## Introduction

We derive the rupture process of the Mj 7.3 2016 Kumamoto earthquake (mainshock) at 1:25 on April 16 (JST) using near-source strong-motion data.

## Data

Strong motion data recorded at 14 stations (11 K-NET surface stations, 1 KiK-net borehole station, and 2 F-net stations) shown in Fig. 1 are used in the inversion analysis. The velocity waveforms (converted by integration of the original K-NET and KiK-net acceleration waveforms) are band-pass filtered between 0.05 and 0.5 Hz, resampled to 5 Hz, and windowed from 1 s before S-wave arrival for 31 s.

## Fault model and discretization of the rupture process

We assume the 72km x 20km rectangular fault model that has a strike of 224 degrees and a dip of 88 degrees based on the F-net moment tensor solution.
The rupture starting point is set at 32.75389N, 130.76481E, and at a depth of 13.12km, referring to the hypocenter information by Hi-net.

The rupture process is spatially and temporally discretized following the multi-time-window linear waveform inversion scheme (Olson and Apsel, 1982; Hartzell and Heaton, 1983).
For the spatial discretization, the fault plane is divided into 18 subfaults along the strike and 5 subfaults along dip directions, with a size of 4km x 4km each.
For the temporal discretization, the moment rate function of each subfault is represented by 7 smoothed-ramp functions (time windows) progressively delayed by 1.0 s and having a duration of 2.0 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 the Green's function.

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 underground structure model.
The underground structure model is obtained for each station from the 3-D structure model (Fujiwara et al., 2009).
Logging information is also used for the KiK-net station.

## 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 around the F-net rake angle (-154 degrees), using the non-negative least-squares scheme (Lawson and Hanson, 1974). In addition, we impose the spatio-temporal smoothing constraint on the slip (Sekiguchi et al., 2000).

## Results

Figure 2 shows the total slip distribution.
Figure 3 shows the comparison between the observed and the synthetic waveforms.
Figure 4 shows the rupture progression.
Figure 5 shows the moment rate function of each subfault.
Vftw, the maximum slip, and the seismic moment are 3.2km/s, 3.3m, and 5.61×10^{19}Nm (Mw7.1), respectively.
The large slip area is found from 10km to 30km to the northeast of the rupture starting point.
The rupture mainly propagated to the northeast, developed into the large moment release between 8 s and 16 s, and almost ceased after 20 s.

Please note that this is the result from the first analysis and will be modified after the further examination.