The 1992 Landers and 1994 Northridge earthquakes produced detectable rotations of the stress axes, and the mainshock-induced static stress changes appear to have produced some aftershocks. 56 3.6 Stress orientation profile, different inversion method 57 3.7 Stress orientation profile, different binning 58 3.8 Stress orientation profiles, according to depth.
Summary
Chapter 1 Stress Orientation in Southern California
- Introduction
- Data and Method
- Observations
- Transverse Ranges
- Eastern California Shear Zone
- Southern Sierra Nevada
- Greater Los Angeles Area
Hauksson [1994] concluded from the heterogeneous stress orientation that the northern part of the Landers rupture experienced a complete stress drop. The greater Los Angeles area is at the southern end of the thrust regime associated with the Transverse Ranges.
Temporal Evolution of the Stress Field
The distribution of spins is approximately Gaussian, with a mean of r-v0° and a standard deviation of rv9°, suggesting that much of the variation may be noise. Rotations related to the tectonic loading of an individual fault may be difficult to detect given the length of the study.
1.3. 7 Modeling the Temporal Evolution of the Stress Field
Discussion
The high-resolution stress orientation model presented in this chapter demonstrates that the stress field in southern California is highly heterogeneous. On the rv20 year time scale of the data used in this study, large earthquakes appear to be the dominant cause of temporal evolution of the stress field.
Conclusions
If the orientation of CJH is indistinguishable from N7E at 95%. the confidence level of the inversion, it is shown as N7E. Figure 1.5: Relative magnitude of the three principal stress axes, for the same inversions as shown in Figure 1.4. The rotation rate was found by fitting a least squares linear trend to the results of the 4 time periods.
![Figure 1.1: Shaded relief map of southern California. Mapped surface traces of faults , from J ennings [1975], are shown as t hin black lines, the San Andreas Fault as a thick black line](https://thumb-ap.123doks.com/thumbv2/123dok/10412530.0/28.810.101.669.164.770/figure-shaded-southern-california-mapped-surface-ennings-andreas.webp)
Chapter 2 Stress Magnitude at Seismogenic Depths
- Int roduction
- Two-Dimensional Solution
- Method
- Results
- Three-Dimensional Inversion
- Met hod
- Results
- Discussion
A general two-dimensional solution can be found for the relationship between the near-field rotation of the stress tensor and the ratio of the earthquake stress drop, !:iT, to the background deviatoric stress magnitude, T. The Camp Rock segment experiences gave a rotation of rv21±14°, which qualitatively suggests a high I~T/TI, but the rotation appears to be in the wrong direction, i.e. the direction that would be expected.
2. 5 Conclusions
Chapter 3 Stress State and the Strength of the San Andreas Fault
- Introduction
- M e t hod
To understand the operation of the plate boundary region in Southern California, it is important to constrain the strength of the San Andreas Fault. The San Andreas is also thought to be weak compared to other faults in the region, based on the apparent misorientation of the fault with respect to the surrounding stress field. In this chapter I re-examine the hypothesis that the San Andreas is weak in a relative sense.
Stress orientation versus distance from the fault is determined for eight profiles across relatively straight segments of the San Andreas Fault (SAF), San Jacinto Fault (SJF), and Elsinore Fault (EF).
Discussion
Observations of stress orientation very close to the San Andreas contradict the model of a relatively weak fault. There are two possibilities: that the San Andreas is strong, or that the environment is weak. Scholz [2000] interpreted this stress rotation, originally published by Hardebeck and Hauksson [1999] , to mean that the San Andreas is actually a strong fault.
Another possibility is that the San Andreas is a weak fault in a weak crust, as suggested by the low anomalous stress magnitude found in Chapter 2.
Chapter 4 Earthquake Stress Drop and Background Stress
- Introduction
- Data and Methods
- Computing Stress Drop
- Uncertainty Estimates
The slip that occurs during an earthquake, and therefore the stress drop of the event, must be related to the stress and friction parameters of the fault. In this chapter, I investigate whether the stress drop increases with depth for small aftershocks (ML=2.5-4.0) of the Northridge earthquake. When the stress drop is combined for all stations, the stress drop of the first event is about 0.9 bar and that of the second is about 10 bar.
It appears, therefore, that there is a significant amount of current distribution at the static stress points of the aftershocks.
Most of these error bars are less than a factor of 5, indicating that measurement uncertainty is not responsible for the three orders of magnitude scatter in voltage drop estimates.
Stress Drop Variations with Depth
For most events, those between 5 km and 15 km depth, no systematic increase in minimum, maximum or average stress drop is observed with depth. The null hypothesis, that the static voltage drops of events at depths between 5 and 15 km and at depths greater than 15 km come from populations with the same mean, can be rejected at a 95% confidence level. The observed change in the average voltage drop at 15 km depth is mainly due to an increase in the lowest observed voltage drop.
The stress drop trend with magnitude was removed prior to the statistical test, so the increase in the minimum apparent stress drop at 15 km depth cannot be due to a disproportionate number of higher magnitude events (and thus larger decreases high stress) at depth.
Mainshock-induced Stress Changes
Spatial Variations in Stress Drop
Discussion
- S t a t ic Stress Drop
- Stress Drop Variations with Magnitude
- Stress Drop Variations with Depth
The observations of Archuleta et al. [1982), that the voltage drop increases with magnitude only for M < 3 events, is consistent with this model. The simple model summarized in Equation 4.2 predicts that the voltage drop should scale with effective normal stress. Alternatively, the fault friction model may be incorrect and the earthquake stress drop may not scale with the magnitude of the effective normal stress on the fault.
