Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, Japan

ESTIMATION OF STRONG MOTION DURINGTHE 2011 OFF THE PACIFIC COAST OF TOHOKU
EARTHQUAKE BY A GROUND MOTIONPREDICTION MODELKATAOKA Shojiro1 and KANEKO Masahiro2
1Senior Researcher, Earthquake Disaster Prevention Division, National Institute for Land andInfrastructure Management, Tsukuba, Japan, kataoka-s92rc@nilim.go.jp
2Head, Earthquake Disaster Prevention Division, National Institute for Land andInfrastructure Management, Tsukuba, Japan, kaneko-m92pq@nilim.go.jp

ABSTRACT: A Ground motion prediction model that was derived prior to the 2011 off
the Pacific coast of Tohoku earthquake is applied to simulation of ground motion during
the giant earthquake. Saturation of ground motion intensity with magnitude isinvestigated using the observed records and estimated ground motion during hypothetical
Suruga-Nankai trough earthquakes by the Central Disaster Prevention Council. The
simulated waveforms and observed records are compared and discussed.
Key Words: the 2011 off the Pacific coast of Tohoku earthquake, ground motion
prediction equation, acceleration response spectrum, group delay time

INTRODUCTION
Empirical equations for ground motion, or ground motion prediction equations (GMPEs), are still oneof the reliable methods for ground motion prediction among others such as semi-empirical methods
and theoretical methods. New empirical equations for acceleration response spectrum and groupdelay time that enable prediction of time history waveform of ground motion were developed prior to
the 2011 off the Pacific coast of Tohoku earthquake. This paper presents the results of estimation ofstrong motion during the Mw9.0 earthquake and examines applicability of the GMPEs to giantearthquakes.

GROUND MOTION PREDICTION EQUATION
GMPE for acceleration response spectrum
Fig. 1 shows 29 earthquakes, which are not crustal earthquakes, and 1,609 strong motion stations ofwhich strong motion records were used for the following regression analyses. The largest earthquake
among them is the 2003 off Tokachi earthquake (moment magnitude Mw8.2, No. 7 in Fig. 1). The371

total of 7,592 records was used; these records were obtained by Japan Meteorological Agency (JMA)
and National Research Institute for Earth Science and Disaster Prevention (K-NET and KiK-net).
Distance-moment magnitude relationship of the strong motion records is shown in Fig. 2.
The following model was employed for the regression analysis for acceleration response spectrum.
log SA (T)＝a1(T) Mw+a2(T) D－log(X d(T)+p(T)10qMw)－b(T) X + c0(T) + cj(T)（1）

where SA is acceleration response spectrum [cm/s2] (critical damping ratio h=0.05), T is natural period[s], D is focal depth [km], X is distance to source fault [km], a1, a2, b, c0, d, p, and q are regressioncoefficients, and cj is correction coefficient for station j.
The two-step regression analysis (Kataoka et al., 2008) was employed. The coefficients a1, a2, b,and c0 derived by the regression analysis are shown in Fig. 3. Coefficient d was found to be 1.0
throughout the target period range, T = 0.1-10[s], and q was set to 0.4.
GMPE for group delay time
The following models were employed for the regression analysis for average and variance of groupdelay time. Eq. (2) is the same as the model of Satoh et al. (2010), while Eq. (3) is different for R isused in Satoh et al. (2010) instead of R2.

 (T) = a(T) M01/3 + b(T) R + cj(T)2 (T) = a(T) M01/3 + b(T) R2 + cj(T)

(2)
(3)

where  and 2 are average [s] and variance [s2] of group delay time, M0 is seismic moment [N･m], T isperiod [s], R is hypocentral distance [km], a and b are regression coefficients, and cj is correction
coefficient for station j. The coefficients a and b derived by the regression analysis are shown in Figs. 4and 5.
The combination of GMPEs for acceleration response spectrum and group delay time enables toestimate time history waveform of ground motion (Satoh et al., 2010).

