Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanINVESTIGATION OF SEISMIC RECORDS OF THE
2011 OFF THE PACIFIC COAST OF TOHOKU
EARTHQUAKE AT A DAM SITE USING THE
EMPIRICAL GREEN’S FUNCTION METHOD
Hiroshi ASAHARA1, Masayuki KASHIWAYANAGI2 and Tsuneo OHSUMI3
1Department of Civil and Environmental Engineering, Graduate School of Advanced Technology ofScience, The University of Tokushima, Tokushima, Japan, asahara@astom.co.jp
2Adviser, Civil Planning & Design Office, Civil & Electrical Engineering Department, Electric Power
Development Co., Ltd., Tokyo, Japan, masayuki_kashiwayanagi@jpower.co.jp
3Professor, Department of Civil and Environmental Engineering, Graduate School of Advanced
Technology of Science, The University of Tokushima, Tokushima, Japan,t_ohsumi@ce.tokushima-u.ac.jp

ABSTRACT: Seismic waveforms of the 2011 off the Pacific coast of Tohoku
Earthquake recorded at the base of a dam site in Fukushima prefecture are reproduced
based on the empirical Green’s function method. Three empirical Green’s functions areprepared to five strong-motion-generation-areas (SMGAs) model. The shape and peakacceleration of the observed waveform are roughly explained. Nearly simultaneous
arrivals from SMGAs at off-shore Miyagi prefecture and off-shore Fukushima prefecture
contributed to the maximum acceleration value at the target site.
Key Words: empirical Green’s function method, the 2011 off the Pacific coast of Tohoku
Earthquake, aftershock, dam site

INTRODUCTION
Dam sites located in Tohoku area have recorded many seismic waveforms of the 2011 off the Pacificcoast of Tohoku Earthquake, Japan, which occurred on March 11, 2011 (main shock, Mw 9.0) and its
aftershocks. Several kinds of rupture processes of the main shock have been proposed using
teleseismic waveforms (e.g., Ide et al., 2011, Ammon et al., 2011) or strong motions (e.g., Furumura etal., 2011, Kurahashi and Irikura, 2011). It is common that every rupture model shows complex rupture
propagation though the results vary from the focused frequencies or the analysis methods. The authors
reproduced the waveforms of the main shock using the empirical Green’s function (EGF) method(Irikura, 1986).
The EGF method is a technique to synthesize seismic records of a large event using the recorded
data at small events as Green’s functions. After the second proposal of Japan Society of Civil
Engineering (JSCE), following the Southern Hyogo prefecture earthquake in 1995, simulation ofearthquake ground motions using the Green’s function approach for a potential rupturing fault, has322

been included in one of the seismic resistant design codes (JSCE, 1996). Since the EGF method
mainly depends on and uses small ground motion histories, small events selected as Green’s functions
are necessary to share the same path and site effects with the target event. Seismic waveforms
recorded at the base of dam sites are suitable for this analysis, where seismic motion is less affected by
sedimentary layers. Seismic records at the base of dam sites are affected by the structure above at highfrequency range, whereas show the characteristics similar to those on the bedrock at frequency range
approximately lower than 1 Hz.
The authors reproduced the waveform of the main shock by the EGF method using waveforms ofsmall events as the Green’s functions. The influence rate of rupture processes to the waveforms wasdiscussed, comparing the synthesized data and the recorded waveform.

Iwate Pref.
SMGA2

Miyagi Pref.
SMGA1

Fukushima Pref.

SMGA3

Target dam site
SMGA4

IbarakiPref.

SMGA5

Fig.1 The location of the target dam site (filled triangle), the fault zone (large dashed rectangle),characterized source model consisting of five SMGAs in the fault zone (small solid rectangles).
The small rectangles and the closed circles inside them show the SMGAs and their initiation
points. The open star and the closed stars show the epicenters of the main shock and the small
events which are candidates for EGFs, respectively. EGF-A, B and C are selected as EGFs.

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Table 1 The source parameters of the main shock and the small events which are candidates for EGFs.
The origin times and the locations were determined by JMA. The CMT solutions and moments
were reported by F-net. Stress drops and areas for EGFs were determined in this study.
Origin time

Latitude Longitude
(deg)
(deg)

Depth(km)MWStrike(deg)Dip(deg)Rake(deg)M0(N m)Stress drop(MPa)Area(km2)

