Source process of the 2016 Kumamoto earthquake (Mj7.3) inferred from kinematic inversion of strong-motion records
Keywords2016 Kumamoto earthquake Source process Kinematic inversion Near-fault strong motion
Akaike’s Bayesian information criterion
global navigation satellite system
interferometric synthetic aperture radar
Japan Meteorological Agency
peak moment rate
The 2016 Kumamoto earthquake, with Japan Meteorological Agency (JMA) magnitude (Mj) of 7.3, occurred at 01:25 JST on April 16, 2016, following the Mj6.5 earthquake occurring at 21:26 on 14 April. During these earthquakes, a JMA intensity scale of 7 was recorded at several stations near the source faults. These abundant near-fault strong-motion records have enabled us to analyze detailed source characteristics. Many surface ruptures (e.g., Shirahama et al. 2016) and significant crustal deformations (e.g., Geospatial Information Authority of Japan 2016a) have been investigated for these earthquakes.
Several source models of the Mj7.3 of the 2016 Kumamoto earthquake have been proposed on the basis of the strong motions (e.g., Asano and Iwata 2016), teleseismic waveforms (Yagi et al. 2016), and crustal deformation (e.g., Himematsu and Furuya 2016). Most of these studies based on seismic data assume northwest-dipping fault planes. However, several studies based on the crustal deformation data obtained by interferometric synthetic aperture radar (InSAR) and global navigation satellite system (GNSS) networks suggest a southeast-dipping fault mechanism in the Aso caldera region (e.g., Ozawa et al. 2016). Determining the fault plane dip direction based on the aftershock distribution is difficult because of the seismicity gap in the western part of the Aso caldera region (Aso gap in Fig. 1, Uchide et al. 2016). Although we have previously proposed a source model with a northwest-dipping fault model using strong-motion data (Irikura et al. 2017), it is important to rediscuss a source model with a southeast-dipping fault model based on strong motion.
In this study, we infer the rupture process of the mainshock of the 2016 Kumamoto earthquake by applying the multiple-time window linear kinematic waveform inversion method to strong-motion data. In order to obtain detailed source models, velocity structure models are improved by using waveform modeling of moderate earthquakes that occurred near the mainshock. We discuss behavior of rupture near the Earth surface by using total slip and moment rate functions. Moreover, we compare the crustal deformations calculated from the inverted source model with those observed by InSAR.
Initial model parameters of fault planes assumed in the waveform inversion
Velocity structure model
In order to obtain accurate Green’s functions, we determine a 1D stratified velocity models for each station, inverting waveforms of small events. Several previous studies (Ichinose et al. 2003; Hikima and Koketsu 2005; Asano and Iwata 2009) constructed proper layered structure models to individual stations based on the waveform modeling of small events and succeeded in obtaining a detailed source rupture process.
Velocity structure models of the 20 sites were inverted with fixed point source parameters and layer thicknesses using strong-motion data from three moderate-magnitude earthquakes within the rupture area of the main shock (S1, S2, and S3 in Fig. 1). The target acceleration seismograms were band-pass-filtered between 0.3 and 1.0 Hz and were integrated into velocities. The focal mechanism and seismic moment provided by F-net were used. The inverted velocity structure models are shown in Fig. 2.
Estimation of source process
We applied a two-step approach of the multi-time window linear waveform inversions of strong-motion data (Hartzell and Heaton 1983) to estimate the rupture process for the fault model. First, the slip distribution was inverted using the 0.05–0.5 Hz band-pass strong-motion data. The proper rupture area of the earthquake was estimated applying the trimming criterion of Somerville et al. (1999) into the derived slip model. Second, the slip distribution was reanalyzed from the 0.05–1.0 Hz waveform inversion of strong-motion data including higher-frequency motions for the reduced fault plane in order to estimate the detailed rupture process.
We used near-fault strong-motion data obtained from 20 stations of K-NET and KiK-net (borehole data); their structures were estimated in the previous section. The data were windowed for 27 s, starting at the P-wave arrival time, and were band-pass-filtered with the respective passband. The accelerograms were integrated into ground velocities, and the data were then resampled with the frequency of 8 Hz.
