Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanSTRONG MOTION ESTIMATION AT THE ELEVATED
BRIDGES OF THE TOHOKU SHINKANSENDAMAGED BY THE 2011 OFF THE PACIFIC COAST
OF TOHOKU EARTHQUAKE BASED ON EXTENDED
SITE EFFECTS SUSTITUTION METHOD
Yoshiya HATA1, Atsushi NOZU2, Susumu NAKAMURA3,
Yoshikazu TAKAHASHI4 and Hiroyuki GOTO5
1

Senior Researcher, R&D Center, Nippon Koei Co., Ltd., Tsukuba, Japanhata-ys@n-koei.jp
2
Head of Engineering Seismology Division, Port and Airport Research Institute, Yokosuka, Japannozu@pari.go.jp
3
Professor, Faculty of Civil Engineering, Nihon University, Koriyama, Japans-nak@civil.ce.nihon-u.ac.jp
4
Associate Professor, DPRI, Kyoto University, Uji, Japan
yos@catfish.dpri.kyoto-u.ac.jp
5
Assistant Professor, DPRI, Kyoto University, Uji, Japan
goto@catfish.dpri.kyoto-u.ac.jp

ABSTRACT: The 2011 off the Pacific coast of Tohoku, Japan, earthquake caused
significant damage to engineering structures, not only due to tsunamis but also due tostrong ground motions. In this paper, an extended site effects substitution method wasused to estimate strong ground motions at the site of damaged elevated bridges of the
Tohoku Shinkansen in Kitakami City, Iwate Prefecture, Japan, for the 2011 main shock,with the site amplification and phase effects evaluated based on temporary aftershockobservation records at the proximity of the site.
Key Words: Strong motion, site effects, aftershock observation, elevated bridges

INTRODUCTION
The 2011 off the Pacific coast of Tohoku, Japan, earthquake caused significant damage to engineering
structures, not only due to tsunamis but also due to strong ground motions (e.g., JGS 2011). It is
important to estimate strong ground motions during the earthquake at sites where engineering structures
were damaged for the purpose of investigating the damage mechanism.
Currently, Japan is covered with nationwide strong motion networks such as K-NET (e.g., Aoi etal. 2004), KiK-net (e.g., Aoi et al. 2004) and the Japan Meteorological Agency (JMA) network

418

(Nishimae 2004), with 1031, 688 and 637 stations, respectively, at the end of the year 2011. Thus, it isusually possible to obtain a record of strong ground motions within 20 km from a target site. The
spatial variation of strong ground motions due to local geology, however, is quite significant (e.g.,
Hata et al. 2011a) and it is often insufficient to employ the observed ground motions at a nearby
station. Examples of the significance of the spatial variation of strong ground motions can also befound later in this article. It is necessary, therefore, to take into account the effects of local geology(site effects) to estimate strong ground motions at a particular site.
On the other hand, after a large earthquake, it is often possible to conduct aftershock observations
and/or microtremor observations at a site of engineering interest (e.g., Hata et al. 2011b). Thus, it isdesirable to make an efficient use of the aftershock and/or microtremor observation results at the siteof interest, in conjunction with the record of a large event at a nearby station, to estimate strong
ground motions during the large event at the site of interest.
Conventional approaches to estimate strong ground motions at a site of interest using aftershock
and/or microtremor records, fall into two categories. One of them is based on full strong motion
simulation using fault models and aftershock records as empirical Green’s functions. In theseapproaches, because the time history of strong ground motion is generated, one can obtain any groundmotion parameters such as peak amplitude, duration, etc. based on the time history. In theseapproaches, however, the reliability of the result is obviously dependent on the quality of the fault
model and it may not always be possible to obtain a fault model with sufficient reliability.
As the other category, a practical estimation method of strong ground motion (called ‘site effectsubstitution method’) was proposed by Hata et al. (2011c). The method is based on records ofaftershocks both at the site of interest and at a nearby permanent strong motion observation station,and on a record of the main shock at the observation station. Because it focuses not only on the
difference of site amplification factors but also on the difference of site phase effects between the siteof interest and the observation station, it can compute time histories of strong ground motions at thesite of interest with high accuracy (e.g., Hata et al. 2011b; 2011c). Another advantage of the method is
its simplicity. Unlike full strong motion calculations such as those based on the Stochastic Green’s
Function Method (e.g., Nozu et al. 2009), the method does not require a fault model of the large event.
Therefore, it can be applied at an early stage of response to the large event even if a reliable fault
model is not available.
The method, however, cannot be directly applied to a multiple-shock event such as the 2011 off
the Pacific coast of Tohoku Earthquake, especially when contributions from two or more sub-events
are remarkable for the site of interest. In this article, an extended site effect substitution method is
proposed for solving this problem. In the extended method, the original method is applied to each
sub-event successively. To validate the extended method, it is applied to strong motion records atpermanent observation stations around the site of damaged elevated bridges of the Tohoku Shinkansen
in Kitakami City, Iwate Prefecture, Japan, for the 2011 main shock. The estimated strong groundmotions at the stations with the extended site effect substitution method are very consistent with theobserved ones, indicating the validity of the extended method. As an application of the extended
method, it was used to estimate strong ground motions at the site of the damaged bridges, with the site
amplification and phase effects evaluated based on temporary aftershock observation records at theproximity of the site.