Main shock

2011/03/11
14:46:18.12

38.103142.86123.7

9.0

22/20091/88

63/27

1.07E+22

Event-1

2011/04/12
14:07:42.28

37.053140.643

15.1

5.9

76/167

89/51

141/2

7.05E+17

Event-2

2011/04/12
17:16:12.02

36.946140.673

6.4

6.6

132/301

50/41 -82/-99 9.58E+18

Event-3

2011/04/07
23:32:43.46

38.204141.92065.9

7.1

211/20

50/40

97/81

4.74E+19

Event-4

2011/03/11
16:14:56.80

36.555142.069

20.0

6.5

15/22071/21 81/113

6.16E+18

Event-5

2011/03/11
15:15:34.47

36.108141.265

43.2

7.8

26/209

59/31

89/92

5.66E+20

Event-6(EGF-B)

2010/03/14
17:08:04.1837.724

141.818

39.8

6.5

20/199

69/21

91/89

6.83E+18

21.2

84.6

Event-7(EGF-C)

2008/05/08
01:45:18.77

36.228141.608

50.6

6.8

18/21668/24 83/107

1.97E+19

31.2

132

Event-8(EGF-A)

2005/08/16
11:46:25.74

38.150142.278

42.0

7.1

29/194

69/22

96/76

5.43E+19

21.3

339

Event-9

2003/05/26
18:24:33.42

38.821141.65172.0

7.0

190/350

69/22

97/71

3.49E+19

WAVEFORM REPRODUCTION OF THE MAIN SHOCK
The target dam site is located in the Tohoku area, and the location is marked by a filled triangle in Fig.
1. This dam is a rock-fill dam. Seismographs are installed at the tops and the base of the dam. This site
has recorded seismic waves of the main shock and its aftershocks. Seismic waveforms of horizontal
upstream-downstream (orthogonal to the enclosing bund) component recorded at the base of the damsite were used in this study.
To simulate strong motions using EGF method, the characterized source model and the EGFs areneeded. The characterized source model was constructed using Kurahashi and Irikura (2011) model,
which consists of five strong-motion-generation-areas (SMGAs). EGFs were selected from theaftershock records and the past records prior to the main shock, considering the propagation path andthe radiation characteristic from the source.
Selection of the EGF
The target dam site has 9 seismic records other than that of the main shock, whose record length
exceed 40 seconds and whose epicenters are inside or around the fault zone of the main shock. These 9records are the candidates for EGFs. The hypocenters and CMT solutions of these records are shownin Fig. 1. The source parameters of the main shock and the small events reported by the Japan
Meteorological Agency (JMA) and the CMT solutions reported by F-net (Okada et al., 2004) areshown in Table 1. Event-1 to -5 occurred after the main shock, whereas event-6 to -9 occurred prior tothe main shock.

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(a) EGF-B(b) EGF-C
1.E+08

Unit Distance Source Spectra (cm*s*km)

Unit Distance Source Spectra (cm*s*km)

1.E+06f c = 0.25 Hz
1.E+05

1.E+04

1.E+03

1.E+020.01

0.1
1Frequency (Hz)f c = 0.20 Hz
1.E+07

1.E+06

1.E+05

1.E+040.01

100.11Frequency (Hz)10Fig. 2 Displacement spectra estimated from bore-hole motion records at KiK-net stations on rock fromthe small events ((a) EGF-B and (b) EGF-C) used as the empirical Green’s functions. The
shadow areas at low frequencies lower than 0.15 Hz show unreliable frequency range that was
not used for the simulation.

The small events’ records used as EGFs have to share the propagation path and site effects as wellas the radiation characteristic from the source. Event-8 (August 16, 2005, Mw 7.1) was commonly
selected as the EGF for SMGA 1 and 2. We call this event as EGF-A. In a similar way, event-6 (March14, 2010, Mw 6.5) was selected as the EGF for SMGA 3 and 4 (EGF-B), and event-7 (May 8, 2008,Mw 6.8) was selected for SMGA 5 (EGF-C). Event-3 was not selected as an EGF, on the grounds that
this event was not an inter-plate earthquake but an intra-slab one (Ohta et al., 2011), although theepicenter was inside the fault zone. The moment magnitude of event-5 (MW 7.8) was too large to useas EGF.
The information of stress drop and fault area is needed to use the waveforms as EGF. The cornerfrequencies of EGF-B and EGF-C were estimated using bore-hole motion records of KiK-net (Aoi etal., 2000) as shown in Fig. 2. The stress drop of these small events was calculated from the cornerfrequency and seismic moment relation (Boore, 1983). The fault area of the small event was obtainedby the circular clack model by Brune (1970, 1971). Conversely, the source models of EGF-A had been
estimated (e.g., Kamae, 2006, Suzuki and Iwata, 2007). The estimated models showed that thisearthquake consisted of two large slips. We decided the fault size of EGF-A considering total size oflarge slips. Stress drop was obtained from the size and seismic moment using the circular crack
formula (Eshelby, 1957). In this study, the observed records used as the EGFs were band-pass-filteredfrom 0.15 Hz to 10 Hz, considering the reliable frequency range of the observed records.
Characterized Source Model and Ground Motion Simulation
The characterized source model was constructed using Kurahashi and Irikura (2011) model, slightly
modifying the source parameters for our EGFs. The source parameters of each SMGA, such as thelength, width, seismic moment, stress drop and delay time from the origin time of each SMGA arelisted in Table 2. To calculate ground motions from each SMGA, the area of the SMGA was divided
into equally-sized square sub faults, the area of which was set to be the same as the small events area
as shown in Fig. 1. SMGA 1 and SMGA 3 are located off-shore Miyagi prefecture. SMGA 2, SMGA 4and SMGA 5 are located off-shore Iwate prefecture, Fukushima prefecture and Ibaraki prefecture,325

