The slip history of the 2011 Mw 7.4 Sanriku-Oki, Japan earthquake, which occurred fifty-one hours before the Mw 9.1 Tohoku earthquake, is constrained by jointly inverting waveforms of teleseismic body waves, long period surface waves and local strong motions as well as GPS observations, after first relocating its hypocenter using a double difference approach and teleseismic P waves. The inverted results indicate that the rupture of this Sanriku-Oki earthquake was dominated by the failure of an elliptical shape asperity, elongating roughly along the plate motion direction. The rupture initiated at the southeast corner of this asperity and propagated mainly in the west-northwest direction with a rupture velocity of 3.1 km/s in the beginning 15 s and 1.1 km/s in the next 40 s. It released a total seismic moment of 1.6 × 1020 Nm, with 82% occurring in the first 25 s. The rupture had an average slip of 1 m and produced an average stress drop of 0.9 MPa. The Sanriku-Oki earthquake did not break the hypocenter region of the Mw 9.1 Tohoku earthquake but slightly increased the Coulomb stress there. A correlation between the high slip region and the high Vp/Vs ratio of the overriding plate right above the plate interface has been found, which suggests the Sanriku-Oki earthquake and its frequent predecessors might have broken a relatively weaker patch within a large strongly coupled asperity.
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 On 9 March, 2011, a large thrust earthquake shook the middle portion of the Japan trench, where the Pacific Plate is subducting beneath the Okhotsk Plate at a convergent rate of 9.2 cm/yr [DeMets et al., 2010]. The analyses of long period seismic waves (e.g., GCMT, http://www.globalcmt.org) yielded a moment magnitude of 7.4, with a low angle nodal plane orienting N189°E and dipping 10° to the west. According to Japan Meteorological Agency (JMA), this so-called Sanriku-Oki earthquake nucleated beneath the (38.328°N, 143.278°E) at a depth of 8 km, 25 km north and 36 km west of the epicenter of the devastating March 11th Mw 9.1 off the Pacific coast of Tohoku earthquake (38.103°N, 142.86°E), which occurred 51 hours later. The small temporal separation and close spatial locations between these two events have drawn wide attention to their potential interaction [e.g., Ando and Imanishi, 2011]. However, the slip distribution of the Sanriku-Oki event has not been as well studied as that of the Tohoku earthquake.
 The March 9th Sanriku-Oki earthquake occurred in the middle of a large seismically quiescent region in the forearc of the Northeast Japan arc inferred from the seismicity from 1990 to 2009 (Figure S1 in the auxiliary material). This seismic gap has a dimension of approximately 120 km along strike by 150 km downdip. The plate interface within this gap failed eventually during the March 11th Tohoku earthquake with an average slip of over 20 m [e.g., Shao et al., 2011]. In contrast, the rupture area of the Sanriku-Oki earthquake as outlined by the JMA aftershocks in the first 2 days (Figure 1a), particularly its northeast corner, was associated with high seismic activity and possible creeping [Uchida et al., 2006]. It is of interest to investigate whether the dynamic and kinematic parameters of the March 9th Sanriku-Oki earthquake are significantly different from other M7 subduction-zone thrust earthquakes.
 The Sanriku-Oki earthquake was well recorded by modern seismic and geodetic instruments. Researchers could freely access the broadband waveforms of over 1000 global seismic stations archived at the IRIS Data Management Center (DMC) and hundreds of borehole strong motion stations located on Honshu Island (KiK-Net, http://Oki.kik.bosai.go.jp). Meanwhile, the Caltech-JPL Advanced Rapid Imaging and Analysis (ARIA) project also distributed the co-seismic static displacements at hundreds of continuous GPS stations. Combining these data provides good coverage to the March 9th Sanriku-Oki earthquake and allows a clear image of its rupture process.
