normal faults and their hanging-wall deformation: an ... · 4golder associates incorporated, 4104...

ABSTRACT

We have used clay models to study the effects offault shape and displacement distribution on defor-mation patterns in the hanging wall of a masternormal fault. The experimental results show thatfault shape influences the style of secondary fault-ing and folding. Mostly antithetic normal faultsform above concave-upward fault bends, whereasmostly synthetic normal faults form above low-angle fault segments and convex-upward faultbends. Beds dip toward the master normal faultabove concave-upward fault bends and away fromthe master normal fault above low-angle fault seg-ments and convex-upward fault bends. Generally,secondary faulting and folding are youngest at faultbends and become progressively older past faultbends.

Hanging-wall deformation patterns differ signifi-cantly when a basal plastic sheet imposes a con-stant-magnitude displacement distribution on themaster normal fault. In models without a plasticsheet, numerous secondary normal faults form inthe hanging wall of the master normal fault. Mostsecondary normal faults propagate upward and,consequently, have greater displacement at depth.In models with a plastic sheet, few visible sec-ondary normal faults develop. Most of these faultspropagate downward and, consequently, have lessdisplacement at depth. Hanging-wall folding iswider and bedding dips are gentler in models with-out a plastic sheet than in identical models with aplastic sheet.

The observed particle paths, displacement distri-butions, bedding dips, and orientations of the prin-cipal-strain axes in our physical models with andwithout a basal plastic sheet are compatible withthe assumption that homogeneous, inclined simpleshear accommodates the hanging-wall deforma-tion. Not all of our modeling observations, however,are consistent with this assumption. Specifically,the observed variability with depth of the distribu-tion and intensity of deformation is incompatiblewith homogeneous, inclined simple shear as thehanging-wall deformation mechanism.

INTRODUCTION

For more than 60 yr, geologists have used physi-cal models to simulate normal faults and theirhanging-wall deformation (Cloos, 1928; Cloos,1930; Cloos, 1968; McClay and Ellis, 1987a, b; Ellisand McClay, 1988; McClay, 1989; Islam et al., 1991;McClay and Scott, 1991; McClay et al., 1992;Withjack and Islam, 1993). These experimentalstudies have guided the structural interpretation offield, well, and seismic data. Additionally, they haveprovided data for testing and calibrating geometricmodels of normal faults (Groshong, 1990; Dula,1991; White and Yielding, 1991; Kerr and White,1992; White, 1992; Xiao and Suppe, 1992).

Physical models of normal faults differ in termsof modeling materials (wet clay vs. dry sand) andexperimental constraints placed on fault shape,development, and displacement distribution. Inphysical models by Cloos (1968), the shape anddevelopment of the master normal fault and its dis-placement distribution are unconstrained (Table1). A master normal fault develops in clay or sandabove two diverging, overlapping metal sheets andpropagates upward. In physical models by McClayet al. (1992), the shape and development of themaster normal fault and its displacement distribu-tion are completely constrained (Table 1). A rigidblock and horizontal base act as the footwall of themaster normal fault, and sand represents the hang-ing-wall strata. During modeling, a plastic sheetcarries the sand down the sloping surface of the

AAPG Bulletin, V. 79, No. 1 (January 1995), P. 1–18.

Copyright 1995. The American Association of Petroleum Geologists. Allrights reserved.

1Manuscript received January 11, 1994; revised manuscript receivedAugust 8, 1994; final acceptance September 7, 1994.

2Mobil Research and Development Corporation, P.O. Box 65032, Dallas,Texas 75265.

3Bureau of Land Management, 411 Briarwood Drive, Suite 404, Jackson,Mississippi 39206.

4Golder Associates Incorporated, 4104 148th Avenue NE, Redmond,Washington 98052.

We thank ARCO Oil and Gas Company and Mobil Research andDevelopment Corporation for their support during the study. We also thankWilliam Brown, Sybil Callaway, Gloria Eisenstadt, Jack Howard, DavidKlepacki, and Eric Peterson for their careful and thoughtful reviews of themanuscript.

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

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

1

footwall block and along the horizontal base. Inthese models, the rigid footwall block and horizon-tal base predetermine the shape of the master nor-mal fault. The plastic sheet prevents the fault shapefrom changing during modeling and imposes aconstant-magnitude displacement distribution onthe master normal fault.

We have conducted our own physical models ofnormal faults to study how fault shape and dis-placement distribution affect hanging-wall defor-mation (Table 1). In our models, a rigid block andhorizontal base act as the footwall of the masternormal fault, and a layer of wet, homogeneous clayrepresents the hanging-wall strata. The sloping

surface of the footwall block is either planar or hasa single concave-upward or convex-upward bend.Our models differ from those of Cloos (1968) inthat the rigid footwall block and horizontal basedefine the initial shape of the master normal fault.Unlike the models of McClay et al. (1992), theshape of the master normal fault can change dur-ing modeling and the displacement distribution onits sloping surface can vary in all but one of ourexperiments. In that experiment, a mylar sheetbeneath the clay layer prevents the master normalfault from changing during the experiment andimposes a constant-magnitude displacement distri-bution on the master normal fault.