THE ORIGINAL AND EXTENDED METHOD
The original method
Fig. 1 shows the framework of the original method (Hata et al. 2011c). In Fig. 1, the original method
is simply composed of three steps. First, the Fourier amplitude of strong motion at a target site (Site A)
for a large earthquake is evaluated by correcting the Fourier amplitude at a nearby permanent
strong-motion station (Site B) for the same event based on the difference of the site amplification
factors at the two sites (Site A and Site B). Then, the Fourier phase of strong motion at the target site419

Site A

Main shock of the earthquake

Site B
Fourier amplitude and phaseof surface ground motion
at Site B

Correction for thedifference of path effects
between Site A and B

Fault

Correction for the differenceof site amplification factors
between Site A and B

Aftershock observation
at Site A

Making sure that the radiation
coefficient does not change
quickly from Site A to Site B

Fourier phase at Site A

Fourier amplitude at Site A
Inverse Fourier transform(Parzen window)

Consideration of causality

Estimation of seismic
waveform at Site A

Fig. 1 The framework of the original method (Hata et al. 2011c)(Site A) for the large earthquake is approximated by the Fourier phase at the same site (Site A) for asmall earthquake that occurred close to the main rupture area of the large earthquake. Finally, an
inverse Fourier transform is conducted to obtain the time histories of strong ground motions at thetarget site (Site A) for the large earthquake.
The extended method
One of the key assumptions of the original method is that the Fourier phase for the large event can beapproximated by the Fourier phase for a small event, and, in fact, it has been shown that theassumption is appropriate for many of recent damaging earthquakes in Japan (e.g., Nozu and Irikura2008). It is obvious, however, that the assumption cannot be directly applied to a multiple-shock event
such as the 2011 off the Pacific coast of Tohoku Earthquake, especially when contributions from two
or more subevents are comparable for the target site (Site A). In fact, contributions from at least two
subevents are quite evident in the waveforms observed in Iwate, Miyagi and Fukushima Prefecture,
Japan, during the 2011 main shock (e.g., Towhata et al. 2011). Even in such cases, one could still
expect that the Fourier phase corresponding to each subevent is approximated by the Fourier phase fora small event (this part will be confirmed later in “Application to the 2011 off the Pacific coast of
Tohoku Earthquake” section).
Thus, the authors extend the original method and propose a new method that can be applied torecords for a multiple-shock event. Fig. 2 shows the framework of the extended method. In Fig. 2,420

Main shock of the earthquake

Division with Taper (Second section)

Observed seismic waveformat Site B
Division with Taper(First section)
Observed surface groundmotion at Site B(First section)

Observed surface ground
Motion at Site B(Second section)

Fourier amplitude and phaseof surface ground motion
at Site B (First section)

Fourier amplitude and phaseof surface ground motion
at Site B (Second section)

