Aftershocks are well aligned with the background stress field, contradicting the hypothesis of highly heterogeneous crustal stress

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi:10.1029/2010jb007586, 2010 Aftershocks are well aligned with the background stress field, contradicting the hypothesis of highly heterogeneous crustal stress Jeanne Hardebeck 1 Received 23 March 2010; revised 27 July 2010; accepted 24 August 2010; published 3 December 2010. [1] It has been proposed that the crustal stress field contains small length scale heterogeneity of much larger amplitude than the uniform background stress. This model predicts that earthquake focal mechanisms should reflect the loading stress rather than the uniform background stress. So, if the heterogeneous stress hypothesis is correct, focal mechanisms before and after a large earthquake should align with the tectonic loading and the earthquake induced static stress perturbation, respectively. However, I show that the off fault triggered aftershocks of the 1992 M7.3 Landers, California, earthquake align with the same stress field as the pre Landers mechanisms. The aftershocks occurred on faults that were well oriented for failure in the pre Landers stress field and then loaded by the Landers induced static stress change. Aftershocks in regions experiencing a 0.05 to 5 MPa coseismic differential stress change align with the modeled Landers induced static stress change, implying that they were triggered by the stress perturbation. Contrary to the heterogeneous stress hypothesis, these triggered aftershocks are also well aligned with the pre Landers stress field obtained from inverting the pre Landers focal mechanisms. Therefore, the inverted pre Landers stress must represent the persistent background stress field. Earthquake focal mechanisms provide an unbiased sample of the spatially coherent background stress field, which is large relative to any small scale stress heterogeneity. The counterexample provided by the Landers earthquake is strong evidence that the heterogeneous stress model is not widely applicable. Citation: Hardebeck, J. (2010), Aftershocks are well aligned with the background stress field, contradicting the hypothesis of highly heterogeneous crustal stress, J. Geophys. Res., 115,, doi:10.1029/2010jb007586. 1. Introduction [2] Some have argued for small scale spatial heterogeneity in the crustal stress field with large amplitude compared to the uniform background stress [e.g., Smith, 2006; Smith and Dieterich, 2010; see also http://resolver.caltech. edu/caltechetd:etd 05252006 191203]. There are reasonable arguments both for and against highly heterogeneous stress in the crust. Earthquake slip models exhibit large changes in displacement over 1 km distances, implying large localized stress changes that could produce heterogeneity [e.g., Wald and Heaton, 1994; Aagaard and Heaton, 2008]. However, finite slip models are nonunique because slip at depth is usually underdetermined [e.g., Liu et al., 2006; Page et al., 2009], so it is unclear how well resolved apparently sharp changes in displacement actually are. Large changes in surface displacement over 1 km along strike distances [McGill and Rubin, 1999] have also been cited as evidence for localized high stress [e.g., Smith, 2006; Smith and Dieterich, 2010]. However, large changes in displacement only imply large stresses if the deformation is elastic. Given the relatively low strength of near surface 1 U.S. Geological Survey, Menlo Park, California, USA. This paper is not subject to U.S. copyright. Published in 2010 by the American Geophysical Union. materials, it is much more likely that the deformation reflects permanent deformation of near surface materials, as the original authors concluded [McGill and Rubin, 1999]. [3] Borehole breakouts indicate that stress orientations in the upper few kilometers can sometimes change significantly over length scales as small as 10 m [e.g., Wilde and Stock, 1997; Hickman and Zoback, 2004]. The breakout heterogeneity, if present, does not necessarily extrapolate to seismogenic depths, however, where greater confining stresses may dampen the relative amplitude of fluctuations. At depth, heterogeneous focal mechanisms have been observed for aftershocks along parts of the rupture surfaces of large earthquakes, including the 1989 M6.9 Loma Prieta [Michael et al., 1990] and 1992 M7.3 Landers [Hauksson, 1994] main shocks in California, implying local stress heterogeneity caused by the main shock. A similar argument, based on the apparent variability of the full southern California focal mechanism catalog, has also been made for heterogeneous stress in the entire upper crust [Rivera and Kanamori, 2002]. However, when differences in tectonic regime and the sizable focal mechanism uncertainties are accounted for, the southern California mechanisms appear much more uniform [Hardebeck, 2006]. [4] One of the predictions of the heterogeneous stress model is that earthquake focal mechanisms during the interseismic period provide a biased sample of the stress field 1of10

