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[1] The three largest recent great subduction zone earthquakes (2011 M9.0 Tohoku, Japan; 2010 M8.8 Maule, Chile; and 2004 M9.2 Sumatra-Andaman) exhibit similar coseismic rotations of the principal stress axes. Prior to each mainshock, the maximum compressive stress axis was shallowly plunging, while immediately after the mainshock, both the maximum and minimum compressive stress axes plunge at ∼45°. Dipping faults can be oriented for either reverse or normal faulting in this post-mainshock stress field, depending on their dip, explaining the observed normal-faulting aftershocks without requiring a complete reversal of the stress field. The significant stress rotations imply near-complete stress drop in the mainshocks, with >80% of the pre-mainshock stress relieved in the Tohoku and Maule earthquakes and in the northern part of the Sumatra-Andaman rupture. The southern part of the Sumatra-Andaman rupture relieved ∼60% of the pre-mainshock stress. The stress axes rotated back rapidly in the months following the Tohoku and Maule mainshocks, and similarly in the southern part of the Sumatra-Andaman rupture. A rapid postseismic rotation is possible because the near-complete stress drop leaves very little “background” stress at the beginning of the postseismic reloading. In contrast, there has been little or no postseismic rotation in the northern part of the Sumatra-Andaman rupture over the 7 years since the mainshock. All M ≥8.0 subduction earthquakes since 1990 with an adequate number of pre- and post-mainshock events were evaluated, and not all show similar coseismic stress rotations. Deeper earthquakes exhibit smaller coseismic stress rotations, likely due to increasing deviatoric stress with depth.

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[2] One surprising observation following the 2011 M9.0 Tohoku, Japan, subduction zone earthquake was the large number of normal faulting aftershocks near the mainshock rupture [e.g., Asano et al., 2011; Nettles et al., 2011]. These events imply that the stress drop of the mainshock was large enough, relative to the background stress, to locally reverse the style of faulting. The rotation of the stress field due to the Tohoku earthquake, constrained by inversion of earthquake moment tensors, was used to estimate the ratio of the stress drop to the pre-mainshock stress, and the results implied near-complete stress drop [Hasegawa et al., 2011]. Rupture models of the mainshock also suggest dynamic overshoot [Ide et al., 2011]. These results imply that the subduction zone interface is quite weak at seismogenic depths, with strength on the order of the earthquake stress drop, consistent with models of weak subduction zones [e.g., Wang and He, 1999]. I perform a systematic search for stress rotations due to other great subduction zone earthquakes, in order to study general strength properties of subduction zones.

2. Data and Method

[3] Stress orientations are found before and after M ≥8.0 subduction zone mainshocks by inverting the moment tensors of smaller earthquakes. Moment tensors are obtained from the Global Centroid Moment Tensor (GCMT) catalog [Ekström et al., 2012]. Only events near the mainshock rupture plane are used, excluding events in the outer rise or associated with back-arc spreading (Figure 1). I consider all M ≥8.0 mainshocks since 1990 with ≥30 events both before the mainshock (from the beginning of the GCMT catalog in 1976) and in the first 6 months after the mainshock. Then, to obtain better temporal resolution and search for post-mainshock stress rotations, all post-mainshock events (through November 2011) are divided equally into as many as 4 windows of ∼30 or more consecutive events.

