pseudo point-source models for shallow crustal …pseudo point-source models for shallow crustal...

PSEUDO POINT-SOURCE MODELS FOR SHALLOW CRUSTAL EARTHQUAKES IN JAPAN

Yoshiya HATA1 and Atsushi NOZU2

INTRODUCTION In recent years, to evaluate and predict strong ground motions in seismic design and practice, a characterized source model, which consists of several rectangular subevents, is often used in Japan. In terms of the applicability of the characterized source models, many researchers have reported that the characterized source models can explain strong ground motions from past large earthquakes as long as the model parameters are appropriately determined.

On the other hand, in a recent study (Nozu, 2012), a more simplified source model called the “the pseudo point-source model” was proposed. In the study, the pseudo point-source model was applied to the 2011 off the Pacific coast of Tohoku Earthquake. According to the results, in spite of its simplicity, the pseudo point-source model can explain the observed velocity waveforms at least as well as the characterized source model. In addition, the pseudo point-source model can explain the observed Fourier spectra better than the characterized source model.

To utilize the pseudo point-source model for the evaluation and prediction of strong ground motions, it is important to study its applicability to various types of earthquakes. So far, its applicability has been studied for subduction earthquakes (e.g., the 2011 off the Pacific coast of Tohoku earthquake, Mw9.0, Nozu (2012)) and intraslub earthquakes (e.g., the 2003 off Miyagi intraslab earthquake, Mj7.1, Wakai et al. (2014)). However, its applicability to shallow crustal earthquakes has not been studied yet.

In this study, we investigate the applicability of the pseudo point-source model to four damaging shallow crustal earthquakes in Japan (Figure 1), namely, the 2000 Western Tottori Prefecture Earthquake (2000/10/06; Mj7.3), the 2005 West Off Fukuoka Prefecture Earthquake (2005/03/20; Mj7.0), the 2007 Noto Hanto Earthquake (2007/03/25; Mj6.9) and the 2007 Off Mid-Niigata Prefecture Earthquake (2007/07/16; Mj6.8). Strong ground motions from these earthquakes caused serious damage to a concrete dam (the 2000 Western Tottori Prefecture Earthquake, e.g., Ohmachi et al., 2003), a fishery port (the 2005 West Off Fukuoka Prefecture Earthquake, e.g., Hata et al., 2012a), and an airport (the 2007 Noto Hanto Earthquake, e.g., Hata et al., 2012b). Strong ground motions from the 2007 Off Mid-Niigata Prefecture Earthquake caused landslides (e.g., Hata et al., 2012c). Thus, it is significantly important to develop a source model which can explain strong ground motions from these earthquakes.

Parameters of the pseudo point-source models were basically determined referring to the parameters of the characterized source models developed for the same earthquakes in the past study (Nozu, 2011). Then, we calculated the velocity waveforms and the Fourier spectra at strong motion observation stations (see Table 1). Finally, we compared the estimated velocity waveforms and Fourier spectra with the observed ones in order to confirm the application of the pseudo point-source models to shallow crustal earthquakes.

1 Graduate School of Engineering, Osaka University, Suita, Japan, [email protected] 2 Engineering Seismology Division, Port and Airport Research Institute, Yokosuka, Japan, [email protected]

The 2000 Western TottoriPrefecture Earthquake （MJ 7.3）

The 2005 West Off FukuokaPrefecture Earthquake （MJ 7.0）

The 2007 Noto HantoEarthquake （MJ 6.9）

The 2007 Off Mid-NiigataPrefecture Earthquake （MJ 6.8）

Tokyo

Osaka

Figure 1. Locations of the shallow crustal earthquakes to be studied

Table 1. List of the strong motion observation stations

(a) The 2000 Western Tottori Pref. EQ. (b) The 2005 West Off Fukuoka Pref. EQ. Abbreviation Station Name

