Rupture process of the Mj6.5, April 14, foreshock of the 2016 Kumamoto earthquake, obtained from strong-motion data


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.


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).


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 1.24×1018Nm (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.

The first report in Japanese was released on April 15th, 2016.
English page was created on May 9th, 2016.


Figure 1: Station distribution and fault model on the map. Blue and red triangles denote the K-NET and KiK-net stations, respectively. A star denotes the rupture starting point.


Figure 2: Total slip distribution on the fault. The vectors denote the direction and amount of the slip of the hanging wall side. A star denotes the rupture starting point.


Figure 3: Comparison between the observed and the synthetic waveforms. The maximum values are shown on the upper right of each waveform.


Figure 4: Rupture progression in terms of slip amount for each 0.9 second time window.


Figure 5: Moment rate function of each subfault. A star denotes the rupture starting subfault.