Strong ground motions are more closely related to regions of slip heterogeneity rather than the entire rupture area and total seismic moment (Irikura and Miyake 2011). Therefore, a characterized source model was proposed that consisted of one or several asperities with large slips and a background area with less slip (Miyake et al. 2003) based on source characterizations defined using slip distributions from the waveform inversion of strong-motion data.
Asperities are regions that have large slip relative to the average slip in the rupture area (Somerville et al. 1999). These asperity areas, as well as the total rupture area, scale with the seismic moment (Fig. 4). The majority of strong-motion records are reproduced with motions generated from asperities. Contributions from the background area of the characterized source model are not important for strong-motion records but must match long-period motions, including the seismic moment (Miyake et al. 2003; Irikura and Miyake 2011).
Therefore, the synthetic ground motions were calculated with the assumption that ground motions were only generated within the SMGAs, which were redefined based on asperity location and area information (Kamae and Irikura 1998; Miyake et al. 2003). The synthetic ground motions from the SMGAs approximately agree with the observed motions (Kamae and Irikura 1998). For the 1995 Hyogo-ken Nanbu earthquake (M
6.9), which was nearly the same size as the 2016 Kumamoto earthquake, the period range available for the SMGA model is shorter than 5 s. We found that for crustal earthquakes, the SMGAs coincide approximately with asperity area (Miyake et al. 2003). Therefore, this characterized source model consisting of SMGAs with large stress parameters and a background area with a zero stress parameter is called the SMGA source model.
We estimated the SMGA source model by comparing the synthetic and observed ground motions from the 2016 Kumamoto earthquake. Whether the SMGAs coincide with the asperity areas of large slip is discussed below. The empirical Green’s function (EGF) method was used to simulate strong ground motions to avoid difficulty in obtaining accurate velocity structures.
First, we constructed a characterized source model with the SMGAs based on the slip distribution model of Yoshida et al. (2016). This model consists of four segments, as shown in Fig. 1a. As shown in the left panel of Fig. 5, we assumed an SMGA in each segment, except the northeast segment (Seg. 4) of the Futagawa fault zone located near the Mount Aso volcano. The northeast segment generated relatively small peak-moment-rate motions compared to the other three segments (Fig. 6, lower).
The EGF events whose records are used as the EGFs were carefully selected to have hypocenters close to the SMGAs with radiation characteristics nearly identical to those of the target events. We selected records of a foreshock (M
4.9, EGF1) and an aftershock (M
5.1, EGF2) for the EGFs. The EGF1 event occurred very close to SMGA1 and inside SMGA2, with predominant strike-slip faulting similar to the focal mechanism of the mainshock (Fig. 5, left). Therefore, the records of EGF1 were used as the EGFs for SMGA1 and SMGA2. However, the EGF2 event occurred very close to SMGA3, with strike-slip faulting and a normal-faulting component (Fig. 5, left) similar to the focal mechanism around SMGA3 during the mainshock. Therefore, we selected the records of EGF2 for the EGFs for SMGA3.
We calculated the spectral ratios between the mainshock and the EGF events to estimate the corner frequency of the EGF events (Fig. 5, right). The source areas and the stress parameters of these events were estimated from the seismic moment and the corner frequency using Brune’s (1970, 1971) formula. The parameters of these events are listed in Table 2. We found that the records of the EGF events were reliable within the frequency range of 0.2–10 Hz because the spectral ratios follow the omega-squared model in this frequency range and deviate from it below 0.2 Hz and beyond 10 Hz.
Each SMGA area was divided into N × N subfaults, the areas of which were taken to be equal to the fault area of each EGF event. The location and size of each SMGA and the rupture starting point, rupture velocity and slip duration inside each SMGA were estimated based on comparison of the timing, shape and amplitude of the synthetic and observed waveforms through trial and error.
A map view of the three SMGAs is shown in the upper panel of Fig. 6. The fit between the synthetic and observed waveforms in this analysis was judged via visual inspection, because the parameters for the three SMGAs are by necessity optimized simultaneously. The three best-fit SMGAs in this analysis are plotted in the lower panel of Fig. 6, with the peak moment-rate distributions drawn in warm colors on the three segments of Yoshida et al. (2016). The source parameters of the SMGAs are listed in Table 3. The observed and synthetic ground motions are shown in Fig. 7a–c. The agreement is satisfactory for acceleration, velocity, and displacement at most of the stations.
