experiments. The hanging-wall folds are narrower in Figure 7—Close-up photograph of experiment 3 after 2 cm of displacement of the moveable wall. Location is experiments 1 and 2 than in experiment 3. shown in Figure 6b. Deformation zone is near the slop- The hanging-wall folds in experiments 3 and 4 ing footwall of the master normal fault. differ considerably, even though the master normal faults are identical in the two models (Figure 10c, d). The hanging-wall fold in experiment 4 is never deformation zones (Figure 8b). The first zone synclinal, even during the early stages of the exper- extends upward from the fault bend separating the iment. The clay near the master normal fault is 30°-dipping and flat segments of the master normal either flat-lying or dips toward the fault. Also, the fault. The second zone extends upward from the fold is much narrower and the folded clay dips fault bend separating the 45°- and 30°-dipping seg- more steeply (25–30°) in experiment 4 than in ments of the master normal fault. The folded clay experiment 3 (15–20°). within both zones dips toward the master normal fault. Unlike experiments 1, 2, and 3, little visible faulting accompanies the folding in experiment 4. Particle Paths and Inclined Shear Angles The few visible faults have small normal displacements. They commonly form at the top surface of Figure 11 shows particle paths for the four the clay layer and propagate downward. Conse- experiments in both a footwall and hanging-wall quently, their displacement decreases with depth. reference frame. In the footwall reference frame, As in experiment 3, deformation zones move points in the hanging wall have paths that parallel past fault bends and become inactive, and new the surface of the master normal fault. In the hang- deformation zones emanating from the same fault ing-wall reference frame, points in the hanging bends replace them (Figure 8c). This process con- wall near the master normal fault have sloping tinues throughout the experiment. After 6 cm of paths. In experiments 1, 2, and 3 without the displacement of the moveable wall, the hanging- mylar sheet, the sloping paths dip between 50 and wall deformation consists of a wide monocline, 60°. In experiment 4 with the mylar sheet, the generally unaffected by visible faulting (Figure 8d). sloping paths dip between 70 and 75°. Several authors have proposed that homogeneous, inclined simple shear accommodates the Displacement Distribution deformation in the hanging walls of normal faults (e.g., White et al., 1986; Dula, 1991; White and Figure 9 shows the displacement distribution on Yielding, 1991; Kerr and White, 1992; White, the master normal fault for the four experiments 1992; Xiao and Suppe, 1992; Withjack and 10 Normal Faults and Their Hanging-Wall Deformation

Figure 8—Line drawings from photographs of experiment 4 (with mylar sheet) showing deformation after (a) 0 cm, (b) 2 cm, (c) 4 cm, and (d) 6 cm of displacement of the moveable wall. Gray areas with dashed boundaries define the deformed clay. Bold black lines are faults that were active since the preceding drawing. Thin black lines are inactive faults.

Peterson, 1993). White et al. (1986) define the bedding. The magnitude of the maximum exten- inclined shear angle as the acute angle between sion is greater near the base of the clay layer (about the vertical and the inclined shear direction. If the 60 to 70%) than near the top (about 20 to 30%). particle paths in the hanging-wall reference frame Similarly, the magnitude of the maximum shorten- parallel the inclined shear direction, then the ing is greater near the base of the clay layer (about inclined shear angle in our physical models is 30 to –25 to –35%) than near the top (about –10 to –20%). 40° in experiments 1, 2, and 3 and 15 to 20° in The strain state differs significantly in experi- experiment 4 (Figure 11). ment 4. In the deformed clay, the maximum extension direction is about 15° counterclockwise from bedding. The magnitude of the maximum exten- Strain Distributions sion is relatively constant throughout the deformed clay, about 30% near the base of the clay layer and Figure 12 shows the strain state in the four 20% near the top. The magnitude of the maximum experiments after 6 cm of displacement of the shortening is also relatively constant throughout moveable wall. In experiments 1, 2, and 3, the the deformed clay, about –20% near the base of the maximum extension direction is subparallel to clay layer and –10% near the top. Withjack et al. 11

