Normal Faults and Their Hanging-Wall Deformation:
An Experimental Study1
Martha Oliver Withjack,2 Quazi T. Islam,3 and Paul R. La Pointe4
ABSTRACT
We have used clay models to study the effects of
fault shape and displacement distribution on deformation patterns in the hanging wall of a master
normal fault. The experimental results show that
fault shape influences the style of secondary faulting and folding. Mostly antithetic normal faults
form above concave-upward fault bends, whereas
mostly synthetic normal faults form above lowangle fault segments and convex-upward fault
bends. Beds dip toward the master normal fault
above concave-upward fault bends and away from
the master normal fault above low-angle fault segments and convex-upward fault bends. Generally,
secondary faulting and folding are youngest at fault
bends and become progressively older past fault
bends.
Hanging-wall deformation patterns differ significantly when a basal plastic sheet imposes a constant-magnitude displacement distribution on the
master normal fault. In models without a plastic
sheet, numerous secondary normal faults form in
the hanging wall of the master normal fault. Most
secondary normal faults propagate upward and,
consequently, have greater displacement at depth.
In models with a plastic sheet, few visible secondary normal faults develop. Most of these faults
propagate downward and, consequently, have less
displacement at depth. Hanging-wall folding is
wider and bedding dips are gentler in models without a plastic sheet than in identical models with a
plastic sheet.
Copyright 1995. The American Association of Petroleum Geologists. All
rights reserved.
1Manuscript received January 11, 1994; revised manuscript received
August 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 and
Development Corporation for their support during the study. We also thank
William Brown, Sybil Callaway, Gloria Eisenstadt, Jack Howard, David
Klepacki, and Eric Peterson for their careful and thoughtful reviews of the
manuscript.
AAPG Bulletin, V. 79, No. 1 (January 1995), P. 1–18.
The observed particle paths, displacement distributions, bedding dips, and orientations of the principal-strain axes in our physical models with and
without a basal plastic sheet are compatible with
the assumption that homogeneous, inclined simple
shear accommodates the hanging-wall deformation. Not all of our modeling observations, however,
are consistent with this assumption. Specifically,
the observed variability with depth of the distribution and intensity of deformation is incompatible
with homogeneous, inclined simple shear as the
hanging-wall deformation mechanism.
INTRODUCTION
For more than 60 yr, geologists have used physical models to simulate normal faults and their
hanging-wall deformation (Cloos, 1928; Cloos,
1930; Cloos, 1968; McClay and Ellis, 1987a, b; Ellis
and McClay, 1988; McClay, 1989; Islam et al., 1991;
McClay and Scott, 1991; McClay et al., 1992;
Withjack and Islam, 1993). These experimental
studies have guided the structural interpretation of
field, well, and seismic data. Additionally, they have
provided data for testing and calibrating geometric
models 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 terms
of modeling materials (wet clay vs. dry sand) and
experimental constraints placed on fault shape,
development, and displacement distribution. In
physical models by Cloos (1968), the shape and
development of the master normal fault and its displacement distribution are unconstrained (Table
1). A master normal fault develops in clay or sand
above two diverging, overlapping metal sheets and
propagates upward. In physical models by McClay
et al. (1992), the shape and development of the
master normal fault and its displacement distribution are completely constrained (Table 1). A rigid
block and horizontal base act as the footwall of the
master normal fault, and sand represents the hanging-wall strata. During modeling, a plastic sheet
carries the sand down the sloping surface of the
1
2
Normal Faults and Their Hanging-Wall Deformation
Table 1. Comparison of Modeling Parameters and Results
Modeling Parameters
Modeling
Material
Fault
Shape
Fault
Development
Fault
Displacement
Distribution
Wet clay
Unconstrained;
sloping surface
of master
normal fault
forms during the
experiment
Unconstrained;
sloping surface
of master
normal fault
forms during the
experiment
Unconstrained
along sloping
surface;
constant
magnitude on
flat surface
Dry sand
Completely
constrained:
45°-, 30°-,
and
0°-dipping
segments
Completely
constrained
Constant
magnitude
Wet clay
Initially
constrained:
45°- and
0°-dipping
segments;
30°-, 45°–,
and 0°-dipping
segments;
45°-, 30°-,
and 0°-dipping
segments
Lower
two-thirds
initially
constrained
Unconstrained
along sloping
surface;
constant
magnitude on
flat surface
Wet clay
Completely
constrained:
45°-, 30°-, and
0°-dipping
Completely
constrained
Constant
magnitude
Modeling Results*
Dry sand
footwall block and along the horizontal base. In
these models, the rigid footwall block and horizontal base predetermine the shape of the master normal fault. The plastic sheet prevents the fault shape
from changing during modeling and imposes a
constant-magnitude displacement distribution on
the master normal fault.
