Strong ground motion simulation of the 2016 Kumamoto earthquake of April 16 using multiple point sources
© The Author(s) 2017
Received: 1 August 2016
Accepted: 24 January 2017
Published: 2 February 2017
Keywords2016 Kumamoto earthquake Strong ground motion simulation Pseudo point-source model Rupture directivity
Strong ground motions were recorded at many stations during the Kumamoto earthquake of April 16, 2016 that occurred at 01:25 (JST), with M JMA 7.3. Some records exceeded a peak ground velocity (PGV) of 100 cm/s, and devastating damage was caused. Source modeling of the earthquake by simulating strong ground motions is important for predicting strong ground motions and understanding their generation mechanism. Researchers have conducted source process analyses of the earthquake. For example, Yagi et al. (2016) and Yamanaka (2016) estimated the source process using teleseismic records. Koketsu (2016), Asano and Iwata (2016), Kubo et al. (2016), and Nozu (2016) used strong ground motions. These analyses indicated that the rupture propagated mainly toward the northeast from the hypocenter, and the rupture extended almost as far as the western edge of Mount Aso. This kind of rupture propagation can cause the rupture directivity effect, where seismic waves are coherently superposed. In the 2016 Kumamoto earthquake, strong motions observed northeast of the epicenter could be amplified by the forward directivity effect. Strong ground motion simulations using point-source models do not seem appropriate for such earthquakes. However, the pseudo point-source model proposed by Nozu (2012a) has been successfully applied to large earthquakes such as the 2011 Tohoku earthquake (Nozu 2012a) as well as shallow crustal earthquakes (Hata and Nozu 2014), although the source model does not consider the rupture directivity effect.
In this study, a pseudo point-source model of the 2016 Kumamoto earthquake was built, and strong ground motions were simulated with the model. The target frequency range was 0.2–10 Hz, which was higher than that of the waveform inversions, so as to focus on damage caused to structures. Then, the proposed source model and the effect of rupture propagation were investigated by comparing the synthetic and observed records, in both the forward and backward regions.
In the pseudo point-source model, strong ground motions are generated from subevents that are placed on the fault plane. Each subevent is approximated with a point source, and may correspond to strong-motion generation areas (SMGAs) (e.g., Kamae and Irikura 1998) or strong-motion pulse generation areas (SPGAs) (Nozu 2012b) in the characterized source models. However, the pseudo point-source model does not consider the spatiotemporal distribution of the slip within the subevent explicitly for the purpose of simplification. Instead, a subevent is modeled by a source spectrum that follows the omega-square model (Aki and Richards 2002). The current version of the pseudo point-source model assumes the same corner frequency for any azimuth or take-off angle. In this respect, the pseudo point-source model is different from SMGA or SPGA models, in which the rupture propagation within a finite subevent is explicitly modeled to consider the directivity effect. Directivity is one possible source of discrepancy from the observed records when the pseudo point-source model is applied to large earthquakes.
For G(f)s, we basically use the empirical model evaluated by Nozu et al. (2006) with the generalized inversion technique, using many weak motions for K-NET and KiK-net stations (Aoi et al. 2004; Okada et al. 2004). However, as described later, G(f) values for several stations were estimated in this study.
The phase spectrum is also evaluated with an empirical model. O(f) is the Fourier transform of a small earthquake record observed at a target station, and |O(f)|p is the absolute value of O(f) to which a Parzen window of 0.05 Hz bandwidth is applied. Here the absolute value is calculated first, and then the Parzen window is applied. O(f)/|O(f)|p is thus a complex spectrum that has small ripples and whose absolute value is almost one. These small ripples are necessary for generating causal waveforms (Nozu and Sugano 2008). If there is more than one subevent, the contribution from each subevent is superposed with the appropriate delay time. In summary, the source and path spectra are evaluated by simple formulas in the model, whereas the site amplification and phase spectra are evaluated empirically. Because of the simplicity of the source model, only six parameters are necessary for each subevent: longitude, latitude, depth, seismic moment, corner frequency, and rupture time. We need to determine the number of subevents and the parameters for each subevent.
