Introduction
We derived the rupture process of the 2008 Iwate-Miyagi Nairiku earthquake (Mj 7.2), which occurred at 08:43 on June 14 (JST), using near-source strong-motion data.
Data
Strong motion data recorded at 14 stations (1 K-NET station, 1 KiK-net surface station, and 12 KiK-net borehole stations), shown in Figure 1, were used in the inversion analysis. The velocity waveforms (converted by integration of the original K-NET and KiK-net accelerations) were band-pass filtered between 0.1 and 1.0 Hz, resampled to 5 Hz, and windowed from 1 s before S-wave arrival. The inverted data duration, which depends on the station (9, 10, 11, or 16 s), was chosen to avoid the effects of secondary waves.
Fault model
The rupture starting point was located at 39.027°N, 140.878°E, and a depth of 6.5 km, which was the hypocenter determined by Shiomi et al. (2009). We assumed a 40×18 km rectangular fault model with a strike of 209°, from the F-net moment tensor solution. The fault model dip angle was set to 40°, so that the surface trace of the shallower extension of the assumed fault plane would agree with the surface rupture locations reported by AIST (2008).
Discretization of the rupture process
The rupture process was spatially and temporally discretized following a multi-time-window linear waveform inversion scheme (Olson and Apsel, 1982; Hartzell and Heaton, 1983). For spatial discretization, the fault plane was divided into 20 and 9 subfaults, of 2×2 km each, along the strike and dip directions, respectively. For temporal discretization, a moment rate function of each subfault was represented by 7 smoothed-ramp functions (time windows), each having a duration of 0.8 s and progressively delayed by 0.4 s. The first time window starting time is defined as the time prescribed by a circular rupture propagation with a constant speed (Vftw). Thus, the rupture process and strong-motion waveforms were linearly related using Green's functions.
Green's function
Green's functions between each subfault and station were calculated using the discrete wavenumber method (Bouchon, 1981) and the reflection/transmission matrix method (Kennett and Kerry, 1979) assuming 1-D layered velocity structure models. Velocity structure models were assumed for each station based on the 3-D structure model proposed by Fujiwara et al. (2006). Logging data were also referred to for the KiK-net stations. The rupture propagation effect inside each subfault was included in Green's functions by the convolution of the moving dislocation effect (Sekiguchi et al., 2002).
Waveform inversion
The seismic moment of each time window at each subfault was derived by minimizing the difference between the observed and synthetic waveforms using the least-squares method. The data weight of IWTH25 was 4-fold larger than that of other stations, as IWTH25 was the only station located just above the source area. To stabilize the inversion, the slip angle variation was limited to ±45° and centered at 104°, which is the rake angle of the F-net moment tensor solution, using the non-negative least-squares scheme (Lawson and Hanson, 1974). Additionally, we imposed a spatiotemporal smoothing constraint on the slip (Sekiguchi et al., 2000), and determined its weight based on ABIC (Akaike, 1980). Vftw was selected to minimize the data-fit residual.
Results
Figure 2 shows the total slip distribution on the fault. Figure 3 shows the total slip distribution projected on the map. Figure 4 shows the rupture progression projected on the map. Figure 5 shows a comparison between the observed and synthetic waveforms. The Vftw, maximum slip, and seismic moment were 1.8 km/s, 6.2 m, and 2.73×1019 Nm (Mw 6.9), respectively. A large slip area extended from the hypocenter to the southern shallow part of the fault plane, and another large slip patch was located in the northern shallow part. The main rupture propagated southward for approximately 9 s and the northern rupture occurred after the rupture of the southern patch. The slip just below IWTH25 is considered to contribute to the large ground motion at IWTH25.