We have conducted our own physical models of
normal faults to study how fault shape and displacement distribution affect hanging-wall deformation (Table 1). In our models, a rigid block and
horizontal base act as the footwall of the master
normal fault, and a layer of wet, homogeneous clay
represents the hanging-wall strata. The sloping
surface of the footwall block is either planar or has
a single concave-upward or convex-upward bend.
Our models differ from those of Cloos (1968) in
that the rigid footwall block and horizontal base
define the initial shape of the master normal fault.
Unlike the models of McClay et al. (1992), the
shape of the master normal fault can change during modeling and the displacement distribution on
its sloping surface can vary in all but one of our
experiments. In that experiment, a mylar sheet
beneath the clay layer prevents the master normal
fault from changing during the experiment and
imposes a constant-magnitude displacement distribution 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
The experimental apparatus has a horizontal
base and three vertical walls (Figure 1). The outer
walls are stationary, whereas the middle wall can
move toward either outer wall. An aluminum
sheet, attached to the moveable wall, covers the
base. A 5-cm-high aluminum block overlies the
sheet and is attached to a fixed wall. The top surface 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 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. In experiment 4, a mylar sheet, attached to the
moveable wall, overlies the sloping side of the aluminum block and the aluminum sheet.
A 7.5-cm-thick layer of clay directly overlies the
aluminum block and aluminum sheet in experiments 1, 2, and 3. In experiment 4, a 5-cm-thick
layer of clay overlies the mylar sheet. In all experiments, the clay density is 1.6 g/cm3, and its cohesive strength is about 10–4 MPa (Sims, 1993). The
top and sides of the clay layer are free surfaces.
Circular markings applied to the top and sides of
the clay layer record strain during modeling.
During experiments 1, 2, and 3, the moveable wall
and the attached aluminum sheet move away from
the aluminum block. In response, the clay above
the aluminum sheet moves away from the block
and 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 sloping
side. The displacement rate of the moveable wall is
0.004 cm/s in all experiments. We repeat each
experiment at least twice to verify the modeling
results.
To ensure geometric and kinematic similarity
between physical models and actual rock deformation (assuming that inertial forces are negligible
and that the density of the modeling material and
rock are identical), the strength of the modeling
material and the model dimensions must be scaled
down by the same factor (Hubbert, 1937). The
cohesive strength of rock is about 105 times greater
than the cohesive strength of the wet clay in the
physical models. The thickness of sedimentary
cover is also about 105 times greater than the clay
thickness in the physical models. Although the criteria for geometric and kinematic similarity have
been satisfied, we emphasize that the physical
models are not exact scale models. Rock may
deform differently than the clay in the models. For
example, rock with preexisting inhomogeneities
(e.g., faults, fractures, bedding) may behave very differently than the homogeneous clay in the models.
MODELING PARAMETERS
The constraints on fault shape, development, and
displacement distribution differ in the four experiments. 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 experiments 1, 2, and 3. The shape of the master normal
fault, however, can change during modeling. For
example, an upward-propagating splay fault can
cut through the clay layer during the experiments,
bypassing the master normal fault and becoming
the new master normal fault. In experiment 4, the
mylar sheet prevents the shape of the master normal fault from changing during modeling. In
experiments 1, 2, and 3, the magnitude of displacement can vary along the sloping surface of
the master normal fault. In experiment 4 with the
mylar sheet, the magnitude of displacement is
constant along the surface of the master normal
fault.