2 Normal Faults and Their Hanging-Wall Deformation

Table 1. Comparison of Modeling Parameters and Results

Modeling Parameters

FaultModeling Fault Fault DisplacementMaterial Shape Development Distribution Modeling Results*

Wet clay Unconstrained; Unconstrained; Unconstrainedsloping surface sloping surface along slopingof master of master surface;normal fault normal fault constantforms during the forms during the magnitude onexperiment experiment flat surface

Dry sand

Dry sand Completely Completely Constantconstrained: constrained magnitude45°-, 30°-,and0°-dippingsegments

Wet clay Initially Lower Unconstrainedconstrained: two-thirds along sloping45°- and initially surface;0°-dipping constrained constantsegments; magnitude on30°-, 45°–, flat surfaceand 0°-dippingsegments;45°-, 30°-,and 0°-dippingsegments

Wet clay Completely Completely Constantconstrained: constrained magnitude45°-, 30°-, and0°-dipping

MODELING PROCEDURE

The experimental apparatus has a horizontalbase and three vertical walls (Figure 1). The outerwalls are stationary, whereas the middle wall canmove toward either outer wall. An aluminumsheet, attached to the moveable wall, covers thebase. A 5-cm-high aluminum block overlies thesheet and is attached to a fixed wall. The top sur-face of the block is square, 25 cm wide and long.The sloping side of the block is planar and dips 45°in experiment 1, has an upper 30°-dipping seg-ment and a lower 45°-dipping segment in experi-ment 2, and has an upper 45°-dipping segment anda lower 30°-dipping segment in experiments 3 and4. In experiment 4, a mylar sheet, attached to themoveable wall, overlies the sloping side of the alu-minum block and the aluminum sheet.

A 7.5-cm-thick layer of clay directly overlies thealuminum block and aluminum sheet in experi-ments 1, 2, and 3. In experiment 4, a 5-cm-thicklayer of clay overlies the mylar sheet. In all experi-ments, the clay density is 1.6 g/cm3, and its cohe-sive strength is about 10–4 MPa (Sims, 1993). Thetop and sides of the clay layer are free surfaces.Circular markings applied to the top and sides ofthe clay layer record strain during modeling.During experiments 1, 2, and 3, the moveable walland the attached aluminum sheet move away fromthe aluminum block. In response, the clay abovethe aluminum sheet moves away from the blockand down its sloping side. During experiment 4,the moveable wall and the attached aluminum and

mylar sheets move away from the aluminum block.The clay, passively carried by the mylar sheet,moves away from the block and down its slopingside. The displacement rate of the moveable wall is0.004 cm/s in all experiments. We repeat eachexperiment at least twice to verify the modelingresults.

To ensure geometric and kinematic similaritybetween physical models and actual rock deforma-tion (assuming that inertial forces are negligibleand that the density of the modeling material androck are identical), the strength of the modelingmaterial and the model dimensions must be scaleddown by the same factor (Hubbert, 1937). Thecohesive strength of rock is about 105 times greaterthan the cohesive strength of the wet clay in thephysical models. The thickness of sedimentarycover is also about 105 times greater than the claythickness in the physical models. Although the cri-teria for geometric and kinematic similarity havebeen satisfied, we emphasize that the physicalmodels are not exact scale models. Rock maydeform differently than the clay in the models. Forexample, rock with preexisting inhomogeneities(e.g., faults, fractures, bedding) may behave very dif-ferently than the homogeneous clay in the models.

MODELING PARAMETERS

The constraints on fault shape, development, anddisplacement distribution differ in the four experi-ments. The aluminum block initially constrains

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 onthe right, the sloping side of the aluminum block is planar and dips 45° in experiment 1, has an upper 30˚-dippingsegment 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 attachedaluminum sheet move toward the right, away from the aluminum block.

the shape of the master normal fault in experi-ments 1, 2, and 3. The shape of the master normalfault, however, can change during modeling. Forexample, an upward-propagating splay fault cancut through the clay layer during the experiments,bypassing the master normal fault and becomingthe new master normal fault. In experiment 4, themylar sheet prevents the shape of the master nor-mal fault from changing during modeling. Inexperiments 1, 2, and 3, the magnitude of dis-placement can vary along the sloping surface ofthe master normal fault. In experiment 4 with themylar sheet, the magnitude of displacement isconstant along the surface of the master normalfault.

