## Introduction

We derive the rupture process of the 2019 Yamagata-oki earthquake (Mj 6.7) at 22:22 on June 18, 2019 (JST) using the near-source strong-motion data.

## Data

Strong motion data recorded at 15 stations (6 K-NET stations, 8 KiK-net borehole stations, and 1 F-net station) shown in Figure 1 are used in the inversion analysis. The velocity waveforms (integrated from 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 22 km × 14 km rectangular fault model that has a strike of 23 degrees and a dip of 36 degrees based on the F-net moment tensor solution.
The rupture starting point is set at 38.6080N, 139.4793E, and a depth of 13.99 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 11 subfaults along the strike and 7 subfaults along dip directions, with a size of 2 km × 2 km each.
For the temporal discretization, the moment rate function of each subfault is represented by 9 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 are also referred to for the KiK-net stations.
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 86 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 the data-fit residual.

## Results

Figure 2 shows the total slip distribution on the fault.
Figure 3 shows the total slip distribution projected on the map.
Figure 4 shows the rupture progression.
Figure 5 shows the comparison between the observed and the synthetic waveforms.
Vftw, the maximum slip, and the seismic moment are 3.0 km/s, 1.0 m, and 4.7×10^{18} Nm (Mw 6.4), respectively.
Large slips are found at the up-dip side of the rupture starting point and overlap the active-aftershock area.
These large slips were caused by the main rupture at 1.5-4.5 s after the rupture initiation.

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