MODELING RESULTS
Experiment 1
During the early stages of experiment 1, the master normal fault propagates upward from the top
edge of the aluminum block to the top surface of
the clay layer. As the experiment progresses, two
deformation zones develop (Figures 2b; 3a, b). One
zone forms above the 45°-dipping segment of the
master normal fault (Figure 3b). The folded clay
within this zone dips gently away from the master
normal fault. Faulting consists predominantly of
steeply dipping synthetic normal faults that propagate 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
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.
1 cm
a
1 cm
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 deformation zone becomes inactive, and a new deformation zone emanating from the fault bend replaces
it. Fold and fault patterns within the new zone are
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, secondar y 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;
5a, b). As in experiment 1, one deformation zone
extends upward from the fault bend separating the
45°-dipping and flat segments of the master normal
fault (Figure 5a). A second deformation zone
extends upward from the fault bend separating the
30°- and 45°-dipping segments of the master normal fault (Figure 5b). The folded clay within this
deformation zone dips away from the master normal fault. Faulting consists of steeply dipping synthetic normal faults and moderately dipping antithetic normal faults. Folding has rotated the faults,
increasing the dip of the synthetic normal faults
and decreasing the dip of the antithetic normal
faults. Generally, the synthetic normal faults have
greater displacements than the antithetic normal
faults. The synthetic normal faults propagate
upward from the fault bend separating the 30°- and
45°-dipping segments. Eventually, one synthetic
normal fault propagates through the entire clay
layer, bypassing the 30°-dipping segment of the
master normal fault (Figure 4c). This through-going
synthetic normal fault becomes the new master
normal fault.
During the later stages of experiment 2, deformation patterns are similar to those in experiment
1. The folded and faulted clay moves past the fault
bend separating the 45°-dipping and flat segments
of the master normal fault. Deformation zones
become inactive, and new deformation zones emanating from the fault bend replace them (Figure 4c,
d). After 6 cm of displacement of the moveable
Withjack et al.
7
Figure 5—Close-up photographs of
experiment 2 after 2 cm of displacement of the moveable wall. Locations
are shown in Figure 4b. (a) Deformation 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
a
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
b
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
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
normal faults propagate upward from the 30°-dipping segment of the master normal fault. Some synthetic normal faults cut the antithetic normal
faults.
As the experiment progresses, the folded and
faulted clay within each deformation zone moves
past the corresponding fault bend. The original
deformation zones become inactive, and new
deformation zones emanating from the same fault
bends replace them (Figure 6c). This process continues throughout the experiment. The synthetic
normal faults associated with the 30°-dipping segment of the master normal fault remain active until
they move past the fault bend separating the 30°dipping and flat segments of the master normal
fault. 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 wide
monocline cut by numerous antithetic and synthetic normal faults (Figure 6d). As in experiments 1
and 2, antithetic faults are generally youngest near
fault bends and oldest far from fault bends. Many of
the synthetic normal faults near the fault bend separating the 30°-dipping and flat segments of the
master normal fault, however, developed during
the early stages of the experiment.
Experiment 4
During the early stages of experiment 4 with the
mylar sheet, folding occurs in two steeply dipping
Withjack et al.
1 cm
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
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
Figure 7—Close-up photograph of experiment 3 after 2
cm of displacement of the moveable wall. Location is
shown in Figure 6b. Deformation zone is near the sloping footwall of the master normal fault.
deformation zones (Figure 8b). The first zone
extends upward from the fault bend separating the
30°-dipping and flat segments of the master normal
fault. The second zone extends upward from the
fault bend separating the 45°- and 30°-dipping segments of the master normal fault. The folded clay
within both zones dips toward the master normal
fault. Unlike experiments 1, 2, and 3, little visible
faulting accompanies the folding in experiment 4.
The few visible faults have small normal displacements. They commonly form at the top surface of
the clay layer and propagate downward. Consequently, their displacement decreases with depth.
As in experiment 3, deformation zones move
past fault bends and become inactive, and new
deformation zones emanating from the same fault
bends replace them (Figure 8c). This process continues throughout the experiment. After 6 cm of
displacement of the moveable wall, the hangingwall deformation consists of a wide monocline,
generally unaffected by visible faulting (Figure 8d).