MODELING RESULTS

Experiment 1

During the early stages of experiment 1, the mas-ter normal fault propagates upward from the topedge of the aluminum block to the top surface ofthe clay layer. As the experiment progresses, twodeformation zones develop (Figures 2b; 3a, b). Onezone forms above the 45°-dipping segment of themaster normal fault (Figure 3b). The folded claywithin this zone dips gently away from the masternormal fault. Faulting consists predominantly ofsteeply dipping synthetic normal faults that propa-gate upward from the surface of the master normal


Figure 2—Line drawings fromphotographs of experiment 1showing deformation after (a) 0cm, (b) 2 cm, (c) 4 cm, and (d) 6cm of displacement of the move-able wall. Gray areas with dashedboundaries define the deformedclay. Bold black lines are faultsthat were active since the preced-ing drawing. Thin black lines areinactive faults. Rectangles arelocations of close-up photographsin Figure 3.

fault. This deformation zone becomes inactive dur-ing the early stages of the experiment. The seconddeformation zone extends upward from the faultbend separating the 45°-dipping and flat segmentsof the master normal fault (i. e., the bottom edge ofthe aluminum block) (Figure 3a). The deformationzone widens upward and dips steeply toward themaster normal fault. The folded clay within the zonedips gently toward the master normal fault. Faultingwithin the zone consists of synthetic and antitheticnormal faults with similar dips relative to bedding.Folding, however, has rotated the faults, decreasingthe dip of the synthetic normal faults and increasingthe dip of the antithetic normal faults (Figure 3a).Generally, the antithetic normal faults have greaterdisplacements than the synthetic normal faults.Most antithetic normal faults form near the base ofthe clay layer and propagate upward. Consequently,their displacements decrease upward.

As the experiment progresses, the faulted andfolded clay within the second deformation zonemoves past the fault bend (Figure 2c). The defor-mation zone becomes inactive, and a new deforma-tion zone emanating from the fault bend replacesit. Fold and fault patterns within the new zone aresimilar to those within the old zone, except thatantithetic normal faults are more steeply dippingand synthetic normal faults are more gently dip-ping. Throughout the experiment, deformationzones move past the fault bend and become inac-tive, and new deformation zones emanating fromthe fault bend replace them. The location of theactive deformation zone, anchored to the faultbend, remains stationary relative to the footwall ofthe master normal fault during the experiment.After 6 cm of displacement of the moveable wall,the hanging-wall deformation consists of a widemonocline cut by numerous antithetic and synthet-ic normal faults (Figure 2d). The folded clay hasthinned and lengthened. Generally, antithetic nor-mal faults are youngest near the fault bend and old-est far from the fault bend. Most of the syntheticnormal faults near the fault bend, however, formedduring the early stages of the experiment.

Experiment 2

During the early stages of experiment 2, sec-ondary faulting and folding occur within two

Withjack et al. 5

1 cm

1 cm

a

b

Figure 3—Close-up photographs of experiment 1 after 2cm of displacement of the moveable wall. Locations areshown in Figure 2b. (a) Deformation zone extendingupward from the fault bend separating the 45°-dippingand flat segments of the master normal fault (i. e., the bot-tom edge of the aluminum block). (b) Deformation zoneabove the 45°-dipping segment of the master normal fault.

upward-widening deformation zones (Figures 4b;5a, b). As in experiment 1, one deformation zoneextends upward from the fault bend separating the45°-dipping and flat segments of the master normalfault (Figure 5a). A second deformation zoneextends upward from the fault bend separating the30°- and 45°-dipping segments of the master nor-mal fault (Figure 5b). The folded clay within thisdeformation zone dips away from the master nor-mal fault. Faulting consists of steeply dipping syn-thetic normal faults and moderately dipping anti-thetic normal faults. Folding has rotated the faults,increasing the dip of the synthetic normal faultsand decreasing the dip of the antithetic normalfaults. Generally, the synthetic normal faults havegreater displacements than the antithetic normal

faults. The synthetic normal faults propagateupward from the fault bend separating the 30°- and45°-dipping segments. Eventually, one syntheticnormal fault propagates through the entire claylayer, bypassing the 30°-dipping segment of themaster normal fault (Figure 4c). This through-goingsynthetic normal fault becomes the new masternormal fault.

During the later stages of experiment 2, defor-mation patterns are similar to those in experiment1. The folded and faulted clay moves past the faultbend separating the 45°-dipping and flat segmentsof the master normal fault. Deformation zonesbecome inactive, and new deformation zones ema-nating from the fault bend replace them (Figure 4c,d). After 6 cm of displacement of the moveable


Figure 4—Line drawings fromphotographs of experiment 2showing deformation after (a) 0cm, (b) 2 cm, (c) 4 cm, and (d) 6cm of displacement of the move-able wall. Gray areas with dashedboundaries define the deformedclay. Bold black lines are faultsthat were active since the preced-ing drawing. Thin black lines areinactive faults. Rectangles arelocations of close-up photographsin Figure 5.

Withjack et al. 7

1 cm

1 cm

a

b

wall, the hanging-wall deformation consists of awide monocline cut by numerous antithetic andsynthetic normal faults. As in experiment 1, anti-thetic faults are generally youngest near the foot-wall block and oldest far from the footwall block.Most of the synthetic normal faults near the foot-wall block, however, formed during the earlystages of the experiment.

