GEOPHYSICAL RESEARCH LETTERS, VOL. 38,, doi:10.1029/2011gl050098, 2011 Joint inversion of strong motion, teleseismic, geodetic, and tsunami datasets for the rupture process of the 2011 Tohoku earthquake Yusuke Yokota, 1 Kazuki Koketsu, 1 Yushiro Fujii, 2 Kenji Satake, 1 Shin ichi Sakai, 1 Masanao Shinohara, 1 and Toshihiko Kanazawa 1 Received 25 October 2011; revised 10 November 2011; accepted 10 November 2011; published 21 December 2011. [1] The 2011 Tohoku earthquake was observed by dense strong motion, teleseismic, geodetic, and tsunami networks. We first inverted each of the datasets obtained by the networks separately, for the rupture process of the earthquake. We then performed checkerboard resolution tests for assessing the resolving power of these datasets. In order to overcome the limited resolutions of the separate inversions and differences in their results, we performed a quadruple joint inversion of all these data to determine a source model most suitable for explaining all the datasets. In the obtained source model, the maximum coseismic slip was approximately 35 m, and the total seismic moment was calculated to be 4.2 10 22 Nm, which yielded M w = 9.0. The main rupture propagated not only in the strike direction but also in the dip direction and included both the deep area called the Miyagi-oki region and the compact shallow area near the Japan Trench. Citation: Yokota, Y., K. Koketsu, Y. Fujii, K. Satake, S. Sakai, M. Shinohara, and T. Kanazawa (2011), Joint inversion of strong motion, teleseismic, geodetic, and tsunami datasets for the rupture process of the 2011 Tohoku earthquake, Geophys. Res. Lett., 38,, doi:10.1029/2011gl050098. 1. Introduction [2] The 2011 Tohoku earthquake occurred at 5:46 a.m. on March 11, 2011 (UTC). The Japan Meteorological Agency (JMA) estimated its moment magnitude (M w )to be 9.0 (available at http://www.jma.go.jp/jma/press/1103/ 25b/201103251730.html, 2011). The W-phase moment tensor solutions obtained by the USGS and us (available at http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/ usc0001xgp/neic_c0001xgp_wmt.php and http://outreach.eri. u-tokyo.ac.jp/eqvolc/201103_tohoku/eng, 2011) show a shallow dipping thrust mechanism, indicating an interplate earthquake due to the subduction of the Pacific plate. The National Police Agency reported that the total number of fatalities and missing people was about twenty thousand (available at http:// www.npa.go.jp/archive/keibi/biki/higaijokyo_e.pdf, 2011), and more than 90% of the fatalities were caused by drowning. Therefore, most of the damage was caused by huge tsunamis; the ground motion damage was moderate [e.g., Si et al., 2011]. [3] This earthquake was observed by dense networks of strong motion, teleseismic, geodetic, and tsunami sensors; 1 Earthquake Research Institute, University of Tokyo, Tokyo, Japan. 2 International Institute of Seismology and Earthquake Engineering, Building Research Institute, Tsukuba, Japan. Copyright 2011 by the American Geophysical Union. 0094-8276/11/2011GL050098 hence, four types of abundant datasets were produced. Various source models were inferred using one of these datasets [e.g., Ide et al., 2011; Simons et al., 2011; Yoshida et al., 2011; Ozawa et al., 2011; Fujii et al., 2011]. However, the features of these models are somewhat different from each other because of the limitations unique to each dataset. In order to overcome such differences and limitations, Koketsu et al. [2011] carried out a triple joint inversion of the teleseismic, strong motion, and geodetic datasets, but performed only a separate inversion for the tsunami dataset. [4] The reason for the above was that the fault model was not appropriate for the tsunami dataset. Accordingly, in this study, we first constructed a new fault model and expanded our geodetic dataset. We then performed separate inversions and checkerboard resolution tests of the individual datasets to confirm their limitations. A quadruple joint inversion of all the datasets was then carried out to obtain a final solution. 