Figure 10—Shape of hanging-wall fold for (a) experiment 1, (b) experiment 2, (c) experiment 3, and (d) experiment 4. Black lines show the smoothed shape of a bed initially 5 cm above the model base. Numbers indi- Figure 9—Magnitude of displacement on the master cate the amount of displacement of the moveable wall. normal fault after 6 cm of displacement of the move- For comparison, the thick black lines show the shape of able wall. Graph shows displacement magnitude as a the bed in the four experiments after 6 cm of displace- function of original vertical distance from the model ment of the moveable wall. base. Points originally near the top edge of the aluminum block were 5 cm from the model base, whereas points originally near the bottom edge of the aluminum block were 0 cm from the model base. The displace- mal fault. When deformation zones move past fault ment magnitude varies along the surface of the master bends, they become inactive, and new deforma- normal fault in experiments 1, 2, and 3 (circles) and is tion zones emanating from the same fault bends constant, 6 cm, in experiment 4 (crosses). replace them. The locations of the active deformation zones, anchored to fault bends, remain stationary relative to the footwall of the master normal SUMMARY OF MODELING RESULTS fault. Generally, secondary faulting and folding are youngest at fault bends and become progressively The physical models show that deformation pat- older past fault bends. terns in the hanging wall of a master normal fault The physical models also show that experimen- depend on fault shape (Table 1). In experiments tal constraints on displacement distribution strong- without a mylar sheet, secondary faulting and fold- ly influence the modeling results (Table 1). In ing occur: (1) above low-angle fault segments, and experiments 1, 2, and 3 without a mylar sheet, the (2) in upward-widening zones that emanate from displacement magnitude varies along the surface of fault bends. Above low-angle fault segments, the master normal fault. Hanging-wall folds are upward-propagating synthetic normal faults form, synclinal during the early stages and monoclinal and folded beds dip away from the master normal during the later stages of the experiments. fault. At concave-upward fault bends, most sec- Numerous antithetic and synthetic normal faults ondary faults are antithetic normal faults with dis- cut the hanging-wall folds. Most of these secondary placements that decrease upward. Folded beds dip normal faults propagate upward and, consequently, toward the master normal fault. At convex-upward have greater displacements at depth. The inclined fault bends, most secondary faults are synthetic shear angle is 30 to 40°, and the direction of maxi- normal faults. The synthetic faults propagate mum extension is subparallel to bedding. In exper- upward and, eventually, bypass the master normal iment 4 with a mylar sheet, the displacement mag- fault. Folded beds dip away from the master nor- nitude is constant along the surface of the master 12 Normal Faults and Their Hanging-Wall Deformation

Figure 11—Particle paths in the footwall reference frame (left) and hanging-wall reference frame (right) for (a) experiment 1, (b) experiment 2, (c) experiment 3, and (d) experiment 4. In experiments 1, 2, and 3, the displacement of the moveable wall is 8 cm; in experiment 4, it is 6 cm. Open and black circles are original and final locations of points, respectively. In the footwall reference frame, the vertical gray lines are the original positions of the moveable wall. In the hanging-wall reference frame, the gray dashed lines show the original positions of the aluminum block. normal fault. The hanging-wall fold is monoclinal master normal fault is not predetermined (Table 1). during the early and late stages of the experiment. In Cloos’ models, a layer of wet clay or dry sand The fold is narrower and bedding dips are steeper covers two overlapping metal sheets. As the sheets than those in experiments 1, 2, and 3. Few visible diverge, a normal fault develops near the base of secondary normal faults develop during experi- the clay or sand layer and propagates upward. The ment 4. Many of these normal faults propagate resultant sloping segment of the master normal downward and, consequently, have less displace- fault is planar and steeply dipping. In the clay ment at depth. The inclined shear angle is 15 to model, a rollover fold and numerous antithetic and 20°, and the direction of maximum extension dips synthetic normal faults form in the hanging wall of more steeply than bedding. the master normal fault. In the sand model, hanging-wall deformation consists mostly of steeply dipping antithetic normal faults. Although deforma- COMPARISON WITH OTHER EXPERIMENTAL tion patterns in Cloos’ clay and sand models resem- MODELS ble those in experiments 1, 2, and 3, some differences exist (Table 1). Few secondary normal faults Physical models by Cloos (1968) differ from form near the planar, high-angle segment of the experiments 1, 2, and 3 in that the shape of the master normal fault in Cloos’ models. In experiments Withjack et al. 13