Experiment 3

During the early stages of experiment 3, the mas-ter normal fault propagates upward from the topedge of the aluminum block to the clay surface. Asthe experiment progresses, secondary faulting andfolding occur within two upward-widening defor-mation zones (Figure 6b). One deformation zoneextends upward from the fault bend separating the 30°-dipping and flat segments of the masternormal fault. A second deformation zone formsabove the sloping footwall of the master normalfault (Figure 7). The folded clay within this zonedips gently away from the master normal fault.Antithetic normal faults propagate upward from the fault bend separating the 45°- and 30°-dipping

Figure 5—Close-up photographs ofexperiment 2 after 2 cm of displace-ment of the moveable wall. Locationsare shown in Figure 4b. (a) Deforma-tion zone extending upward from thefault bend separating the 45°-dippingand flat segments of the master nor-mal fault. (b) Deformation zoneextending upward from the faultbend separating the 30°- and 45°-dip-ping segments of the master normalfault.

segments of the master normal fault, and syntheticnormal faults propagate upward from the 30°-dip-ping segment of the master normal fault. Some syn-thetic normal faults cut the antithetic normalfaults.

As the experiment progresses, the folded andfaulted clay within each deformation zone movespast the corresponding fault bend. The originaldeformation zones become inactive, and newdeformation zones emanating from the same faultbends replace them (Figure 6c). This process con-tinues throughout the experiment. The syntheticnormal faults associated with the 30°-dipping seg-ment of the master normal fault remain active untilthey move past the fault bend separating the 30°-dipping and f lat segments of the master normalfault. As they move past this fault bend, they are

faulted and rotated to gentler dips (Figure 6d).After 6 cm of displacement of the moveable wall,the hanging-wall deformation consists of a widemonocline cut by numerous antithetic and synthet-ic normal faults (Figure 6d). As in experiments 1and 2, antithetic faults are generally youngest nearfault bends and oldest far from fault bends. Many ofthe synthetic normal faults near the fault bend sep-arating the 30°-dipping and flat segments of themaster normal fault, however, developed duringthe early stages of the experiment.

Experiment 4

During the early stages of experiment 4 with themylar sheet, folding occurs in two steeply dipping


Figure 6—Line drawings fromphotographs of experiment 3showing deformation after (a) 0cm, (b) 2 cm, (c) 4 cm, and (d) 6cm of displacement of the move-able wall. Gray areas with dashedboundaries define the deformedclay. Bold black lines are faultsthat were active since the preced-ing drawing. Thin black lines areinactive faults. Rectangle is loca-tion of close-up photograph inFigure 7.

deformation zones (Figure 8b). The first zoneextends upward from the fault bend separating the30°-dipping and flat segments of the master normalfault. The second zone extends upward from thefault bend separating the 45°- and 30°-dipping seg-ments of the master normal fault. The folded claywithin both zones dips toward the master normalfault. Unlike experiments 1, 2, and 3, little visiblefaulting accompanies the folding in experiment 4.The few visible faults have small normal displace-ments. They commonly form at the top surface ofthe clay layer and propagate downward. Conse-quently, their displacement decreases with depth.

As in experiment 3, deformation zones movepast fault bends and become inactive, and newdeformation zones emanating from the same faultbends replace them (Figure 8c). This process con-tinues throughout the experiment. After 6 cm ofdisplacement of the moveable wall, the hanging-wall deformation consists of a wide monocline,generally unaffected by visible faulting (Figure 8d).

Displacement Distribution

Figure 9 shows the displacement distribution onthe master normal fault for the four experiments

after 6 cm of displacement of the moveable wall.In experiments 1, 2, and 3, the displacement mag-nitude varies along the sloping surface of the mas-ter normal fault. Points originally near the top ofthe footwall block move about 4 cm along the sur-face of the master normal fault; points originallynear the middle of the footwall block move about5 cm; and points originally near the bottom of thefootwall block move about 6 cm along the surfaceof the master normal fault. In experiment 4 withthe mylar sheet, the displacement magnitude isconstant, 6 cm, along the entire surface of the mas-ter normal fault.

Fold Shapes

The hanging-wall folds in experiments 1, 2, and3 have similarities and differences (Figure 10a, b,c). During the early stages of the three experi-ments, the folds are synclinal. Near the master nor-mal fault, the folded clay dips away from the fault.Far from the master normal fault, the folded claydips 15 to 20° toward the fault. The folds becomemonoclinal during the later stages of the experi-ments. The hanging-wall folds are narrower inexperiments 1 and 2 than in experiment 3.

The hanging-wall folds in experiments 3 and 4differ considerably, even though the master normalfaults are identical in the two models (Figure 10c,d). The hanging-wall fold in experiment 4 is neversynclinal, even during the early stages of the exper-iment. The clay near the master normal fault iseither flat-lying or dips toward the fault. Also, thefold is much narrower and the folded clay dipsmore steeply (25–30°) in experiment 4 than inexperiment 3 (15–20°).

Particle Paths and Inclined Shear Angles

Figure 11 shows particle paths for the fourexperiments in both a footwall and hanging-wallreference frame. In the footwall reference frame,points in the hanging wall have paths that parallelthe surface of the master normal fault. In the hang-ing-wall reference frame, points in the hangingwall near the master normal fault have slopingpaths. In experiments 1, 2, and 3 without themylar sheet, the sloping paths dip between 50 and60°. In experiment 4 with the mylar sheet, thesloping paths dip between 70 and 75°.