2. New Fault Model and Geodetic Dataset [5] Figure 1a shows all the earthquakes that occurred in the initial 24 hours after the mainshock of the 2011 Tohoku earthquake, as determined by the JMA (the smallest magnitude is 2.9). Koketsu et al. [2011] considered the earthquakes in the black rectangular grid to be aftershocks. This rectangle (dimensions: 480 150 km 2 ) was adopted with a strike and dip of 200 and 12, respectively, to model the source fault of the mainshock. However, using this fault model, they could not obtain a stable solution for the separate inversion of the tsunami dataset, because considerably shallow slips are necessary to recover large peaks in local tsunami waveforms. They extended the fault model to the shallowest part of the plate boundary neighboring the Japan Trench only for the tsunami inversion, as denoted by the white narrow rectangle in Figure 1a. This extended fault model having dimensions of 480 180 km 2 was also used in this study; it was divided into 96 subfaults of 30 30 km 2. In this study, the dips of these subfaults were set to 20, 12, and 5 in every two rows from the relatively deep part (Figure 1b), referring to the shape of the plate boundary in the Japan Integrated Velocity Structure Model (JIVSM) [Koketsu et al., 2008]. The epicenter (latitude: 38.103 N, longitude: 142.861 E) and origin time (5:46:18 a.m. UTC) determined by the JMA were used as the location and time, respectively, of rupture initiation. The vertical location of the hypocenter was assumed to be at a depth of 17 km in order to make the fault model follow the plate boundary in the JIVSM. [6] The strong motion and teleseismic datasets were the same as those used by Koketsu et al. [2011], but the geodetic dataset was expanded to horizontal and vertical 1of5
Figure 1. (a) K-NET/KiK-net stations used in this study (green triangles). The source fault (rectangular grid) is assumed on the basis of the distribution of relatively small earthquakes during the initial 24 hours (yellow circles). The orange star and the orange and white circles denote the epicenters of the mainshock, aftershocks with magnitudes greater than 7.0, and a foreshock, respectively. The blue line denotes the Japan Trench. (b) The cross section of the source fault model (red line), aftershock distribution (yellow circles), subducting Pacific plate (dark blue curve), and the Pacific Ocean floor (purple curve) along the profile (red line drawn in Figure 1a). The orange and hollow red stars denote the assumed rupture initiation point and the hypocenter determined by the JMA, respectively. displacements at 343 stations. In addition, five seafloor displacements were observed by a GPS/acoustic combination technique [Sato et al., 2011], and they were added to the expanded geodetic dataset. The tsunami dataset is almost the same as that of Koketsu et al. [2011], but the waveforms observed by ocean-bottom pressure gauges (TM-1 and TM-2) were also included. 3. Separate Inversions [7] We then performed a separate inversion of each dataset using the method of Yoshida et al. [1996] with the revisions of Hikima and Koketsu [2005]. The inversion was subject to a smoothness constraint with a discrete Laplacian in space and time. The weight of the constraint was determined by minimizing the Akaike s Bayesian Information Criterion (ABIC) [Akaike, 1980]. Slip vectors were represented by a linear combination of two components in the directions of 90 45 for all datasets. When a layered velocity structure was required in the strong motion, teleseismic, and geodetic inversions, we extracted it from the JIVSM. [8] For the inversion of the strong motion dataset, Green s functions were calculated using the method of Kohketsu [1985]. We selected 20 K-NET and KiK-net stations plotted in Figure 1a, applied a bandpass filter of 10 s to 100 s to three-component records, and integrated these filtered records into ground velocities. For the inversion of the teleseismic dataset, Green s functions were calculated using the method of Kikuchi and Kanamori [1991]. Considering the data quality and the azimuthal coverage, we selected 45 GSN (Global Seismographic Network) stations at epicentral distances of 30 to 100 (Figure S1a in Text S1 of the auxiliary material), removed instrumental responses from the P-wave records observed at these stations, and integrated them into ground displacements using a bandpass filter of 4 s to 500 s. 1 For these inversions, ramp functions with a rise time of 10 s were used as the temporal basis functions, with nine time windows at each subfault. The rupture front velocity was set to 2.5 km/s. These parameters were examined in the auxiliary material (Figures S2 S6). For the inversion of the geodetic dataset, Green s functions were calculated using the method of Zhu and Rivera [2002]. We used 343 GEONET stations and calculated two-component static displacements by comparing averages before and immediately after the mainshock using GIPSY-OASIS 2. In addition, we used the seafloor data observed by Sato et al. [2011]. For the inversion of the tsunami dataset, Green s functions were