Theoretical Green’s functions were calculated by using the discrete wave number method (Bouchon 1981) and the reflection/transmission coefficient matrix method (Kennett and Kerry 1979) using the velocity structure models estimated in the previous section (Fig. 2). In the multi-time window linear waveform inversion procedure, the moment release distribution is discretized in both space and time. The fault plane was divided into 13 (along strike) × 9 (along dip) subfaults with a size of 4 km (along strike) × 2 km (along dip) for the first step. We distributed 15 point sources at a 0.8 km (strike) by 0.67 km (dip) interval inside each subfault to consider the rupture propagation effect (e.g. Wald et al. 1991). For the moment rate functions at individual subfaults, we aligned smoothed ramp functions having durations of 1.8 s at intervals of 0.9 s in the first step and those of 0.9 s at intervals of 0.45 s in the second step to represent the moment release of each subfault. Non-negative constraints (Lawson and Hanson 1974) were also adopted to limit the rake angle variation. The rake angles were allowed to vary within ±45° centered at 180°.
The weight of the smoothing constraint for inversion with a certain first-time window propagating velocity (V FT) value was determined on the basis of Akaike’s Bayesian information criterion (ABIC) proposed by Akaike (1980) following previous studies (e.g. Sekiguchi et al. 2000). The number of smoothed ramp functions representing moment release was also determined on the basis of ABIC.
We applied the trimming criterion of Somerville et al. (1999) to remove columns of their average slip below 0.3 times the average slip of the entire fault (0.69 m in this study) from our slip model in order to estimate the proper rupture area of the earthquake. The trimming result removed two columns (8 km) of the southwest edge of the fault plane as shown in Fig. 4. The reduction in moment release was 4%, at 6.7 × 1019 to 6.5 × 1019 Nm.
Estimated fault parameters
Total moment (Nm)
4.7 × 1019
Max. slip (m)
Average slip (m)
Trimmed fault area (km2)
44 × 18 = 792
Initial fault area (km2)
52 × 18 = 936
Combined asperity area (km2)
First-time window velocity (km/s)
The contributions of each segment on the ground motions (Fig. 6) showed that the F1 segment did not dominate the ground motions of the stations even around the F1 segment (KMMH02, KMMH06, KMM004, and KMM007), whereas the F2, F3, and H segments controlled the ground motions at the stations around the respective segments (e.g., KMMH14 and KMMH16). The dominance of the F2, F3, and H segments on the ground motions contributed to the good resolution of the inverted solutions on these segments. In contrast, the ground motions at the stations close to the F1 segment appeared to be not controlled by the contribution of the F1 segment; its contribution on the ground motions was largest at KMM004 but was not larger than that from the F2 segment. Therefore, the solution for the F1 segment of the inverted source model is not well constrained by the ground motion data used in this study. This weak constraint corresponds to the apparently low resolution on the F1 segment shown in the results of checkerboard test (Fig. 7b). That is, the uncertainty of the F1 segment weakly affected the makeup of the synthetic waveforms from the entire fault.
Two asperities were determined from the total slip distribution by using the procedure of Somerville et al. (1999). The major asperity, the A1 asperity, is identified at a depth between 0.5 km at the top of the fault plane and 10 km on the F2 and F3 segments of the fault (Fig. 5a). Another minor asperity, the A2 asperity, was identified on the deep part of the F3 segment. The A1 asperity, at the depth of 0.5 km, corresponded to the location of the surface ruptures during the earthquake (e.g., Shirahama et al. 2016). The proper rupture area S, at 792 km2, and the combined asperity area S a, at 240 km2, agree with the scaling relations of S–M 0 and S a–M 0 (Irikura and Miyake 2001, Miyakoshi et al. 2015) for the seismic moment M 0.
The moment rate functions of subfaults in the deeper part of the A1 asperity have Kostrov-type function (Kostrov 1964), short duration, and high peak moment rate (PMR), whereas those in the shallower part of the A1 asperity (area 1) have bell-like shape, long-duration function, and low PMR (Fig. 5b). The bell shape of the moment rate functions in area 1 is expected to cause weak short-period ground motions owing to low peak of the bell shape moment rate function. Long duration of the moment rate function near the Earth surface has been pointed out in previous studies of the 1995 Hyogo-ken Nanbu earthquake (Sekiguchi et al. 1996) and the 2014 North Nagano earthquake (Hikima et al. 2015).
The PMR distribution shown in Fig. 5b was used to investigate the generation areas of the strong motions. Fault elements with PMRs of at least 1.5 times larger than the average PMRs over the entire fault are enclosed by dotted lines in the figure; this criterion is similar to Somerville’s criterion. The PMR at each subfault was calculated from the maximum moment release of all time windows except that of the last time window. In most cases, a large moment release at the last time window was suggested to be errors owing to uncertainties in the inversion analysis.