Next, we constructed a characterized source model with the SMGAs based on the single fault plane model along the Futagawa fault zone estimated by Kubo et al. (2016) to be the source fault of the 2016 Kumamoto earthquake. It is preferable to use simpler fault geometry to predict strong ground motions for future earthquakes if synthetic motions that fit the observed motions reasonably well can be obtained.
We formulated a simplified SMGA model where “a single SMGA” was put into the single fault plane proposed by Kubo et al. (2016) based on the slip distribution. For the EGFs, we selected records of a foreshock (M
4.4) that had nearly the same focal mechanism as the mainshock and that occurred inside the SMGA. We also calculated the spectral ratios between the mainshock and the EGF event to estimate the corner frequency of the EGF event, the source area, and the stress parameter. The source parameters of this event are listed in Table 4. The reliable frequency range in this case was 0.3–10 Hz.
The entire assumed fault plane and the SMGA are shown in Fig. 8 with the observed stations used for this analysis. The best-fit characterized source model to simulate ground motions using the EGF method was determined through choosing the starting point, rupture velocity, and slip duration by comparing the observed and synthetic waveforms. The criterion for the best-fit is minimizing the residuals between the observed and synthetic waveforms using the fitness function given by Miyake et al. (1999). The residual is defined as the sum of the squared residuals of the displacement waveforms and acceleration envelopes.
The best-fit SMGA to the observed waveforms is shown in Fig. 9 with the slip distribution reported by Kubo et al. (2016) indicated with warm colors. The parameters of the SMGA used for the simulation, such as length, width, rise time, seismic moment, and stress parameter, are listed in Table 5. The synthetic motions agree with the observed motions for acceleration, velocity, and displacement, as shown in Fig. 10, including at KMMH16 (KiK-net Mashiki), KMMH14 (KiK-net Toyono) and KMM005 (K-NET Ohzu), which are located very near the source fault.
The location of the SMGA indicated in Fig. 9 coincides with a large slip area deeper than 5 km but does not correspond to a near-surface slip area in the northeast of the fault plane, which is consistent with the SMGA model in the upper panel of Fig. 6 based on the slip distributions of Yoshida et al. (2016). The inverted slip-velocity time functions in the near-surface areas in the lower panel of Fig. 6 have motions longer than 3 s. Therefore, the ground motions generated by the large near-surface slip may have had little influence on the strong ground motions shorter than 3 s. This finding may explain why there were no SMGAs in the northeast area of the fault plane shown in the upper panel of Fig. 6 based on the model of Yoshida et al. (2016) or in Fig. 9 based on the model of Kubo et al. (2016).
The combined area of the three SMGAs from the four-segment model of Yoshida et al. (2016) is about 204 km2. The SMGA from the single fault plane model of Kubo et al. (2016) is 17.3 km in length and 13.0 km in width, for an area of 224.9 km2. Conversely, the asperity area based on the inverted heterogeneous slip distributions, i.e., the logarithmic average of the three models in Table 1, is about 180 km2. Therefore, we found that both the combined area of the three SMGAs in Fig. 6 and the area of the single SMGA in Fig. 9, which were obtained using different forward modeling approaches, are nearly the same as the asperity area determined based on the slip distributions from waveform inversion using the strong-motion data.
The SMGAs in the upper panel of Fig. 6 obtained based on the four-segments source model of Yoshida et al. (2016) do not always coincide with the SMGA in Fig. 9 from the single segment source model of Kubo et al. (2016). However, the locations and the combined area of the three SMGAs in Fig. 6 are nearly the same as those of the SMGA in Fig. 9. The synthetic ground motions for acceleration, velocity, and displacement shown in Fig. 7 have almost the same amplitudes as those in Fig. 10. These findings indicate that this method of estimating ground motion based on SMGA models is robust because the simulation results do not differ greatly between these different SMGA models.