Corresponding author: Aditya Riadi Gusman, Institute of Seismology and Volcanology, Hokkaido University, Sapporo, Hokkaido, Japan. (firstname.lastname@example.org)
 The slip distribution of the largest foreshock that occurred 2 days before the mainshock of the 2011 Tohoku earthquake is estimated by tsunami waveform inversion. The major slip region was located on the down-dip side of the hypocenter, and the slip amounts ranged from 0.6 to 1.5 m. By assuming the rigidity of 4 × 1010 N m-2, the seismic moment calculated from the slip distribution is 1.2 × 1020 N m (Mw 7.3). The slip distribution suggests that the largest foreshock did not rupture the plate interface where the dynamic rupture of the mainshock was initiated. The largest foreshock increased the Coulomb stress (1.6–4.5 bars) on the plate interface around the hypocenter of the mainshock. This indicates that the 2011 Tohoku earthquake was brought closer to failure by the largest foreshock.
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 An earthquake (Mw 7.3) occurred off the coast of Miyagi (143.28°E and 38.328°N) at 02:45:12 on 9 March 2011 UTC (according to JMA) and generated a small tsunami. This earthquake is the largest foreshock of the 11 March 2011 Tohoku earthquake (Mw 9.0). The epicenters of the largest foreshock and the mainshock are separated by approximately 45 km. According to the JMA catalog, the foreshock sequences of the 2011 Tohoku earthquake began 23 days prior to the main event. Kato et al.  identified two distinct sequences of foreshocks migrating at rates of 2–10 km/day along the trench axis toward the epicenter of the 2011 Tohoku earthquake; the largest foreshock initiated the second sequence that migrates at an average speed of ~10 km/day.
 In this region, the Pacific Plate moves westwards and is subducting beneath northern Honshu at a rate of 80 mm/yr. [Miura et al., 2006]. Two of the most recent M7 class earthquakes occurred in 1978 (Mw 7.6) and in 2005 (Mw 7.2) [Yamanaka and Kikuchi, 2004; Miura et al., 2006]; these earthquakes are located approximately 110 km southwest from the epicenter of the largest foreshock. Great earthquakes have occurred in the subduction zone in 869 (Mw 8.4), 1896 (Mw 8.0), and 1933 (Mw 8.4) [Kanamori, 1971, 1972; Tanioka and Satake, 1996; Minoura et al., 2001; Satake et al., 2008] (Figure 1).
 The tsunami waveforms generated by the 9 March 2011 largest foreshock were recorded by pressure gauges and GPS buoys deployed off the coast of Miyagi. We apply tsunami waveform inversion method [Satake, 1989] to estimate slip distribution of the largest foreshock. We have previously used tsunami waveforms in estimating slip distribution of the great 2011 Tohoku earthquake [Gusman et al., 2012]. Earthquake parameters used in this study are based on the USGS W phase centroid moment tensor solution (strike/dip/rake: 192°/14°/81°). We predict the Coulomb stress change from the slip distribution and evaluate how the largest foreshock led to the rupture of the great 2011 Tohoku earthquake.
 We used tsunami waveforms at TM1, TM2, GPSB802, GPSB803, and GPSB804 stations (Figure 2) to estimate slip distribution of the largest foreshock. The bottom pressure gauges of TM1 and TM2 are operated by University of Tokyo and Tohoku University. The Ministry of Land, Infrastructure, Transport, and Tourism (MLIT) and the Port and Airport Research Institute (PARI) operate the GPS buoys. The TM1 and TM2 sampling rate is 10 Hz, while the GPS buoys sampling rate is 1 Hz.
 These records include ocean tides and high frequency waves, which should be removed to retrieve the tsunami waveform. The ocean tides are approximated by fitting a polynomial function, and are removed from the tide records. The records also include waves with frequencies that are higher than a tsunami, which are removed by applying a low-pass filter. The low-pass filter passed everything below 0.01 Hz and cutoff everything above 0.03 Hz. Accurate bathymetry is crucial for tsunami simulation because tsunami propagation mainly depends of the ocean depth. We use the General Bathymetric Chart of the Oceans (GEBCO) 30 arc-seconds gridded bathymetry dataset for the tsunami simulation.
3 Inversion Method
 To estimate the extent of the ruptured plate interface, we assumed an area on the plate interface with a length of 105 km and a width of 90 km that covers the foreshock area. Then, we divide the plate interface into 42 subfaults with size of 15 × 15 km. The mechanisms for all subfaults are strike = 192°, dip = 14°, and rake = 81° from the USGS W phase centroid moment tensor solution, the shallowest depth of the subfaults is 10 km. Instantaneous rupture on all subfaults is assumed because the tsunami propagation velocity is much smaller than the rupture velocity. Ocean bottom deformation for each subfault is computed with unit amount of slip by Okada  formula. The spatial wavelength of the ocean bottom deformation from the 15 × 15 km subfault at 10 km depth is much larger (~100 km) than the ocean depth (~3 km) (Figure2). Therefore, the initial sea surface deformation is assumed to be the same as the ocean bottom deformation.