Several authors have proposed that homoge-neous, inclined simple shear accommodates thedeformation in the hanging walls of normal faults(e.g., White et al., 1986; Dula, 1991; White andYielding, 1991; Kerr and White, 1992; White,1992; Xiao and Suppe, 1992; Withjack and

Withjack et al. 9

1 cm

Figure 7—Close-up photograph of experiment 3 after 2cm of displacement of the moveable wall. Location isshown in Figure 6b. Deformation zone is near the slop-ing footwall of the master normal fault.

Peterson, 1993). White et al. (1986) define theinclined shear angle as the acute angle betweenthe vertical and the inclined shear direction. If theparticle paths in the hanging-wall reference frameparallel the inclined shear direction, then theinclined shear angle in our physical models is 30 to40° in experiments 1, 2, and 3 and 15 to 20° inexperiment 4 (Figure 11).

Strain Distributions

Figure 12 shows the strain state in the fourexperiments after 6 cm of displacement of themoveable wall. In experiments 1, 2, and 3, themaximum extension direction is subparallel to

bedding. The magnitude of the maximum exten-sion is greater near the base of the clay layer (about60 to 70%) than near the top (about 20 to 30%).Similarly, the magnitude of the maximum shorten-ing is greater near the base of the clay layer (about–25 to –35%) than near the top (about –10 to –20%).

The strain state differs significantly in experi-ment 4. In the deformed clay, the maximum exten-sion direction is about 15° counterclockwise frombedding. The magnitude of the maximum exten-sion is relatively constant throughout the deformedclay, about 30% near the base of the clay layer and20% near the top. The magnitude of the maximumshortening is also relatively constant throughoutthe deformed clay, about –20% near the base of theclay layer and –10% near the top.


Figure 8—Line drawings fromphotographs of experiment 4(with mylar sheet) showing defor-mation after (a) 0 cm, (b) 2 cm, (c)4 cm, and (d) 6 cm of displace-ment of the moveable wall. Grayareas with dashed boundariesdefine the deformed clay. Boldblack lines are faults that wereactive since the preceding draw-ing. Thin black lines are inactivefaults.

SUMMARY OF MODELING RESULTS

The physical models show that deformation pat-terns in the hanging wall of a master normal faultdepend on fault shape (Table 1). In experimentswithout a mylar sheet, secondary faulting and fold-ing occur: (1) above low-angle fault segments, and(2) in upward-widening zones that emanate fromfault bends. Above low-angle fault segments,upward-propagating synthetic normal faults form,and folded beds dip away from the master normalfault. At concave-upward fault bends, most sec-ondary faults are antithetic normal faults with dis-placements that decrease upward. Folded beds diptoward the master normal fault. At convex-upwardfault bends, most secondary faults are syntheticnormal faults. The synthetic faults propagateupward and, eventually, bypass the master normalfault. Folded beds dip away from the master nor-

mal fault. When deformation zones move past faultbends, they become inactive, and new deforma-tion zones emanating from the same fault bendsreplace them. The locations of the active deforma-tion zones, anchored to fault bends, remain station-ary relative to the footwall of the master normalfault. Generally, secondary faulting and folding areyoungest at fault bends and become progressivelyolder past fault bends.

The physical models also show that experimen-tal constraints on displacement distribution strong-ly inf luence the modeling results (Table 1). Inexperiments 1, 2, and 3 without a mylar sheet, thedisplacement magnitude varies along the surface ofthe master normal fault. Hanging-wall folds aresynclinal during the early stages and monoclinalduring the later stages of the experiments.Numerous antithetic and synthetic normal faultscut the hanging-wall folds. Most of these secondarynormal faults propagate upward and, consequently,have greater displacements at depth. The inclinedshear angle is 30 to 40°, and the direction of maxi-mum extension is subparallel to bedding. In exper-iment 4 with a mylar sheet, the displacement mag-nitude is constant along the surface of the master

Withjack et al. 11

Figure 9—Magnitude of displacement on the masternormal fault after 6 cm of displacement of the move-able wall. Graph shows displacement magnitude as afunction of original vertical distance from the modelbase. Points originally near the top edge of the alu-minum block were 5 cm from the model base, whereaspoints originally near the bottom edge of the aluminumblock were 0 cm from the model base. The displace-ment magnitude varies along the surface of the masternormal fault in experiments 1, 2, and 3 (circles) and isconstant, 6 cm, in experiment 4 (crosses).

Figure 10—Shape of hanging-wall fold for (a) experi-ment 1, (b) experiment 2, (c) experiment 3, and (d)experiment 4. Black lines show the smoothed shape of abed initially 5 cm above the model base. Numbers indi-cate the amount of displacement of the moveable wall.For comparison, the thick black lines show the shape ofthe bed in the four experiments after 6 cm of displace-ment of the moveable wall.

normal fault. The hanging-wall fold is monoclinalduring the early and late stages of the experiment.The fold is narrower and bedding dips are steeperthan those in experiments 1, 2, and 3. Few visiblesecondary normal faults develop during experi-ment 4. Many of these normal faults propagatedownward and, consequently, have less displace-ment at depth. The inclined shear angle is 15 to20°, and the direction of maximum extension dipsmore steeply than bedding.