SATURATION OF GROUND MOTION INTENSITY WITH MAGNITUDEFig. 6 compares SA (T=1[s]) of observed ground motion with the GMPE derived above. Two kinds ofobserved SA (T=1[s]) are plotted in Fig. 6; original ones and corrected (site amplification
characteristics are removed by cj) ones. It can be seen that the GMPE overestimate the groundmotion when Mw is set to 9.0. The GMPE was found to have least misfit with the corrected SA(T=1[s]) when Mw was set to 8.3. Fig. 7 summarizes the moment magnitudes that give the GMPE theleast misfit with the corrected SA (T = 0.1-10[s]).
In order to investigate how SA (T) varies with Mw in the range of Mw>8.0, ground motions duringhypothetical Tokai, Tonankai, and Nankai earthquakes (Mw8.0, 8.2, and 8.4) and their coupledearthquakes (Mw8.3-8.7) that had been estimated by the Central Disaster Prevention Council in 2002
were stochastically analyzed. As shown is Fig. 8, SA (T) were found not to get larger with Mw anylonger when the magnitude became larger than 8.2, in other words, SA (T) saturated at Mw8.2.

ESTIMATION OF GROUND MOTION BY THE GMPE
Source fault of the 2011 off the Pacific coast of Tohoku earthquake
A 3-segment source fault was set for estimation of ground motion by the GMPEs as shown in Fig. 9
based on the source model obtained from inversion of strong motions (Yoshida et al., 2011). Seismic372

moments were set to 6.52 x 1021 [N･m] (Mw8.48), 1.85 x 1022 [N･m] (Mw8.78), and 8.63 x 1021 [N･m](Mw8.56), while rupture starting times were set to 0 [s], 40 [s], and 100 [s] (Satoh et al., 2011) for
segment 1, 2, and 3, respectively. Though Mw of all segments are larger than 8.5, they were set to 8.3
for estimation of SA (T) following the results of the previous chapter.
In addition to the 3-segment source fault, a single fault model was set for comparison of time
history waveforms. The seismic moment of the single fault model was set to 3.36 x 1022 [N･m](Mw8.95), which is equivalent to the sum of seismic moments of the 3 segments. Rupture starting
point is the same as segment 1 and 2.
Comparison between observed and estimated ground motions
Figs. 10 and 11 compare the time history waveforms of the observed and the estimated groundmotions. The correction coefficient obtained for each station was applied to compensate the GMPEs
for site amplification and phase characteristics. The waveforms of the 3-segment model show, as awhole, an agreement with observed ones, while those of single fault model seem too simple for groundmotions at stations in Miyagi prefecture, i.e. MYG006, MYGH10, Wakuya Branch, and Naruse Weir.
Detailed investigations are necessary for a better agreement; several research groups have proposedeven more complicated source model such as the one by Kurahashi and Irikura (2011) that consists of
5 strong motion generation areas.
Fig. 12 shows comparisons of the acceleration response spectra. The observed and estimatedresults don’t show a very good agreement, especially at MYG006. Applicability of the site
correction coefficient to giant earthquakes must be improved by taking consideration of various effects,
travel path for instance, neglected in this study.

CONCLUSIONSA Ground motion prediction model that was derived prior to the 2011 off the Pacific coast of Tohoku
earthquake is applied to simulation of ground motion during the giant earthquake. Saturation ofground motion intensity with magnitude is investigated using the observed records and estimatedground motion during hypothetical Suruga-Nankai trough earthquakes by the Central Disaster
Prevention Council. It was found that acceleration response spectra of both of observed andestimated ground motions saturate around Mw 8.3. The simulated waveforms and observed records
are compared and discussed. Further investigation is needed for a better agreement between
observed and estimated ground motions.

ACKNOWLEDGMENTS
The authors are grateful to Dr. Yasuhiro Yoshida, Meteorological Research Institute, JMA, for thedetailed data of the source fault. The strong motion records obtained by National Research Institutefor Earth Science and Disaster Prevention (K-NET and KiK-net), JMA, and Ministry of Land,Infrastructure, Transport and Tourism are used in this study.

REFERENCES
Kataoka, S., Matsumoto, S., Kusakabe, T. and Toyama, N. (2008). “Attenuation relationships andamplification map for ground motion in rather-long period range, Proceedings of Japan Society for
Civil Engineers A, Vol. 64, No. 4, 721-738.
Kurahashi, S. and Irikura, K. (2011). “Source model for generating strong ground motions during the2011 off the Pacific coast of Tohoku Earthquake”, Earth Planets Space, Vol. 63, 571-576.