Displacement Distribution
Figure 9 shows the displacement distribution on
the master normal fault for the four experiments
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
experiments 1 and 2 than in experiment 3.
The hanging-wall folds in experiments 3 and 4
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
synclinal, even during the early stages of the experiment. The clay near the master normal fault is
either flat-lying or dips toward the fault. Also, the
fold is much narrower and the folded clay dips
more steeply (25–30°) in experiment 4 than in
experiment 3 (15–20°).
Particle Paths and Inclined Shear Angles
Figure 11 shows particle paths for the four
experiments in both a footwall and hanging-wall
reference frame. In the footwall reference frame,
points in the hanging wall have paths that parallel
the surface of the master normal fault. In the hanging-wall reference frame, points in the hanging
wall near the master normal fault have sloping
paths. In experiments 1, 2, and 3 without the
mylar sheet, the sloping paths dip between 50 and
60°. In experiment 4 with the mylar sheet, the
sloping paths dip between 70 and 75°.
Several authors have proposed that homogeneous, inclined simple shear accommodates the
deformation in the hanging walls of normal faults
(e.g., White et al., 1986; Dula, 1991; White and
Yielding, 1991; Kerr and White, 1992; White,
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
inclined shear angle as the acute angle between
the vertical and the inclined shear direction. If the
particle paths in the hanging-wall reference frame
parallel the inclined shear direction, then the
inclined shear angle in our physical models is 30 to
40° in experiments 1, 2, and 3 and 15 to 20° in
experiment 4 (Figure 11).
Strain Distributions
Figure 12 shows the strain state in the four
experiments after 6 cm of displacement of the
moveable wall. In experiments 1, 2, and 3, the
maximum extension direction is subparallel to
bedding. The magnitude of the maximum extension is greater near the base of the clay layer (about
60 to 70%) than near the top (about 20 to 30%).
Similarly, the magnitude of the maximum shortening 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 experiment 4. In the deformed clay, the maximum extension direction is about 15° counterclockwise from
bedding. The magnitude of the maximum extension is relatively constant throughout the deformed
clay, about 30% near the base of the clay layer and
20% near the top. The magnitude of the maximum
shortening is also relatively constant throughout
the deformed clay, about –20% near the base of the
clay layer and –10% near the top.
Withjack et al.
Figure 9—Magnitude of displacement on the master
normal fault after 6 cm of displacement of the moveable wall. Graph shows displacement magnitude as a
function of original vertical distance from the model
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 displacement magnitude varies along the surface of the master
normal fault in experiments 1, 2, and 3 (circles) and is
constant, 6 cm, in experiment 4 (crosses).
SUMMARY OF MODELING RESULTS
The physical models show that deformation patterns in the hanging wall of a master normal fault
depend on fault shape (Table 1). In experiments
without a mylar sheet, secondary faulting and folding occur: (1) above low-angle fault segments, and
(2) in upward-widening zones that emanate from
fault bends. Above low-angle fault segments,
upward-propagating synthetic normal faults form,
and folded beds dip away from the master normal
fault. At concave-upward fault bends, most secondary faults are antithetic normal faults with displacements that decrease upward. Folded beds dip
toward the master normal fault. At convex-upward
fault bends, most secondary faults are synthetic
normal faults. The synthetic faults propagate
upward and, eventually, bypass the master normal
fault. Folded beds dip away from the master nor-
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 indicate the amount of displacement of the moveable wall.
For comparison, the thick black lines show the shape of
the bed in the four experiments after 6 cm of displacement of the moveable wall.
mal fault. When deformation zones move past fault
bends, they become inactive, and new deformation zones emanating from the same fault bends
replace them. The locations of the active deformation zones, anchored to fault bends, remain stationary relative to the footwall of the master normal
fault. Generally, secondary faulting and folding are
youngest at fault bends and become progressively
older past fault bends.
The physical models also show that experimental constraints on displacement distribution strongly inf luence the modeling results (Table 1). In
experiments 1, 2, and 3 without a mylar sheet, the
displacement magnitude varies along the surface of
the master normal fault. Hanging-wall folds are
synclinal during the early stages and monoclinal
during the later stages of the experiments.