COMPARISON WITH OTHER EXPERIMENTALMODELS

Physical models by Cloos (1968) differ fromexperiments 1, 2, and 3 in that the shape of the

master normal fault is not predetermined (Table 1).In Cloos’ models, a layer of wet clay or dry sandcovers two overlapping metal sheets. As the sheetsdiverge, a normal fault develops near the base ofthe clay or sand layer and propagates upward. Theresultant sloping segment of the master normalfault is planar and steeply dipping. In the claymodel, a rollover fold and numerous antithetic andsynthetic normal faults form in the hanging wall ofthe master normal fault. In the sand model, hang-ing-wall deformation consists mostly of steeply dip-ping antithetic normal faults. Although deforma-tion patterns in Cloos’ clay and sand models resem-ble those in experiments 1, 2, and 3, some differ-ences exist (Table 1). Few secondary normal faultsform near the planar, high-angle segment of themaster normal fault in Cloos’ models. In experiments


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 displace-ment of the moveable wall is 8 cm; in experiment 4, it is 6 cm. Open and black circles are original and final loca-tions of points, respectively. In the footwall reference frame, the vertical gray lines are the original positions of themoveable wall. In the hanging-wall reference frame, the gray dashed lines show the original positions of the alu-minum block.

1, 2, and 3, numerous antithetic and syntheticnormal faults develop near fault bends and abovelow-angle fault segments of the master normalfault.

A sand model by McClay et al. (1992) resem-bles experiment 4 (Table 1). A rigid block andhorizontal base act as the footwall of the masternormal fault, and a layer of dry, homogeneoussand represents the hanging-wall strata. The rigidblock has an upper 45°-dipping segment and alower 30°-dipping segment. During modeling, aplastic sheet carries the sand down the slopingsurface of the footwall block and along the hori-zontal base. In response, a rollover fold developsin the hanging wall of the master normal fault.Downward-steepening synthetic and antitheticnormal faults form near the top of the sand layerfar from the master normal fault, producing a

crestal collapse graben. The displacement onmost secondary normal faults decreases withdepth. Hanging-wall deformation patterns in thesand model by McClay et al. resemble those inexperiment 4. The hanging-wall folds have similarshapes. Also, most secondary normal faults formnear the top of the models and propagate down-ward. The secondary faults in the sand model byMcClay et al., however, have much greater dis-placements 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., exper-iment 4 and the model of McClay et al. (1992)]confirm our conclusion that constraints on dis-placement distribution profoundly affect experi-mental results. In clay and sand models without aplastic sheet, numerous secondary synthetic andantithetic normal faults develop near fault bends.Most secondary antithetic normal faults propagateupward. Consequently, their displacement decreas-es upward. In clay and sand models with a plasticsheet, secondary faults are much less numerous.Most secondary faults form near the top surface ofthe model and propagate downward. Consequent-ly, their displacement increases upward.

ANALYSIS AND DISCUSSION OF MODELINGRESULTS

We have calculated displacement magnitudes,bedding dips, and strain states associated withmovement past a single fault bend assuming thatfinite, homogeneous, inclined simple shear accom-modates the hanging-wall deformation (Appen-dix). Our analysis predicts that the displacementmagnitude on a sloping fault segment should dif-fer from that on an adjacent flat segment, unlessthe value of the inclined shear angle is half of thevalue of the dip of the sloping fault segment.Consequently, in models with a basal mylar sheetand a constant displacement magnitude, the valueof the inclined shear angle should be half of thevalue of the dip of the sloping fault segment. Thisprediction matches observations from the physicalmodels (Table 2). For example, in experiment 4with the basal mylar sheet, the displacement mag-nitude on the 30°-dipping fault segment equalsthat on the adjacent f lat segment. Particle pathsindicate that the inclined shear angle is about 15°,half of the value of the dip of the sloping fault seg-ment. Our analysis also predicts that the directionof maximum extension depends on the inclinedshear angle. In experiment 3 with an inclinedshear angle of 40°, the direction of maximumextension should be subparallel to bedding. In

Withjack et al. 13

Figure 12—Strain distribution for (a) experiment 1, (b)experiment 2, (c) experiment 3, and (d) experiment 4.Thin lines follow bedding. Thick black lines show thedirection of maximum extension. Upper (bold) num-bers are magnitudes of maximum extension, and lowernumbers are magnitudes of maximum shortening.Extension is positive.

experiment 4, with an inclined shear angle of 15°,the direction of maximum extension should beabout 15° counterclockwise from bedding. Thesepredictions also match observations from thephysical models (Table 2). In experiment 3, thedirection of maximum extension is subparallel tobedding. In experiment 4, the direction of maxi-mum extension is about 15° counterclockwisefrom bedding.

