1. Introduction

A gigantic interplate earthquake occurred on March 11, 2011 at 14:46 (JST) to the northeast of mainland Japan. The hypocenter determined by the Japan Meteorological Agency (JMA) was at 38.10N, 142.86E, depth 23.7 km. A very large tsunami hit the Pacific coastline of the Tohoku and Kanto area with maximum heights greater than 10 m. JMA estimated Mw to be 9.0 from centroid moment tensor (CMT) analysis using long-period global data. It was the greatest earthquake ever recorded by seismometers around Japan. Tens of thousands of fatalities occurred, mainly from the tsunami.

In this region, the Pacific plate is subducting beneath northeastern Japan at the Japan Trench. The convergence rate is about 8 cm/yr in the WNW direction (Wei and Seno, 1998). Many M 7 class earthquakes have occurred in this region (Yamanaka and Kikuchi, 2004), but few events greater than M 8 have occurred in the last several hundred years. The Meiji-Sanriku earthquake of 1896, which triggered an abnormally large tsunami, is one such event. The average slip during this event was 5.9–6.7 m (Tanioka and Seno, 2001), yet the total slip released by seismic waves was far less than that accumulated from plate coupling over the last several hundred years. This suggests a high coupling rate as pointed out by GPS analysis (Nishimura et al., 2004). The mechanism of releasing the slip deficit in this region is a topic of much research. One candidate for this kind of event is the Jogan earthquake of AD 869, for which Mw has been estimated at more than 8.4 by comparing the distribution of tsunami deposits with numerical tsunami simulations (Satake et al., 2008; Namegaya et al., 2010), but the size and mechanism of this event are uncertain.

In this study, we have estimated the source process of the 2011 Tohoku Earthquake by using both teleseismic P waves and regional strong motion data. We then considered the relation between the large slip area and interplate coupling in the source region.

2. Teleseismic Waveform Analysis

2.1 Data and method

We retrieved broadband data with vertical components of teleseismic P waves from the Data Management Center of the Incorporated Research Institutions for Seismology (IRIS), selecting 41 stations with epicentral distances between 30° and 100°. The data were integrated to displacement and band-pass filtered between 0.002 and 1.0 Hz. Figure 1 shows locations of the mainshock and aftershocks (M > 5.0) from the unified JMA catalog. The initial size of the fault plane was taken to be 510 km × 240 km from the aftershock distribution, and the rupture was assumed to start at the hypocenter of the mainshock. We divided the fault into subfaults 30 km × 30 km in size, each with strike and dip angles fixed at 201° and 9°, respectively, in accordance with the quick Global CMT solution. This mechanism is almost identical to the strike and dip angles of the subducting Pacific plate. The moment rate function for each subfault was expressed by 10 basic triangle functions with 8 s durations overlapping by 4 s, which can cover a 44-s rupture duration at each subfault. The spatiotemporal distribution of slip on the fault plane was inverted by the teleseismic body-wave inversion program (Kikuchi and Kanamori, 2003) developed by Kikuchi and Kanamori (1991). The body-wave Green’s functions were computed for a simple-layered oceanic model with a 3 km water depth referred to the Jeffreys-Bullen model. No time adjustments were used for waveform alignments and weights on waveforms were equal. An optimal maximum rupture velocity of 1.8 km/s, minimizing residuals between observed and calculated waveforms, was selected by trial and error.

Fig. 1.
figure 1

Finite-source model from inversion of teleseismic waves. (a) Focal mechanism. (b) Moment rate function. (c) Slip distribution on the fault. The large green star represents the epicenter of the mainshock (Mw = 9.0), and gray circles represent aftershocks (M ≥ 5.0) within 24 h of the mainshock. Crosses represent grid points on the fault plane for calculating synthetic waveforms. Contour interval in slip distribution is 4 m.

