## Introduction

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

## Data

Strong motion data recorded at 27 stations (13 K-NET stations, 11 KiK-net stations, and 3 F-net stations) 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 0.05 and 1.0 Hz, resampled to 5 Hz, and windowed from 1 s before S-wave arrival for 30 s.

## Fault model and discretization of the rupture process

We assume the 56 km x 24 km rectangular fault model that has a strike of 224 degree based on the F-net moment tensor solution.
The dip angle of the fault model is set to 65 degree based on the hypocenter distribution of aftershocks and the surface-rupture distribution, and the static coseismic displacements inferred by InSAR and GNSS.
The rupture starting point is set at 32.7557N, 130.7616E, and a depth of 13.58 km, determined by the double-difference method.

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 28 subfaults along the strike and 12 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 13 smoothed-ramp functions (time windows) progressively delayed by 0.8 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 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 station.
To consider the rupture propagation effect, 25 point-sources are uniformly distributed over each subfault in the calculation of Green's functions.

## 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 -142 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 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.
Figure 6 shows the comparison of the map projection of slip distribution with the surface traces of active faults and the aftershock activity.
Vftw, the maximum slip, and the seismic moment are 2.8 km/s, 4.6 m, and 5.3×10^{19}Nm (Mw7.1), respectively.
The large slips are found from 10 km to 30 km to the northeast of the rupture starting point. The rupture mainly propagated to the northeast, developed into the large moment release between 5 s and 15 s, and almost ceased after 20 s. The slip distribution in the shallow part is consistent the observed surface-rupture distribution. In addition, the large slip area does not overlap with the active aftershock area.

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