 In the following sections, after relocating the hypocenter of the March 9th event relative to the March 11th Tohoku earthquake using teleseismic broadband P waves, we first constrain the rupture process of the Sanriku-Oki earthquake by jointly inverting the seismic waveforms of teleseismic broadband and local strong-motion stations, and the co-seismic static displacements of GPS stations. We then investigate the tectonic cause of this event by comparing the inverted slip distribution with the slip zones of previous large earthquakes, high-resolution bathymetry map, and velocity tomography of the overriding plate right above the fault zone. In the end, we develop a hypothesis to link these independent observations.
2. Finite Fault Inversion of the 2011 Sanriku-Oki Earthquake
2.1. Hypocenter Relocation
 Finite fault studies, particularly those based on teleseismic data, often result in relative rather than absolute spatial-temporal variation of the fault rupture. The references are the hypocenter location and earthquake origin time after preforming some standard processes, such as aligning the data with their first P or S arrivals. In order to investigate the interaction of the March 9th and 11th earthquakes, a double-difference relocation analysis using teleseismic P waves has been preforming to correct the relative location between those two earthquakes. This work is discussed in detail in the auxiliary material. The relocated hypocenter of the March 9th Sanriku-Oki earthquake is (38.34°N, 143.12°E, 14 km), 14 km west of its JMA epicenter.
 We selected the strong-motion waveforms recorded at 23 KiK-net borehole stations in this study (Figure 1a). These data have been bandpass filtered between 3 s and 50 s before being integrated into displacements. For each trace, we windowed 80 s seismic signals starting at its first P-wave arrival. Although near-field strong motion waveforms are very sensitive to the earthquake rupture process, all those strong motion stations are located on the west side of the source region, with a limited azimuthal coverage of 111° (from 231° to 332°). We improved the azimuthal coverage by further incorporating 30 broadband teleseismic P waves and 21 SH waves (Figure 1a). These data were downloaded from IRIS DMC and bandpass filtered between 2 s and 166 s before being converted into ground displacements. Moreover, 29 Rayleigh and 19 Love waves in the period range from 166 s to 333 s were used to constrain the overall fault parameters such as total seismic moment, focal mechanism, and centroid location. Finally, we estimated the co-seismic static displacements of the Sanriku-Oki earthquake by comparing averages of continuous GPS data one-week before and one-day after the earthquake. These static measurements have relatively small amplitudes. The maximum observed horizontal displacement is 3.2 cm. We selected 42 horizontal displacements in this study (Figure 1a).
2.3. Inversion Setup
 We adopted a 80 km by 104 km rectangular plane to model the fault geometry of the Sanriku-Oki earthquake. This planar fault has a strike of 190° and dips 11° to the west, consistent with the GCMT solution. We discretized the fault plane into 130 8 km by 8 km subfaults and further sampled each subfault with 81 uniformly distributed point sources to take into account its finiteness [Ji et al., 2002]. We let the rupture initiate at the relocated hypocenter (38.34°N, 143.12°E, 14 km). We used a 1D layered velocity model (Table S1 in the auxiliary material), interpolated from the global CRUST2.0 [Bassin et al., 2000] and a local seismic velocity profile [Miura et al., 2005], to approximate the structure in the source region. The synthetic seismograms of body waves and long period surface waves were calculated using the first motion approximation [Langston and Helmberger, 1975] and the normal mode superposition algorithm [e.g., Dahlen and Tromp, 1998], respectively. The static response of this layered structure was generated using the algorithm of Xie and Yao .
 We apply a finite fault inversion method that performs the waveform inversion in the wavelet domain and applies a simulated annealing method to simultaneously invert slip amplitude, rake angle, rupture initiation time, and the shape of an asymmetric slip rate function for each subfault [Ji et al., 2002, 2003]. We let the slip amplitude vary from 0 to 4 m and the rake angle change from 45° to 105°. We allow the starting time and ending time of the asymmetric slip rate function [Ji et al., 2003] to change from 0.8 to 6.4 s. The value of rise time is therefore limited between 1.6 and 12.8 s. Overall, there are 650 free model parameters, constrained by 8000 wavelet coefficients extracted from the seismic data accompanying with 42 GPS vectors. Because many of these wavelet coefficients are correlated, we stabilize the inversions by applying a derivative minimization smooth constraint of fault slip [Ji et al., 2002], as well as a temporal constraint proposed recently [Shao et al., 2011]. The latter aims to compress the irresolvable roughness of the rupture front, which is not well constrained because of the intrinsic trade-off between rupture initiation time and rise time [Ji et al., 2003].