Table 2 The source parameters of each SMGA.
SMGA 1SMGA 2SMGA 3

SMGA 4SMGA 5

L (km)

55.2

36.8

92.0

36.8

34.5

W (km)

36.8

36.8

55.2

36.8

34.5

NL×NW×ND

3×2×7

2×2×3

10×6×11

4×4×4

3×3×2

M0 (N m)

2.28E+21

6.52E+20

4.51E+214.37E+20

3.55E+20

Stress drop (MPa)

39.9

23.4

29.7

16.3

25.9

Delay time fromorigin time (sec)

15.64

66.42

68.41

109.71

118.17

Rise time (sec)

3.3

3.3

4.9

3.3

3.1

EGF

EGF-A

EGF-A

EGF-B

EGF-B

EGF-C

Fig.3 Comparison of the observed (black traces) and synthetic (red traces) seismographs by the EGF
method at the dam site. The acceleration (left) and velocity (right) are composed.

respectively.
The rise times inside each SMGA were given by the empirical relations by Kataoka et al. (2003).
The average S wave velocity and the rupture velocity were given to be 3.5 km/s and 2.8 km/s,
respectively. The QS value for plate boundary earthquakes in Eastern Japan area, which was proposedby Kawase and Matsuo (2004), was used as the propagation property at this area; QS = 93 f 0.89 . Here f
is frequency (Hz).

DISCUSSION
The observed and synthetic waveforms (acceleration and velocity) at the dam site are shown in Fig. 3.
The base time at these graphs is the start time of the observed, 58 seconds after the origin time. The
shape and peak acceleration of the observed waveform were roughly explained by the synthetic using
five SMGAs. The observed peak acceleration was 23 gal, whereas the synthetic peak was 24 gal. The
acceleration waveforms had two peaks: the first appeared around 30 sec. and the second appeared
around 100 sec. The synthetic first peak was calculated larger than that of the observed, though the326

Fig.4 Fourier spectra of observed (black trace) and synthetic (red trace) accelerations shown in Fig. 3.

Fig.5 Comparison of synthetic waveforms from five SMGAs (red trace) and from individual SMGAs(black traces) from SMGA1 to SMGA5.

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synthetic second peak was similar to that of the observed. The initial tremor of the observed was notrecreated on the grounds that the EGF data started just before the S wave arrival, lacking the initial P
wave data because of the specification of the observation system.
The observed and synthetic Fourier spectra are shown in Fig. 4. The synthetic Fourier spectrum
was well consistent with the observed at all frequency range. The observed and synthetic hadcommonly peaks at about 0.4 Hz and 1.0 Hz, and bottom at 1.8Hz. The observed bottom at 1.5 Hz was
not recreated.
The waveforms synthesized from individual SMGAs were shown in Fig. 5. The waveform before
70 sec. only depended on SMGA1, and SMGA2 had a little impact on the waveform. The low
acceleration period between the first and second peaks showed the interval between SMGA1 andSMGA3. The influences from SMGA 3 to 5 reached in sequence. Comparing waveforms of individual
SMGAs with the observed waveform, it was found that SMGA3 and SMGA4 had the largest influenceon the waveform. Though the fracture start times of these SMGAs were about 40 seconds away, thearrival times at the target site were came closer. The nearly arrivals made the peak acceleration around
100 sec.

CONCLUSIONSThe seismic waveform of the 2011 off the Pacific coast of Tohoku Earthquake recorded at the target
dam site was reproduced using the empirical Green’s function method. Three empirical Green’sfunctions were prepared to five SMGAs. The shape and peak acceleration of the observed waveform
were roughly explained by the model using five SMGAs. The comparison of the observed andsynthetic waves made it clear that nearly simultaneous arrivals of wave packets from SMGAs at
off-shore Miyagi and off-shore Fukushima contributed to the maximum acceleration value at the site.

ACKNOWLEDGMENTS
The authors are grateful to the National Institute for Earth Science and Disaster Prevention (NIED),
Japan for providing strong motion data of the KiK-NET and the CMT solutions by the F-net.

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