## Introduction

We derive the rupture process of the 2018 Hokkaido Eastern Iburi earthquake (Mj 6.7) at 03:08 on September 6 (JST) using the near-source strong-motion data.

## Data

Strong motion data recorded at 20 stations (4 K-NET stations, 14 KiK-net stations in borehole, and 2 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 0.5 Hz, resampled to 5 Hz, and windowed from 1 s before S-wave arrival for 25 s.

## Fault model and discretization of the rupture process

Based on the spatial distribution of aftershocks and the F-net moment tensor solution, 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 22 km and its width is 20 km.
The dip angle is 65 degree, which is based on the F-net moment tensor solution.
The rupture starting point is set at 42.6908N, 142.0067E, and a depth of 37.04 km, determined by JMA.

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 15 subfaults along the strike and 10 subfaults along dip directions, with a maximum size of 2km x 2km.
For the temporal discretization, the moment rate function of each subfault is represented by 8 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 107 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 and Figure 4 show the total slip distribution by map projection and planar projection, respectively.
Figure 5 shows the rupture progression.
Figure 6 shows the source time rate function of each subfault.
Figure 7 shows the comparison between the observed and the synthetic waveforms.
The maximum slip and the seismic moment are 3.8 m and 2.5×10^{19}Nm (Mw 6.9), respectively.
Vftw of 1.4 km/s is selected to minimize the data-fit residual.
A large slip area was found at a depth of 25-30 km in the up-dip direction from the hypocenter.
During the first 6 s, the rupture slowly grows around the hypocenter with small slips.
Subsequently, the rupture develops with a large moment release between 6 s and 12 s in the large slip area.

*For details of this analysis, we refer the reader to Kubo *et al.* (2020).

*et al.*2019a) had been published in Earth, Planets and Space on September 18, 2019. After the publication, we noticed that the source inversion was not done with the intended setting on the rupture starting point. So, we retracted the previous paper on December 23, 2019 (Kubo

*et al.*2019b) and resubmitted the corrected version of the paper as a new paper to Earth, Planets and Space. This paper was published on Feburary 18, 2020 (Kubo

*et al.*2020). Please refer to Kubo

*et al.*(2020) instead of the previous papaer.