2.4. Inversion Results
Figures 1a and 1b display the spatial slip distributions of our preferred source model. The distribution of rise time is shown in Figure S4a in the auxiliary material. We define the average slip velocity as the ratio of static slip and rise time, and present its distribution in Figure S4b in the auxiliary material. Before discussing the rupture characteristics of this event, we compare the observations with synthetics predicted with this preferred model.
 Our preferred model explains the data very well. Figure 1a shows the comparison of observed and synthetic static displacements. Their misfits have a spatially random distribution (Figure S5 in the auxiliary material). Their mean value is only 0.2 cm, compatible with the typical GPS observational error. Figure 2 shows the comparisons of observed and synthetic waveforms at several representative stations. The comparisons of all waveforms could be found in the auxiliary material (Figures S6–S8 in the auxiliary material). Quantitatively, the preferred model produces a variance reduction of 83.2% for teleseismic body waves, 84.2% for teleseismic surface waves, and 81.5% for local strong motion data. Note that the strong motion observations show a clear sign of directivity. The peak amplitudes at stations located northwest of the epicenter are significantly larger than those at stations southwest (Figure 2b).
 The inverted slip distribution is characterized by a single elliptical shape asperity. It elongates for ∼90 km mainly in the west-northwest (WNW) direction in a map view, which is close to the plate motion direction (Figure 1a). The rupture initiated at the shallower portion of the fault plane, at a depth of 14 km, and then propagated mainly toward Honshu Island in the WNW direction. The rupture front in the first 15 s migrated a distance of 47 km in this direction, suggesting an average velocity of 3.1 km/s or about 80% of local shear wave speed. It then slowed down to only 1.1 km/s but continuously expanded for another 40 s. The inverted total seismic moment (Mo) is 1.6 × 1020 Nm, equivalent to a moment magnitude of 7.4, consistent with the GCMT solution. Eighty-nine percent of the total seismic moment occurred in the subfaults with slip larger than 25 cm. The accumulated area of these subfaults is 4160 km2. Although the inverted total rupture process lasted for about 55 s, over 82% of the seismic moment was released in the first 25 s (Figure 1a). We shall point out that the WNW extension of fault slip is well constrained by the inland GPS and strong motion data, but the rupture velocity is sensitive to the hypocenter location. Using the original JMA epicenter would lead to a faster rupture velocity.
 It is noteworthy that the centroid of this asperity is located about 27 km northwest of the relocated epicenter, agreeing remarkably well with the centroid location of the GCMT solution (Figure 1a). In Figure 1a, we have superimposed on the slip distribution, JMA ML > 2 aftershocks within the first 51 hours, GCMT focal mechanisms of the three largest foreshocks, and the JMA epicenter of the March 11th Tohoku earthquake. Although these aftershocks might not all occur on the plate interface, they cluster around the high slip region in the map view. The JMA epicenter of the March 11th Tohoku earthquake is located ∼20 km south of the 25 cm iso-slip contour of the March 9th event. It is then unlikely that the co-seismic rupture extended to it. All three Mw > 6 aftershocks occurred between the slip region of the March 9th event and the JMA epicenter of the March 11th Tohoku earthquake. According to GCMT, the largest aftershock has a moment magnitude of 6.5. This earthquake occurred about 33 hours before the Tohoku earthquake with a centroid location 23 km north of the latter's epicenter.