crestal collapse graben. The displacement on most secondary normal faults decreases with depth. Hanging-wall deformation patterns in the sand model by McClay et al. resemble those in experiment 4. The hanging-wall folds have similar shapes. Also, most secondary normal faults form near the top of the models and propagate downward. The secondary faults in the sand model by McClay et al., however, have much greater displacements than those in experiment 4. Comparisons of models without a plastic sheet [i.e., experiments 1, 2, and 3 and Cloos’ (1968) models] with those with a plastic sheet [i.e., experiment 4 and the model of McClay et al. (1992)] confirm our conclusion that constraints on displacement distribution profoundly affect experimental results. In clay and sand models without a plastic sheet, numerous secondary synthetic and antithetic normal faults develop near fault bends. Most secondary antithetic normal faults propagate upward. Consequently, their displacement decreases upward. In clay and sand models with a plastic sheet, secondary faults are much less numerous. Most secondary faults form near the top surface of the model and propagate downward. Consequent- ly, their displacement increases upward.

ANALYSIS AND DISCUSSION OF MODELING RESULTS Figure 12—Strain distribution for (a) experiment 1, (b) experiment 2, (c) experiment 3, and (d) experiment 4. We have calculated displacement magnitudes, Thin lines follow bedding. Thick black lines show the bedding dips, and strain states associated with direction of maximum extension. Upper (bold) num- movement past a single fault bend assuming that bers are magnitudes of maximum extension, and lower finite, homogeneous, inclined simple shear accom- numbers are magnitudes of maximum shortening. modates the hanging-wall deformation (Appen- Extension is positive. dix). Our analysis predicts that the displacement magnitude on a sloping fault segment should differ from that on an adjacent flat segment, unless 1, 2, and 3, numerous antithetic and synthetic the value of the inclined shear angle is half of the normal faults develop near fault bends and above value of the dip of the sloping fault segment. low-angle fault segments of the master normal Consequently, in models with a basal mylar sheet fault. and a constant displacement magnitude, the value A sand model by McClay et al. (1992) resem- of the inclined shear angle should be half of the bles experiment 4 (Table 1). A rigid block and value of the dip of the sloping fault segment. This horizontal base act as the footwall of the master prediction matches observations from the physical normal fault, and a layer of dry, homogeneous models (Table 2). For example, in experiment 4 sand represents the hanging-wall strata. The rigid with the basal mylar sheet, the displacement mag- block has an upper 45°-dipping segment and a nitude on the 30°-dipping fault segment equals lower 30°-dipping segment. During modeling, a that on the adjacent flat segment. Particle paths plastic sheet carries the sand down the sloping indicate that the inclined shear angle is about 15°, surface of the footwall block and along the hori- half of the value of the dip of the sloping fault seg- zontal base. In response, a rollover fold develops ment. Our analysis also predicts that the direction in the hanging wall of the master normal fault. of maximum extension depends on the inclined Downward-steepening synthetic and antithetic shear angle. In experiment 3 with an inclined normal faults form near the top of the sand layer shear angle of 40°, the direction of maximum far from the master normal fault, producing a extension should be subparallel to bedding. In 14 Normal Faults and Their Hanging-Wall Deformation

Table 2. Comparison of Experimental Observations and Strain-Analysis Predictions*

Predicted from Predicted from Strain Analysis Strain Analysis Observed in (with γ = 30° Observed in (with γ = 30° Experiment 3** and α = 40°) Experiment 4** and α = 15°) Inclined shear 35° to 40° 15° to 20° angle (α) Displacement on ~0.8 to 1.0 0.78 to 1.0 1.0 1.00 sloping segment/ displacement on flat segment (d/D) Bedding dip (δ) 15° to 20° 16° 25° to 30° 24° Principal strain ~20°, –70° 14°, –76° ~40°, –50° 37°, –53° orientations (ψ, ψ + 90°) Principal ~0.70, –0.30 at base 0.39, –0.28 ~0.30, –0.20 at base 0.30, –0.23 strain ~0.30, –0.05 at top ~0.20, –0.15 at top magnitudes ε ε ( 1, 2)

*Counterclockwise is positive. Extension is positive. **After 6 cm of displacement of the moveable wall in clay originally above the 30¡-dipping segment of the master normal fault.

