Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanSTRONG GROUND MOTIONS DURING
THE 2011 PACIFIC COAST OFF TOHOKU, JAPAN
EARTHQUAKE
Kojiro IRIKURA1 and Susumu KURAHASHI2
1

Professor, Disaster Prevention Research Center, Aichi Institute of Technology,
Toyota, Japan, irikura@geor.or.jp
2
Lecturer, Disaster Prevention Research Center, Aichi Institute of Technology,
Toyota, Japan, susumu@ aitech.ac.jp

ABSTRACT: The 2011 Tohoku Earthquake occurred along the plate boundary east ofnortheastern Japan. Huge tsunami caused tremendous disasters near the Pacific coast ofnortheastern Japan. In addition, strong ground motions affected ground failures, thencausing liquefaction, subsequently infrastructure and building damage over soft-groundareas. Slip and moment rate distributions were inverted using long-period strong motion
data (20 – 200 sec). Very large slip was obtained on the shallower part of the fault plane.
Large peak moment rate was shown on deeper part as well as on shallower part. The
source model for generating short-period motions was estimated from short-period strong
motion data. The acceleration records at stations show several isolated wave-packets
arriving from different origins on the source fault. Such origins are considered to be thestrong motion generation areas (SGMA). We identified five wave-packets in theobserved seismograms, which were arriving from five SMGAs on the source fault. The
source model is estimated from the forward modeling, comparing short-period groundmotions simulated using the empirical Green’s functions with those observed. The final
model has five SMGAs over the source fault located west of the hypocenter and along
the down-dip edge of the source fault. Attenuation-distance relationship of peak ground
velocity (PGV) from this earthquake was virtually equivalent to the empirical one fromMw 8.0 determined by Si and Modorikawa (1999). On the other hand, peak groundacceleration (PGA) was also virtually equivalent to the empirical one from Mw 8.0 in the
distance over 100 km, but clearly larger than that from Mw 8.0 near the source fault.
Ground motions with extremely high-accelerations can be explained by two different
causes. One is nonlinear site responses due to surface geology with decreased S wave
velocities (nonlinear soil behavior). The other is source characteristics, such as rupture
directivity effects, heterogeneous slip velocity inside the strong motion generation areasand so on. Very little damage during this earthquake is explained by spectral
characteristics of ground motions with predominant periods shorter than 0.5 sec,
although accelerations were so high.
Key Words: 2011 Tohoku earthquake, strong ground motions, strong motion generationarea, characterized source model, attenuation-distance relationship9INTRODUCTION
The 11 March 2011 giant earthquake with Mw 9.0 occurred off the Pacific coast of Tohoku, and is thelargest historical earthquake to strike in or near Japan. The rupture was initiated approximately 100 km
off-shore of Miyagi prefecture and extended about 450 km in length and about 200 km in width along
the subducting Pacific plate. The focal mechanism showed a reverse fault with a compression axis in a
WNW-ESE direction.
The huge tsunami generated by this earthquake struck the east-coast along Tohoku, resulting in morethan 19,000 people being killed or missing. The tsunami waves were also responsible for severe
accidents at the nuclear reactors in the Fukushima Daiichi Nuclear Power Plant, which further
intensified the scope of the disaster.
Strong ground motions with high seismic intensity such as 6-upper and 6-lower in the JMA scale
extends from the Tohoku to the Kanto district, over an area of about 400 km × 100 km (Hoshiba et al.,2011). A maximum seismic intensity 7 (corresponding to greater than 10 on the Modified Mercalli
scale) was recorded at Tsukidate (MYG004) in Kurihara about 175 km from the epicenter. Even atsome stations in Tokyo Metropolitan area more than 350 km from the epicenter, 6-lower intensity arerecorded.
More than 120 thousands houses and buildings were totally destroyed and more than 240 thousands
were half collapsed. Such damaged buildings were caused mostly by tsunami. Damage by shaking was
relatively less.
For the source regions of this earthquake, the Headquarters for Earthquake Research Promotion ofJapan (HERP) have made long-term evaluation of seismic activity based on an idea of so-called“characteristic earthquake model” (HERP 2009a). The entire area is divided into eight regions fromthe seismic activity for past 400 years. For each region, the presence of characteristic earthquake was
evaluated by analyzing the pattern of earthquake occurrences. For example, in offshore of Miyagi
prefecture, so-called Miyagi-oki earthquakes have repeatedly occurred with almost the same size andfairly close in location each other such as the sequence of the 1936, 1978, and several other earlier
events. The probability of the earthquake occurrence with M 7.4 - 7.5 is evaluated earthquake in thenext 30 years is 99%. M= 7.6-7.8 at 80 % for the Southern-Sanriku-oki in the region east of the
Miyagi-oki earthquake. An earthquake with M=7.3-7.5 is forecasted at less than 7 % for the
Fukushima-oki and that with M=6.7-7.2, at more than 90 % for the Ibaragi-oki, respectively. The
rupture of the 2011Tohoku earthquake seems to start from the source region of the SouthernSanriku-oki earthquake which is evaluated as 80 % probability in the next 30 years.
Slip distribution models have been inverted using teleseismic, geodetic, and tsunami data by many
researchers (e.g. Ide et al., 2011; Iinuma el al., 2011; Fujii and Satake, 2011; Yagi and Nishimura,
2011; Yamanaka, 2011). However, these initial modeling results exhibit significant variability, withnotably dissimilar features. For example, some of the models have the main slip distribution west of
the hypocenter, while others locate it east of the hypocenter toward the Japan Trench zone. The slip
distributions from the tsunami data show large slip near the Trench zone. A unified source model wasconstructed through joint inversion of teleseismic, strong motion, and geodetic datasets by Koketsu etal. (2011) and Yokota et al. (2011). Their results showed that the main rupture propagated not onlyin the strike direction but also in the dip direction and included both the deep area called the
Miyagi-oki region and the compact shallow area near the Japan Trench.
Strong motion data in the near-source region provide more detailed information about the shorter
period rupture process during the earthquakes. In our study, we estimate a source model for generatingstrong ground motions from this earthquake by comparing the observed records from the mainshockwith synthesized motions based on a characterized source model and the empirical Green’s function
method. The characterized source model consists of several strong-motion-generation-areas (SMGAs)
with large slip velocity or high stress drop, distributed across the entire rupture area of the earthquake.
One of features of this earthquake is relatively small damage caused by ground motions. To clarify thereasons of less damage are discussed about the characteristics of attenuation-distance relationships
such as PGV and PGA in relation of the long period and short period source models.