Numerous antithetic and synthetic normal faults
cut the hanging-wall folds. Most of these secondary
normal faults propagate upward and, consequently,
have greater displacements at depth. The inclined
shear angle is 30 to 40°, and the direction of maximum extension is subparallel to bedding. In experiment 4 with a mylar sheet, the displacement magnitude 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
during the early and late stages of the experiment.
The fold is narrower and bedding dips are steeper
than those in experiments 1, 2, and 3. Few visible
secondary normal faults develop during experiment 4. Many of these normal faults propagate
downward and, consequently, have less displacement at depth. The inclined shear angle is 15 to
20°, and the direction of maximum extension dips
more steeply than bedding.
COMPARISON WITH OTHER EXPERIMENTAL
MODELS
Physical models by Cloos (1968) differ from
experiments 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 sand
covers two overlapping metal sheets. As the sheets
diverge, a normal fault develops near the base of
the clay or sand layer and propagates upward. The
resultant sloping segment of the master normal
fault is planar and steeply dipping. In the clay
model, a rollover fold and numerous antithetic and
synthetic normal faults form in the hanging wall of
the master normal fault. In the sand model, hanging-wall deformation consists mostly of steeply dipping antithetic normal faults. Although deformation patterns in Cloos’ clay and sand models resemble those in experiments 1, 2, and 3, some differences exist (Table 1). Few secondary normal faults
form near the planar, high-angle segment of the
master normal fault in Cloos’ models. In experiments
Withjack et al.
13
crestal collapse graben. The displacement on
most secondar y 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. Consequently, 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.
Thin lines follow bedding. Thick black lines show the
direction of maximum extension. Upper (bold) numbers are magnitudes of maximum extension, and lower
numbers are magnitudes of maximum shortening.
Extension is positive.
1, 2, and 3, numerous antithetic and synthetic
normal faults develop near fault bends and above
low-angle fault segments of the master normal
fault.
A sand model by McClay et al. (1992) resembles experiment 4 (Table 1). A rigid block and
horizontal base act as the footwall of the master
normal fault, and a layer of dry, homogeneous
sand represents the hanging-wall strata. The rigid
block has an upper 45°-dipping segment and a
lower 30°-dipping segment. During modeling, a
plastic sheet carries the sand down the sloping
surface of the footwall block and along the horizontal base. In response, a rollover fold develops
in the hanging wall of the master normal fault.
Downward-steepening synthetic and antithetic
normal faults form near the top of the sand layer
far from the master normal fault, producing a
We have calculated displacement magnitudes,
bedding dips, and strain states associated with
movement past a single fault bend assuming that
finite, homogeneous, inclined simple shear accommodates the hanging-wall deformation (Appendix). Our analysis predicts that the displacement
magnitude on a sloping fault segment should differ from that on an adjacent flat segment, unless
the value of the inclined shear angle is half of the
value of the dip of the sloping fault segment.
Consequently, in models with a basal mylar sheet
and a constant displacement magnitude, the value
of the inclined shear angle should be half of the
value of the dip of the sloping fault segment. This
prediction matches observations from the physical
models (Table 2). For example, in experiment 4
with the basal mylar sheet, the displacement magnitude on the 30°-dipping fault segment equals
that on the adjacent flat segment. Particle paths
indicate that the inclined shear angle is about 15°,
half of the value of the dip of the sloping fault segment. Our analysis also predicts that the direction
of maximum extension depends on the inclined
shear angle. In experiment 3 with an inclined
shear angle of 40°, the direction of maximum
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*
Observed in
Experiment 3**
Predicted from
Strain Analysis
(with γ = 30°
and α = 40°)
Observed in
Experiment 4**
Predicted from
Strain Analysis
(with γ = 30°
and α = 15°)
Inclined shear
angle (α)
35° to 40°
Displacement on
sloping segment/
displacement on
flat segment
(d/D)
~0.8 to 1.0
0.78 to 1.0
1.0
1.00
Bedding dip (δ)
15° to 20°
16°
25° to 30°
24°
Principal strain
orientations
(ψ, ψ + 90°)
~20°, –70°
14°, –76°
~40°, –50°
37°, –53°
~0.70, –0.30 at base
~0.30, –0.05 at top
0.39, –0.28
~0.30, –0.20 at base
~0.20, –0.15 at top
0.30, –0.23
Principal
strain
magnitudes
(ε1, ε2)
15° to 20°
*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°,
the direction of maximum extension should be
about 15° counterclockwise from bedding. These
predictions also match observations from the
physical models (Table 2). In experiment 3, the
direction of maximum extension is subparallel to
bedding. In experiment 4, the direction of maximum extension is about 15° counterclockwise
from bedding.