experiment 4, with an inclined shear angle of 15°, of each deformation zone should parallel each the direction of maximum extension should be other and the inclined shear direction. In the about 15° counterclockwise from bedding. These physical models, especially experiments 1, 2, and predictions also match observations from the 3, strain magnitudes significantly decrease from physical models (Table 2). In experiment 3, the the base to the top of the deformed clay, and the direction of maximum extension is subparallel to boundaries of the deformation zones diverge bedding. In experiment 4, the direction of maxi- upward. This observed variability with depth is mum extension is about 15° counterclockwise incompatible with finite, homogeneous, inclined from bedding. simple shear as the hanging-wall deformation Generally, our analysis shows that the observed mechanism. particle paths, displacement distributions, bed- Our experimental results support many of the ding dips, and principal strain orientations in the conclusions of the geometric forward modeling by physical models are compatible with the assump- Xiao and Suppe (1992). For example, both the tion that finite, homogeneous, inclined simple physical and geometric models predict that hang- shear accommodates the hanging-wall deforma- ing-wall folding occurs in zones that emanate from tion. Not all modeling results, however, are con- fault bends and that folding ceases when hanging- sistent with this assumption. If finite, homoge- wall rocks move past fault bends. As discussed by neous, inclined simple shear accommodates the White and Yielding (1991) and Xiao and Suppe hanging-wall deformation, then the magnitudes of (1992), geometric models provide little informa- the principal strains should be constant through- tion about the small-scale deformation mechanisms out the deformed clay. Also, the two boundaries that accommodate the hanging-wall folding. Our Withjack et al. 15 experimental study complements the geometric synthetic normal faults that intersect the fault sur- study by Xiao and Suppe (1992) by providing this face at fault bends are active today. Antithetic nor- important information. For example, the physical mal faults that intersect the fault surface below models show that antithetic normal faults develop concave-upward fault bends are inactive and near concave-upward fault bends and synthetic become progressively older below the fault normal faults develop near convex-upward fault bends. bends. These results support the assertion of Xiao and Suppe (1992) that antithetic simple shear is associated with concave-upward fault bends and CONCLUSIONS synthetic simple shear is associated convex- upward fault bends. Our experimental results also We have used clay models to study how the suggest that the basic premise of most geometric shape of a master normal fault and its displacement models (i.e., homogeneous, inclined simple shear distribution affect the hanging-wall deformation. accommodates the hanging-wall deformation) has The modeling results show that the hanging-wall limitations. For example, contrary to the geometric deformation depends on both fault shape and dis- models of Xiao and Suppe (1992), the physical placement distribution. models indicate that the width of the deformed (1) Fault shape controls the style of secondary zones and the intensity of deformation can vary faulting and folding. In models without a basal significantly with depth, even in strata deposited mylar sheet, mostly antithetic normal faults form before faulting. near concave-upward fault bends, whereas mostly synthetic normal faults form near convex-upward fault bends and above low-angle fault segments. APPLICATION Beds generally dip toward the master normal fault near concave-upward fault bends and away from The Corsair (Brazos Ridge) fault of offshore the master normal fault near convex-upward fault Texas is a gently dipping, northeast-trending nor- bends and above low-angle fault segments. When mal fault that detaches at depth, probably within deformation zones move past fault bends, they the Louann Salt (Christiansen, 1983; Worrall and become inactive and new deformation zones ema- Snelson, 1989). The growth fault developed dur- nating from the same fault bends replace them. ing Miocene to Holocene time. Locally, its dis- Consequently, most secondary faults and folds are placement exceeds 15 km. The shape of the youngest at fault bends and become progressively Corsair fault varies along strike. At some loca- older beyond fault bends. tions, the fault surface has a single concave- (2) Displacement distribution also affects the upward bend between 2 and 3 km depth (Figure patterns of hanging-wall deformation. In models 13a). At these sites, numerous antithetic normal without a mylar sheet, the displacement magni- faults cut the hanging-wall strata. Antithetic faults tude varies along the surface of the master normal that intersect the surface of the Corsair fault at fault. Numerous secondary normal faults form in the fault bend are recently active. Antithetic faults the hanging wall. Most secondary normal faults that intersect the fault surface below the fault propagate upward and, consequently, have greater bend are inactive and become progressively older displacement at depth. The inclined shear angle is below the fault bend. At other locations, the 30 to 40°, and the direction of maximum extension Corsair fault has a concave-upward bend and a is subparallel to bedding. In models with a mylar convex-upward bend at about 3 km depth (Figure sheet, the displacement magnitude is constant 13b). At these sites, numerous antithetic and syn- along the surface of the master normal fault. Few thetic normal faults cut the hanging-wall strata. visible secondary normal faults form in the hanging Many synthetic faults splay from the surface of wall. Most of these faults propagate downward the Corsair fault near the convex-upward fault and, consequently, have less displacement at bend and are recently active. Antithetic faults that depth. The inclined shear angle is 15 to 20°, and intersect the fault surface near the fault bends are the direction of maximum extension dips more also active, whereas antithetic faults that intersect steeply than bedding. Hanging-wall folds are wider the surface of the Corsair fault below both fault and bedding dips are gentler in models without a bends are inactive. mylar sheet than in identical models with a mylar The fault patterns in the hanging wall of the sheet. Corsair fault resemble those in our physical mod- The particle paths, displacement distributions, els. At concave-upward fault bends, most sec- bedding dips, and orientations of the principal- ondary faults are antithetic normal faults. At con- strain axes in our physical models with and with- vex-upward fault bends, most secondary faults are out a basal mylar sheet are compatible with the synthetic normal faults. Secondary antithetic and assumption that finite, homogeneous, inclined 16 Normal Faults and Their Hanging-Wall Deformation

