## Introduction

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

## Data

Strong motion data recorded at 27 stations (13 K-NET stations, 9 KiK-net borehole stations, 2 KiK-net surface station, 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

Based on the observations of surface ruptures, the spatial distribution of aftershocks, and the geodetic data such as InSAR and GNSS, the realistic curved fault model was developed for the source-process analysis of this event (Figure 2). The top length of the curved fault model is approximately 53 km and its width is 24 km. 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 approximately 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 0.4 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 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 inside each subfault, 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). The weight of the smoothing constraint is determined based on ABIC (Akaike, 1980). Vftw is selected to minimize data-fit residual.

## Results

Figure 3, Figure 4, and Figure 5 show the total slip distribution by map projection, perspective illustration, and planar projection, respectively.
Figure 6 shows the comparison between the observed and the synthetic waveforms.
Figure 7 shows the rupture progression.
Figure 8 shows the moment rate function of each subfault.
Vftw, the maximum slip, and the seismic moment are 2.6 km/s, 3.8 m, and 5.5×10^{19}Nm (Mw7.1), respectively.
Large slips (> 2.4 m) are found 10-30 km northeast of the rupture starting point and are distributed from the depth of approximately 15 km to the top of the fault model. The northeastern edge of this large slip region reaches the northwestern part of the caldera of Mt. Aso. These large slips were caused by the main rupture at 4-16 s after rupture initiation, which propagated toward the northeast shallow area. It is also found that another rupture propagated toward the surface from the rupture starting point at 2-6 s, and then propagated toward the northeast along the near surface at 6-10 s. The extent of the large near-surface slips in this source model is roughly consistent with the extent of the observed large surface ruptures.

*For details of this analysis, we refer the reader to Kubo et al. (2016)