The high PMR subfaults generally overlap with the identified asperity except in area 1 at depths <2 km (Fig. 5b). The low PMR of the near-Earth surface subfault suggests that generation of strong motion from this depth is weak. The depth difference in the moment rate function implies different constitutive relations of friction between the shallow and the deeper parts (e.g., Ide and Takeo 1997).
We also calculated the static displacements from our previous model with northwest-dipping F1 segment (Irikura et al. 2017, in which segment 4 corresponds the F1 segment in the present paper). The resulting total slip and the synthetic seismic velocity waveforms from the previous model were nearly consistent with the results of the present model. The consistency of the synthetic seismic velocity waveforms between both models suggests that the dip angle of the F1 segment is not well constrained from the sparse seismic data near the fault used in this study. However, the calculated vertical static displacements for the present southeast-dipping F1 model (Fig. 9a) and the previous northwest-dipping F1 model (Fig. 9c) clearly show different polarity on the east of the F1 segment. The vertical displacements calculated from the southeast-dipping F1 model are consistent with the subsidence around the central cones of Aso volcano obtained from the 2.5-D InSAR analysis (Fig. 9b). Ozawa et al. (2016) also explained the crustal deformation obtained from InSAR and GNSS data with a southeast-dipping fault model similar to our southeast-dipping F1 segment model. Our present fault model (Fig. 9a) explains both the strong motions and the observed subsidence around the central cones of Aso volcano.
The source process of the 2016 Kumamoto earthquake was investigated from the near-fault strong-motion records by applying a two-step approach of the inversion with different frequency ranges to discuss generation of strong motions and to explain crustal deformations. Four segments, F1, F2, F3, and H, were set as the fault model consisting of segment H along the Hinagu fault zone, segment F3 along a plane connecting the Futagawa and Hinagu fault zones, and segments F2 and F1 along the Futagawa fault zone. Three western segments, H, F3, and F2, were northwest-dipping, and the most eastern segment (F1) under the Aso caldera was set to be southeast-dipping. The fault size was determined to be 44 km × 18 km (792 km2) by the first-step inversion result of 0.05–0.5 Hz strong-motion data. The second-step inversion result of 0.05–1.0 Hz strong-motion data indicated 4.7 × 1019 Nm for the total moment release and 1.8 m average slip for the entire fault. The combined area (S a) of two asperities estimated around the shallow and deep parts of the fault was 240 km2, which agrees with the scaling relationship S a versus M 0 reported by Irikura and Miyake (2001). The asperity area was estimated in the seismogenic zone and in the shallow part of the fault plane. The distribution of the high peak moment rate area correlated with the deeper part of the asperity but not near-surface part. The moment rate functions near the Earth surface had low peak, bell shape, and long duration. These long-duration subfaults are expected to cause weak short-period ground motions. The location of the shallow asperity with large slip corresponds to the locations of the observed surface rupture (e.g., Shirahama et al. 2016). The overall patterns of vertical static displacements calculated from the derived source model agree with those of the observed ones acquired by InSAR. The subsidence of the static displacement on the east of the F1 segment supports the southeast-dip of the F1 segment.
KY led and designed the entire research and drafted the manuscript. KM, KS and KI contributed to the discussion of the results. All authors discussed the results and commented on the manuscript. All authors read and approved the final manuscript.
The authors thank National Research Institute for Earth Science and Disaster Resilience (NIED) for providing K-NET and KiK-net data. F-net mechanism solutions were also provided by NIED. This study was based on the 2016 research project “Examination for uncertainty of strong ground motion prediction” by the Nuclear Regulation Authority (NRA), Japan. The authors also acknowledge valuable comments provided by Haruo Horikawa, Peter Martin Mai, and two anonymous reviewers.