calculated using the method of Fujii and Satake [2007]. We selected the 33 stations shown in Figure S1b. [9] We examined the resolution of these datasets by means of a checkerboard test. We generated synthetic datasets for the checkerboard-like slip distributions shown in Figure 2a. These synthetic datasets were inverted using the same parameters as those for the separate inversions. Figures 2b 2e show the results of the checkerboard tests for the separate inversions of the strong motion, teleseismic, geodetic, and tsunami datasets, respectively. The overall spatial resolution of the teleseismic inversion (Figure 2c) was not sufficient to discuss the rupture process in detail. Such a problem of low resolution of the teleseismic inversion was also reported by Delouis et al. [2010] for the 2010 Maule earthquake. [10] The GEONET was set up only on the Japanese islands in the west of the fault model; hence, the azimuthal coverage of the geodetic dataset was not sufficiently good to resolve the easternmost part near the Japan Trench (Figure 2d), even when we used the seafloor data. In the result for the strong motion inversion (Figure 2b), this tendency was weak but still visible for a similar reason. On the other hand, the resolution of the tsunami inversion (Figure 2e) was not high in the southwestern part because there were few local tsunami stations close to this part. We also performed the 1 Auxiliary materials are available in the HTML. doi:10.1029/ 2011GL050098. 2of5
Figure 2. (a) Target model used for the checkerboard resolution tests (slips of 0 m and 25 m on alternating groups of 4 2 subfaults and 2 2 subfaults), and the results of the checkerboard resolution tests for the separate inversions of (b) strong motion, (c) teleseismic, (d) geodetic, and (e) tsunami datasets, and (f) the joint inversion. checkerboard test for assessing the resolving power of the joint inversion, which will be discussed in the following section. The checkerboard pattern was recovered well in the result shown in Figure 2f. [11] Figures 3a 3d show the slip distributions derived from the results of the separate inversions of the strong motion, teleseismic, geodetic, and tsunami datasets, respectively. The maximum coseismic slips were approximately 31, 25, 31, and 38 m, respectively. The seismic moments were calculated to be 4.2 10 22, 4.3 10 22, 4.0 10 22, and 3.4 10 22 Nm, respectively, all of which yielded M w = 9.0, using the rigidity structure derived from the JIVSM. In the strike direction, although the slip pattern in the south was different, all the considered distributions found the largest slips in the central part of the fault model. In contrast, there were considerable differences in the dip direction. For example, the longitudinal location of the largest slip varied among the distributions. 4. Joint Inversion [12] In order to overcome the limited resolutions of the separate inversions and the differences in the results of these inversions, we carried out a quadruple joint inversion of the strong motion, teleseismic, geodetic, and tsunami datasets by using the same method as that for the separate inversions. All the data were weighted equally after flattening the difference in the amount of data. Although the teleseismic dataset is not necessary owing to its low resolving power, we included it in Figure 3. Slip distributions obtained by the separate inversions of (a) strong motion, (b) teleseismic, (c) geodetic, and (d) tsunami datasets. Arrows indicate the subfault slips on the hanging wall. The white circle and the sky-blue ellipse in Figure 3d denote the compact shallow rupture and the area to its south, respectively. 3of5
joint inversion result correspond fairly well to the observations, as shown in Figures S7 S10. [14] The joint inversion result revealed that the main rupture was located around the hypocenter. This feature is similar to that indicated by the result of the joint inversion without the tsunami dataset by Koketsu et al. [2011]. However, this rupture was extended to the easternmost part near the Japan Trench, which is different from that shown by the source model of Koketsu et al. [2011], because of the inclusion of the tsunami dataset, even though the area of this shallow rupture (white circle in Figure 4a) was considerably more compact than that indicated by the tsunami inversion result (white circle and sky-blue ellipse in Figure 3d). No aftershocks generated in the initial 24 hours were located in this compact rupture area. [15] We also took snapshots of slip distribution every 10 s after the rupture initiation