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2.2 Inversion results

The results of our teleseismic waveform inversion are shown in Fig. 1. Figure 2 shows the observed and calculated waveforms and the distribution of stations used in this analysis. The total seismic moment is 4.3 × 1022 N m (Mw = 9.0). There are three major stages of slip (asperities) during the event at about 20–40 s, 40–90 s, and after 100 s following the initiation of rupture (Fig. 1(b)). The rupture duration is more than 150 s, but we cannot discuss the exact duration because of the contamination of PP or PcP phases. The first asperity corresponds to the first peak in the observed data and is located near the hypocenter. The second and largest one, corresponding to the second peak in the observed data, is distributed on the shallower side (east) of the fault plane near the hypocenter. The third one is about 200–300 km SSW of the hypocenter. The maximum slip is about 28 m if the rigidity is assumed to be 30 GPa. The reduction of variance in our inversion is about 75%, and the overall fit between observed and calculated data is good.

Fig. 2.
figure 2

(a) P wave waveform fits for the teleseismic inversion. Selected stations used in the inversion are displayed, with observed and calculated waveforms shown as black (top) and red (lower) lines, respectively. The number above the station code is the peak-to-peak amplitude of the observed waveform (micro-meter) and the number below the station code is the source-to-station azimuth and epicentral distance. (b) Distribution of stations, with red circles representing epicentral distances between 30° and 100° from the mainshock in 10° increments.

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3. Regional Strong Motion Waveform Analysis

3.1 Data and method

Twenty-three strong motion seismograms from K-NET (Kinoshita, 1998) and KiK-net stations (Aoi et al., 2000), deployed by the National Research Institute for Earth Science and Disaster Prevention (NIED) and from the JMA, were used in this analysis (Fig. 3). We did not use seismic data from JMA stations in the Tohoku district, where the telemetric system failed. Acceleration seismograms were integrated to velocity, then the data were band-pass filtered between 0.01 and 0.15 Hz and decimated to 0.5 Hz. We used 250 s of data, starting from 10 s before the P wave arrivals. The strike and dip angles of the fault plane was fixed at the same values used in teleseismic waveform analysis. The fault size was taken to be 475 km × 175 km, and the rupture was assumed to start at the hypocenter of the main-shock. We divided the fault into subfaults 25 km × 25 km in size.

Fig. 3.
figure 3

Finite-source model from inversion of strong motion waves. (a) Moment rate function. (b) Slip distribution on the fault. The large green star represents the epicenter of the mainshock (Mw = 9.0), and gray circles represent aftershocks (M ≥ 5.0) within 24 h of the mainshock. Crosses represent grid points on the fault plane for calculating synthetic waveforms. Triangles denote seismic stations used in this analysis. Contour interval in slip distribution is 4 m. The light blue rectangle shows the estimated peak of the highly uplifted area obtained from tsunami arrival times (Hayashi et al., 2011).

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The Green’s function for each subfault was calculated by the discrete wavenumber method (Bouchon, 1981) using reflection-transmission matrices (Kennett and Kerry, 1979). The anelasticity effect was included by the use of complex velocity (Takeo, 1985). A stratified layered structure (Wu et al., 2008) was assumed in calculating the Green’s functions. The moment rate function for each subfault was expressed by 20 basic triangle functions with 8 s duration overlapping by 4 s, which can cover an 84-s rupture duration at each subfault. The maximum rupture velocity was set at 2.5 km/s to minimize variance. We used the linear multiple time window inversion method with constraints on the smoothness of the spatiotemporal slip distribution (e.g., Ide et al., 1996; Nakayama and Takeo, 1997). The smoothness parameters (hyperparameters) were selected to minimize Akaike’s Bayesian information criterion (ABIC) (Akaike, 1980; Fukahata et al., 2003). Waveforms were aligned by onset time and weights on waveforms were equal for all stations.

3.2 Inversion results

Figure 3 shows the slip distribution obtained from the regional strong motion data analysis. The total seismic moment was 3.4 × 1022 N m (Mw = 9.0), which is slightly smaller than that obtained by the teleseismic waveform inversion but comparable. The slip area extends eastwards from the hypocenter to the shallower part of the fault plane. The maximum slip amount is 38 m. The overall fit between observed and calculated waveforms is quite good (Fig. 4), with a reduction in variance of about 91%.

Fig. 4.
figure 4

Comparison of observed (black lines) and calculated (red lines) waveforms for selected stations. The velocity amplitude scale for each station is displayed to the right of the waveforms in cm/s.