Generally, our analysis shows that the observedparticle paths, displacement distributions, bed-ding dips, and principal strain orientations in thephysical models are compatible with the assump-tion that finite, homogeneous, inclined simpleshear accommodates the hanging-wall deforma-tion. Not all modeling results, however, are con-sistent with this assumption. If finite, homoge-neous, inclined simple shear accommodates thehanging-wall deformation, then the magnitudes ofthe principal strains should be constant through-out the deformed clay. Also, the two boundaries

of each deformation zone should parallel eachother and the inclined shear direction. In thephysical models, especially experiments 1, 2, and3, strain magnitudes significantly decrease fromthe base to the top of the deformed clay, and theboundaries of the deformation zones divergeupward. This observed variability with depth isincompatible with finite, homogeneous, inclinedsimple shear as the hanging-wall deformationmechanism.

Our experimental results support many of theconclusions of the geometric forward modeling byXiao and Suppe (1992). For example, both thephysical and geometric models predict that hang-ing-wall folding occurs in zones that emanate fromfault bends and that folding ceases when hanging-wall rocks move past fault bends. As discussed byWhite and Yielding (1991) and Xiao and Suppe(1992), geometric models provide little informa-tion about the small-scale deformation mechanismsthat accommodate the hanging-wall folding. Our


Predicted from Predicted fromStrain 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 1.00sloping segment/displacement onflat 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, –0.23strain ~0.30, –0.05 at top ~0.20, –0.15 at topmagnitudes(ε1, ε2)

*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.

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

experimental study complements the geometricstudy by Xiao and Suppe (1992) by providing thisimportant information. For example, the physicalmodels show that antithetic normal faults developnear concave-upward fault bends and syntheticnormal faults develop near convex-upward faultbends. These results support the assertion of Xiaoand Suppe (1992) that antithetic simple shear isassociated with concave-upward fault bends andsynthetic simple shear is associated convex-upward fault bends. Our experimental results alsosuggest that the basic premise of most geometricmodels (i.e., homogeneous, inclined simple shearaccommodates the hanging-wall deformation) haslimitations. For example, contrary to the geometricmodels of Xiao and Suppe (1992), the physicalmodels indicate that the width of the deformedzones and the intensity of deformation can varysignificantly with depth, even in strata depositedbefore faulting.

APPLICATION

The Corsair (Brazos Ridge) fault of offshoreTexas is a gently dipping, northeast-trending nor-mal fault that detaches at depth, probably withinthe Louann Salt (Christiansen, 1983; Worrall andSnelson, 1989). The growth fault developed dur-ing Miocene to Holocene time. Locally, its dis-placement exceeds 15 km. The shape of theCorsair fault varies along strike. At some loca-tions, the fault surface has a single concave-upward bend between 2 and 3 km depth (Figure13a). At these sites, numerous antithetic normalfaults cut the hanging-wall strata. Antithetic faultsthat intersect the surface of the Corsair fault atthe fault bend are recently active. Antithetic faultsthat intersect the fault surface below the faultbend are inactive and become progressively olderbelow the fault bend. At other locations, theCorsair fault has a concave-upward bend and aconvex-upward bend at about 3 km depth (Figure13b). At these sites, numerous antithetic and syn-thetic normal faults cut the hanging-wall strata.Many synthetic faults splay from the surface ofthe Corsair fault near the convex-upward faultbend and are recently active. Antithetic faults thatintersect the fault surface near the fault bends arealso active, whereas antithetic faults that intersectthe surface of the Corsair fault below both faultbends are inactive.

The fault patterns in the hanging wall of theCorsair fault resemble those in our physical mod-els. At concave-upward fault bends, most sec-ondary faults are antithetic normal faults. At con-vex-upward fault bends, most secondary faults aresynthetic normal faults. Secondary antithetic and

synthetic normal faults that intersect the fault sur-face at fault bends are active today. Antithetic nor-mal faults that intersect the fault surface belowconcave-upward fault bends are inactive andbecome progressively older below the faultbends.

CONCLUSIONS

We have used clay models to study how theshape of a master normal fault and its displacementdistribution affect the hanging-wall deformation.The modeling results show that the hanging-walldeformation depends on both fault shape and dis-placement distribution.

(1) Fault shape controls the style of secondaryfaulting and folding. In models without a basalmylar sheet, mostly antithetic normal faults formnear concave-upward fault bends, whereas mostlysynthetic normal faults form near convex-upwardfault bends and above low-angle fault segments.Beds generally dip toward the master normal faultnear concave-upward fault bends and away fromthe master normal fault near convex-upward faultbends and above low-angle fault segments. Whendeformation zones move past fault bends, theybecome inactive and new deformation zones ema-nating from the same fault bends replace them.Consequently, most secondary faults and folds areyoungest at fault bends and become progressivelyolder beyond fault bends.