I see higher average voltage drops for deeper aftershocks due to an increase in the minimum voltage drop at 15 km depth.
Conclusions
LAOO
The vertical error bars indicate the 95%. confidence interval of the static voltage drop, while the horizontal error bars indicate the 95% confidence level of the hypocentral depth. e) Combined estimate (averaged over all stations). The vertical error bars indicate the 95% confidence interval of the static voltage drop, while the horizontal error bars indicate the 95%. The static stress change shown is the change in shear stress in the direction of slip.
Chapter 5 Static Stress Change Triggering of Earthquakes
- Introduction
- Method
- Observed Sequences
- S y nthetic Sequences
- Statistical Test
- Results
- Discussion
- Conclusions
This suggests that Coulomb stress changes played a significant role in triggering the aftershock sequences. For both series, the CI for events within 2-5 km of the main shock fault is low. Other spatial variations in the performance of the Coulomb stress trigger model can be seen in Figures 5.4 and 5.5.
The Coulomb model for inducing stress changes was tested on the aftershock sequences of the 1992 Landers and 1994 Northridge earthquakes.
A .l Int roduction
Inversion Methods
- Linear Inversion Method
All methods for reversing focal stress orientation mechanisms rely on the assumption that earthquakes slide in the direction of the resolved shear stress on the fault plane. The orientation of the fracture plane is not generally considered to provide information about the stress state because it may be an arbitrary oriented, pre-existing plane of weakness. For a reliable inversion, the orientations of the fracture surfaces must be sufficiently diverse to sample the entire stress tensor.
The first is that the four voltage parameters are constant over the spatial and temporal extent of the data set.
A .2.2 Grid Search M e thod
Testing the Inversion Methods
- Synthetic Data Sets
- Testing
The accuracy of the inversion methods, and the appropriateness of their uncertainty estimates, is tested by inverting each of the synthetic data sets using both methods. First, I test the accuracy of the inversion results, defined as the angle between the correct and best-fit stress orientations and the difference in R value. If the confidence regions are appropriate, the correct stress state should fall within the X% confidence region for approximately X% of the data sets, for all X.
In FMSI evaluation, the correct stress state is considered to be within the X% confidence zone if Ecor ~ Ex, where Ecor is the total discrepancy of the nearest grid point with the correct stress state.
Results
- Accuracy
- Confidence Regions
The correct stress state generally falls within the X% confidence region for (X ±10)% of the inversions, indicating that the LSIB confidence regions are approximately correct. The exception applies to large data sets, N = 300, in which case the confidence areas are much too small (Figure A.5). The suitability of the LSIB confidence regions does not decrease as mechanism errors increase (Figure A.6), indicating that the bootstrap technique successfully integrates data errors into the uncertainty estimates.
In most cases, the confidence regions of the FMSI are far too large, with the correct stress state falling within the X% confidence region for 'X% of the inversions.
Discussion
- Problems with LSIB
In the axisymmetric case (R = 0 or R= 1), the FMSI confidence regions are clearly too small when considering all four model parameters (Figure A.7). This, together with the observation that FMSI determines axisymmetric values of R with poor accuracy (Figure A.4), suggests that the problem is primarily an incorrect estimate of R. These same data will also be repeated in resampled data sets more often than other data.
The confidence regions found using the modified resampling method are of a more appropriate size (Figure A.8).
A.5.2 Problems with FMSI
This implies that the assumption of an inappropriate normal distribution, although not strictly correct, is not the cause of the large confidence regions. The calculation of the threshold value of the confidence region, ~x, is based on the assumption that the minimum observed total discrepancy, ~min, is the expected value of the total discrepancy due to data errors for the correct stress state, aestE[m ]. The limited grid of parameter space may affect the apparent adequacy of uncertainty estimates in cases where the size of the grid partition is larger than, or comparable to, the appropriate X% confidence region size.
However, this is not a general explanation for the large confidence regions, as the 68% and 95% confidence regions typically contain many grid points.
A .6 Con clusions
If the plot falls above this line, it means that the correct answer falls within the X% confidence region » X% of the time and the confidence regions are too large. Similarly, if the plot falls below the line, the correct answer falls within the X% confidence region «X%. Results of an experiment with perfect confidence regions will have a 95% probability of falling within the shaded zone, which is the 95% confidence region of the binomial probability distribution for 200 trials with an X% probability of success each trial.
If the confidence areas are too large or too small, the function will fall above or below the shaded area, respectively (see Figure A.2).
Bibliography
Zoback, Mechanism diversity of the Lorna Prieta aftershocks and the mechanics of mainshock–aftershock interaction, Sci. Sanders, Evidence from precise earthquake hypocenters for segmentation of the San Andreas fault in San Gorgonio Pass, J. Zoback, Implications of earthquake focal mechanisms for the frictional strength of the San Andreas fault system, presented at Geological Society of London Conference on Weak Faults, 2000.
Hauksson, Seismogenic deformation field in the Mojave block and implications for the tectonics of the eastern California shear zone, J.
![Figure 1.11: The stress field in 1812, as predicted from the stress evolution model of D eng and Sykes [1997], which includes earthquake induced stress changes and tectonic stress loading from 1812 to 1992](https://thumb-ap.123doks.com/thumbv2/123dok/10412530.0/38.811.106.743.148.564/figure-predicted-evolution-includes-earthquake-induced-changes-tectonic.webp)