[e.g., Smith and Dieterich, 2010]. In this model, earthquakes should preferentially occur in volumes of crust where the stress field is aligned with the tectonic loading, as the tectonic loading would tend to push the well oriented faults in those volumes closer to failure, much more than faults in other volumes. Focal mechanisms should reflect the orientation of the tectonic loading, and stress inversion of focal mechanisms [e.g., Michael, 1984] during interseismic periods would return the loading tensor. Similarly, after a large earthquake, the focal mechanisms of triggered aftershocks would reflect the stress perturbations from the earthquake, because faults in volumes where stress was aligned with the earthquake induced stress changes would be preferentially pushed toward failure. Smith and Dieterich [2010] hypothesized that apparent stress rotations due to large earthquakes [e.g., Michael, 1987; Hauksson, 1994] may be artifacts from sampling different spatial volumes in a heterogeneous stress field. [5] The prediction that focal mechanisms should reflect the loading stress, rather than the background stress, provides an opportunity to test the heterogeneous stress hypothesis. Large earthquakes are known to change the stress field [e.g., King et al., 1994], producing a temporary loading stress that differs from the usual tectonic loading. Therefore, if the heterogeneous stress hypothesis is correct, the pre earthquake events and the triggered aftershocks should reflect different stress fields. This can be tested by inverting the pre earthquake focal mechanisms for the apparent prestress and checking whether the aftershocks are aligned with this stress field. [6] The heterogeneous stress model predicts that the apparent prestress found from inversion of pre earthquake focal mechanisms is actually the tectonic loading stress. The aftershock focal mechanisms should not be preferentially aligned with the prestress, as they should be independent of the tectonic loading, assuming that the cumulative tectonic loading over the time period of the aftershock catalog is negligible. Alternatively, if the homogeneous part of the stress field is larger than the local variations, inversion of the pre earthquake focal mechanisms for prestress would result in the uniform background stress. In this case, the aftershock focal mechanisms should be consistent with a combination of the background and earthquake induced stress fields. The aftershocks should therefore be consistent with the prestress, assuming they are far enough away from the main shock that the stress change is sufficiently small compared to the background stress that a true rotation of the stress field could not occur. Therefore, the key test is whether or not the focal mechanisms of triggered aftershocks align with the inverted pre earthquake stress field. 2. Data [7] The 1992 M7.3 Landers, California, earthquake triggered aftershocks over a large region, and most aftershocks are consistent with the Landers induced static stress change field [King et al., 1994; Hardebeck et al., 1998]. The Landers aftershocks were well recorded by the Southern California Seismic Network [Hauksson et al., 1993] and provide an ideal data set to test whether the triggered aftershocks were also aligned with the apparent pre Landers stress field. Southern California exhibits complex fault structure, associated with the large scale bend in the San Andreas Fault, and so it is a good candidate location for a heterogeneous stress field. The complex fault geometry also ensures that there are a variety of available fault orientations, so changes in preferred failure orientation should be detectable. [8] I use a focal mechanism catalog for southern California generated by the method of Hardebeck and Shearer [2002], selecting only quality A C mechanisms without multiples. The pre Landers catalog is complicated by the occurrence of the M6.2 Joshua Tree earthquake 2 months prior to the Landers main shock, and the post Landers catalog is complicated by the occurrence of the M6.5 Big Bear aftershock a few hours after Landers. To simplify this situation, the Joshua Tree, Landers, and Big Bear earthquakes are considered together as the main shock. The pre Landers catalog (Figure 1a) uses event from 1984 until the time of the Joshua Tree earthquake, and the post Landers catalog (Figure 1b) starts just after the Big Bear earthquake. The focal mechanisms are shown by the P axes and T axes in the insets to Figures 1a and 1b. [9] Two stress fields are required for the test: the inverted pre Landers stress field and