[4] Stress orientations are computed for all of the time windows simultaneously, using the damped stress inversion method of Hardebeck and Michael [2006], which minimizes any temporal stress changes not required by the data. Uncertainty is computed using multiple bootstrap resamplings of the data, where one of the two nodal planes is randomly selected. Because noisy data may lead to apparent stress rotations, it is important to verify that any observed stress change is significant. I compare the total data misfit with the data misfits for a suite of inversions using random partitions of the data, preserving the number of pre- and post-mainshock events, followingHardebeck and Hauksson [2001]. If the misfit for the data divided into the pre- and post-mainshock time windows is less than the misfits for ≥95% of the random data partitions, then the difference between pre- and post-mainshock events is unlikely to have occurred by chance due to random errors. I use the smallest damping for which the misfit is significant when compared to the misfits for random partitions, followingHardebeck and Michael [2006]. For many mainshocks, zero damping fits this criterion, meaning that the time windows are inverted independently. The regions are not divided into spatial bins, so the inversions may average over some spatial stress variations. Michael [1991]found that stress inversions return the average stress for a moderately varying stress field, and a misfit of ≥45° indicates too much variation. All of the inversions with ∼30-event temporal resolution show misfit <45° (Table S2 in theauxiliary material).

3. Results

[5] The three largest mainshocks (2011 M9.0 Tohoku, 2010 M8.8 Maule, and 2004 M9.2 Sumatra-Andaman) show substantial stress rotations between the pre- and post-mainshock periods (Figure 1). During the pre-mainshock period, the maximum compressive stress axis,σ1, is typically shallowly plunging, opposite to the dip-direction of the subduction zone, as in numerical models of weak subduction zones [e.g.,Wang and He, 1999]. The minimum compressive axis, σ3, is more steeply plunging, and σ2 is near-horizontal. After the mainshock, theσ1 and σ3 axes have rotated about a horizontal axis such that the post-mainshock plunges of theσ1 and σ3 axes are similar (Figure 2a). With both the σ1 and σ3 axes plunging at ∼45°, dipping faults can be oriented for either reverse or normal faulting, depending on their dip. The observed dips of reverse and normal faulting aftershocks have different distributions, with the reverse faults generally more shallowly dipping and the normal faults more steeply dipping (choosing the nodal plan that dips in the same direction as the megathrust), as predicted (Figure 2b). If the trenchward dipping nodal planes were chosen instead, the normal events would be more shallowly dipping and the reverse events more steeply dipping, consistent with the predictions for trenchward dipping planes (Figure 2a, inset). The post-mainshock stress state can therefore explain the normal-faulting aftershocks observed after the Tohoku [e.g.,Asano et al., 2011; Nettles et al., 2011], Maule [e.g., Farías et al., 2011] and Sumatra-Andaman [e.g.,Dewey et al., 2007] earthquakes, without requiring a complete reversal of the stress field (e.g., as suggested by Kato et al. [2011]).

[6] The rotation of the σ1 and σ3 axes can be used to estimate the ratio of the stress drop to the background deviatoric stress level. The stress rotation, Δθ, is theoretically a function of the original angle of the σ1 axis to the fault, θ, and the ratio of the mainshock stress drop, Δτ, to the background deviatoric stress magnitude, τ = 0.5*(σ1 − σ3) [Hardebeck and Hauksson, 2001]. The theoretical rotation is found from the eigenvectors of the post-mainshock stress tensor, which is the sum of the background stress and the mainshock stress change. The observed stress rotations for the Tohoku, Maule, and northern Sumatra-Andaman (zones B and C) mainshocks imply that these events relieved at least >80% of the deviatoric stress present before the mainshock (Figure 3). The southern part of the Sumatra-Andaman rupture (zone A) relieved ∼60% of the pre-mainshock deviatoric stress.

[7] The southern two zones of the Sumatra-Andaman earthquake (zones A and B) also experienced rotations of the maximum horizontal compressive stress, SHmax (Figures 1 and 3a). The pre-mainshock SHmax axis is not perpendicular to the strike of the trench, and instead loads the megathrust in a right-lateral sense. In zones A and B, the post-mainshock SHmax axes are normal to the trench strike, implying that most of the right-lateral stress was relieved by the right-lateral slip in the mainshock rupture [e.g.,Banerjee et al., 2007; Chlieh et al., 2007]. The SHmax rotation implies that the mainshock relieved >20% and >85% of the deviatoric stress in zones A and B, respectively, similar to the results for the rotation of the σ1 and σ3 axes in these zones. Interestingly, there is no significant rotation of SHmax in zone C, despite the large component of right-lateral slip present in the kinematic source models [e.g.,Banerjee et al., 2007; Chlieh et al., 2007]. However, SHmax does rotate slowly during the postseismic period (Figure S2e), suggesting that some right-lateral stress may have been relieved by shallow postseismic slip.

