The Strength of Active Faults
George Hilley, Department of Geology, Arizona State University, Tempe,
Arizona 85281
Abstract
The strength of active faults in the lithosphere influences the orientation
of the stresses acting on the fault. For faults with low shear strength,
stresses applied remotely must reorient themselves such that the shear
traction applied to the fault does not exceed the strength of the fault.
In this study, we take the formuations of Zoback et. al (1987) relating
the stress rotation around a weak fault as a function of fault strength,
and rederive the equation to relate the stress rotation to fault friction.
We show that changes in strike of a strike slip fault can be used to
calculate the driving stresses responsible for movement along the fault as
well as fault friction.
We use these formulations relating fault friction and stress rotation to
evaluate which processes may be responsible for frictional weakening of
major strike-slip faults and which cannot. In particular, we investigate
the hypothesis that frictional weakening along the fault occurs as the
result of hyperbrecciation along the fault surface. We compare the stress
rotation around two strike-slip faults with similar total displacment to
determine the possible frictions acting on these faults. In the case that
frictional weakening results from hyperbrecciation, two strike-slip faults
with similar total displacement should have similar fricitonal strengths.
We investigate the validity of this hypothesis by comparing the stress
rotation around the Altyn Tagh fault in Central Asia and the San Andreas
Fault in California. The San Andreas Fault shows significant stress
rotation in the vicinity of the fault, indicating a low frictional strength
of the fault. In contrast, the Altyn Tagh fault shows no such rotation,
indicating that it is a well-oriented, strong fault. Both faults have
accumulated hundreds of kilometers of total displacement. These results
suggest that hyperbrecciation does not play a role in reducing the faults'
frictional strength. We are currently investigating a total of 12
strike-slip faults in order to strengthen this suggestion and evaluate the
correlation of low fault strength with strike-slip faults that are
plate boundaries.
I. Introduction
Faults in the brittle upper crust behave as frictional sliding surfaces. In
these types of faults, the displacement occurs after some critical
combination of shear stress and normal stress is applied to the fault
surface. This critical value scales linearly with the ratio of the normal
stress to shear stress. Laboratory samples and most active faults have
critical values at ratios of normal stress to shear stress around 0.6-0.8.
However, a certain class of faults fail at anomalously
low ratios. Three mechanisms have been invoked to explain this behavior.
First, high pore pressure (near hydrostatic stresses) in the fault zone may act to
weaken the fault. Second, accumulated slip along the fault may lead to
hyperbrecciation which weakens the fault. Third, minerology of the fault
zone may act to lubricate the fault surface, reducing the fault friction.
Laboratory experiments show that only pure
clay is sufficient to minerologically lubricate the fault zone.
The stability of clays above 100C precludes the presence of the
minerals' presence at seismogenic depths. Therefore, high pore pressures
and hyperbrecciation may be the realistic processes that produce a weak
fault.
Faults with low frictional strength will cause a rotation of the remote
stresses near to the fault. The strength of the fault cannot be exceded
without failure; therefore, the principle stress orientations must rotate
into an orientation such that the shear traction resolved from the local
stress tensor onto the fault surface equals the strength of the fault
(Zoback et. al, 1989). This relationship can be derived as (from Zoback
et. al, 1989):
Where alpha is the orientation of the greatest compressive stress relative
to the fault plane in the area near the fault, SHmax is the maximum
horizontal compressive stress, Shmin is the minimum horizontal compressive
stress, Co is the fault strength (in MPa), and beta is the angle of
the greatest compressive stress relative to the fault plane in the
far-field. Hence, the driving stresses responsible for the formation of
the fault and subsequent movement are oriented at an angle, beta, to the
fault surface. As one approaches the fault, the driving stresses rotate to
an orientation where alpha is the angle between the fault surface and the
direction of the maximum horizontal compressive stress (SHmax).
We can write the strength of the fault (Co) in terms of the normal
traction (sigma(n)) and the friction(mu) as:
These two sets of equations can be solved itteratively to determine the
induced rotation due to the presence of a weak fault. Figure
1 shows the relationship between beta and alpha for faults of various
strengths (dashed lines, using Zoback et. al (1989) formulation) and
frictions (solid lines, using itterative technique described
above).
Figure 1: Relationship between alpha (angle between fault plane and SHmax
near the weak fault) and beta (angle between far-field driving stresses and
fault plane) for different strengths (in MPa, dashed lines) and frictions
(solid lines).
II. Frictional Strength of the San Andreas Fault
Heat anonmalies, stress drops during earthquakes, and stress rotations
adjacent to the San Andreas Fault suggest that the fault has low frictional
strength. In the vicinity of the San Andreas Fault, the orientation of
SHmax rotates nearly orthogonal to the fault (Figure 2).