(2) Displacement distribution also affects thepatterns of hanging-wall deformation. In modelswithout a mylar sheet, the displacement magni-tude varies along the surface of the master normalfault. Numerous secondary normal faults form inthe hanging wall. Most secondary normal faultspropagate upward and, consequently, have greaterdisplacement at depth. The inclined shear angle is30 to 40°, and the direction of maximum extensionis subparallel to bedding. In models with a mylarsheet, the displacement magnitude is constantalong the surface of the master normal fault. Fewvisible secondary normal faults form in the hangingwall. Most of these faults propagate downwardand, consequently, have less displacement atdepth. The inclined shear angle is 15 to 20°, andthe direction of maximum extension dips moresteeply than bedding. Hanging-wall folds are widerand bedding dips are gentler in models without amylar sheet than in identical models with a mylarsheet.

The particle paths, displacement distributions,bedding dips, and orientations of the principal-strain axes in our physical models with and with-out a basal mylar sheet are compatible with theassumption that finite, homogeneous, inclined

Withjack et al. 15

simple shear accommodates the hanging-walldeformation. The observed variability with depthof the distribution and intensity of deformation,however, is not compatible with this assumption.Thus, our experimental results suggest that

geometric models of normal faults based on theassumption that finite, homogeneous, inclinedsimple shear accommodates the hanging-walldeformation may not accurately represent thechanges in deformation patterns with depth.


Figure 13—Interpreted, depth-migrated seismic lines from the Corsair (Brazos Ridge) fault of offshore Texas (afterChristiansen, 1983). (a) Section showing Corsair fault with concave-upward fault bend and secondary normalfaults. (b) Section showing Corsair fault with concave-upward and convex-upward fault bends and secondary nor-mal faults.

APPENDIX

If finite, homogeneous, inclined simple shear accommodatesthe hanging-wall deformation associated with movement past asingle fault bend, then the displacement magnitude for points onthe sloping segment of the master normal fault that do not movepast the fault bend is

where D is the displacement magnitude of points on the flat seg-ment, α is the inclined shear angle, and γ is the dip of the slopingsegment (Table 2). For points on the sloping segment that movepast the fault bend,

Based on Jaeger (1969), bedding dip is

where c = sinγ/[cosα][cos(γ—α)] and counterclockwise is posi-tive. The magnitudes of the principal strains are

where extension is positive. The axes of the principal strainstrend ψ and ψ + 90° relative to the horizontal where ψ =[tan—1(—2/c) — α]/2 and counterclockwise is positive.

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Ellis, P. G., and K. R. McClay, 1988, Listric extensional fault sys-temsÑresults of analogue model experiments: Journal of BasinResearch, v. 1, p. 55—70.

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study of geological structures: Geological Society of AmericaBulletin, v. 48, p. 1459—1520.

Islam, Q., P. La Pointe, and M. Withjack, 1991, Experimental andnumerical models of basement-detached normal faults (abs.):AAPG Bulletin, v. 75, p. 600.

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McClay, K. R., and P. G. Ellis, 1987a, Analogue models of exten-sional fault geometries, in M. P. Coward, J. F. Dewey, and P. L.Hancock, eds., Continental extensional tectonics: GeologicalSociety of London Special Publication 28, p. 109—125.

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ε ε12 1 2 2 1 24 2 1 4 2 1= + + − = + − −[( ) ]/ [( ) ]/c c c c and 2

δ α α= +( ) −−tan tan1 c

D d D .cos / cosα γ α−( ) < <

d D= −( )cos /cosα γ α

Withjack et al. 17

Martha Oliver Withjack

Martha Oliver Withjack receivedher Ph.D. from Brown University,Providence, Rhode Island, in 1978,focusing on the mechanics of con-tinental rifting. Before joiningMobil Research and DevelopmentCorporation in 1988, she workedas a research geologist at CitiesService Oil and Gas Company andARCO Oil and Gas Company. Herresearch interests include exten-sional tectonics, structural interpretation of seismicdata, and physical, analytical, and geometric modelingof structures. She was an AAPG Distinguished Lecturer(1984—1985) and a recipient of the J. C. ÒCamÓ SprouleMemorial Award (1986), and is a fellow of theGeological Society of America.

Quazi T. Islam

Quazi T. Islam obtained hisB.Sc. (Hons) and M.Sc. degrees ingeology from the University ofDhaka, Bangladesh. He moved tothe United States in 1978, afterworking with Petrobangla as ageologist. From 1978 to 1982, heworked with Oil and Gas Consul-tants in Houston and Dallas. Afterreceiving his M.S. degree in geolo-gy from the University of Texas atDallas, he was employed with the Research andTechnical Service Division of ARCO (1985—1991). Heworked primarily on regional geology and structural andseismic modeling projects. Before joining the Bureau ofLand Management, he was employed with Entech Inc.

Paul R. La Pointe

Paul La Pointe is a senior project manager for GolderAssociates Inc., where he is engaged in providing frac-tured reservoir, fracture flow, and stochastic reservoirmodeling consulting services to the petroleum industryand to international high-level radioactive-waste pro-grams. Prior to joining Golder in 1991, he spent 10 yrwith the research division of ARCO Oil and Gas compa-ny in Plano, Texas. He received his Ph.D. in 1980 fromthe University of Wisconsin.


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