- 1.Reevaluate the G(f) at the surface of KMMH16 by multiplying the observed Fourier spectral ratio (KMMH16 surface/previous KMM006) and the G(f) at the previous KMM006 by Nozu et al. (2006). The observed Fourier spectral ratio was evaluated using five weak motions before the relocation of KMM006 (Table 1).Table 1
Earthquakes used to reevaluate the G(f) at KMMH16 (surface)
- 2.Evaluate G(f) at the present KMM006 by multiplying the observed Fourier spectral ratio (present KMM006/KMMH16 surface) and the reevaluated G(f) at the surface of KMMH16. The observed Fourier spectral ratio was evaluated using eight weak motions after the relocation of KMM006 (Table 2).Table 2
Earthquakes used to reevaluate the G(f) at KMM006 after relocation
Evaluate G(f) at the borehole of KMMH16 by multiplying the observed Fourier spectral ratio (KMMH16 borehole/KMMH16 surface) by the reevaluated G(f) at the surface of KMMH16. The observed Fourier spectral ratio was evaluated using the same eight weak motions as in step 2 of the procedure (above).
- 4.Compare the G(f)s before and after modification. These three newly evaluated G(f)s are shown in Fig. 2, which shows that G(f) for the surface of KMMH16 increased slightly, although not significantly.
Parameters of the subevents
Along-strike distance from the epicenter
4.0 × 1017 Nm
7.0 × 1017 Nm
8.0 × 1018 Nm
For all target stations
Used only for KMM004, KMM005, KMM007, and KMMH06
Difference of the arrival time and the shortest distance from Subevent 1
Time delay (s)
Difference of the shortest distance from Subevent 1 (km)
KMMH16 to KMMH14 (borehole)
KMM006 to KMMH16 (surface)
Nonlinear parameter ν1 and the peak frequencies of G(f) and observed Fourier spectrum of the mainshock
Peak frequency of G(f) (Hz)
Peak frequency of observed fourier spectrum (Hz)
Results and discussion
On the other hand, discrepancies can be found between the synthetic and observed Fourier spectra that can be attributed to the simplicity of the pseudo point-source model. One of them is the underestimation of components lower than 0.5 Hz for almost all the stations. One possible cause of the underestimation is the shallow large slip that causes fling steps. For the 2016 Kumamoto earthquake, source process analyses using teleseismic records (Yagi et al. 2016; Yamanaka 2016) indicate that a large slip occurred near the surface, which may have contributed to the low-frequency components of the observed records. As mentioned previously, only the subevents that generate strong ground motions are modeled; therefore, shallow large slips, or fling steps, were not covered in the pseudo point-source model. Revealing the effect of shallow slip on strong ground motions is one of the important issues to be addressed. At KMMH14, located southwest of the epicenter, the synthetic Fourier spectrum overestimated the observation between 0.5 and 3 Hz. This result may indicate that the actual rupture proceeded northeast and that the backward directivity effect might appear in the observed Fourier spectrum at KMMH14.
We developed a pseudo point-source model for the 2016 Kumamoto earthquake of April 16 with M JMA 7.3 for the purpose of simulating strong ground motions in the frequency range of 0.2–10 Hz. Three subevents were placed on the fault plane considering the characteristics of the observed records. The synthesized Fourier spectra and velocity waveforms generally explained the observed records, such as troughs in the Fourier spectra and strong pulses. However, underestimation in the low frequency range was found. The underestimation is presumably due to the following two reasons. The first is that the target of the pseudo point-source model is only the subevents that generate strong ground motions, and it does not consider the shallow large slip. The second reason is that the current version of the pseudo point-source model does not consider the rupture directivity effect. Consequently, strong pulses were not reproduced enough at stations northeast of Subevent 3, such as KMM004, where the effect of rupture directivity was significant. This result indicates the necessity for improving the pseudo point-source model so that it can incorporate the effect of rupture directivity by, for example, introducing azimuth-dependent corner frequency.
Japanese standard time
Japan Meteorological Agency
Peak ground velocity
National Research Institute for Earth Science and Disaster Resilience
Strong-motion generation area
Strong-motion pulse generation area
YN conducted the source modeling and strong ground motion simulation. YN and AN investigated and interpreted the simulation results. Both authors read and approved the final manuscript.
We used the waveform data from K-NET and KiK-net operated by the NIED and information about the source from JMA and F-net. We would like to thank Dr. Haruo Horikawa and anonymous reviewers for their valuable comments.
The authors declare that they have no competing interests.