A-JSK JMA SakaiminatoA-JYN JMA YonagoA-KHR K-NET HiroseA-KKF K-NET KofuA-KKK KiK-net HakutaA-KKM KiK-net MihonosekiA-KKN KiK-net HinoA-KKS KiK-net ShingouA-KMH K-NET MihonosekiA-KNC K-NET NichinanA-KYN K-NET YonagoA-SKG Sakaiminato-G

Abbreviation Station Name

B-JFO JMA FukuokaB-JFT JMA FukutsuB-JIT JMA ItoshimaB-KCK K-NET ChikushinoB-KFK K-NET FukuokaB-KGN K-NET GenkaiB-KKG KiK-net GenkaiB-KKU KiK-net UmiB-KMB K-NET Maebaru

(c) The 2007 Noto Hanto EQ. (d) The 2007 Off Mid-Niigata Pref. EQ. Abbreviation Station Name

C-JNN JMA NanaoC-JNT JMA NotoC-JTG JMA TogiC-JWJ JMA WajimaC-KKS KiK-net SuzuC-KKY KiK-net YanagitaC-KNN K-NET NanaoC-KNT K-NET NotoC-KOY K-NET OhyaC-KSH K-NET ShoinC-KTG K-NET TogiC-KWJ K-NET Wajima

Abbreviation Station Name

D-JIZ JMA IzumozakiD-JNG JMA NagaokaD-JOJ JMA OjiyaD-KNP Kashiwazaki-kariha Nuclear PlantD-KMT K-NET MatsugasakiD-KNG K-NET NagaokaD-KOG K-NET OgiD-KOJ K-NET OjiyaD-KTR K-NET TeradomariD-MYN MLIT YoneyamaD-NKK NEXCO Kakizaki InterChangeD-NKS NEXCO Kashiwazaki InterChange

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The 2005 West OffFukuoka Prefecture Earthquake

The 2007 Noto Hanto Earthquake The 2007 Off Mid-NiigataPrefecture Earthquake

A-JSK A-JYN A-KHRA-KKF A-KKK A-KKMA-KKN A-KKS A-KMHA-KNC A-KYN A-SKG

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C-JNN C-JNT C-JTGC-JWJ C-KKS C-KKYC-KNN C-KNT C-KOYC-KSH C-KTG C-KWJ

D-JIZ D-JNG D-JOJD-KNP D-KMT D-KNGD-KOG D-KOJ D-KTRD-MYN D-NKK D-NKS

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Frequency (Hz) Figure 2. Site amplification factors at strong motion observation stations

OUTLINE OF THE PSEUDO POINT-SOURCE MODEL In the pseudo point-source model, for each of the subevents which contribute to strong motion generation, the spacio-temporal distribution of slip within the subevent is not modelled. Instead, the source spectrum associated with the rupture of the subevent is modelled. There are two motivations to perform such simplification. Firstly, since the Fourier phase of an earthquake motion is mainly controlled by the path effect and the local site effect, it is less important to evaluate the influence of the rupture process inside a subevent on the Fourier phase. Secondly, the Fourier amplitude of the earthquake motion observed at a rock site during a large earthquake has a shape without significant peaks and troughs. When an earthquake motion is calculated by a characterized source model, artificial peaks and troughs will often appear in the calculated Fourier amplitude, which is not in agreement with the observations.

In the pseudo point-source model, the source spectrum associated with the rupture of a subevent is assumed to follow the omega-square model (Aki, 1967). By multiplying the source spectrum with the path effect (Boore, 1983) and the site amplification factor (Nozu et al., 2007; Hata et al., 2012c; 2012d; see Figure 2), the Fourier amplitude spectrum at a site of interest can be obtained. Then, combining it with the Fourier phase characteristics of a smaller event, the time history of strong

ground motions from the subevent can be obtained. Finally, by summing up contributions from the subevents, strong ground motions from the entire rupture can be obtained.