Generally, our analysis shows that the observed
particle paths, displacement distributions, bedding dips, and principal strain orientations in the
physical models are compatible with the assumption that finite, homogeneous, inclined simple
shear accommodates the hanging-wall deformation. Not all modeling results, however, are consistent with this assumption. If finite, homogeneous, inclined simple shear accommodates the
hanging-wall deformation, then the magnitudes of
the principal strains should be constant throughout the deformed clay. Also, the two boundaries
of each deformation zone should parallel each
other and the inclined shear direction. In the
physical models, especially experiments 1, 2, and
3, strain magnitudes significantly decrease from
the base to the top of the deformed clay, and the
boundaries of the deformation zones diverge
upward. This observed variability with depth is
incompatible with finite, homogeneous, inclined
simple shear as the hanging-wall deformation
mechanism.
Our experimental results support many of the
conclusions of the geometric forward modeling by
Xiao and Suppe (1992). For example, both the
physical and geometric models predict that hanging-wall folding occurs in zones that emanate from
fault bends and that folding ceases when hangingwall rocks move past fault bends. As discussed by
White and Yielding (1991) and Xiao and Suppe
(1992), geometric models provide little information about the small-scale deformation mechanisms
that accommodate the hanging-wall folding. Our
Withjack et al.
experimental study complements the geometric
study by Xiao and Suppe (1992) by providing this
important information. For example, the physical
models show that antithetic normal faults develop
near concave-upward fault bends and synthetic
normal faults develop near convex-upward fault
bends. These results support the assertion of Xiao
and Suppe (1992) that antithetic simple shear is
associated with concave-upward fault bends and
synthetic simple shear is associated convexupward fault bends. Our experimental results also
suggest that the basic premise of most geometric
models (i.e., homogeneous, inclined simple shear
accommodates the hanging-wall deformation) has
limitations. For example, contrary to the geometric
models of Xiao and Suppe (1992), the physical
models indicate that the width of the deformed
zones and the intensity of deformation can vary
significantly with depth, even in strata deposited
before faulting.
APPLICATION
The Corsair (Brazos Ridge) fault of offshore
Texas is a gently dipping, northeast-trending normal fault that detaches at depth, probably within
the Louann Salt (Christiansen, 1983; Worrall and
Snelson, 1989). The growth fault developed during Miocene to Holocene time. Locally, its displacement exceeds 15 km. The shape of the
Corsair fault varies along strike. At some locations, the fault surface has a single concaveupward bend between 2 and 3 km depth (Figure
13a). At these sites, numerous antithetic normal
faults cut the hanging-wall strata. Antithetic faults
that intersect the surface of the Corsair fault at
the fault bend are recently active. Antithetic faults
that intersect the fault surface below the fault
bend are inactive and become progressively older
below the fault bend. At other locations, the
Corsair fault has a concave-upward bend and a
convex-upward bend at about 3 km depth (Figure
13b). At these sites, numerous antithetic and synthetic normal faults cut the hanging-wall strata.
Many synthetic faults splay from the surface of
the Corsair fault near the convex-upward fault
bend and are recently active. Antithetic faults that
intersect the fault surface near the fault bends are
also active, whereas antithetic faults that intersect
the surface of the Corsair fault below both fault
bends are inactive.
The fault patterns in the hanging wall of the
Corsair fault resemble those in our physical models. At concave-upward fault bends, most secondary faults are antithetic normal faults. At convex-upward fault bends, most secondary faults are
synthetic normal faults. Secondary antithetic and
15
synthetic normal faults that intersect the fault surface at fault bends are active today. Antithetic normal faults that intersect the fault surface below
concave-upward fault bends are inactive and
become progressively older below the fault
bends.
