Introduction
We derive the rupture process of the Mj 6.5 event of the 2016 Kumamoto earthquake at 21:26 on April 14 (JST) using the near-source strong-motion data.
Data
Strong motion data recorded at 16 stations (5 K-NET stations, 8 KiK-net borehole stations, 2 KiK-net surface stations, and 1 F-net station) 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 0.1 and 1.0 Hz, resampled to 10 Hz and windowed from 1 s before S-wave arrival for 10 s.
Fault model and discretization of the rupture process
We assume the 22 km x 14 km rectangular fault model that has a
strike of 212 degrees and a dip of 89 degrees based on the F-net moment
tensor solution.
The rupture starting point is set at 32.7417N, 130.7994E, and a
depth of 12.49 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 11
subfaults along the strike and 7 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 5 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 -164 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 2 shows the total slip distribution on the fault.
Figure 3 shows the perspective illustration of the total slip distribution.
Figure 4 shows the comparison between the observed and the synthetic waveforms.
Figure 5 shows the rupture progression.
Figure 6 shows the moment rate function of each subfault.
Vftw, the maximum slip, and the seismic moment are 2.5 km/s, 0.7 m, and 1.7×1018Nm
(Mw6.1), respectively.
Large slips (> 0.4m) are found in the region around the rupture
staring point and in the shallow region north-northeast of the rupture
starting point.
The ruptures in these regions occurred at 1–3 s and 3–6 s after rupture initiation, respectively.
Please note that this is the first analysis and will be modified after the further examination.