The source model consists of six parameters for each subevent, namely, longitude, latitude, depth, rupture time, seismic moment and corner frequency of the subevent. Finite size of the subevent can be taken into account in the model, because the corner frequency of the subevent is included in the model, which is inversely proportional to the length of the subevent.

It should be noted that the pseudo point-source model studied in this article is the original model, in which an averaged radiation coefficient is assumed and the effect of rupture directivity is neglected. In the actual strong ground motions, the effects of radiation pattern and the influence of rupture directivity will be more or less included (e.g., Satoh, 2011). And it is not difficult to extend the pseudo point-source model so that these effects can be taken into consideration, if necessary.

However, there are also drawbacks in directly introducing these effects into strong motion simulations. For example, it is recognized that, if we use the conventional frequency-dependent radiation coefficient, the effects of radiation pattern appears too strongly in the synthetic ground motions (e.g., Katoh et al., 2013). In terms of rupture directivity, it is reported that some of the shallow crustal earthquakes in Japan generated damaging strong ground motions without the effect of forward directivity (Nozu, 2011). Thus, more efforts are required to really identify the roles played by these effects (the effects of radiation pattern and the influence of rupture directivity) in the actual strong ground motions. Therefore, in this study, we would like to start from the simplest model, in which both of these effects are not included. If these effects are really important in the actual strong ground motions, errors will appear in the calculated results. Thus, this study will serve as a test case to identify the importance of the effects of radiation pattern and the influence of rupture directivity.

The parameters of the pseudo point-source models are determined as follows.

CONSTRUCTION OF THE PSEUDO POINT-SOURCE MODELS Parameters of the pseudo point-source models were basically determined referring to the parameters of the characterized source models developed for the same earthquakes in the past study (Nozu, 2011). The location and rupture time of each subevent are determined referring to the location and rupture time of corresponding asperity. In terms of the rupture time, we performed minor adjustment to be consistent with the observed velocity waveforms. The seismic moment of each subevent is initially determined from the seismic moment of the corresponding asperity, and it was adjusted to be consistent with the observed velocity waveforms. We calculated the corner frequency of each subevent by Brune’s Equation (Brune, 1970; 1971) from the corresponding asperity area and the shear wave velocity. Here, typical values were used for the shear wave velocities of the source region for crustal earthquakes (e.g., Nozu, 2011). The locations and parameters of the pseudo point-source models which were identified by the above process are shown in Figure 3 and Table 2.

Based on the pseudo point-source model thus constructed, we calculated strong ground motions at strong motion observation stations. Here, typical values were used for the medium density for crustal earthquakes (e.g., Nozu, 2011). The mean value (0.63) to all the directions was used for the radiation coefficient. Another mean value (0.71) was used for PRTITN (Boore, 1983), which is a coefficient indicating the partition of energy into two horizontal components. The Q values estimated in the past studies (Satoh and Tatsumi, 2002; Kato, 2001) were used to represent the path effects.

The strong motion stations (Aoi et al., 2004; Nishimae, 2004; Uehara and Kusakabe, 2004; Maruyama et al., 2010) were selected so that they include stations which were used for the construction of the characterized source models in the past study (Nozu, 2011). In the future study, the authors’ intention is to evaluate the relative performance of the pseudo point-source model and the characterized source model.

Following the previous study (Nozu, 2011), we used the records of the aftershocks which occurred near a subevent to consider the path and site effects appropriately (see Figure 3 and Table 3). In particular, in the case of the 2000 Western Tottori Earthquake, at the southern stations (A-KKF, A-KKN, A-KNC and A-KKS), we adopted the records of Aftershock_A1. On the other hand, at the northern stations (A-KKK, A-KHR, A-KYN, A-JYN, A-KMH, A-JSK, A-SKG and A-KKM), we adopted the records of Aftershock_A2. In the cases of the 2005 West Off Fukuoka Prefecture Earth-

35.0°N133.0°E

A-KKS

A-KNC

A-KKF

A-KKN

A-KKK

A-KHR

A-JYN

A-KYN

A-KMHA-KKM

A-JSK

A-SKG

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Aftershock_A1 Main shock_A

Subevent_A2

Subevent_A1

35.6°N

133.7°E

B-KGN B-KKG

B-JFT

B-JIT

B-KMBB-JFO

B-KFK

B-KCK

B-KKU

Main shock_B

Subevent_B1

Subevent_B2

Aftershock_B

130.0°E 130.6°E33.4°N

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(a) The 2000 Western Tottori Pref. EQ. (b) The 2005 West Off Fukuoka Pref. EQ.