Correction for thedifference of path effects
between Site A and B

Correction for thedifference of path effects
between Site A and B

Correction for the differenceof site amplification factors
between Site A and B

Correction for the differenceof site amplification factors
between Site A and B

Aftershock observation
at Site A

Fourier amplitude at Site A(First section)

Fourier amplitude at Site A(Second section)

Fourier phase at Site A

Inverse Fourier transform(Parzen window)

Inverse Fourier transform(Parzen window)

Estimation of seismic waveformat Site A (First section)

Estimation of seismic waveformat Site A (Second section)
The first section and the second sectionof the seismic waveform at Site A are superposed.
Estimation of seismic
waveform at Site A

Fig. 2 The framework of the extended method
first, the waveform at Site B is divided into parts corresponding to each subevent (the first and thesecond sections) with a taper. Then, the original method (see Fig. 1) is applied to each section (the first
and the second sections), and the waveform at Site A corresponding to each subevent is obtained.
Finally, the waveforms are superposed to obtain the total waveform at Site A.

APPLICATION TO THE 2011 OFF THE PACIFIC COAST OF TOHOKU EARTHQUAKE
Outline of application
In this chapter, to validate the extended method (called ‘extended site effect substitution method’), it isapplied to the 2011 off the Pacific coast of Tohoku Earthquake. The validation is conducted by applying themethod to estimate ground motions at strong motions stations and by comparing the estimated groundmotions with the observed ones. Then the extended method is applied to estimate strong ground motions at
the site of damaged bridges.
The earthquake occurred on 11 March 2011 off the Pacific coast of Tohoku and Kanto district,Japan. According to the Japan Meteorological Agency (JMA) unified source catalog, the hypocentral
parameters are origin time 14:46 (Japan Standard Time); epicenter, 38.1°N, 142.9° E; depth, 24 km;
and the moment magnitude MW 9.0. According to the F-net of the National Research Institute for Earth
Science and Disaster Prevention, the moment magnitude is MW 8.7. As reported by Takahashi and
Goto (2011), the earthquake caused serious damage to elevated bridges of the Tohoku Shinkansen in421

Iwate prefecture, Japan (see Photo. 1). In order to analyze the damage mechanism, it is very importantto evaluate the strong seismic motion at the elevated bridge site with high accuracy. The location of
the hypocenter of the 2011 main shock and the site of the damaged bridges of the Tohoku Shinkansen
is shown in Fig. 3.
Strong ground motions from the 2011 main shock were observed in nationwide strong-motion
networks in Japan including K-NET, KiK-net, etc. A large amount of strong motion records was obtained in
the earthquake. The locations of the strong motion stations around the damaged bridges of the Tohoku
Shinkansen are shown in Fig. 4, with peak ground velocities (PGVs) and JMA seismic intensities (e.g.,
Nishimae 2004). The list of the stations with abbreviations can be found in Table 1.
Strong ground motions observed at these sites show significant variability due to site effects. For
instance, although TUW and KTK are close to each other, the PGVs and JMA seismic intensities atthese sites are quite different (see Fig. 4), which indicates the significant difference of the site effects
at these stations. In addition, strong ground motions observed at these sites are characterized bycontributions from at least two distinct subevents as shown in Fig. 5 (a) and (b). Therefore, the records
are quite suitable for the validation of the extended method. In the following, these records will be
used for the validation.

Photo. 1 The damaged columns of an elevated bridge of the Tohoku Shinkansen (Takahashi and Goto 2011)N

ISD（17.7, 5.1）

SNK
N

Rikuzentakata City

Minamisanriku City

HNM（38.3, 5.6）
SNK

Ishinomaki City

TUW（12.7, 4.9）

Aftershock
KTK（50.8, 5.9）

Main shock
Station Name [Abbreviation]（PGV(cm/s), JMA Seismic Intensity）

Fig. 3 The location of the damaged bridges

0

5 km

Fig. 4 The observation results of strong ground motions422

Table 1 List of strong motion stations

Abbreviation

Station Name

SNK

Damaged piers site of Tohoku Shinkansen(Temporary aftershock observation site)
KiK-net Touwa
K-NET Kitakami
K-NET Ishidoriya
KiK-net Hanamaki-South