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Snapshots of the distribution of released seismic moment at 10-s intervals are shown in Fig. 5. In the first stage of the rupture (0–40 s), the rupture expands outwards from the hypocenter, which corresponds to the first peak of the observed data in the Tohoku area (Fig. 4). In the next stage (40–80 s), the rupture area extends towards the shallow part of the fault plane in both north and south directions. This stage corresponds to the second peak of observed data in Tohoku and causes large slip amounts and may be related to the generation of the large tsunami. The rupture velocity is very slow (~1 km/s) during the first and second stages, and the rupture duration is long (~80 s). In the third stage (after 80 s), the rupture extends southwards, reaching the southern end of the fault plane at 160 s. The amplitude peaks in the southern part of the rupture area are due to the superposition of moment release from the second and third stages.

Fig. 5.
figure 5

Snapshots of the rupture propagation at 10-s intervals derived from strong motion inversion. The area of the figures corresponds to the grids in Fig. 3. The seismic moment release during each interval is shown by colors. Contour interval is 0.5 × 1020 N m. The star indicates the hypocenter. Diamonds corresponding to strong high-frequency radiation sources during the first, second, and third rupture stages (see Section 4) are shown in magenta, light blue, and blue, respectively.

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4. Discussion and Conclusions

A large slip area near, and offshore of, the hypocentral region with maximum slip exceeding 25 m is obtained by both teleseismic and regional source process analyses. The shape of the large slip area is similar in both analyses, but the points at the maximum slipped area near the trench differ somewhat (about 50 km). This might be due to the location error of these analyses. The maximum slip is larger in the regional analysis because of a spatially finer resolution. This region also coincides with the area of large coseismic slip obtained by GPS analysis (GIJ, 2011) except near the trench, where a small coseismic slip was estimated by GPS. The difference partly reflects the poor resolution of GPS data near the trench. In the tsunami waveform inversion (Fujii and Satake, 2011), the area of large slip also can be seen near the trench just east of the hypocenter. The region where tsunami back-propagation curves of initial crests are concentrated (Hayashi et al., 2011), shown in Fig. 3, is almost coincident with the area of large slip obtained in this study. These results strongly suggest the existence of a strong asperity near the trench. However, the inferred slip distribution in the southern part of the rupture area is not identical in the teleseismic and regional analyses. This suggests that the location error is greater than that in the northern part, but the slip amount we inferred is necessary to explain the strong waveform peaks at stations in the Kanto area (e.g., station HITACH in Fig. 4).

Interplate coupling in northeastern Japan has been investigated by many researchers using the GPS network. Nishimura et al. (2004) found that interplate coupling was strong during 1995–2002 in the epicentral region, where a very large slip was estimated by this study. A low ratio of the number of small repeating earthquakes to the total number of earthquakes was observed in the area of large slip (Uchida et al., 2002), which is also suggestive of strong interplate coupling in this region. These observations suggested the potential for the occurrence of earthquakes.

Aoki et al. (2011) carried out a rough estimation of the sources of high-frequency energy using the Source-Scanning Algorithm developed by Kao and Shan (2007). The short period (4–8 Hz) RMS velocity envelopes of K-NET and KiK-net stations were used. Five high-frequency sources (HFS) were imaged during this event (Fig. 5). The first HFS was in the first rupture stage, the second and third HFSs in the second stage, and the fourth and fifth HFSs in the third stage. The rupture progress of HFSs in a NS direction was almost the same as that estimated by the strong motion data analysis. The HFSs are generally located on the rim of the large slip patch obtained by the strong motion data analysis. This result is similar to that of the 1994 Sanriku-Haruka-Oki earthquake (Nakayama and Takeo, 1997).

In source process analyses with the combination of tele-seismic and regional strong motion data, we have found the following features: The main rupture is located to the shallower side of the hypocenter, and maximum slip amounts were more than 25 m. The size of the main fault was about 450 km in length and 200 km in width; the duration of rupture was more than 150 s; and Mw was 9.0. The initial rupture gradually expanded near the hypocenter (0–40 s) and subsequently propagated both southwards and northwards. But there are some differences between the two approaches. Constructing a source process model by joint inversion of teleseismic and regional strong motion data such as Yagi et al. (2004) is an important next step.