the Landers induced static stress change field. The pre Landers focal mechanisms were inverted for a spatially varying stress field using the 2 D damped stress inversion method of Hardebeck and Michael [2006] (Figure 1c). This inversion assumes that the stress field does not change significantly over the 8 years of the pre Landers catalog and that the stress orientations do not change with depth. These assumptions are justified by Hardebeck and Hauksson s [2001] observation that stress orientations in southern California do not change substantially with depth and do not change significantly with time except in areas with recent large earthquakes. To test the sensitivity to the grid configuration, I tried four binning schemes, two with 8 km grid spacing and two with 10 km spacing, with each pair shifted relative to each other by half the grid spacing. I allow 8 10 km scale variations in the pre Landers stress field because my tests target stress heterogeneity on much smaller scales of 10 m to 1 km. [10] The earthquake induced static stress changes (Figure 1d) were computed using DLC software codes (R. Simpson, personal communication) based on the Okada [1992] subroutines for dislocations in an elastic half space. Because the Joshua Tree, Landers, and Big Bear earthquakes are being considered together as the main shock, the static stress changes induced by all three were modeled. Wald and Heaton s [1994] source model was used for the Landers earthquake, and uniform slip models were constructed for Joshua Tree and Big Bear earthquakes (Table 1) on the basis of their seismic moments and apparent fault orientations defined by seismicity [Hauksson et al., 1993]. [11] A subset of the focal mechanism catalog is selected such that the Landers induced stress change at each event hypocenter is large relative to the tectonic loading over the time scale of the aftershock data set, but small enough that it could not cause a true rotation of the uniform background stress. The magnitude of the stress change is measured as the differential stress (s1 s3) of the stress change tensor, where s1 and s3 are the maximum and minimum compressive stresses, respectively. The upper cutoff of the differential stress change is chosen to be 5 MPa, which is small compared to most estimates of the magnitude of the crustal 2of10

deviatoric stress, and so should not cause a true stress rotation. Additionally, all aftershocks within 5 km of the modeled fault planes are removed, because the stress changes this close to the fault are poorly constrained due to the coarse slip distribution model, and it is undesirable for the data set to be dominated by events with high but poorly modeled stress changes. The lower cutoff differential stress is chosen to be 5 kpa, based on the observation of Jackson et al. [1997] that most of the region under consideration exhibits <0.15 microstrain/yr, or <4.5 kpa/yr, of tectonic Figure 1 3of10

Table 1. Parameters for the Uniform Slip Source Models for the Joshua Tree and Big Bear Main Shocks End Point 1 End Point 2 Longitude (deg) Latitude (deg) Longitude (deg) Latitude (deg) Dip (deg) Width (km) Rake (deg) Slip (m) Joshua Tree 116.3000 33.9550 116.3450 34.0567 90.00 15.00 160.00 0.2616 Big Bear 116.8217 34.1650 116.6883 34.2433 85.00 13.00 10.00 0.3411 loading. The aftershock catalog ends 1 year after the Big Bear earthquake, so the cumulative tectonic loading is less than the earthquake induced loading over most of the region. Hardebeck et al. [1998] found significant aftershock triggering at Landers for stress changes of 10 kpa to 1 MPa, so this data set should encompass most of the off fault triggered aftershocks. 3. Method [12] I found the misfit of each focal mechanism in the catalog with respect to two stress tensors: the inverted stress field prior to the main shock (Figure 1c) and the static stress change due to the main shock (Figure 1d). The pre Landers stress is taken at the nearest stress inversion grid point, whereas the Landers induced stress change is computed at each hypocenter. Misfit is calculated as the angle between the rake vector and the shear stress vector projected on the fault plane, as is often done in stress inversions [e.g., Michael, 1984]. [13] The misfits of pre Landers events to the prestress are expected to be low, because the stress field was inverted from these events. These events are independent of the Landers stress change, so their misfits to the static stress change field should somewhat uniformly fill the range of possible misfit values, 0 180. If the heterogenous stress hypothesis is correct, aftershocks are controlled only by the main shock stress change and are independent of the inverted prestress. So aftershocks should have low misfit relative to the modeled static stress change and somewhat uniformly fill the range of possible misfit