10

LONG-PERIOD SOURCE MODEL
Data and Velocity-Structure Model
Long-period source model by Yishida et al. (2011) are here introduced to compare not only slip but
also peak moment-rate distributions with source model for generating strong ground motions in thenext section. They used the strong-motion data obtained from 37 stations of F-net and KiK-net, and 1
station (MYR, Sasatani et al., 2002) of Hokkaido University as shown in Fig. 1. These stations arelocated on relatively hard rock. The velocity-type broadband seismometers used for F-net(VSE-355G3) and MYR (VS3, Muramatsu et al., 2001) are very capable of recording very long-period
components excited by this M 9 earthquake.
The data were windowed for 300 s, starting at P-wave arrival time, and band-pass filtered between
periods of 200 s to 20 s (0.005–0.05 Hz) for waveform inversion. The accelerograms obtained fromthe KiK-net were integrated into ground velocities with a sampling time of 4 s.
A single fault plane was assumed for the waveform inversion analysis having a fault size, 468 km longin strike and 228 km wide in dip, referring to the aftershock distribution. The strike and dip angle weretaken to be N193◦E and 10◦, respectively, referring to the JMA CMT solution. The rupture starting
point is located at the hypocenter determined by JMA: 38.103◦N, 142.861◦E, 23.7 km.
The velocity structure model proposed by Wu et al. (2008, 2009) for the waveform inversion of the
1979 and 2005 Miyagi-oki earthquake was used for calculating the theoretical Green’s functions. We
use an identical structure model for all stations, because the stations used in the inversion are locatedon almost hard rock, so it is expected that the observed seismograms are less affected by local site
effects in the long-period range.
Theoretical Green’s functions are calculated using the discrete wavenumber method (Bouchon,1981) and the reflection/transmission-coefficient matrix method (Kennet and Kerry, 1979) using astratified medium. A multi-time-window linear waveform-inversion procedure ( Hartzell and Heaton,
1983) was used, in which the moment-release distribution is discretized in both space and time.
To suppress instability or excessive complexity, a smoothing constraint is introduced to reduce
differences in moment release values close in space. The smoothing constrained parameter used in the
inversion was determined to choose the solution with a total slip which agrees with that expected fromthe geodetic data. Nonnegative constraints (Lawson and Hanson, 1974) to limit the rake-angle
variation are also adopted, allowing to vary within 45◦ centered at 90◦.
Slip and Peak Moment-Rate Distribution
Inversion results of total slip and peak moment rate distributions are shown in Fig. 2. Large asperity
areas with large slip in the shallow part of the fault plane are remarkably seen. The asperity size isabout 300 km × 100 km, and the slip on the asperity is about 20 to 47 m in Fig. 2. The slip vectors
indicate an almost pure dip-slip fault mechanism. The total moment release is 4.3 × 1022 N m (Mw9.0). This moment is similar to the seismic moment of 3.43 ×1022 N m which is derived from GPSdata (Ozawa et al., 2011). Synthetics calculated from the estimated rupture process agree well withcompared with the observed data.
Slip models by tsunami inversion are proposed by Fujii and Satake (2011). The overall slip
patterns and the average slip in the shallow part of the fault along the trench in this study are nearly thesame as their results (the maximum slip of about 30 m).
The time progression of the rupture shows that the source process of the earthquake consists of 3
rupture stages. In order to explain the contributions to the waveforms in the three stages, we divided
the source model into Areas 1, 2 and 3: the deeper part of the fault, the shallower asperity area of thenorthern part of the fault, and the southern part of the fault. In the first stage of the fault rupture,
moderate moment-rate areas are found at the southern and deeper side of the rupture starting point (theframe of 15–30 s). The rupture front also reached the shallower part of the fault (asperity area) at
about 40 s after the rupture initiation, and rupture progression seems to be suspended in that part. At