 We estimate the weighted average values of inverted source parameters (Umean). It is defined as, Umean = Σ(UiDi)/ΣDi, where Ui, Di are the parameter value and slip amplitude of the i-th subfault. These average values are much more robust than the results of individual subfaults [Ji et al., 2002]. For the preferred model, the weighted average slip amplitude and rake angle are 1.0 m and 76.4°, respectively. The average rise time is 5.7 s, with 3.2 s for the starting time and 2.5 s for the ending time [Ji et al., 2003]. The slip velocity defined above changes up to 1.2 m/s, with a weighted average of 0.2 m/s.
 We further calculate the on-fault static stress changes for the motion in the average rake angle direction using the software Coulomb 3.2 [Lin and Stein, 2004] and our inverted slip distribution. Only the subfaults with slip larger than 25 cm were used in this calculation. The calculated stress changes have been scaled with a reasonable shear modulus (μ) of 3.6 × 1010 Nm based on the velocity model mentioned above. As shown in Figure 1c, the on-fault shear stress changes vary from −3.2 MPa to 1.5 MPa. The average static stress drop weighted by slip is 0.9 MPa. This result is smaller than the average stress drop of interplate earthquakes (3 MPa [Kanamori and Anderson, 1975]), but this discrepancy might not be significant. In a recent global survey, the median stress drop of Mw 7 reverse faulting earthquakes is about 1 MPa [see Allmann and Shearer, 2009, Figure 11a]. Adopting the USGS estimation of the radiated seismic energy (ER = 1.3 ± 0.2 × 1015 J), the apparent stress drop (μER/M0) is then about 0.3 MPa, consistent with the median value of subduction earthquakes (0.31 MPa [Choy and Boatwright, 1995]). Hence, the March 9th earthquake is apparently a typical Mw 7 earthquake in terms of its rupture velocity, average stress drop and apparent stress drop.
 Our stress calculation also indicates that the March 9th earthquake caused only a small Coulomb stress increase of 0.06 MPa for the thrust motion at JMA hypocenter of the March 11th Mw 9.1 Tohoku earthquake.
3. Discussions and Implications
 The fact that the giant March 11th Tohoku earthquake ruptured the aforementioned seismic gap (Figure S1 in the auxiliary material) with an average slip over 20 m [e.g., Shao et al., 2011; Simons et al., 2011] suggests that this seismically quiescent region was strongly coupled before this earthquake, which could be caused by structural heterogeneities in the megathrust zone [Zhao et al., 2011]. However, distinguishably different with its surrounding region, the background seismic activity in the slip zone of the March 9th event is characterized by frequent M 5–7 earthquakes (Figure S1 in the auxiliary material). For instance, according to JMA catalog, two M7 events occurred on this portion of the plate interface in the twentieth century. The latest one occurred on January 18th, 1981 [Yamanaka and Kikuchi, 2004]. In Figure 3a, the slip distribution of the 1981 event, the 1978 Mw 7.4 Miyagi-Oki earthquake, and the March 9th event are depicted as grey, green, and red contours, respectively. Their epicenters are denoted as the grey, green, and red stars. The slip models of these two previous earthquakes were constrained using local strong motion data [Yamanaka and Kikuchi, 2004]. Although the 1981 rupture initiated in the north boundary of its slip zone and propagated southward for about 40 km along the plate interface [Yamanaka and Kikuchi, 2004], it can be seen that the major slip area of the 1981 event overlaps with that of the March 9th event. With a plate convergence rate of 9.2 cm/yr [DeMets et al., 2010], the accumulated tectonic load is up to 2.8 m since its 1981 predecessor, but the average co-seismic slip of the March 9th event (∼1 m) accounts for only about one third of that value. Such a slip deficit is in fact similar to what was found during previous studies of the repeated Miyagi-Oki earthquake sequence [e.g., Yamanaka and Kikuchi, 2004].