Figure 13—Interpreted, depth-migrated seismic lines from the Corsair (Brazos Ridge) fault of offshore Texas (after Christiansen, 1983). (a) Section showing Corsair fault with concave-upward fault bend and secondary normal faults. (b) Section showing Corsair fault with concave-upward and convex-upward fault bends and secondary normal faults. simple shear accommodates the hanging-wall geometric models of normal faults based on the deformation. The observed variability with depth assumption that finite, homogeneous, inclined of the distribution and intensity of deformation, simple shear accommodates the hanging-wall however, is not compatible with this assumption. deformation may not accurately represent the Thus, our experimental results suggest that changes in deformation patterns with depth. Withjack et al. 17

APPENDIX study of geological structures: Geological Society of America Bulletin, v. 48, p. 1459—1520. If finite, homogeneous, inclined simple shear accommodates Islam, Q., P. La Pointe, and M. Withjack, 1991, Experimental and the hanging-wall deformation associated with movement past a numerical models of basement-detached normal faults (abs.): single fault bend, then the displacement magnitude for points on AAPG Bulletin, v. 75, p. 600. the sloping segment of the master normal fault that do not move Jaeger, J. C., 1969, Elasticity, fracture and flow with engineering past the fault bend is and geological applications: London, Chapman & Hall, p. 23—29. dD=−cosαγα /cos() Kerr, H. G., and N. White, 1992, Laboratory testing of an automat- ic method for determining normal fault geometry at depth: where D is the displacement magnitude of points on the flat seg- Journal of Structural Geology, v. 14, p. 873—885. ment, α is the inclined shear angle, and γ is the dip of the sloping McClay, K. R., 1989, Physical models of structural styles during segment (Table 2). For points on the sloping segment that move extension, in A. J. Tankard and H. R. Balkwill, eds., Extensional past the fault bend, tectonics and stratigraphy of the North Atlantic margins: AAPG Memoir 46, p. 95—110. DdD.cosαγα / cos()−<< McClay, K. R., and P. G. Ellis, 1987a, Analogue models of extensional fault geometries, in M. P. Coward, J. F. Dewey, and P. L. Based on Jaeger (1969), bedding dip is Hancock, eds., Continental extensional tectonics: Geological Society of London Special Publication 28, p. 109—125. δαα=+−1()− McClay, K. R., and P. G. Ellis, 1987b, Geometries of extensional tanc tan fault systems developed in model experiments: Geology, v. 15, γ α γ α p. 341—344. where c = sin /[cos ][cos( — )] and counterclockwise is posi- McClay, K. R., and A. D. Scott, 1991, Experimental models of tive. The magnitudes of the principal strains are hangingwall deformation in ramp-flat listric extensional fault systems: Tectonophysics, v. 188, p. 85—96. εε=+[(421421cc212 ) + ]/ − and =+ [( cc 212 ) − ]/ − McClay, K. R., T. Dooley, P. Hollings, J. Keller, L. Thompson, and 1 2 M. White, 1992, Analogue modelling: Fault Dynamics Project Report No. 3, Part II, p. 15—36. where extension is positive. The axes of the principal strains ψ ψ ψ Sims, D., 1993, The rheology of clay: a modeling material for geo- trend and + 90¡ relative to the horizontal where = logic structures (abs.): EOS Transactions, American Geophysical —1 α [tan (—2/c) — ]/2 and counterclockwise is positive. Union, v. 74, p. 569. White, N., 1992, A method for automatically determining normal fault geometry at depth: Journal of Geophysical Research, v. 97, REFERENCES CITED p. 1715—1733. White, N. J., and G. Yielding, 1991, Calculating normal fault Christiansen, A. F., 1983, An example of a major syndepositional geometries at