 Synthetic tsunami waveforms generated from all subfaults at the stations were numerically computed by solving the linear shallow water equations with spherical coordinate system [Johnson, 1998]. The numerical model solved the governing equations with the finite difference method. The computation area extends from 140°E to 150°E and 35°N to 41°N. The GEBCO 30 arc-seconds dataset were resampled to build a bathymetric grid system with grid size of 90 arc-seconds (approximately 2.7 km). For the tsunami inversion, the first cycle of tsunami waveforms are used because it contains most information about the slip distribution of the earthquake. Because the sea level observation instruments use different sampling rates of 10 Hz and 1 Hz, we resample the observed tsunami waveforms at 1 s interval.
 To estimate the slip distribution of the largest foreshock we used non-negative least square method [Lawson and Hanson, 1974] and included a spatial smoothness constraint. The optimal value of smoothing factor (α2 = 0.1) was obtained to minimize the value of Akaike's Bayesian Information Criterion (ABIC) [Akaike, 1980]. For more details of our inversion method, see Gusman et al. . We calculated the standard error of the estimated slip distribution by “delete-half” Jackknife technique [Tichelaar and Ruff, 1989].
4 Results and Discussion
 The major slip region of the inferred slip distribution has a dimension of 45 × 45 km which is located on the down-dip side of the hypocenter (Figure 3). The slip amounts on the major slip region range from 0.6 to 1.5 m. The major slip region is centered at a depth of approximately 19 km. By assuming the rigidity of 4 × 1010 N m-2, the seismic moment calculated from the slip distribution is 1.2 × 1020 N m which is equivalent to Mw 7.3. Centroid for this event that was determined by the USGS is located near the center of the major slip region (Figure 3).
 Tsunami waveforms simulated from the slip distribution agree with the observed ones at all stations (Figure 4). Standard error of the estimated slip distribution is obtained using 50 models from the Jackknife resamples (the slip distribution with its standard error can be seen in the Supporting Information). The maximum standard error for the slip distribution is ± 1.6 cm, which is relatively small (4.8%) compared with the slip amount on the corresponding subfault. We also estimate source models with the shallowest subfaults depths of 5 and 15 km, in addition to the initial source model with the shallowest subfault depth of 10 km. The RMS of residual between simulated and observed tsunami waveforms from the slip distribution with the shallowest depth of 10 km (RMS(10) = 0.0116) is smaller than those from the other slip distributions (RMS(5) = 0.0147 and RMS(15) = 0.0173). The geometry of the preferred slip distribution is consistent with the SLAB1.0 geometry in this region [Hayes et al., 2012].
 The estimated slip distribution suggests that the 9 March 2011 largest foreshock (Mw 7.3) did not rupture the plate interface where the dynamic rupture of the mainshock of the 11 March 2011 Tohoku earthquake (Mw 9.0) was initiated (Figure 3). The epicenter of the mainshock is located adjacent to the southern termination of the slip distribution. This indicates that highly resistive patch around the epicenter of the mainshock was able to withstand the stress caused by the largest foreshock. Stress increases larger than 0.1 bars commonly raise regional seismicity and thus potentially bring a major fault to failure with delays ranging from seconds to decades [Stein, 1999; Parsons et al., 2008]. From the slip distribution, we calculated the Coulomb stress change on thrust faults with the same geometry as the largest foreshock (Figure 5). Friction coefficient of 0.4 and rigidity of 4 × 1010 N m-2 are assumed. The calculation shows that the Coulomb stress increased by 1.6–4.5 bars within a 4 km radius of the hypocenter of the mainshock (depth = 23.7 km). At the hypocenter, the stress increased by 3.5 bars. This indicates that the 2011 Tohoku earthquake was brought closer to failure by the largest foreshock.
 Moreover, the stress changes caused by the largest foreshock triggered the subsequent foreshocks. The foreshocks occurred on 9 March 2011 were mostly located on the upper part of the major slip region of the largest foreshock. From 10 March until before the 11 March 2011 Tohoku earthquake occurred, the foreshocks moved toward the epicenter of the mainshock (JMA catalog) (Figure 3). The foreshock migration was interpreted as propagation of slow slip by Kato et al. , the slow slip also increased the static stress on the plate interface in addition to that by the largest foreshock. These static stress increases might have finally brought the 2011 Tohoku earthquake to failure.
 We estimated the slip distribution of the largest foreshock of the 2011 Tohoku earthquake by using tsunami waveforms at near-field stations. The major slip region has a dimension of 45 × 45 km which is located on the down-dip side of the hypocenter. The slip amounts on the major slip region range from 0.6 to 1.5 m. By assuming the rigidity of 4 × 1010 N m-2, the seismic moment calculated from the slip distribution is 1.2 × 1020 N m which is equivalent to Mw 7.3. The inferred slip distribution shows that the largest foreshock did not rupture the plate interface where the dynamic rupture of the mainshock was initiated. However, the largest foreshock increased the Coulomb stress by 3.5 bars on the plate interface at the hypocenter of the mainshock. The static stress changes from the largest foreshock might have brought the great 2011 Tohoku earthquake closer to failure.
 The Coulomb stress change is calculated using Coulomb3.3 software. We thank the editor Andrew Newman and two anonymous reviewers for their constructive reviews of the manuscript.