for illustrating the progress of the source rupture (Figure 4b). The first small rupture began to propagate bilaterally westward and northeastward (0 40 s). Next, the rupture propagated to the easternmost shallow area and generated the compact shallow slip (40 60 s). Later, the main rupture began to propagate northwestward and southward and became dominant with the largest final slip of 35 m (60 100 s). At this time, the slip propagated to the westmost area, including the Miyagi-oki region, for which the Earthquake Research Committee of the Japanese Government reported the probability of having another M7 earthquake during the 30-year period to be greater than 90%, before this earthquake. The southward rupture finally reached west off Fukushima Prefecture, approximately 200 km south of the hypocenter (100 120 s). Figure 4. (a) Slip distributions obtained by the joint inversion. The yellow circles denote aftershocks in the initial 24 hours. The orange star and the orange and white circles denote the epicenter of the mainshock, aftershocks with magnitudes greater than 7.0, and a foreshock, respectively. The arrows indicate the subfault slips on the hanging wall. The white circle and the sky-blue ellipse denote the compact shallow rupture and the area to its south, respectively. (b) The progress of the source rupture is represented by the snapshots of the slip distribution every 10 s after rupture initiation. the joint inversion because of our purpose of constructing a source model suitable for explaining all the datasets. [13] The slip distribution of the source model obtained through this joint inversion is shown in Figure 4a as the detailed rupture pattern of the 2011 Tohoku earthquake. The maximum coseismic slip was approximately 35 m. The seismic moment of this model was calculated to be 4.2 10 22 Nm, which again yielded M w = 9.0. The synthetic waveforms and displacement vectors calculated from the 5. Discussion and Conclusions [16] As mentioned above, the separate inversions revealed different source models owing to the limited resolution of each single dataset. In particular, the resolution of the teleseismic-data-only inversion is low over the entire source region, as shown in Figure 2. Among the published source models for the 2011 Tohoku earthquake, several models based on inversions of teleseismic data only [Ide et al., 2011; Lay et al., 2011; Hayes, 2011; Shao et al., 2011] show slip distributions that are different from those of our joint and separate inversions because of this low resolution. Each of these models has a peak slip zone to the east of the epicenter close to the Japan Trench, while our models have a peak slip zone around the epicenter, except for the tsunami inversion. Consequently, in order to obtain the detailed rupture process of a megathrust event in a subduction zone, a joint inversion of various datasets is necessary. [17] We performed the quadruple joint inversion of all the datasets and determined the source model most suitable for explaining all the datasets. Although previous megathrust events such as the 2004 Sumatra-Andaman and the 2010 Maule earthquakes propagated mainly in the strike direction [Ammon et al., 2005; Lorito et al., 2011], the 2011 Tohoku earthquake rupture propagated not only in the strike direction but also in the dip direction. This rupture included both the deep area called the Miyagi-oki region and the compact shallow area near the Japan Trench (white circle in Figure 4a). The absence of shallow rupture was also found in the results of the separate strong motion, teleseismic, and 4of5
geodetic inversions (Figures 3a 3c), and in the inversion results for the Sumatra-Andaman and Maule earthquakes. Therefore, Koketsu et al. [2011] suggested the slips in the shallow area to be inelastic deformations, which did not affect ground motions and static displacements but only tsunamis. However, we have shown that the source model, which including the compact shallow rupture (white circle in Figure 4a), explained all the datasets. This implies another possibility that the compact shallow rupture might be a usual fault slip rather than an inelastic deformation. Nevertheless, to improve the fit of the observed and synthetic tsunami waveforms (Figure S10) to the level for the separate tsunami inversion, we still need an inelastic deformation in the south of the compact rupture (sky-blue ellipse in Figure 4a), as shown in Figure 3d. [18] Acknowledgments. We thank Martin Mai and an anonymous reviewer for their helpful comments. 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