depth: theory and examples, in A. M. Roberts, G. listric fault, in A. W. Bally, ed., Seismic expression of structural Yielding, and B. Freeman, eds., The geometry of normal faults: styles: AAPG Studies in Geology 15, p. 2.3.1-36—40. Geological Society Special Publication 56, p. 251—260. Cloos, E., 1968, Experimental analysis of Gulf Coast fracture pat- White, N. J., J. A. Jackson, and D. P. McKenzie, 1986, The relation- terns: AAPG Bulletin, v. 52, p. 420—444. ship between the geometry of normal faults and that of the Cloos, H., 1928, Experimente zur inneren tektonik: Centralblatt sedimentary layers in their hanging walls: Journal of Structural fur Mineralogie, Abt. B, p. 609—621. Geology, v. 8, p. 897—909. Cloos, H., 1930, Kunstliche gebirge, II: Natur und Museum, v. 60, Withjack, M. O., and Q. Islam, 1993, Origin of rollover: discus- p. 258—269. sion: AAPG Bulletin, v. 77, p. 657—658. Dula, W. F., 1991, Geometric models of listric normal faults and Withjack, M. O., and E. T. Peterson, 1993, Prediction of normal- rollover folds: AAPG Bulletin, v. 75, p. 1609—1625. fault geometriesa sensitivity analysis: AAPG Bulletin, v. 77, Ellis, P. G., and K. R. McClay, 1988, Listric extensional fault sys- p. 1860—1873. temsresults of analogue model experiments: Journal of Basin Worrall, D. M., and S. Snelson, 1989, Evolution of the northern Research, v. 1, p. 55—70. Gulf of Mexico, in A. W. Bally and A. R. Palmer, eds., The geol- Groshong, R., 1990, Unique determination of normal fault shape ogy of North America; an overview: Geological Society of from hanging-wall bed geometry in detached half grabens: America, v. A, p. 97—138. Eclogae Geologicae Helvetiae, v. 83, p. 455—471. Xiao, H., and J. Suppe, 1992, Origin of rollover: AAPG Bulletin, v. 76, Hubbert, M. K., 1937, Theory of scale models as applied to the p. 509–529. 18 Normal Faults and Their Hanging-Wall Deformation

ABOUT THE AUTHORS

Martha Oliver Withjack Paul R. La Pointe Martha Oliver Withjack received Paul La Pointe is a senior project manager for Golder her Ph.D. from Brown University, Associates Inc., where he is engaged in providing frac- Providence, Rhode Island, in 1978, tured reservoir, fracture flow, and stochastic reservoir focusing on the mechanics of con- modeling consulting services to the petroleum industry tinental rifting. Before joining and to international high-level radioactive-waste pro- Mobil Research and Development grams. Prior to joining Golder in 1991, he spent 10 yr Corporation in 1988, she worked with the research division of ARCO Oil and Gas compa- as a research geologist at Cities ny in Plano, Texas. He received his Ph.D. in 1980 from Service Oil and Gas Company and the University of Wisconsin. ARCO Oil and Gas Company. Her research interests include extensional tectonics, structural interpretation of seismic data, and physical, analytical, and geometric modeling of structures. She was an AAPG Distinguished Lecturer (1984—1985) and a recipient of the J. C. Cam Sproule Memorial Award (1986), and is a fellow of the Geological Society of America.

Quazi T. Islam Quazi T. Islam obtained his B.Sc. (Hons) and M.Sc. degrees in geology from the University of Dhaka, Bangladesh. He moved to the United States in 1978, after working with Petrobangla as a geologist. From 1978 to 1982, he worked with Oil and Gas Consul- tants in Houston and Dallas. After receiving his M.S. degree in geology from the University of Texas at Dallas, he was employed with the Research and Technical Service Division of ARCO (1985—1991). He worked primarily on regional geology and structural and seismic modeling projects. Before joining the Bureau of Land Management, he was employed with Entech Inc.