## Introduction

We derive the rupture process of the Mj 6.5 foreshock of the 2016 Kumamoto earthquake at 21:26 on April 14 (JST) using the near-source strong-motion data.

## Data

Strong motion data recorded at 11 stations (6 K-NET surface and 5 KiK-net borehole stations) shown in Fig. 1 are used in the inversion analysis. The velocity waveforms converted by integration of the original accelerations are band-pass filtered between 0.1 and 0.5 Hz, resampled to 5 Hz and windowed from 1 second before S-wave arrival for 10 seconds.

## Fault model and discretization of the rupture process

We assume the 12km x 10km fault model that has a strike of 211 degrees and a dip of 87 degrees based on the F-net moment tensor solution.
The rupture starting point is set at 32.743N, 130.806E, and at a depth of 12.6km, 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 6 subfaults along the strike and 5 subfaults along dip directions, with a size of 2km x 2km each.
For the temporal discretization, the moment rate function of each subfault is represented by 4 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 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 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 (-174 degrees), using the non-negative least-squares scheme (Lawson and Hanson, 1974). In addition, we impose the spatio-temporal smoothing constraint on 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 1.6km/s, 2.7m, and 1.24×10^{18}Nm (Mw6.0), respectively.
The large slip is found around the rupture starting point.

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