137.4°E136.6°E37.0°N

37.6°N

C-KKS

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138.2°E 139.0°E (c) The 2007 Noto Hanto EQ. (d) The 2007 Off Mid-Niigata Pref. EQ.

Figure 3. The pseudo point-source models for the shallow crustal earthquakes quake and the 2007 Noto Hanto Earthquake, we adopted the records of Aftershock_B or Aftershock_C. In the case of the 2007 Off Mid-Niigata Prefecture Earthquake, we adopted the records of Aftershock_D1 at D-JIZ and D-KTR sites, the records of Aftershock_D2 at D-KNP sites and the records of Aftershock_D3 at remaining sites. In the inverse Fourier transform, we generate causal time histories using smoothing technique (Nozu et al., 2009).

STRONG MOTION ESTIMATION Figure 4 shows the observed (black) and synthetic (red) Fourier amplitude spectra at strong motion stations for the 2000 Western Tottori Earthquake, the 2005 West Off Fukuoka Prefecture Earthquake, the 2007 Noto Hanto Earthquake and the 2007 Off Mid-Niigata Prefecture Earthquake. The spectra are smoothed with a Parzen window with a band width of 0.05Hz. It should be noted that the spectra are corrected for the non-linear response effects from engineering bedrock to ground surface using equivalent linear analysis (Yoshida et al., 2002) and the model for the shallow soil layers (Ooi and Fujiwara, 2013). In Figure 4, the agreement between the observed and synthetic Fourier spectra is quite satisfactory.

Figure 5 shows the observed (black) and synthetic (red) velocity waveforms at strong motion stations for the 2000 Western Tottori Earthquake, the 2005 West Off Fukuoka Prefecture Earthquake,

Table 2. List of parameters for the pseudo point-source models for the shallow crustal earthquakes

Latitude(deg.)

Longitude(deg.)

Depth(km)

Subevent_A1 35.245 133.371 6.5 13:30:22.4 0.9E+18 0.68

Subevent_A2 35.300 133.358 2.0 13:30:24.6 0.7E+18 0.50

Latitude(deg.)

Longitude(deg.)

Depth(km)

Subevent_B1 33.715 130.216 7.2 10:53:43.0 1.0E+18 0.66

Subevent_B2 33.780 130.105 9.2 10:53:43.7 0.8E+18 0.48

Latitude(deg.)

Longitude(deg.)

Depth(km)

Subevent_C1 37.226 136.698 12.1 09:41:58.4 0.3E+18 0.68

Subevent_C2 37.209 136.640 6.9 09:41:59.7 0.7E+18 0.48

Subevent_C3 37.283 136.740 2.1 09:42:01.6 0.1E+18 0.52

Latitude(deg.)

Longitude(deg.)

Depth(km)

Subevent_D1 37.517 138.579 12.6 10:13:24.3 0.6E+18 0.88

Subevent_D2 37.467 138.584 15.5 10:13:26.1 0.7E+18 0.43

Subevent_D3 37.409 138.505 14.7 10:13:29.6 1.1E+18 0.53

CornerFrequency

(Hz)

Rupture Time(h:m:s)

SeismicMomentM0 (Nm)

CornerFrequency

(Hz)

Location***Rupture Time

(h:m:s)


CornerFrequency

(Hz)


(h:m:s)



(h:m:s)


CornerFrequency

(Hz)

*** Based on the Characterized Source Models by NOZU (2011)

(a) The 2000 Western Tottori Prefecture Earthquake

(b) The 2005 West Off Fukuoka Prefecture Earthquake

(c) The 2007 Noto Hanto Earthquake

(d) The 2007 Off Mid-Niigata Prefecture Earthquake

Location***

Table 3. List of aftershocks used to determine phase characteristics

DateTime

(hour:min.)Latitude*

(deg.)Longitude*

(deg.)Depth*

(km)Mj* M0**

(Nm)(strike, dip, rake)**

(deg.)

