## Introduction

We derive the rupture process of the 2015 Miyagi-oki earthquake (Mj 6.8) at 06:13 on May 13 (JST) using the near-source strong-motion data.

## Data

Strong motion data recorded at 18 stations (6 K-NET stations, 11 KiK-net stations, and 1 F-net station) shown in Figure 1 are used in the inversion analysis. The velocity waveforms (converted by integration of the original K-NET and KiK-net accelerations) are band-pass filtered between 0.1 and 1.0 Hz, resampled to 5 Hz and windowed from 1 s before S-wave arrival for 15 s.

## Fault model and discretization of the rupture process

We assume the 26 km x 28 km rectangular fault model that has a strike of 177 degrees and a dip of 25 degrees based on the F-net moment tensor solution.
The rupture starting point is set at 38.86N, 142.15E, and a depth of 46 km, which is the hypocenter determined by JMA.

The rupture process is spatially and temporally discretized following the multiple-time-window linear waveform inversion scheme (Olson and Apsel, 1982; Hartzell and Heaton, 1983).
For the spatial discretization, the fault plane is divided into 13 subfaults along the strike and 14 subfaults along dip directions, with a size of 2 km x 2 km each.
For the temporal discretization, the moment rate function of each subfault is represented by 7 smoothed-ramp functions (time windows) progressively delayed by 0.4 s and having a duration of 0.8 s each.
The first time window starting time is defined as the time prescribed by a circular rupture propagation with the constant speed of Vftw.
Thus, the rupture process and the strong-motion waveforms are linearly related via Green's functions.

The Green's functions between each subfault and each station are 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.
The underground structure model is obtained for each station from the 3-D structure model (Fujiwara et al., 2009).
Logging data is also referred to for the KiK-net stations.
The rupture propagation effect inside each subfault is included in the Green's function by the convolution of the moving dislocation effect, following Sekiguchi et al. (2002).

## Waveform inversion

Moment of each time window at each subfault is derived by minimizing the difference between the observed and the synthetic waveforms using the least-squares method. To stabilize the inversion, the slip angle is allowed to vary within ±45 centered at 64 degrees, which is the rake angle of the F-net moment tensor solution, using the non-negative least-squares scheme (Lawson and Hanson, 1974). In addition, we impose the spatiotemporal smoothing constraint on slips (Sekiguchi et al., 2000). The weight of the smoothing constraint is determined based on ABIC (Akaike, 1980). Vftw is selected to minimize data-fit residual.

## Results

Figure 2 shows the total slip distribution on the fault.
Figure 3 shows the rupture progression.
Figure 4 shows the moment rate function of each subfault.
Figure 5 shows the comparison between the observed and the synthetic waveforms.
Vftw, the maximum slip, and the seismic moment are 4.0 km/s, 1.5 m, and 1.3×10^{19} Nm (Mw 6.7), respectively.
Large slips are found in the region around the rupture staring point and the regions approximately 10 km southeast of the rupture starting point.
These regions had the down-dip ruptures at 0－2.4 s and 2.4－4.8 s after rupture initiation, respectively.
Through the check of the synthetic waveforms generated by each slip region, we confirmed that the two pulses in the observed waveforms were radiated from the two regions, respectively.

Please note that this analysis is tentative and may be modified after the further examination.