values relative to the inverted prestress. However, if stress is more homogeneous, the aftershocks are controlled by both the stress change and the prestress and should exhibit low misfit relative to both. Any background events misidentified as aftershocks will have misfits in the same range as the pre Landers events. Therefore, simple scatterplots or histograms of the misfit of each aftershock relative to the two stress fields provide a qualitative evaluation of the heterogeneous stress hypothesis. [14] I also performed a quantitative test of whether or not the pre Landers and post Landers focal mechanisms differ significantly in their misfits to the two stress tensors. In this quantitative test, I considered the magnitude of the Landersinduced stress change and divided the catalog into nine subcatalogs based on the differential (s1 s3) stress change at the event hypocenter. For each subcatalog, I subtracted the average misfit of events before Landers from the average misfit of events after Landers to find the change in misfit. If the post Landers events are dominated by aftershocks, the misfit change should be negative with respect to the Landers induced static stress change. For heterogeneous stress, the misfit change relative to the prestress should be positive for catalogs dominated by aftershocks, which should be less dependent on the prestress than the pre Landers events. For homogeneous stress, the misfits of the aftershocks and pre Landers events to the prestress should be approximately the same. [15] The significance of the misfit change is assessed by comparison to the null hypothesis that the pre Landers and post Landers events sample the same stress field. Another way to state the null hypothesis is that it is unimportant which events come before or after Landers. This null hypothesis is implemented by reshuffling, in each of the nine subcatalogs, which events occur before and after Landers, keeping the original number of each. For the misfit with respect to the Landers induced static stress changes, 3000 reshufflings are performed. The misfit with respect to the background stress requires a new inversion for background stress for each reshuffled catalog, and I performed 1000 reshufflings for each of the four inversion grid configurations. 4. Results [16] The post Landers focal mechanisms are concentrated toward low misfits with respect to the Landers induced Figure 1. (a) Pre Landers earthquakes, from 1 January 1984 until the time of the 23 April 1992 M6.2 Joshua Tree earthquake, 2 months prior to the 28 June 1992 M7.3 Landers main shock. Color reflects the magnitude of the modeled Landers static stress change at the event hypocenter, expressed as the differential stress (s1 s3). Only the 2223 events with differential stress changes between 5 kpa and 5 MPa are plotted and used in the analysis. Inset shows the P axes (red) and T axes (blue) of the focal mechanisms for these events. (b) Post Landers earthquakes, from just after the 28 June 1992 M6.5 Big Bear aftershock until 28 June 1993. Only events with differential stress changes between 5 kpa and 5 MPa are used, and all aftershocks <5 km from the modeled main shock source are excluded, leaving 725 events in the catalog. Inset shows the P axes (red) and T axes (blue) of the focal mechanisms for these events. Blue lines represent the Landers surface rupture and model fault planes for Joshua Tree and Big Bear. SAF, San Andreas Fault. (c) Pre Landers stress field, inverted from the events in Figure 1a. Arrows show the orientation and magnitude of the horizontal principal axes of the normalized deviatoric stress tensor. The 8 km 8 km inversion grid has been decimated for plotting purposes. The inset shows stress orientation around Cajon Pass, the only location where the change in stress orientation is not fully captured by the decimated stress field. (d) Main shock static stress changes, from the combined Landers, Joshua Tree, and Big Bear earthquakes. Arrows show the orientation and magnitude of the horizontal principal axes of the normalized deviatoric stress tensor. 4of10

Figure 2. (a) Misfits of the pre Landers earthquakes, with respect to the inverted pre Landers stress field (Figure 1c) and modeled static stress change field (Figure 1d). Misfit is calculated as the angle between the rake vector and the shear stress vector projected on the fault plane. (b) Misfits of the post Landers earthquakes, with respect to the inverted prestress field and modeled static stress change field. Note that most post Landers earthquakes are consistent with both the prestress and the main shock static stress change, and very few appear to be independent of the prestress. stress change, indicating that the post Landers catalog is dominated by aftershocks that are consistent with triggering by the coseismic static stress