Main shock_A 2000/10/06 13:30 N 35.273 E 133.348 9 7.3 8.62E+18 (150, 85, －9)

Aftershock_A1 2000/10/17 22:16 N 35.193 E 133.425 11 4.5 2.84E+15 (218, 72, 177)

Aftershock_A2 2000/11/03 16:33 N 35.357 E 133.293 9 4.6 5.23E+15 (165, 84, －3)

DateTime


(deg.)Longitude*

(deg.)Depth*

(km)Mj* M0**


(deg.)

Main shock_B 2005/03/20 10:53 N 33.738 E 130.175 9 7.0 7.80E+18 (122, 87, －11)

Aftershock_B 2005/04/20 06:11 N 33.677 E 130.287 14 5.8 1.31E+17 (312, 90, 14)

DateTime


(deg.)Longitude*

(deg.)Depth*

(km)Mj* M0**


(deg.)

Main shock_C 2007/03/25 09:41 N 37.220 E 136.685 11 6.9 1.36E+19 (58, 66, 132)

Aftershock_C 2007/06/11 03:45 N 37.243 E 136.653 7 5.0 2.04E+16 (224, 44, 143)

DateTime


(deg.)Longitude*

(deg.)Depth*

(km)Mj* M0**


(deg.)

Main shock_D 2007/07/16 10:13 N 37.557 E 138.608 17 6.8 9.30E+18 (49, 42, 101)

Aftershock_D1 2007/07/16 15:37 N 37.503 E 138.643 23 5.8 3.26E+17 (24, 44, 79)

Aftershock_D2 2007/07/16 21:08 N 37.508 E 138.628 20 4.4 5.21E+15 (39, 41, 115)

Aftershock_D3 2007/07/18 16:53 N 37.442 E 138.615 23 4.3 4.08E+15 (39, 62, 95)

* after JMA ** after F-net (www.fnet.bosai.go.jp)





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Figure 4. Comparison of the observed and synthetic horizontal Fourier spectra

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Figure 4. Comparison of the observed and synthetic horizontal Fourier spectra (Cont.)

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T ime (s) Time (s) Time (s) (a) The 2000 Western Tottori Prefecture Earthquake

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Obs. Syn.

Obs. Syn.

Obs. Syn.

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Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

[N-S]

[E-W]

[N-S]

[E-W]

[N-S]

[E-W]

[N-S]

[E-W]

[N-S]

[E-W]

[N-S]

[E-W]

[N-S]

[E-W]

[N-S]

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[N-S]

[E-W]

B-JIT

B-JIT

B-KMB

B-KMB

B-JFO

B-JFO

B-KFK

B-KFK

B-KCK

B-KCK

B-KKU

B-KKU

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B-JFT

B-KGN

B-KGN

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B-KKG

Ve

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Ve

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T ime (s) Time (s) Time (s) (b) The 2005 West Off Fukuoka Prefecture Earthquake

Figure 5. Comparison of the observed and synthetic velocity waveforms (0.2-2Hz)

0 1 0 2 0 3 0 4 0 5 0-100

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0 1 0 2 0 3 0 4 0 5 0-100

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Obs. Syn.

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Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

Obs. Syn.