CONCLUSIONS
We have used clay models to study how the
shape of a master normal fault and its displacement
distribution affect the hanging-wall deformation.
The modeling results show that the hanging-wall
deformation depends on both fault shape and displacement distribution.
(1) Fault shape controls the style of secondary
faulting and folding. In models without a basal
mylar sheet, mostly antithetic normal faults form
near concave-upward fault bends, whereas mostly
synthetic normal faults form near convex-upward
fault bends and above low-angle fault segments.
Beds generally dip toward the master normal fault
near concave-upward fault bends and away from
the master normal fault near convex-upward fault
bends and above low-angle fault segments. When
deformation zones move past fault bends, they
become inactive and new deformation zones emanating from the same fault bends replace them.
Consequently, most secondary faults and folds are
youngest at fault bends and become progressively
older beyond fault bends.
(2) Displacement distribution also affects the
patterns of hanging-wall deformation. In models
without a mylar sheet, the displacement magnitude varies along the surface of the master normal
fault. Numerous secondary normal faults form in
the hanging wall. Most secondary normal faults
propagate upward and, consequently, have greater
displacement at depth. The inclined shear angle is
30 to 40°, and the direction of maximum extension
is subparallel to bedding. In models with a mylar
sheet, the displacement magnitude is constant
along the surface of the master normal fault. Few
visible secondary normal faults form in the hanging
wall. Most of these faults propagate downward
and, consequently, have less displacement at
depth. The inclined shear angle is 15 to 20°, and
the direction of maximum extension dips more
steeply than bedding. Hanging-wall folds are wider
and bedding dips are gentler in models without a
mylar sheet than in identical models with a mylar
sheet.
The particle paths, displacement distributions,
bedding dips, and orientations of the principalstrain axes in our physical models with and without a basal mylar sheet are compatible with the
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
deformation. The observed variability with depth
of 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 the
assumption that finite, homogeneous, inclined
simple shear accommodates the hanging-wall
deformation may not accurately represent the
changes in deformation patterns with depth.
Withjack et al.
APPENDIX
If finite, homogeneous, inclined simple shear accommodates
the hanging-wall deformation associated with movement past a
single fault bend, then the displacement magnitude for points on
the sloping segment of the master normal fault that do not move
past the fault bend is
d = Dcos α /cos( γ − α )
where D is the displacement magnitude of points on the flat segment, α is the inclined shear angle, and γ is the dip of the sloping
segment (Table 2). For points on the sloping segment that move
past the fault bend,
Dcos α / cos( γ − α ) < d < D .
Based on Jaeger (1969), bedding dip is
δ = tan −1 (c + tanα ) − α
where c = sinγ/[cosα][cos(γ—α)] and counterclockwise is positive. The magnitudes of the principal strains are
ε1 = [( 4 + c 2 )1 2 + c]/ 2 − 1 and ε 2 = [( 4 + c 2 )1 2 − c]/ 2 − 1
where extension is positive. The axes of the principal strains
trend ψ and ψ + 90° relative to the horizontal where ψ =
[tan—1(—2/c)— α]/2 and counterclockwise is positive.
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18
Normal Faults and Their Hanging-Wall Deformation
ABOUT THE AUTHORS
Martha Oliver Withjack
Martha Oliver Withjack received
her Ph.D. from Brown University,
Providence, Rhode Island, in 1978,
focusing on the mechanics of continental rifting. Before joining
Mobil Research and Development
Corporation in 1988, she worked
as a research geologist at Cities
Service Oil and Gas Company and
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 Consultants 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.
Paul R. La Pointe
Paul La Pointe is a senior project manager for Golder
Associates Inc., where he is engaged in providing fractured reservoir, fracture flow, and stochastic reservoir
modeling consulting services to the petroleum industry
and to international high-level radioactive-waste programs. Prior to joining Golder in 1991, he spent 10 yr
with the research division of ARCO Oil and Gas company in Plano, Texas. He received his Ph.D. in 1980 from
the University of Wisconsin.