changes (Figure 2b). The mechanisms of the post Landers events also exhibit low misfits with respect to the prestress and appear more consistent with the prestress than with the Landers induced stress changes. So, while the aftershock mechanisms are clearly responding to the Landers stress change, they remain aligned with the pre Landers stress field. For comparison, the misfits of the pre Landers events are low with respect to the prestress, as expected, and span the full misfit range with respect to the Landers stress changes (Figure 2a). The misfit of the post Landers events to the prestress appears slightly larger than the misfit of the pre Landers events, which is expected because the stress field was fit to the pre Landers focal mechanisms. [17] Post Landers events in regions experiencing a 0.05 5 MPa stress change have an average misfit to the modeled Landers static stress change that is 45 62 less than the pre Landers events (Figure 3a). This misfit decrease is outside of what would occur by chance, at >99% confidence, implying that the post Landers events with 0.05 5 MPa stress change are dominated by aftershocks aligned with the static stress change. This stress threshold is an order of magnitude greater than the estimated tectonic loading for the duration of the catalog, so the aftershocks should not be affected by the tectonic loading stress. However, the aftershocks show only a modest increase of 5 38 in average misfit with respect to the prestress, compared to the pre Landers mechanisms used to fit the prestress (Figure 3b). For most subcatalogs, the average misfit change is indistinguishable from the reshuffled data at 95% confidence. For subcatalogs with stress changes of 0.05 0.1 MPa and 1 5of10

Figure 3. (a) Difference in mechanism misfit before versus after Landers, with respect to the modeled Landers static stress change (Figure 1d), as a function of differential stress change. The misfit change is defined as the average misfit of events after Landers minus the average misfit of events before Landers. Black lines represent the results for the real data, with the horizontal error bars representing the range of differential stress values and the vertical error bars representing nodal plane uncertainty. Shading shows the range of results expected from random chance, found by reshuffling the data. The middle 90% of 3000 reshufflings are shown. The numbers at the top of each bin indicate the number of pre Landers and post Landers events in that bin. (b) Difference in mechanism misfit before versus after Landers, with respect to the inverted pre Landers stress field (Figure 1c), as a function of differential stress change. Black lines represent the real data, with the horizontal error bars representing the range of differential stress values and the vertical error bars representing nodal plane uncertainty and different stress inversion grid configurations. Shading shows the range of results expected from random chance, found by reshuffling the data. The middle 90% of 4000 reshuffling results are shown. 2 MPa, the average misfit change is different from that of the reshuffled data at 95% confidence, although, when the nodal plane ambiguity and inversion grid effects are accounted for, the 90% confidence ranges overlap. These two bins together contain only 7% of the aftershock catalog, so this marginally significant movement away from the pre Landers stress tensor is limited to a small number of aftershocks. The majority of triggered aftershocks are well aligned with the prestress, inconsistent with the predictions of the heterogeneous stress hypothesis. [18] I repeated this test, using only events within 10 km of the San Andreas Fault, to test whether stress heterogeneity along this major fault could have been missed in the analysis of the larger data set. The results are quite similar. The post Landers events experiencing a 0.1 MPa stress change have an average misfit to the modeled stress change that is 27 73 less than the pre Landers events (Figure 4a). This misfit decrease is outside of what would occur by chance at >99% confidence, implying that the post Landers events along the San Andreas are dominated by aftershocks. These aftershocks show only a modest increase of 3 17 in average 6of10