[N-S]

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[E-W]

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[N-S]

[E-W]

[N-S]

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[N-S]

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[E-W]

C-JWJ

C-JWJ

C-KWJ

C-KWJ

C-KKY

C-KKY

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C-KOY

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T ime (s) Time (s) Time (s) (c) The 2007 Noto Hanto Earthquake

0 1 0 2 0 3 0 4 0 5 0-90

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D-NKS

D-NKS

D-NKK

D-NKK

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D-NYN

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D-KOG

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T ime (s) Time (s) Time (s) (d) The 2007 Off Mid-Niigata Prefecture Earthquake

Figure 5. Comparison of the observed and synthetic velocity waveforms (0.2-2Hz) (Cont.)

the 2007 Noto Hanto Earthquake and the 2007 Off Mid-Niigata Prefecture Earthquake. Here, again, the agreement between the observed and synthetic velocity waveforms is quite satisfactory.

CONCLUSION In this study, the pseudo point-source model was applied to explain strong ground motions from some shallow crustal earthquakes. The pseudo point-source model is simpler, and involves less model parameters, than the conventional characterized source model, which itself is a simplified expression of actual earthquake source. In the pseudo point-source model, the spacio-temporal distribution of slip within a subevent is not modelled. Instead, the source spectrum associated with the rupture of a subevent is modelled and it is assumed to follow the omega-square model. By multiplying the source spectrum with the path effect and the site amplification factor, the Fourier amplitude at the sites of interest can be obtained. Then, combining it with the Fourier phase characteristics of a smaller event, the time history of strong ground motions from the subevent can be calculated. Finally, by summing up contributions from the subevents, strong ground motions from the entire rupture can be obtained.

The source model consists of six parameters for each subevent, namely, longitude, latitude, depth, rupture time, seismic moment and corner frequency of the subevent. Finite size of the subevent can be taken into account in the model, because the corner frequency of the subevents is included in the model, which is inversely proportional to the length of the subevent.

To examine the applicability of the model to shallow crustal earthquakes, pseudo point-source models were developed for the 2000 Western Tottori Prefecture Earthquake, the 2005 West Off Fukuoka Prefecture Earthquake, the 2007 Noto Hanto Earthquake and the 2007 Off Mid-Niigata Prefecture Earthquake. The velocity waveforms (0.2-2Hz) and the Fourier spectra (0.2-10Hz) at strong motion stations calculated with the pseudo point-source models agree well with the observed ones, indicating the applicability of the pseudo point-source model to shallow crustal earthquakes. Recall that the pseudo point-source model studied in this article is the original model, in which an averaged radiation coefficient is assumed and the effect of rupture directivity is neglected. The excellent results presented in this article may be suggesting that the roles played by these effects (the effects of radiation pattern and the influence of rupture directivity) was not significant at least for these earthquakes. As a future work, the results should be compared with the results of characterized source models for the same earthquakes.

REFERENCES Aki, K. (1967) “Scaling law of seismic spectrum”, Jour. Geophys. Res., 72: 1217-1231. Aoi, S., Kunugi, T. and Fujiwara, H. (2004) “Strong-motion seismograph network operated by NIED: K-NET

and KiK-net”, Jour. of Japan Association for Earthquake Engineering, 4(3): 65-74. Boore, D. M. (1983) “Stochastic simulation of high-frequency ground motions based on seismological models of

the radiated spectra”, Bulletin of the Seismological Society of America, 73:1865-1894. Brune, J. N. (1970) “Tectnic stress and the spectra of seismic shear waves from earthquakes”, Jour. Geophys.

Res., 75: 4997-5009. Brune, J. N. (1971) “Correction”, Jour. Geophys. Res., 76: 5002. Hata, Y., Ichii, K. and Sakai, H. (2012a) “Strong motion estimation at the Genkai fishing port damaged by the

2005 West Off Fukuoka Prefecture Earthquake based on empirical site amplification and phase effects”, Journal of JSCE, Division A1, 68(2): 242-247.

Hata, Y., Ichii, K. and Nozu, A. (2012b) “Three-dimensional non-linear FEM analysis of a seismic induced crack at an airport runway”, Soil Dynamics and Earthquake Engineering, 42:105-118.

