## Introduction

We derived the rupture process of the 2008 Northern Iwate earthquake (Mj 6.8), which occurred at 00:24 on July 24 (JST), using near-source strong-motion data.

## Data

Strong motion data recorded at 22 stations (2 K-NET stations and 20 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 for 16 s.

## Fault model

The Hi-net first motion focal mechanism and F-net moment tensor solution shown in Figure 1 largely deviate from each other. Hence, a preliminary inversion analysis with a single planar fault model based on the F-net moment tensor was insufficient to explain the waveforms at stations within specific azimuths. Therefore, we derived a two-segment fault model consisting of southern and northern segments. The southern segment was 16×30 km with a strike of 223° and dip of 65° (Hi-net first motion), while the northern segment was 14×30 km with a strike of 179° and a dip of 71° (F-net moment tensor). The rupture starting point was located on the southern segment at 39.7391°N, 141.6704°E, and a depth of 115 km, which was the hypocenter determined by the Hi-net.

## 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 model was divided into subfaults of 2×2 km each. Therefore, the southern and northern segments were divided into 8×15 and 7×15 subfaults, 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 a 1-D layered velocity structure model (Ukawa et al., 1984). 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. To stabilize the inversion, the slip angle variation was limited to ±45° and centered at the rake angles of each segment (-107° for the southern segment and -93° for the northern segment), 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 a comparison between the observed and synthetic waveforms.
The Vftw, maximum slip, and seismic moment were 3.6 km/s, 2.4 m, and 2.82×10^{19} Nm (Mw 6.9), respectively.
The largest slip area was found in the northern segment, extending from the area around the point connecting the two segments to the shallower part of the fault model.

Figure 4 shows the contributions of the southern and northern segments to the synthetic waveforms.
The observed waveforms at stations located around and north of the epicenter, had one main pulse wave generated mainly from the large slips on the northern segment.
In contrast, the observed waveforms at stations located south of the epicenter (e.g., IWTH04, IWTH22, and IWTH27), had two main pulse waves, each generated from the southern and northern segments, respectively.
Use of the Hi-net focal mechanism in the southern segment improved the waveform fittings for IWT018 and IWTH19.