Figure 4. As in Figure 3, but for earthquakes within 10 km of the San Andreas Fault. misfit with respect to the prestress, compared to the pre Landers mechanisms (Figure 4b). This average misfit change is indistinguishable from the reshuffled data at >95% confidence. Therefore, I conclude that the heterogeneous stress hypothesis can be rejected near the San Andreas Fault as well as for the rest of southern California. [19] Interestingly, the triggered aftershocks are simultaneously consistent with two stress fields: the pre Landers stress field and the Landers induced stress change field. One possible explanation is that aftershocks may preferentially occur in locations where the main shock stress change aligns with the background stress. This idea is the basis for modeling aftershock triggering using Coulomb stress changes on optimally oriented planes [e.g., King et al., 1994]. However, as McKenzie [1969] demonstrated, a single focal mechanism may be consistent with a range of different stress tensors if the fault is not assumed to be optimally oriented. Therefore, another possible explanation is that the stress fields are different and the triggered aftershocks represent the subset of focal mechanisms that are consistent with both stress fields. [20] The data suggest a combination of these two explanations. The background stress and the Landers induced stress change are in general not very similar, as measured by the normalized tensor dot product (Figure 5). The post Landers events preferentially occur where the two stress tensors are somewhat more similar. The distribution of the normalized tensor dot product is shifted toward higher values when sampled at the locations of the aftershocks compared to the locations of the pre Landers earthquakes or a uniform sample. However, many aftershocks occur in locations where the two stress tensors are dissimilar: about two thirds occur where the normalized tensor dot product is less than 0.5, and one third occurs where the tensor dot product is negative. Figure 6 shows a set of aftershocks that occurred where the two stress fields are quite dissimilar, with a normalized tensor dot product of 0.44, yet the orientation of the shear stress projected onto the fault planes is similar. 5. Discussion [21] The heterogeneous stress hypothesis predicts that triggered aftershocks should occur in volumes of the crust 7of10

Figure 5. The similarity between the pre Landers stress field and the Landers induced stress change field, measured by the normalized tensor dot product between the deviatoric parts of the stress tensors. The solid black line shows the cumulative distribution of the similarity sampled at each grid node used in the stress inversion. The dashed and shaded lines show the similarity sampled at the locations of the pre Landers and post Landers earthquakes, respectively. where stress is aligned with the Landers stress change, whereas the pre Landers events should occur in volumes where stress is aligned with the tectonic loading stress. The results, however, show that the triggered aftershocks are aligned with the same stress field as the pre Landers mechanisms. One might argue that, in a heterogeneous stress field, the aftershocks might preferentially align with the tectonic loading if years of loading have brought many faults in well oriented stress volumes near failure, while also perhaps moving faults in other stress volumes away from failure. However, the accumulated stress owing to past tectonic loading, which is a persistent spatially coherent stress field, should actually be considered part of the uniform background stress. If the background stress is large enough to have a significant impact on the orientations of faults near failure, the heterogeneous part of the stress field must be small in comparison, implying a relatively uniform stress field. [22] The simplest explanation of the focal mechanism catalog is that the prestress is the persistent spatially coherent background stress, which is large enough compared to any heterogeneity that it can be successfully retrieved using standard stress inversion techniques [e.g., Michael, 1984; Hardebeck and Michael, 2006]. The aftershocks are consistent with both the background stress and the Landers induced stress change, in part because they preferentially occur in regions where the two stress fields are more similar and in part because a single focal mechanism can be consistent with a range of different stress tensors. This requires failure of nonoptimally oriented planes, such as preexisting faults, which are not included in Smith and Dieterich s [2010] modeling. These faults failed because they were well aligned within the dominant background stress field and then received a small additional stress load from the Landers main shock. [23] The heterogeneous stress model, if it applies anywhere, should apply to the complex active fault system in southern California. Therefore, the counterexample provided by the Landers earthquake is strong evidence that the heterogeneous stress model is not widely applicable. The Landers counterexample also disproves the hypothesis that focal mechanisms are biased toward the stress loading direction and implies that focal mechanism stress inversion techniques [e.g., Michael, 1984], when used properly, correctly return the background stress orientations. Reported stress rotations due to large earthquakes, including