 In Figure 3b, we superimpose the inverted slip distribution on the Vp/Vs ratio of the overriding plate right above the plate interface, which is obtained from a recent tomography study using high-quality arrival times from thousands of local earthquakes [Huang et al., 2011]. It can be seen that in a map view, the high slip region of the March 9th earthquake is closely correlated with the region with high Vp/Vs ratios (up to 10%). Since the Japan forearc region features cold (<400°c) mantle [Wiens et al., 2008], high Vp/Vs ratios might indicate the existence of high fluid contents on the plate interface. Furthermore, the presence of fluids will increase the pore pressure in the fault zone [e.g., Zhao et al., 2009]. Generally, we can represent the fault zone strength as μ0(σn − P), where μ0 denoting the static friction coefficient. σn − P is the effective normal stress with σn and P denoting the normal stress and the pore pressure [e.g., Scholz, 2002]. Higher pore pressure then would lead to lower effective normal stress and weaker fault zone strength. Hence, the 2011 March 9th Sanriku-Oki earthquake might represent the failure of a relatively weaker patch inside a strongly coupled plate interface.
 The barrier model [Aki, 1979] and the asperity model [Kanamori, 1981] are two end-member models that explain the relationship between the spatial heterogeneities of the fault and the earthquake cycle. In the barrier model, the shear stress that acts in the plane of a fault before an earthquake is relatively uniform, but the fault strength is spatially variable. During a large earthquake, slip occurs on weaker parts of the fault but does not propagate through relatively high-strength barriers. In the asperity model, the shear stress before an earthquake is spatially variable and the highly stressed asperities break in the earthquake. Both models are required to explain the complex seismic activity in this region. The giant March 11th Tohoku earthquake is probably an example that the largest earthquake occurs when the largest strong region in a plate boundary segment breaks. The strength of such a large strongly coupled plate interface could be heterogeneous as well [see Zhao et al., 2011]. The repeated M7 earthquakes in the source region of the March 9th Sanriku-Oki earthquake suggest that relatively weaker patches fail more frequently but are arrested by the surrounding relatively stronger patches before turning into a Tohoku type earthquake, consistent with the barrier model.
 However, the relationship between high Vp/Vs ratio at the bottom of the overriding plate and weaker coupled plate interface is not unique. Further evidence is required to support the above hypothesis. The kinematic and dynamic parameters of this type of M7 events might not be distinguishable from other subduction-zone thrust earthquakes with a similar magnitude. The slip deficit, inferred from the studies of this event and the previous Miyagi earthquake sequence [e.g., Yamanaka and Kikuchi, 2004], is worth further investigation. It is of interest to know whether the slip deficit is a unique feature for this type of earthquakes.
 It is also not clear yet why the overriding plate right above this region is associated with a high fluid content. It might simply be a long standing heterogeneity of the overriding plate, but it is worth noting that a subducted seamount can erode the base of the overriding plate and entrain fluid-rich sediment [e.g., Ranero and von Huene, 2000]. The overriding plate above the seamount could create a fluid pressure gradient that drains fluid from the seamount flanks and concentrates it at the crest [Le Pichon et al., 1993], leading to a localized high fluid region as well. Further investigations are needed.
 The authors benefited from discussions with Takahiro Maeda and Ralph Archuleta. We thank editor, Kelin Wang and an anonymous reviewer for their constructive comments. We also thank to IRIS data center for providing broadband teleseismic waveforms, KiK-net for providing strong motion data, ARIA team at JPL and Caltech for sharing the continuous GPS data, and Japan Oceanographic Data Center (JODC) for sharing the bathymetry data (J-EGG500). All the figures are made using Generic Mapping Tools (GMT) software written by Paul Wessel and Walter H.F. Smith. This work was supported by NSF grant EAR-0911769, USGS Award G09AP00023, and the Southern California Earthquake Center, which is funded by NSF Cooperative Agreement EAR-0109624 and USGS Cooperative Agreement 02HQAG0008.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper. The SCEC contribution number for this paper is 1513.