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- Aki K, Richards PG (2002) Quantitative seismology, 2nd edn, University Science Books
- Aoi S, Kunugi T, Fujiwara H (2004) Strong-motion seismograph network operated by NIED: K-NET and KiK-net. J Jpn Assoc Earthq Eng 4:65–74Google Scholar
- Asano K, Iwata T (2016) Source rupture processes of the foreshock and mainshock in the 2016 Kumamoto earthquake sequence estimated from the kinematic waveform inversion of strong motion data. Earth Planets Space 68:147. doi:10.1186/s40623-016-0519-9 View ArticleGoogle Scholar
- Boore DM (1983) Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra. Bull Seism Soc Am 73:1865–1894Google Scholar
- Fukuyama E, Ishida M, Dreger DS, Kawai H (1998) Automated seismic moment tensor determination by using on-line broadband seismic waveforms. Zisin 51:149–156 (in Japanese with English abstract) Google Scholar
- Hata Y, Nozu A (2014) Pseudo point-source models for shallow crustal earthquakes in Japan. Paper presented at the second European conference on earthquake engineering and seismology, Istanbul, 25–29 August 2014
- Irikura K, Miyakoshi K, Kurahashi S (2016) Methodology of simulating ground motions from crustal earthquakes and mega-thrust subduction earthquakes: application to the 2016 Kumamoto earthquake (crustal) and the 2011 Tohoku earthquake (mega-thrust). In: 5th IASPEI/IAEE international symposium: effects of surface geology on seismic motion, Taipei, 15–17 August 2016
- Japan Meteorological Agency (2016) Webpage of the hypocenter list on April 16, 2016. http://www.data.jma.go.jp/svd/eqev/data/daily_map/20160416.html. Accessed 18 Oct 2016 (in Japanese)
- Kamae K, Irikura K (1998) Source model of the 1995 Hyogo-ken Nanbu Earthquake and simulation of near-source ground motion. Bull Seism Soc Am 88:400–412Google Scholar
- Kato K (2001) Evaluation of source, path, and site amplification factors from the K-NET strong motion records of the 1997 Kagoshima-Ken-Hokuseibu earthquakes. J Struct Constr Eng 543:61–68 (in Japanese with English abstract) Google Scholar
- Koketsu K (2016) http://taro.eri.u-tokyo.ac.jp/saigai/2016kumamoto/index.html#C. Accessed July 31 2016 (in Japanese)
- Kubo H, Suzuki W, Aoi S, Sekiguchi H (2016) Source rupture processes of the 2016 Kumamoto, Japan, earthquakes estimated from strong-motion waveforms. Earth Planets Space 68:161. doi:10.1186/s40623-016-0536-8 View ArticleGoogle Scholar
- Nozu A (2012a) A simplified source model to explain strong ground motions from a huge subduction earthquake -simulation of strong ground motions for the 2011 off the Pacific Coast of Tohoku Earthquake with a pseudo point-source model. Zisin 65:45–67. doi:10.4294/zisin.65.45 (in Japanese with English abstract) View ArticleGoogle Scholar
- Nozu A (2012b) A super asperity model for the 2011 Off the Pacific Coast of Tohoku Earthquake. J Jpn Assoc Earthq Eng 12:221–240. doi:10.5610/jaee.12.2_21 (in Japanese with English abstract) Google Scholar
- Nozu A (2016) http://www.pari.go.jp/bsh/jbn-kzo/jbn-bsi/taisin/research_jpn/research_jpn_2016/jr_46.html. Accessed 31 July 2016 (in Japanese)
- Nozu A, Sugano T (2008) Simulation of strong ground motions based on site-specific amplification and phase characteristics–accounting for causality and multiple nonlinear effects. Technical Note of the Port and Airport Research Institute 1173. (in Japanese with English abstract)
- Nozu A, Nagao T, Yamada M (2006) Simulation of strong ground motions based on site-specific amplification and phase characteristics. In: Proceedings of the third international symposium on the effects of surface geology on seismic motions, Grenoble
- Okada Y, Kasahara K, Hori S, Obara K, Sekiguchi S, Fujiwara H, Yamamoto A (2004) Recent progress of seismic observation networks in Japan-Hi-net, F-net. K-net and KiK-net. Earth Planets Space 56(8):xv–xxviii. doi:10.1186/BF03353076 View ArticleGoogle Scholar
- Yagi Y, Okuwaki R, Enescu B, Kasahara A, Miyakawa A, Otsubo M (2016) Rupture process of the 2016 Kumamoto earthquake in relation to the thermal structure around Aso volcano. Earth Planets Space 68:118. doi:10.1186/s40623-016-0492-3 View ArticleGoogle Scholar
- Yamanaka Y (2016) http://www.seis.nagoya-u.ac.jp/sanchu/Seismo_Note/2016/NGY60.html. Accessed 31 July 2016 (in Japanese)