Strong ground motion simulation of the 2016 Kumamoto earthquake of April 16 using multiple point sources
 Yosuke Nagasaka^{1}Email author and
 Atsushi Nozu^{1}
DOI: 10.1186/s4062301706128
© The Author(s) 2017
Received: 1 August 2016
Accepted: 24 January 2017
Published: 2 February 2017
Abstract
Keywords
2016 Kumamoto earthquake Strong ground motion simulation Pseudo pointsource model Rupture directivityBackground
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 pointsource models do not seem appropriate for such earthquakes. However, the pseudo pointsource 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 pointsource 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.
Methods
In the pseudo pointsource 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 strongmotion generation areas (SMGAs) (e.g., Kamae and Irikura 1998) or strongmotion pulse generation areas (SPGAs) (Nozu 2012b) in the characterized source models. However, the pseudo pointsource 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 omegasquare model (Aki and Richards 2002). The current version of the pseudo pointsource model assumes the same corner frequency for any azimuth or takeoff angle. In this respect, the pseudo pointsource 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 pointsource 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 KNET and KiKnet 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.
Parameters
 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)
Date
Time
Lat.
Lon.
M_{w}
2002/05/20
22:19
32.6420
130.8145
3.9
2002/09/02
05:48
32.7248
130.8068
3.6
2005/01/15
15:42
32.6345
130.8453
3.9
2011/10/05
23:33
32.9140
130.8503
4.4
2012/03/12
07:58
32.9200
130.8550
3.8
 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
Date
Time
Lat.
Lon.
M_{w}
2016/04/14
21:26
32.7417
130.8090
6.1
2016/04/14
22:38
32.6768
130.7350
4.9
2016/04/14
23:43
32.7670
130.8270
4.9
2016/04/15
00:03
32.7007
130.7780
6.0
2016/04/15
01:53
32.7008
130.7530
4.7
2016/04/16
7:23
32.7867
130.7740
4.6
4016/04/16
8:20
32.7015
130.6790
4.5
2016/04/16
14:27
32.6508
130.7432
4.5
 3.
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
Subevent 1  Subevent 2  Subevent 3  

Longitude  130.78°  130.80°  130.89° 
Latitude  32.77°  32.78°  32.84° 
Depth  18.0 km  18.0 km  15.0 km 
Alongstrike distance from the epicenter  2.3 km  4.6 km  15.0 km 
Seismic moment  4.0 × 10^{17} Nm  7.0 × 10^{17} Nm  8.0 × 10^{18} Nm 
Corner frequency  0.50 Hz  0.60 Hz  0.12 Hz 
Rupture time  0.0 s  1.1 s  5.7 s 
Note  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)  1.3  4.7 
KMM006 to KMMH16 (surface)  0.8  2.3 
Nonlinear parameter ν_{1} and the peak frequencies of G(f) and observed Fourier spectrum of the mainshock
ν_{1}  Peak frequency of G(f) (Hz)  Peak frequency of observed fourier spectrum (Hz)  

KMM003  0.86  2.36  2.03 
KMM007  0.91  3.46  3.15 
KMM008  0.89  0.86  0.77 
KMM009  0.70  7.88  3.96 
KMM011  0.87  3.11  2.71 
KMMH03  0.57  1.79  1.02 
KMMH14  0.78  0.89  0.60 
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 pointsource 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 lowfrequency 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 pointsource 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.
Conclusions
We developed a pseudo pointsource 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 pointsource 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 pointsource 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 pointsource model so that it can incorporate the effect of rupture directivity by, for example, introducing azimuthdependent corner frequency.
Abbreviations
 JST:

Japanese standard time
 JMA:

Japan Meteorological Agency
 PGV:

Peak ground velocity
 NIED:

National Research Institute for Earth Science and Disaster Resilience
 SMGA:

Strongmotion generation area
 SPGA:

Strongmotion pulse generation area
Declarations
Authors’ contributions
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.
Acknowledgements
We used the waveform data from KNET and KiKnet operated by the NIED and information about the source from JMA and Fnet. We would like to thank Dr. Haruo Horikawa and anonymous reviewers for their valuable comments.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 Aki K, Richards PG (2002) Quantitative seismology, 2nd edn, University Science Books
 Aoi S, Kunugi T, Fujiwara H (2004) Strongmotion seismograph network operated by NIED: KNET and KiKnet. 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/s4062301605199 View ArticleGoogle Scholar
 Boore DM (1983) Stochastic simulation of highfrequency 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 online broadband seismic waveforms. Zisin 51:149–156 (in Japanese with English abstract) Google Scholar
 Hata Y, Nozu A (2014) Pseudo pointsource 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 megathrust subduction earthquakes: application to the 2016 Kumamoto earthquake (crustal) and the 2011 Tohoku earthquake (megathrust). 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 Hyogoken Nanbu Earthquake and simulation of nearsource ground motion. Bull Seism Soc Am 88:400–412Google Scholar
 Kato K (2001) Evaluation of source, path, and site amplification factors from the KNET strong motion records of the 1997 KagoshimaKenHokuseibu earthquakes. J Struct Constr Eng 543:61–68 (in Japanese with English abstract) Google Scholar
 Koketsu K (2016) http://taro.eri.utokyo.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 strongmotion waveforms. Earth Planets Space 68:161. doi:10.1186/s4062301605368 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 pointsource 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/jbnkzo/jbnbsi/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 sitespecific 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 sitespecific 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 JapanHinet, Fnet. Knet and KiKnet. 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/s4062301604923 View ArticleGoogle Scholar
 Yamanaka Y (2016) http://www.seis.nagoyau.ac.jp/sanchu/Seismo_Note/2016/NGY60.html. Accessed 31 July 2016 (in Japanese)