Hata, Y., Ichii, K. and Sakai, H. (2012c) “Seismic waveform estimation at the Oumigawa landslide induced by the 2007 Niigataken Chuetsu-Oki Earthquake based on site effect substitution method”, Journal of JSCE, Division A1, 68(2): 265-270.

Hata, Y., Ichii, K. and Sakai, H. (2012d) “Seismic waveform estimation at the Higashitakezawa landslide induced by the 2004 Mid Niigata Prefecture Earthquake based on empirical site amplification and phase effects”, Journal of Japan Landslide Society, 49(2): 51-60.

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”, Jour. of Struct. Constr. Eng., AIJ, (543): 61-68.

Kato, K., Hisada, Y., Manabe, S., Nozu, A., Nobata, A., Morikawa, J., Ohno, S. and Yamamoto, Y. (2013) “The benchmark test of the statistical green function method for the Southeast Off Kii Peninsula earthquake”, Proc. of the 10th Annual Meeting of Japan Association for Earthquake Engineering, 181-182.

Maruyama, Y., Yamazaki, F., Mizuno, K., Tsuchiya, Y. and Yogai, H. (2010) “Fragility curves for expressway embankments based on damage datasets after recent earthquakes in Japan”, Soil Dynamics and Earthquake Engineering, 30(11): 1158-1167.

Nishimae, Y. (2004) “Observation of seismic intensity and strong ground motion by Japan Meteorological Agency and local governments in Japan”, Jour. of Japan Association for Earthquake Engineering, 4(3): 75-78.

Nozu, A., Nagao, T. and Yamada, M. (2007) “Site amplification factors for strong-motion sites in Japan based on spectral inversion technique and their use for strong-motion evaluation”, Jour. of Japan Association for Earthquake Engineering, 7(3): 215-234.

Nozu, A., Nagao, T. and Yamada, M. (2009) “Simulation of strong ground motions using empirical site amplification and phase characteristics: modification to incorporate causality”, Journal of JSCE, Division A, 65(3): 808-813.

Nozu, A. (2011) “Modeling semi-short-period ground motions from crustal earthquakes using characterized source models”, Report of the Port and Airport Research Institute, 50(4): 133-195.

Nozu, A. (2012) “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–”, Journal of the Seismological Society of Japan. 2nd ser., 65: 45-67.

Ohmachi, T., Kojima, N., Murakami, A. and Komaba, N. (2003) “Near field effects of hidden seismic faulting on a concrete dam”, Journal of Natural Disaster Science, 25(1): 7-15.

Ooi, M. and Fujiwara, H. (2013) “Integration and provision of geotechnical information –Geo-Station–”, Geotechnical Engineering Magazine, 61(6): 24-27.

Satoh, T. and Tatsumi, Y. (2002) “Source, path, and site effects for crustal and subduction earthquakes inferred from strong motion records in Japan”, Jour. of Struct. Constr. Eng., AIJ, (556): 15-24.

Satoh, T. (2011) “Correction-factor model of rupture directivity and radiation pattern for empirical ground-motion attenuation relations of crustal earthquakes”, Jour. Struct. Constr. Eng., AIJ, (661): 499-508.

Uehara, H. and Kusakabe, T. (2004) “Observation of strong earthquake motion by National Institute for Land and Infrastructure Management”, Jour. of Japan Association for Earthquake Engineering, 4(3): 90-96.

Wakai, A., Nagasaka, Y. and Nozu, A. (2014) “A pseudo point-source model for off Miyagi intraslab earthquake on May 26, 2003”, Journal of JSCE, Division A1, 70(4).

Yoshida, N., Kobayashi, S., Suetomi, I. and Miura, K. (2002) “Equivalent linear method considering frequency dependant characteristics of stiffness and damping”, Soil Dynamics and Earthquake Engineering, 22(3): 205-222.

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