TUW
KTK
ISD
HNM

Table 2 Parameters for the main shock and the analyzed aftershock
Time
Latitude* Longitude* Depth* M W **(hh/mm JST)(deg.)(deg.)(km)

Main shock 2011/03/11

14:46

N 38.103

E 142.860

24

8.7

M 0**
(strike, dip, rake)**(deg.)(N・m)
1.07E+22(200, 27, 88)

Aftershock 2011/07/13

00:37

N 38.330

E 142.007

47

4.9

2.64E+16

Date(195, 61, 103)

* After Japan Meteorological Agency (JMA)** After F-net (see Data and Resources section)
Acc. (Gal)350

Peak= 251 Gal
0

-350
0

(a)
30

60

90

120

Time (s)Acc. (Gal)

350

0

(b)
30

60

90
Acc. (Gal)

0

(c)

-350
0

30

Time (s)60

Acc. (Gal)(d)
Time (s)60

90

TUW [E-W]: ground surface
180
210
240
Second section (70-220 sec)

0

(e)
100

130

350

0

30

150

Time (s)

-350
90
70

350 First section (0-90 sec)

-350
0

120

350

350 First section (0-90 sec)
Acc. (Gal)

TUW [N-S]: ground surface
180
210
240
Peak= 325 Gal-350
0Acc. (Gal)150Time (s)TUW [N-S]: ground surface
160
190
220
Second section (70-220 sec)

0

(f)

-350
70

100

130

Time (s)TUW [E-W]: ground surface
160
190
220

Fig. 5 The observed acceleration waveforms for the 2011 main shock at TUW
Although the main shock was observed at TUW, KTK, ISD and HNM sites, there was no strong
motion observation station at the site of damaged bridges during the 2011 main shock. In this study, as
shown in Fig. 6, temporary aftershock observation site (SNK) was created at the proximity of thedamaged bridges, where commercial power supply was available. The observation was conducted forabout 3 months from 18 April to 14 July, 2011. As the temporary observation results, a lot of seismic
waveforms due to aftershock events were recorded. One of them is the July 13 aftershock (2011/07/13
00:37 off Miyagi Prefecture), which was observed at all sites including TUW, KTK, ISD and HNM(see Table 1). The source parameters of the main shock and the aftershock are listed in Table 2. The

423

hypocenters and the focal mechanisms of the main shock and the aftershock are shown in Fig. 3. The
July 13 aftershock will later be used for the evaluation of the site phase effects (see “Estimation of
Fourier phase” section).
We estimate strong ground motions at KTK, ISD and HNM based on the records at TUW by means of
the extended method. Then, by comparing the estimated and observed strong ground motions, theapplicability of the extended method to the target area is investigated. Finally, using the extended method,strong ground motions at the site of damaged bridges during the 2011 main shock are estimated.
Division of waveforms
The observed acceleration waveforms at TUW are tapered off between 70 and 90 s to obtain the firstsection (see Fig. 5 (c) and (d)) and the second section (see Fig. 5 (e) and (f)) as shown in Fig. 5, eachcorresponding to different subevents.
Estimation of Fourier amplitude
Ratios of Fourier amplitude spectra at SNK with respect to TUW for 43 aftershocks are plotted using
gray traces in Fig. 7. In Fig. 7, all of the spectra are smoothed with a Parzen window with a band
width of 0.05Hz. In addition, the spectral ratios are corrected for the difference of the path effects, i.e.,the difference of the hypocentral distances for the 43 aftershocks at SNK and TUW. The black trace
indicates the average for the 43 aftershocks. The authors think that it is important to average theFourier amplitude ratios over several aftershocks to achieve robust estimation of strong groundmotions. Although the ratios are around 1.0 from 0.2 Hz to 1.0 Hz, the ratios exceed 1.0 in thefrequency range from 1.0 Hz to 6.0 Hz. In other words, in the frequency range from 1.0 Hz to 6.0 Hz,
the site amplification factor for SNK is larger than for TUW.
The Fourier amplitude spectrum for the NS component at SNK during the 2011 main shock was
obtained by multiplying the Fourier amplitude spectrum for the NS component at TUW with theaverage spectral ratio (see black trace in Fig. 7). The Fourier amplitude spectrum for the EW
component at SNK was obtained in the same way from the EW component at TUW. The Fourier
amplitude spectra for the horizontal components at KTK, ISD and HNM during the 2011 main shock
were calculated in the same way, based on the records of the same 43 aftershocks. Fig. 8 shows theestimated Fourier amplitude spectra at KTK, ISD, HNM and SNK. In Fig. 8, the estimated spectra at
KTK, ISD and HNM are compared with the observed ones. The agreement between the estimated andthe observed spectra is quite satisfactory. In other words, the validity of the estimation method of theFourier amplitude is well confirmed.
20 m