[8] Of the M <8.7 mainshocks, only the 2006 Kuril Islands earthquake exhibits a rotation implying an unambiguously large value of Δτ/τ, which implies it relieved 60–85% of the pre-mainshock deviatoric stress. The 1994 Kuril Islands, 2003 Tokachi-Oki, Japan, and 2007 Sumatra-Mentawai earthquakes, on the other hand, exhibit small rotations corresponding to low Δτ/τ, relieving <1% to <45% of the pre-mainshock deviatoric stress. Therefore, the near-complete stress drop of the three largest mainshocks does not appear to be a universal feature of great megathrust earthquakes. The ratio Δτ/τ is smaller, in general, for mainshocks with larger median aftershock depth (Figure 3c), which roughly reflects the depth range of the mainshock rupture. Therefore, deeper mainshocks tend to relieve a smaller portion of the background deviatoric stress, consistent with increasing deviatoric stress with depth. The smaller mainshocks show a trenchward plunge of the σ1 axis, similar to that of the largest mainshocks (Figure S2).

[9] The stress rotation decayed rapidly in the months following the Tohoku and Maule mainshocks, as well as in the southern portion of the Sumatra-Andaman rupture (zone A), but has not yet decayed significantly along the northern Sumatra-Andaman rupture (zones B and C) (Figure 4). The rapid post-mainshock rotation is possible because the near-complete stress drop leaves very little “background” deviatoric stress at the beginning of the post-seismic period. Small amounts of postseismic reloading can therefore produce substantial stress rotations. The observed postseismic stress rotations can be modeled using the same dependence of Δθ_{post} on θ_{post} and Δτ_{post}/τ_{post}, with negative Δτ_{post} representing stress reloading of the fault rather than stress drop (Figure 3b). The values of Δτ/τ and Δτ_{post}/τ_{post}can then be used to estimate what fraction of the pre-mainshock stress has been reloaded so far in the post-seismic period.

[10] The large post-mainshock rotations in the Tohoku and Maule regions correspond to a reloading of ∼180% of the deviatoric stress present at the beginning of the post-seismic period. Because of the near-complete stress drop in the Tohoku and Maule mainshocks, this corresponds to only a small fraction of the seismic cycle stress. About 6% of the total stress present before the Tohoku mainshock (and, therefore, ∼6% of the stress drop) appears to have been reloaded in the first 8 months following the mainshock, although the uncertainty is quite large. The postseismic rotation occurs over ∼0.2% of the duration of the seismic cycle, so a ∼6% reloading can't be entirely due to tectonic motion, and must include contributions from deep postseismic slip and/or viscoelastic relaxation. The inferred reloading is on the same order as the postseismic slip, estimated to be ∼10% of the coseismic slip over the first 2 weeks [Ozawa et al., 2011], much of which is down-dip of the mainshock slip.

[11] For Sumatra-Andaman zone A, the post-seismic rotation corresponds to reloading of about 70% of the deviatoric stress present at the beginning of the post-seismic period, or ∼30% of the deviatoric stress existing prior to the earthquake, again with large uncertainty. This is too large to be entirely due to tectonic motion, but is consistent with postseismic GPS measurements which show displacements of ∼10% the coseismic displacement over the first 2 weeks [Vigny et al., 2005]. In the northern part of the Sumatra-Andaman rupture zone, zones B and C, the post-mainshock stress rotation corresponds to a smaller reloading of ∼25–30% of the deviatoric stress present at the beginning of the post-seismic period, although the stress rotations are not distinguishable from zero at 1-sigma uncertainty, so it is possible that there has been no reloading over the 7 years since the mainshock. Tectonic reloading may be slow for the northern Sumatra-Andaman rupture zone due to the very oblique plate convergence [e.g.,Paul et al., 2001].