373

Satoh, T., Okawa, I., Nishikawa, T., Sato, T. and Seki, M. (2010). “Prediction of waveforms oflong-period ground motions for hypothetical earthquakes using empirical regression relations ofresponse spectra and phase spectra, Journal of Structural and Construction Engineering(Transactions of AIJ), Vol. 75, No. 649, 521-530.
Satoh, T., Okawa, I., Nishikawa, T., and Sato, T. (2011). “Simulation of long-period ground motions
during the 2011 off the Pacific coast of Tohoku earthquake using empirical regression relations,
Proceeding of the 8th Annual Meeting of Japan Association for Earthquake Engineering, 430-431.
Yoshida, Y., Ueno, H., Muto, D., and Aoki, S. (2011). “Source process of the 2011 off the Pacific coastof Tohoku Earthquake with the combination of teleseismic and strong motion data.” Earth Planets
Space, Vol. 63, 565-569.

凡例
Rangeof Mw
Mwの範囲
7.5 - 9(1)7 - 7.5 (7)6.5 - 7(17)6 - 6.5 (3)5.5 - 6(1)Strong motion
観測点（1609）
stations

Fig. 1 Epicenters of 29 earthquakes and 1609 strong motion stations of which strong motion records
were used for the regression analyses in this study.

374

Mw

8.5
8.0
7.5
7.0
6.5
6.0
5.5100100

1000

Distance to source fault [km]

0.9

0.009

0.8

0.008

0.7

0.007

0.6

0.006

0.5

0.005

a2a1

Fig. 2 Distance-moment magnitude relationship of the strong motion records used in this study.

0.4

0.004

0.3

0.003

0.2

0.002

0.1

0.001

0.0

0.000
0.1

1T(s)

10

0.1

1T(s)

100.1

1T(s)

10

1.0

0.004

0.5
0.0

0.003

-0.5

0.002

c0ｂ-1.0
-1.5
-2.0
-2.5

0.001

-3.0
-3.5

0

-4.0

0.1

110T(s)Fig. 3 Coefficients a1, a2, b, and c0 derived from the regression analysis for acceleration response
spectra.

375

0.40

1.E-080.35
Coefficient b

Coefficient a

8.E-09
6.E-094.E-090.30

0.25

2.E-090.20

0.E+00
0.1

10.1

10110

Period [s]Period [s]Fig. 4 Coefficients a and b derived from the regression analysis for average group delay time, .
0.008

5.E-070.006
Coefficient b

Coefficient a

4.E-07
3.E-07
2.E-07

0.004

0.002

1.E-070.000

0.E+000.1

10.1

10110Period [s]Period [s]Fig. 5 Coefficients a and b derived from the regression analysis for variance of group delay time, 2.

376

Peak response acceleration [cm/s/s]

10000

1000

100

OriginalCorrected
Mw9.0
Mw8.3

101
10100
Distance to source fault [km]1000

Fig.6 Observed and corrected strong motion (SA(T = 1[s])) compared with the GMPE.
gives the least misfit with the observed SA(T = 1[s]) when Mw is set to 8.3.

The GMPE

Moment magnitude

8.4
8.3
8.2
8.1
8.0
7.9
7.8
7.7
0.1

1
Natural period [s]10Fig. 7 Moment magnitude that gives the GMPE for SA(T) the least misfit with observed SA(T).

377

T=0.20s

T=0.50s

最大加速度応答(cm/s)
Peak response
acceleration [cm/s/s]

100022最大加速度応答(cm/s)
Peak response
acceleration [cm/s/s]

1000

100

Tokai東海S-1(Mw7.96)
S-1 (Mw7.96)
Tokai東海S-2(Mw7.96)
S-2 (Mw7.96)
東南海(Mw8.2)
Tonankai(Mw8.2)
東海・東南海(Mw8.3)
Tokai-Tonankai(Mw8.3)
Tokai-Tonankai-Nankai(Mw8.7)
東海・東南海・南海(Mw8.7)
10

100

Tokai東海S-1(Mw7.96)
S-1 (Mw7.96)
Tokai東海S-2(Mw7.96)
S-2 (Mw7.96)
東南海(Mw8.2)
Tonankai(Mw8.2)
東海・東南海(Mw8.3)
Tokai-Tonankai(Mw8.3)
Tokai-Tonankai-Nankai(Mw8.7)
東海・東南海・南海(Mw8.7)