LG direction(N15°E)N

TR direction(N105°E)

D am
aged
a

rea o
n

eleva
t

ed br
i

dge

0

Ratio of Fourier Amp. （ SNK / TUW ）100

Temporary aftershockobservation site

Fig. 6 Temporary aftershock observation site SNK

Reference= 1.0
Ratio (43 waves)
Mean

10

1

0.1
0.1

1
Frequency (Hz)10

Fig. 7 The ratios of the Fourier amplitude spectra424

Fourier spectra (Gal ・ s)

10 3 KTK [N-S]
1st section

10 3 KTK [E-W]
1st section

10 3 KTK [N-S]
2nd section

10 3 KTK [E-W]
2nd section

10 2

10 2

10 2

10 2

10 1

10 1

10 1

10 1

Obs .

Obs.

Obs.

Syn.

Syn.

Syn.

Fourier spectra (Gal ・ s)

1
0.1

1

Fourier spectra (Gal ・ s)

1
0.1

1
0.1

10

Syn.

1

10

1
0.1

1

10 3 ISD [E-W]
1st section

10 3 ISD [N-S]
2nd section

10 3 ISD [E-W]
2nd section

10 2

10 2

10 2

10 2

10 1

10 1

10 1

10 1

Obs .

Obs.

Obs.

Syn.

Syn.

Syn.

1

10

1
0.1

1

1
0.1

10

Syn.

1

10

1
0.1

1

10 3 HNM [E-W]
1st section

10 3 HNM [N-S]
2nd section

10 3 HNM [E-W]
2nd section

10 2

10 2

10 2

10 2

10 1

10 1

10 1

10 1

Obs .

Obs.

Obs.

Syn.

Syn.

Syn.

1

10

1
0.1

1

1
0.1

10

Syn.

1

10

1
0.1

1

10 3 SNK [TR-N105 ° E]
1st section

10 3 SNK [LG-N15 ° E]
2nd section

10 3 SNK [TR-N105 ° E]
2nd section

10 2

10 2

10 2

10 2

10 1

10 1

10 1

10 1

Syn.

Syn.

1

10

1
0.1

Syn.

1

1
0.1

10

1

10

1

10 3 TUW [E-W]
1st section

10 3 TUW [N-S]
2nd section

10 3 TUW [E-W]
2nd section

10 2

10 2

10 2

10 2

10 1

10 1

10 1

10 1

Obs .

1
Frequency (Hz)

Obs.

10

1
0.1

1
Frequency (Hz)

Obs.

10

1
0.1

10

Syn.

1
0.1

10 3 TUW [N-S]
1st section

1
0.1

10

Obs .

10 3 SNK [LG-N15 ° E]
1st section

1
0.1

10

Obs .

10 3 HNM [N-S]
1st section

1
0.1

Fourier spectra (Gal ・ s)1

10 3 ISD [N-S]
1st section

1
0.1

Fourier spectra (Gal ・ s)

10

Obs .

1
Frequency (Hz)

10

Obs .