4. Discussion and Conclusions

[12] The observed coseismic stress rotations constrain the ratio between the stress drop and the background deviatoric stress in the volume near and above the megathrust interface. The rotations observed for the Tohoku, Maule, and Sumatra-Andaman earthquakes imply that the stress drop in these earthquakes was >80% of the pre-mainshock deviatoric stress. However, other mainshocks, including the 2003 Tokachi-Oki and 2007 Sumatra-Mentawai earthquakes, exhibit much smaller stress rotations implying stress drops <20% of the deviatoric stress. This implies variations of at least a factor of 4 in the stress drops of great subduction zone earthquakes and/or in the deviatoric stress. Deeper earthquakes exhibit smaller coseismic stress rotations, implying that the variation is likely due to increasing deviatoric stress with depth.

[13] The near complete stress drop of the Tohoku earthquake poses a problem for our understanding of the coupling of this subduction zone. The Tohoku event released less than the expected total moment accumulation since the 869 Jogan earthquake [Minoura et al., 2001]. Ozawa et al. [2011] estimate that, even accounting for large afterslip and incomplete plate coupling, a M ∼9 earthquake would need to occur every 350–700 years to match the modeled rate of moment accumulation. Studies of coupling based on repeating earthquakes find that the Tohoku event was equivalent to 260–880 years of moment accumulation [Uchida and Matsuzawa, 2011]. The Tohoku earthquake released only 0.23–0.77 of the moment predicted to have accumulated in the 1142 years since the Jogan earthquake. Because the Tohoku earthquake appears to have released all of the accumulated moment, this implies that the plate interface is not as coupled as current models predict, that the coupling and/or convergence rate is time-dependent, or that additional great earthquakes or slow-slip events since the Jogan event are missing from the historical record.

[15] Normal faulting aftershocks were observed following the Tohoku, Maule, and Sumatra-Andaman mainshocks [e.g.,Dewey et al., 2007; Asano et al., 2011; Nettles et al., 2011; Farías et al., 2011]. Toda et al. [2011]proposed that normal faulting aftershocks reflect stress heterogeneity, and indicate the presence of local normal faulting regimes that are activated by static stress changes. This hypothesis is plausible in locations where normal faulting is expected, for example back-arc spreading [Dewey et al., 2007], bending in the outer rise [e.g., Obana et al., 2012], or in some shallow onshore settings [e.g., Kato et al., 2011]. But for the events used in this study, which are close to the megathrust interface, this hypothesis would require pockets of normal-faulting regime to exist close to the megathrust interface prior the mainshock, which seems unlikely.

[16]McKenzie and Jackson [2012]propose that normal faulting in subduction zones is driven by gravitational collapse, and brought on by dynamic weakening of normal faults during a great earthquake. For normal faulting to continue in the aftershock period, even at reduced frictional strength, the faults must be oriented for normal faulting in the post-mainshock stress field. Normal faulting near the mainshock rupture zone can be explained by the observed post-mainshock stress field in which theσ1 and σ3 axes both plunge at ∼45°. In this stress field, dipping faults can produce either reverse or normal earthquakes, depending on their dip. For gravitational stresses to be important at depth, the overall stress level would have to be low, consistent with the implications of the observed stress rotations.

Acknowledgments

[17] I am grateful to the Global Centroid Moment Tensor (GCMT) project for making their moment tensor catalog publically available. I thank Fred Pollitz, Andy Michael, Roland Bürgmann, and an anonymous reviewer for helpful comments on an earlier version of this paper.

[18] The Editor thanks Roland Burgmann and an anonymous reviewer for their assistance in evaluating this paper.