Figure 2: Stress orientations in California (taken from Zoback et.
al, 1989; scan courtesey of Zack Washburn). Note the near-orthogonality
of the orientation of SHmax to the San Andreas Fault.
The far-field driving stresses responsible for movement along the San
Andreas Fault are complicated by the scale of the fault and the presence
of other stress provinces in the area. In order to determine the
orientation of the far-field driving stresses, we study stress orientations
in the region of the Big Bend. If the San Andreas is being fueled by a
relatively constant far-field stress orientation, then the change in the
strike of the fault results in a change in beta in Figure 1. Therefore,
the angular relationship between the fault strike and the strike of SHmax
near the fault
should change through the bend. We use this fact to calculate the
best-fit stress orientations driving the San Andreas Fault and the
corresponding fault friction required to rotate the stresses to the angle
that they make with the strike of the fault. We take two populations of
stress measurements, one north of the Big Bend and one south of the Bend.
Since beta in Figure 1 must be 33 degrees greater than Beta in Figure 1
south of the bend, we can perform a least squares inversion minimizing the
misfit between the data and the predicted rotation from Figure 1 and
backsolve for the orientation of SHmax in the far-field and the friction
of the fault. The results of this inversion are shown in Figures 3 and
4. Figure 3 lets all variables optimize (free variables are differential
stress, friction, and orientation of the far-field driving stresses).
Figure 4 shows the inversion fixing the differential stress estimated by
Zoback et. al (1989). The differential stress determined from the full
optimization was 150.0800 MPa heuristically agrees well with the Zoback et.
al (1989) estimate of a differential stress of 136 MPa. Computed orientations of
SHmax is almost exactly N-S and computed frictions were low (mu = 0.0282
for full optimization and mu = 0.0090 for constrained differential stress
optimization).
Figure 3: Constrained optimization of stress data around San
Andreas Fault. Friction, differential stress, and remote stress
orientation were optimized in this calculation. Note the N-S orientation
of SHmax (strike of SAF for points in left half of figure is 315
degrees) and the low fault friction (mu = 0.0090).
Figure 4: Constrained optimization of stress data around San
Andreas Fault. Friction and remote stress orientation were optimized in
this calculation with a constant differential stress of 136 MPa. Again,
the fault friction and SHmax orientation are consistent with the results of
the fully optimized model and the heat flow data collected along the San
Andreas Fault.
III. Processes responsible for the formation of a low-friction fault
From the above investigation, we conclude that the San Andreas Fault is a
weak fault. If we assume that this weakening is the result of
hyperbrecciation resulting from accumulated displacement along the fault,
then faults with similar displacement should have similar frictions.
These low frictions should be apparent in the stress data as rotations of
the remote stress near the fault. In order to test this hypothesis, we
consider the Altyn Tagh fault in Central Asia. Slip along the Altyn Tagh
is on the order of the San Andreas fault; however, the fault is not
accomodating direct plate motion as a transform fault (as is the San
Andreas) but is likely accomodating the escape of Asia from the
Indo-Eurasian collision to the south. The location and some of the stress
data from the region is shown in Figure 5.
Figure 5: Location and stress orientations of the Alytn Tagh Fault,
Central Asia.
Data from the World Stress Map Project was used to determine the degree of
rotation in the vicinity of the Altyn Tagh fault. Table 1 shows the mean
and standard deviation of the stress measurements for the different data
quality classes defined by the World Stress Map Project and the mean and
standard deviation for the entire population of stress data. In short,
there is strong evidence of no stress rotation around the Altyn Tagh
fault. From this, we infer that the fault is strong. Based on a
comparison with the San Andreas Fault which has similar amounts of total
displacement, we find it difficult to accept hyperbrecciation as a process
of fault weakening.
Table 1: Results from Stress Analysis of Altyn Tagh Fault
| Quality Ranking | Mean | Std. Deviation |
| A | 35.5 | 10.6 |
| B | 51.3 | 14.9 |
| C | 40.2 | 16.7 |
| D | 41.6 | 10.5 |
| E | 18.9 | 4.6 |
| All | 40 | 16.7 |
IV. Conclusions and Future Work
We conclude that 1) the San Andreas Fault is a weak fault as evidenced
from the stress rotation surrounding the fault, 2) by comparison of the
Altyn Tagh fault with the San Andreas Fault, we feel that hyperbrecciation
may not be responsible for decreases in fault friction. It is extrememly
tenuous to base such grandiose conclusions on two data points. Therefore,
we are currently investigating other active strike-slip faults in order to
determine the relationship between total accumulated offset, tectonic
setting (plate-bounding faults and non-plate-bounding faults) and fault
friction.
V. References:
Zoback, M. D., and 12 others, New Evidence on the State of Stress of the
San Andreas Fault System, Science, November 1987, pp. 1105-1111