The authors declare that they have no competing interests.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
- Akaike H (1980) Likelihood and the Bayes procedure. In: Bernardo JM, DeGroot MH, Smith AFM (eds) Bayesian statistics. University Press, Valencia, pp 143–166Google Scholar
- Bouchon M (1981) A simple method to calculate Green’s functions for elastic layered media. Bull Seismol Soc Am 71:959–971Google Scholar
- Fujiwara H, Kawai S, Aoi S, Morikawa N, Senna S, Azuma H, Ooi M, Hao KX, Hasegawa N, Maeda T, Iwaki A, Wakamatsu K, Imoto M, Okumura T, Matsuyama H, Narita A (2012) Some improvements of seismic hazard assessment based on the 2011 Tohoku earthquake. Technical note of the National Research Institute for Earth Science and Disaster Prevention, No. 379Google Scholar
- Geospatial Information Authority of Japan (2016a) Information about 2016 Kumamoto earthquake, http://www.gsi.go.jp/BOUSAI/H27-kumamoto-earthquake-index.html. Accessed 28 July 2016
- Geospatial Information Authority of Japan (2016b) http://maps.gsi.go.jp/#10/32.773997/130.904846/&base=std&ls=std%7Curgent_earthquake_20160414kumamoto_p023dr_p135ar_qu_25d%2C0.7%7Ctoshiken_katsudansouzu%7C20160414kumamoto_epicenter%7C_20160414kumamoto_epicenter%7Curgent_earthquake_qugrd_cont10cm_cut10%2C0.7&disp=111111&lcd=toshiken_katsudansouzu&vs=c1j0l0u0f1&d=vl. Accessed 30 Nov 2016
- Hartzell SH, Heaton TH (1983) Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake. Bull Seismol Soc Am 73:1553–1583Google Scholar
- Hikima K, Nakamura R, Uetake T (2015) Source process of the 2014 Nagano-Ken Hokubu Earthquake (Mj6.7)—analysis using the near-field Broadband Waveforms in the source region. In: proceedings of the Seismological Society of Japan Fall meeting, S15-14 (in Japanese) Google Scholar
- Irikura K, Miyake H (2001) Prediction of strong ground motions for scenario earthquakes. J Geol 110:849–875 (in Japanese with English abstract) Google Scholar
- Irikura K, Miyakoshi K, Kamae K, Yoshida K, Somei K, Kurahashi S, Miyake H (2017) Applicability of scaling relationships of source parameters for crustal earthquakes: examination of ground motion estimation of the 2016 Kumamoto earthquake. Earth Planets Space 69:10. doi: 10.1186/s40623-016-0586-y CrossRefGoogle Scholar
- Kitsunezaki C, Goto N, Kobayashi Y, Ikawa T, Horike M, Saito T, Kurota T, Yamane K, Okuzumi K (1990) Estimation of P- and S-wave velocities in deep soil deposits for evaluating ground vibrations in earthquake. J Nat Disaster Sci 9–3:1–17 (in Japanese with English abstract) Google Scholar
- Kostrov BV (1964) Selfsimilar problems of propagation of shear cracks. PMM 28:889–898Google Scholar
- Lawson CL, Hanson RJ (1974) Solving least square problems. Prentice Hall, Englewood CliffsGoogle Scholar
- Miyakoshi K, Irikura K, Kamae K (2015) Re-examination of scaling relationships of source parameters of the inland crustal earthquakes in Japan based on the waveform inversion of strong motion data. J Jpn Assoc Earthq Eng 15(7):141–156 (in Japanese with English abstract) Google Scholar
- Nakata T, Imaizumi T (eds) (2002) Digital active fault map of Japan. University of Tokyo Press, Tokyo (in Japanese) Google Scholar
- National Institute of Advanced Industrial Science and Technology (2012) Active fault database of Japan. Research Information Database DB095. https://gbank.gsj.jp/activefault/index_e_gmap.html. Accessed 30 June 2016
- Okada Y (1992) Internal deformation due to shear and tensile faults in a half-space. Bull Seismol Soc Am 82:1018–1040Google Scholar
- Shirahama Y, Yoshimi M, Awata Y, Maruyama T, Azuma T, Miyashita Y, Mori H, Imanishi K, Takeda N, Ochi T, Otsubo M, Asahina D, Miyakawa A (2016) Characteristics of the surface ruptures associated with the 2016 Kumamoto earthquake sequence, central Kyushu, Japan. Earth Planets Space 68:191. doi: 10.1186/s40623-016-0559-1 CrossRefGoogle Scholar
- Wald DJ, Helmberger DV, Heaton TH (1991) Rupture model of the 1989 Loma Prieta earthquake from the inversion of strong-motion and broadband teleseismic data. Bull Seismol Soc Am 81:1540–1572Google Scholar
- Yoshida K, Somei K, Miyakoshi K, Ling SQ (2016) Microtremor observations for the strong-motion stations around source region of the 2016 Kumamoto earthquake. In: Proceedings of the 135th SEGJ conference, Muroran Institute of Technology, Muroran, Japan, 26–28 Oct 2016 (in Japanese) Google Scholar
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