in the near field of the Landers main shock [Hauksson, 1994], are therefore not sampling artifacts and imply true rotations of the background stress. [24] The only convincing focal mechanism evidence for heterogeneous stress comes from a few data sets, typically aftershock sequences, where the focal mechanism variability is too large to be explained by a uniform stress tensor. The best studied example is the aftershock sequence of the 1989 M6.9 Loma Prieta earthquake [e.g., Michael et al., 1990], which exhibited right lateral, left lateral, thrust, and normal faulting mechanisms. The heterogeneity is restricted to the events along and directly above the main shock rupture surface, whereas the rest of the aftershocks are more homogeneous [Michael et al., 1990; Hardebeck, 2006]. Other earthquakes, such as the Landers main shock [Hauksson, 1994], exhibit aftershock heterogeneity along only some parts of the rupture surface. This suggests that, although large earthquakes can produce heterogeneous stress, the effects are very localized. The heterogeneity also cannot be long lived; otherwise stress heterogeneity would be apparent along all major faults. This suggests either that the aftershocks significantly reduce the stress heterogeneity or that some other stress relaxation mechanism is in effect. [25] The general homogeneity of the stress field also has important implications for the dynamics of earthquake rupture. Assuming that earthquake slip distributions are as heterogeneous as they appear in kinematic slip models, the initial stress distribution, the fault constitutive properties, or both must be heterogeneous [e.g., Aagaard and Heaton, 2008]. Low heterogeneity in the stress field implies that significant spatial variation is required in the fault constitutive properties. 6. Conclusions [26] I used earthquakes before and after the 1992 M7.3 Landers, California, earthquake to test the hypothesis that the crustal stress field contains large amplitude, small lengthscale heterogeneity. The heterogeneous stress hypothesis predicts that triggered aftershocks should occur in volumes of the crust where stress is aligned with the Landers stress change, whereas the pre Landers events should occur in volumes where stress is aligned with the tectonic loading stress. However, both the pre Landers and aftershock focal mechanisms are well aligned with the inverted prestress, indicating that they are in fact sampling the same stress field. The pre Landers stress field and the Landers stress change field are quite different over much of the region, ruling out coincidental alignment. The alignment of the aftershock 8of10

Figure 6. Examples of Landers aftershocks with focal mechanisms that are consistent with both the pre Landers stress field and the Landers induced static stress change. These mechanisms occurred in a region where the two stress tensors are dissimilar, with a normalized tensor dot product of 0.44. The open red and blue symbols show the pre Landers stress and Landers stress change tensors, respectively. The black and shaded lines show the fault plane in the lower and upper hemispheres, respectively, and the rake is shown as a solid black or shaded circle. The solid red and blue circles show the projected shear stress direction of the two stress tensors onto the fault plane, with lighter colors indicating the upper hemisphere. focal mechanisms with the prestress is inconsistent with the prediction of the heterogeneous stress model that the pre Landers events and triggered aftershocks should sample crustal volumes with different stress orientations. Therefore, the inverted pre Landers stress must be the persistent background stress field. The aftershocks are consistent with both the background stress and the Landers induced stress change, in part because they preferentially occur in regions where the two stress fields are more similar and in part because a single focal mechanism can be consistent with a range of different stress tensors. If heterogeneous stress were common in the crust, it should be expected in southern California, given the complexity of the fault system. The Landers counterexample is therefore strong evidence that the heterogeneous stress model is not widely applicable. [27] Acknowledgments. IamgratefultoAndyMichaelandBrad Aagaard for constructive reviews of an earlier version of this manuscript, to the associate editor and two anonymous reviewers for their comments, and to Debbie Smith and Tom Heaton for many interesting discussions about stress heterogeneity. I thank the Southern California Seismic Network (SCSN) and the Southern California Earthquake Data Center (SCEDC) for collecting and providing access to the earthquake first motion data used to generate the focal mechanism catalog. 9of10

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