In this study, we estimated source process of the 2016 Kumamoto earthquake from strong-motion data by using the multiple-time window linear kinematic waveform inversion method to discuss generation of strong motions and to explain crustal deformation pattern with a seismic source inversion model. A four-segment fault model was assumed based on the aftershock distribution, active fault traces, and interferometric synthetic aperture radar data. Three western segments were set to be northwest-dipping planes, and the most eastern segment under the Aso caldera was examined to be a southeast-dipping plane. The velocity structure models used in this study were estimated by using waveform modeling of moderate earthquakes that occurred in the source region. We applied a two-step approach of the inversions of 20 strong-motion datasets observed by K-NET and KiK-net by using band-pass-filtered strong-motion data at 0.05-0.5 Hz and then at 0.05-1.0 Hz. The rupture area of the fault plane was determined by applying the criterion of Somerville et al. (Seismol Res Lett 70:59-80, 1999) to the inverted slip distribution. From the first-step inversion, the fault length was trimmed from 52 to 44 km, whereas the fault width was kept at 18 km. The trimmed rupture area was not changed in the second-step inversion. The source model obtained from the two-step approach indicated 4.7 × 10 19 Nm of the total moment release and 1.8 m average slip of the entire fault with a rupture area of 792 km 2 . Large slip areas were estimated in the seismogenic zone and in the shallow part corresponding to the surface rupture that occurred during the Mj7.3 mainshock. The areas of the high peak moment rate correlated roughly with those of large slip; however, the moment rate functions near the Earth surface have low peak, bell shape, and long duration. These subfaults with long-duration moment release are expected to cause weak short-period ground motions. We confirmed that the southeast dipping of the most eastern segment is more plausible rather than northwest-dipping from the observed subsidence around the central cones of the Aso volcano.

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We analyzed a kinematic earthquake rupture generator that combines the randomized spatial field approach of Graves and Pitarka (Bull Seismol Soc Am 106:2136-2153, 2016) (GP2016) with the multiple asperity characterization approach of Irikura and Miyake (Pure Appl Geophys 168:85-104, 2011) (IM2011, also known as Irikura recipe). The rupture generator uses a multi-scale hybrid approach that incorporates distinct features of both original approaches, such as small-scale stochastic rupture variability and depth-dependent scaling of rupture speed and slip rate, inherited from GP2016, and specification of discrete high slip rupture patches, inherited from IM2011. The performance of the proposed method is examined in simulations of broadband ground motion from the 2016 Kumamoto, Japan earthquake, as well as comparisons with ground motion prediction equations (GMPEs). We generated rupture models with multi-scale heterogeneity, including a hybrid one in which the slip is a combination of highslip patches and stochastic small scale variations. We find that the ground motions simulated with these rupture models match the general characteristics of the recorded near-fault motion equally well, over a broad frequency range (0-10 Hz). Additionally, the simulated ground motion is in good agreement with the predictions from Ground Motion Prediction Equations (GMPEs). Nonetheless, due to sensitivity of the ground motion to the local fault rupture characteristics, the performance among the models at near-fault sites is slightly different, with the hybrid model producing a somewhat better fit to the recorded ground velocity waveforms. Sensitivity tests of simulated near-fault ground motion to variations in the prescribed kinematic rupture parameters show that average rupture speeds higher than the default value in GP2016 (average rupture speed = 80% of local shear wave speed), as well as slip rate durations shorter than the default value in GP2016 (rise time coefficient = 1.6), generate ground motions that are higher than the recorded ones at periods longer than 1 s. We found that these two parameters also affect the along strike and updip rupture directivity effects, as illustrated in comparisons with the Kumamoto observations.

We have investigated the rupture process of the 2011 off the Pacific coast of Tohoku Earthquake using a multitime-window linear waveform inversion method using long-period strong-ground motion data. From the record section of the long-period motion of the 3 phases, it is indicated that the rupture process mainly consists of the 3 stages. We have assumed a single planar fault model of 468 km long in strike and 228 km wide in dip. The seismic moment of this earthquake was estimated to be 4.3 × 10 22 N m (M w 9.0). The inverted slip distribution shows a large asperity with a maximum slip of about 47 m which is located on the shallower part of the fault plane. The rupture process is divided into three stages: a first stage with moderate slip; a second stage with large and long-duration slip in the shallow part of the fault; and a third stage with relatively small and short-duration slip in the southern part of the fault. The feature of the ground motion suggested from the record section is well represented by the peak moment rate distributions, rather than the slip distributions. The rupture velocity is around 3-4 km/s in the first and third stages, while rupture progression was suspended for a while before the rupture of the asperity.

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A two-stage scaling relationship of the source parameters for crustal earthquakes in Japan has previously been constructed, in which source parameters obtained from the results of waveform inversion of strong motion data are combined with parameters estimated based on geological and geomorphological surveys. A three-stage scaling relationship was subsequently developed to extend scaling to crustal earthquakes with magnitudes greater than M w 7.4. The effectiveness of these scaling relationships was then examined based on the results of waveform inversion of 18 recent crustal earthquakes (M w 5.4-6.9) that occurred in Japan since the 1995 Hyogo-ken Nanbu earthquake. The 2016 Kumamoto earthquake, with M w 7.0, was one of the largest earthquakes to occur since dense and accurate strong motion observation networks, such as K-NET and KiK-net, were deployed after the 1995 Hyogo-ken Nanbu earthquake. We examined the applicability of the scaling relationships of the source parameters of crustal earthquakes in Japan to the 2016 Kumamoto earthquake. The rupture area and asperity area were determined based on slip distributions obtained from waveform inversion of the 2016 Kumamoto earthquake observations. We found that the relationship between the rupture area and the seismic moment for the 2016 Kumamoto earthquake follows the second-stage scaling within one standard deviation (σ = 0.14). The ratio of the asperity area to the rupture area for the 2016 Kumamoto earthquake is nearly the same as ratios previously obtained for crustal earthquakes. Furthermore, we simulated the ground motions of this earthquake using a characterized source model consisting of strong motion generation areas (SMGAs) based on the empirical Green's function (EGF) method. The locations and areas of the SMGAs were determined through comparison between the synthetic ground motions and observed motions. The sizes of the SMGAs were nearly coincident with the asperities with large slip. The synthetic ground motions obtained using the EGF method agree well with the observed motions in terms of acceleration, velocity, and displacement within the frequency range of 0.3-10 Hz. These findings indicate that the 2016 Kumamoto earthquake is a standard event that follows the scaling relationship of crustal earthquakes in Japan.

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