We now consider an appropriate source model to explain the observed peculiar tsunami waveform at the two OBPG stations. We assume a source rupture area of approximately 480 km by 200 km over the subducting Pacific Plate as shown in Fig. 2(a), which is divided into 4×3 subfaults with lengths of 160–180 km and widths of 50 km. The geometry of each subfault, such as its strike, dip, and depth is chosen to fit to the upper boundary of the subducting Pacific plate (e.g., Furumura and Kennett, 2005); the dip angles of the subfaults are set to 7, 12, 17, and 22 degrees from the trench axis side to the land and all rake angles are set to 86 degrees following the results of a W-phase moment-tensor inversion of the USGS (2011). The relative depths of each subfault from the ocean bottom are set to 3, 9.09, 19.49, and 34.11 km, from the trench to the land side.
The sea bottom elevation and initial sea height due to the slip over each subfault segment are calculated based on the analytic solution of Okada (1985), assuming a homogeneous half-space model with a Poisson ratio of 0.25. The depth of each subfault is set relative to the ocean bottom rather than the sea surface. The Green’s function of the tsunami waveform for a unit slip over each subfault is then calculated by a tsunami propagation simulation based on the linear long-wave theory (e.g., Goto, 1984). In this simulation, we use a 500-m resolution bathymetry model constructed by combining the ETOPO1 global Earth model and the J-EGG500 Japan coastal model for tsunami computation.
3.1 Source slips and tsunami waveforms
In order to explain the observed offshore tsunami at stations TM1 and TM2 shown in Fig. 1(b), we first examined the case of a uniform slip of 15 m over the entire 12 sub-fault segments and we calculated the co-seismic ground elevation above the source area and the tsunami waveform at TM1 and TM2.
The results for the ground surface deformation pattern and simulated tsunami waveforms at stations TM1 and TM2 are shown in Fig. 2(a). This demonstrates that a large upheaval of the seafloor occurs over the subfaults near the trench, with about 3–4 m uplift of the seafloor around TM1 and TM2. The resultant tsunami traces at TM1 and TM2 derived from the present simulation (inset of Fig. 2(a)) show a gradual fall in sea height from 0 to −1 m at TM2, and to −2 m at TM1 just after the earthquake (Stage A), followed by a sudden drop of the sea surface to −3 to −4 m at a later time (Stage B) at both stations. These characteristics of the simulated tsunami waveforms do not match those of the observed waveforms shown in Fig. 1(b). In this simulation, the large slip below TM1 and TM2 produce a large upheaval of the sea floor as well as the sea surface above TM1 and TM2 after the earthquake. An outflow of seawater at these stations occurs immediately after the coseismic deformation, which gradually reduces the sea level above TM1 and TM2 with increasing time. Therefore, the results of this model strongly suggest that very little sea bottom uplift occurred in the area around TM1 and TM2 during the earthquake.
Based on the above findings, we modified the source slip model to consider subsidence of the sea bottom in the area around TM1 and TM2. We assigned the same amount of slip (15 m) to the six shallower subfaults at the trench side (subfaults a1–2, b1–2, and c1–2), and no slip was assigned to the six deeper subfaults (Fig. 2(b)). The result based on this new source model revealed a subsidence of the sea bottom of −4 m at TM1 and −0.5 m at TM2. The simulated tsunami waveforms at TM1 and TM2 reproduced the observed features of the tsunami qualitatively well, including a gradual uplift of the sea surface from 0 to 4 m at TM1 following the earthquake in Stage A and a sudden uplift to 5 m in Stage B. Also, the shape of the simulated tsunami waveform agrees well with that observed at TM2, with a drop in sea height from 0 to −1 m in the earlier part of Stage A, a gradual uplift due to the tsunami in the later part of Stage A, and a sudden uplift in Stage B (Fig. 1).
Although the modified source slip model shown in Fig. 2(b) explains the observed features of the tsunami waveform at TM1 and TM2 reasonably well, the arrival time of the simulated large, short-wavelength tsunami in Stage B is much earlier than that actually observed. We therefore relocated the area of larger slip on the subfaults to the south (b1–4 and c1–4) in order to introduce a delay in the arrival time of the tsunami at TM1 and TM2 (Fig. 2(c)). After incorporating such a delay, the arrival times of the simulated tsunami at TM1 and TM2 were about 800 and 1100 s after the earthquake origin time, respectively, which shows good agreement with the observations. Thus, we found that the shape of the simulated tsunami waveform matches that of the observed tsunami for both stages. However, the maximum height of the simulated tsunami at TM1 and TM2 is only 2 m. This indicates that a much larger slip is needed for subfault b1 and/or b2 in order to produce a tsunami with a height of more than 5 m at TM1 and TM2, as seen in the observational data (Fig. 1).
3.2 Estimated slip distribution over the fault plane
Based on these findings, we finally construct an appropriate tsunami source model to explain the observed tsunami waveforms at TM1 and TM2 by forward modeling (Fig. 3). The simulated tsunami waveforms reveal a gradual increase in the tsunami height from 0 to 2 m in the first 600 s after the earthquake (Stage A), which was mainly caused by slip at deeper parts of the plate interface (subfaults b3–4), and to some extent by a small amount of slip near the trench off Sanriku (a1–a2). The sudden increase of over 5 m in the height of the tsunami at 700 s (Stage B) was generated by a very large (57 m) slip over the subfault in the plate interface near the trench (b1–2). Our results suggest that no significant slip occurred over the northern segment of the subfault (a3–4), since the arrival times of the main tsunami at TM1 and TM2 are rather late at about 900 and 1100 s, respectively, after the earthquake. We assumed that the slip over the southern segments (c1–4) is 5 m; however, this slip cannot be well constrained by the tsunami records at TM1 and TM2.
In order to confirm the effectiveness of our tsunami source model based on only the tsunami records at TM1 and TM2 off Kamaishi, we compared our simulations with the tsunami waveforms at other DART stations (21401, 21413, 21418) in the Pacific Ocean and OBPGs off Kushiro (PG1 and PG2) (Fig. 4). Very good agreement is found between the simulated and observed tsunami waveforms at the three DART stations, although the arrival times of the simulated tsunami at stations PG1 and PG2 off Kushiro are somewhat later than those observed. This is because the length of the present subfault segment in the fault strike direction (80 km) is too large to provide efficient time resolution for tsunami propagation to PG1 and PG2 along the strike.