100

10Distanceto source (km)fault [km]断層最短距離100

Distance
to source (km)fault [km]断層最短距離1000

1000

T=2.00s2

最大加速度応答(cm/s)
Peak response
acceleration [cm/s/s]

2

Peak response
最大加速度応答(cm/s
acceleration [cm/s/s])

T=1.00s100

Tokai東海S-1(Mw7.96)
S-1 (Mw7.96)
Tokai東海S-2(Mw7.96)
S-2 (Mw7.96)
東南海(Mw8.2)
Tonankai(Mw8.2)
東海・東南海(Mw8.3)
Tokai-Tonankai(Mw8.3)
Tokai-Tonankai-Nankai(Mw8.7)
東海・東南海・南海(Mw8.7)
10
10100

Tokai東海S-1(Mw7.96)
S-1 (Mw7.96)
Tokai東海S-2(Mw7.96)
S-2 (Mw7.96)
東南海(Mw8.2)
Tonankai(Mw8.2)
東海・東南海(Mw8.3)
Tokai-Tonankai(Mw8.3)
Tokai-Tonankai-Nankai(Mw8.7)
東海・東南海・南海(Mw8.7)
10100

10Distanceto source (km)fault [km]断層最短距離100

Distance
to source (km)fault [km]断層最短距離Fig. 8 Attenuation relationships of SA(T) of the ground motion during the Tokai, Tonankai, andNankai earthquakes estimated by the Central Disaster Prevention Council.

378

Segment 1
Segment 2
Segment 3

MYG010
MYG010Kaihokubashi
Kaihokubashi

2

Kesennuma
Kesennuma
Branch

1&WakuyaWakuyaBranch

gme
nt

Osaki
Osaki Branch
MYG006
MYG006poin

MYG015
MYG015ting

NaruseNaruseWeir
Highway
SendaiSendai Koji
Koji

t fo

r Se

YamazakiYamazakiu restar

MYGH10
MYGH10

Rupt

Sakumagawa
Sakumagawa
FKS024
FKS024nt 3

HighwayIwaki
Iwaki kokudo
kokudo

IBR003
IBR003point for SeTCG014
TCG014
TCGH16
TCGH16gme

TCG006
TCG006

IBR005
IBR005

Ruptu restarting

BranchIwase
Iwase kokudo
kokudoFig. 9 The 3-Segment source fault used in the ground motion simulation. Point sources are locatedwith interval of 25 [km]. The estimated ground motions at highlighted stations are shown inFig. 10. Moment magnitudes are 8.48, 8.78, and 8.56 and rupture starting times are 0, 40, 100[s] for Segments 1, 2, and 3, respectively.

379

MYG006

MYGH10TCG006

Fig. 10 Comparisons of time history waveforms of observed and estimated ground motions atMYG006, MYGH10, and TCG006.

380Wakuya
BranchNaruseWeir

IwaseBranch

Fig. 11 Comparisons of time history waveforms of observed and estimated ground motions at Wakuya
Branch, Naruse Weir, and Iwase Branch.

381

10000
MYG006
Cal: 3-segment
Cal: single fault

Peak response acceleration [cm/s/s]

Peak response acceleration [cm/s/s]

10000

1000

100

MYGH10Cal: 3-segment
Cal: single fault
1000

10100.1

1
Natural period [s]

0.1

101
Natural period [s]1010000

TCG006
Cal: 3-segment
Cal: single fault

Peak response acceleration [cm/s/s]

Peak response acceleration [cm/s/s]

10000

1000

100

Wakuya Branch
Cal: 3-segment
Cal: single fault
1000

10010100.1

1Natural period [s]0.11010000

10000
Naruse Weir
Cal: 3-segment
Cal: single fault

Peak response acceleration [cm/s/s]

Peak response acceleration [cm/s/s]

100

1000

100

1
Natural period [s]10Iwase Branch
Cal: 3-segment
Cal: single fault

1000

10010100.11
Natural period [s]

0.1

101
Natural period [s]10Fig. 12 Comparisons of acceleration response spectra of observed and estimated ground motions.

382