10

1
0.1

1
Frequency (Hz)10

Fig. 8 The comparison of the observed and synthetic Fourier amplitude spectra for the 2011 main shock425

Estimation of Fourier phase
In the site effect substitution method, it is desirable to select a small event that is close to the target
event for the evaluation of Fourier phase. Therefore, in this study, the July 13 aftershock, shown in
Table 2, was selected both for the first and the second sections, referring to its relative location to themain rupture area of the 2011 off the Pacific coast of Tohoku Earthquake (e.g., Kurahashi and Irikura2011) (see Fig. 3). Validity of this selection can be confirmed as follows. In Fig. 9, the observed
velocity waveforms for the 2011 main shock on the ground surface at TUW are shown as black traces,
both for the first and the second sections. On the other hand, the red traces indicate the synthetic
velocity waveforms with the same Fourier amplitude and the Fourier phase of the July 13 aftershock(see Table 2 and Fig. 3) on the ground surface at TUW. Both traces are band pass filtered between 0.2
and 3.0 Hz (Note that all of the velocity waveforms in this article are band pass filtered between 0.2
and 3.0 Hz). The left panels are for the first sections, and the right panels are for the second sections.
In Fig. 9, we can recognize the similarity of the synthetic waveforms (red traces) to the observed ones
(black traces), both for the first and the second sections. The similarity of the waveforms indicates thateach of the first and the second sections of the main shock ground motion has almost the same Fourierphase as the aftershock ground motion, that is, although the 2011 main shock was a multiple-shock
event, the Fourier phase for the first and the section sections of the main shock waveforms can still beapproximated by the Fourier phase of the aftershock, at least for the target area. Thus, the Fourierphase of the aftershock at KTK, ISD, HNM and SNK is used in the following waveform estimation.
Waveform estimation
The first and the second sections of strong ground motions on the ground surface at KTK, ISD and
HNM are respectively estimated by making use of the Fourier amplitude and the Fourier phaseestimated above. Here, we generate causal time histories using the smoothing technique mentioned
earlier. Finally, by superposing the first and the second sections, strong ground motions from the 2011
main shock on the ground surface at KTK, ISD, HNM and SNK are estimated. In the superposition,
the relative arrival time of the S waves at TUW is considered.
The observed velocity waveforms (black traces) and the estimated velocity waveforms (red traces)
at KTK, ISD and HNM are compared in Fig. 10 for the horizontal components. The similarity of all
traces (see Fig. 10) indicates the applicability of the extended method. Thus, it is suggested that theextended method is applicable to the 2011 off the Pacific Coast of Tohoku Earthquake, at least for thetarget area. From an engineering point of view, it is quite important that a strong motion at a site
without the record of the main shock can be estimated based on the record of the main shock at a
nearby site even when the site effects are quite different for the two sites.
Fig. 11 shows the estimation results of velocity and acceleration waveforms at the ground surface
at the site of the damaged bridges. Here, the velocity waveforms are band pass filtered between 0.2
and 3.0 Hz. Fig. 12 shows the estimated velocity response spectra for the horizontal components(Damping: 5%). Fig. 13 is the comparison of the design response spectrum (Damping: 5%) by
Railway Technical Research Institute (RTRI 1999) and the estimated acceleration response spectra(Damping: 5%). In the natural period range from 0.12 s to 0.48 s, the estimated spectra are larger thanthe design spectrum. In future study, using the estimated strong motions, seismic response analysis forthe elevated bridge shall be carried out.

SUMMARY AND CONCLUSIONS
After a damaging earthquake such as the 2011 off the Pacific coast of Tohoku, Japan, earthquake, there isan urgent need for the estimation of strong ground motions at sites of damaged structures that can be used
for earthquake response analysis of structures, shake table tests and so on. Although the site effectsubstitution method proposed by the authors, is advantageous for the estimation of strong ground motions
because of its simplicity, it cannot be directly applied to a multiple-shock event such as the 2011 off the

426

10
Vel. (cm/s)

Vel. (cm/s)

10 First section (0-90 sec)

TUW [N-S]
0

-10
0

30

Time (s)

60

90

0

30

Time (s)Amplitude= mainshock, Phase= mainshock
Amplitude= mainshock, Phase= aftershock
130
160
190
220
Time (s)100

10

TUW [E-W]

-10
0

0

-10
70
Vel. (cm/s)

Vel. (cm/s)

10 First section (0-90 sec)

Second section (70-220 sec)
TUW [N-S]

60

90

Second section (70-220 sec)
TUW [E-W]

0

-10
70

Amplitude= mainshock, Phase= mainshock
Amplitude= mainshock, Phase= aftershock
130
160
190
220
Time (s)100Fig. 9 The first and the second sections of the observed velocity waveforms

Vel. (cm/s)

40
Obs.

0

Vel. (cm/s)

-40
4030

Vel. (cm/s)
Vel. (cm/s)

50

60

70

80

90

100

110

120

130

KTK [N-S]
140
150
Syn.

0

40

50

60

70

80

90

100

110

120

130

KTK [E-W]
140
150

Obs.

Syn.

0

-20
2030

40

50

60

70

80

90

100

110

120

130

ISD [N-S]
140
150

Obs.

Syn.

0

-20
4030
Vel. (cm/s)

40

Obs.

-40
2030

40

50

60

70

80

90

100

110

120

130

ISD [E-W]
140
150

Obs.

Syn.

0

-40
4030
Vel. (cm/s)

Syn.

40

50

60

70

80

90

100

110

120

130

HNM [N-S]
140
150

Obs.

Syn.

0

-40
30

40

50

60

70

80

90

100

110

120

130

HNM [E-W]
140
150

Time (s)Fig. 10 The observed velocity waveforms and the synthetic velocity waveforms.

427

30
Vel. (cm/s)

Peak= 20.1 cm/s
0

-30
0

30

60

90

120

150

Time (s)30180

SNK [LG-N15 ° E]
210
240

Vel. (cm/s)

Peak= 24.5 cm/s
0

-30
0

30

60

90

120

Time (s)Acc. (Gal)

700

180

SNK [TR-N105 ° E]
210
240
Peak= 568 Gal

0

-700
0

30

60

90

120

150

Time (s)700
Acc. (Gal)

150

180

SNK [LG-N15 ° E]
210
240
Peak= 688 Gal

0

-700
0

30

60

90

120

150

Time (s)180

SNK [TR-N105 ° E]
210
240

Fig. 11 The estimated ground motion at SNK for the 2011 off the Pacific coast of Tohoku Earthquake
10 4
Design spectrum
SNK [LG-N15 ° E]

SNK [LG-N15 ° E]

SNK [TR-N105 ° E]

SNK [TR-N105 ° E]
Abs. Response Acc. (Gal)

Rel. Response Vel. (cm/s)

10 3

10 2

10 1

1
0.1

1
Natural Period (s)

10 2

10 1
0.1

10

Fig. 12 The relative velocity response spectra

10 3

1
Natural Period (s)10Fig. 13 The absolute acceleration response spectra

Pacific coast of Tohoku Earthquake, especially when contributions from two or more subevents arecomparable for the site of interest.
In this article, the authors extend the original site effect substitution method and propose a new methodthat can be applied to ground motions from a multiple-shock event. In the extended method, the waveformat the permanent strong motion station is divided into sections corresponding to each subevent and theoriginal method is applied to each section. The extended method is applied to the 2011 off the Pacific coastof Tohoku Earthquake to confirm its applicability. In terms of velocity waveforms and Fourier amplitude
spectra, the agreement between the estimated and the observed ground motions are quite satisfactory. Thus,
it is suggested that the extended method is applicable the 2011 off the Pacific coast of Tohoku Earthquake,428

at least for the target area. As an application of the extended method, it was used to estimate strong
ground motions at the site of the elevated bridges of the Tohoku Shinkansen damaged by the 2011 main
shock. As a result, it was found that the estimated response spectra exceed the design response spectrum.
Future work should include evaluating the amount of errors quantitatively for the extended method as well
as for other methods.

ACKNOWLEDGMENTS
We would like to thank the National Research Institute for Earth Science and Disaster Prevention(NIED) for providing strong motion data. We would also like to thank the Japan Meteorological
Agency (JMA) and NIED for providing source parameters of the 2011 off the Pacific coast of Tohoku
Earthquake (main shock) and aftershocks. This study was carried out as one of the activities of "Joint
Reconnaissance Committee on the 2011 Great East Japan Earthquake (Chairperson: Prof. Akira Mano
(Tohoku University))". The authors thank the members of the committee for valuable suggestions.

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