11

45–60 s after the rupture initiation, the second stage of the rupture started in the shallower part of thefault. The asperity area, with a length of about 300 km, simultaneously began to rupture with a highmoment rate, and the rupture continued for 30–40 s (the frames of 45–60 s to 75–90 s). Moderate
moment was released in the deeper part of the fault (the frame of 75–90 s). After the moment rate in
the asperity area declined, the third stage of the rupture seemed to be triggered. After that, the rupture
mainly progressed to the southern part of the fault (the frame of 90–105 s), and the deeper part of thefault (the frames after 105–120 s). In the frames of 90–105 s and 105–120 s, some moderate
moment-rate areas in the southern part of the fault plane are recognized. The rupture of these areas
radiated short-period motions with a short pulse width of moment-rate functions corresponding tostrong motion generation area described in the next section.

Fig. 1. (Left) Map showing F-net and KiK-net stations(solid square) and the assumed fault plane (rectangle).
The star shows the epicenter determined by JMA.
(Right) Band-pass filtered velocity seismograms of
the horizontal EW component. Pass-bands are
0.01–0.05 Hz (100–20 s). The waveforms are pasted up
with the delay time from the origin time.

Fig. 2. Upper: Distributions of coseismic slip obtained
for the 2011 Tohoku Earthquake. The star indicatesthe rupture starting point. The rectangle represented
by the dashed line indicates 3 areas, Area 1, 2,
and 3 denoted in the text. Lower: Distributions ofpeak moment rate together with the slip rate function
at each subfault.

SHORT-PERIOD SOURCE MODEL
Locations of strong motion generation areas
Based on the aftershock distribution in the first 24 hours and the CMT solution by Japan
Meteorological Agency (JMA), we define the source fault as roughly 450 km long and 200 km widewith strike of 193 and dip 10. The hypocenter is at 38.1033 N, 142.86 E, and 23.7 km deep by JMA.
The locations of the SMGAs are constrained using the back-propagation method of Kurahashi and
Irikura (2010). The acceleration records at stations along a line from north to south are arranged withthe same time and amplitude scale in Fig. 3. In the aligned records several isolated wave-packets arefound arriving from different origins on the source fault. Such origins are considered to be the strong
motion generation areas (SGMAs).
We identified five wave-packets in the observed seismograms, which originate from five SMGAs on
the source fault. The onsets of the wave-packets are found to propagate with a certain velocity as
shown in Fig. 3. We can estimate the locations of the SMGAs based on the onset times of the

12wave-packets at many stations. The origin of each wave-packet, that is the starting point of each
SMGA, is theoretically determined on the source fault from the arrival times at more than threestations by the back-propagation method taking the coordinates (x, y, and z) and rupture velocity Vr asvariables and assuming unbounded media with constant S wave velocity Vs (Kurahashi and Irikura,2010). However, for the Tohoku earthquake, strong motion data exist only on the west side of thesource fault. Therefore, the initiation of each SMGA cannot be isolated at a point, but rather it isblurred along an area about 20 km in length due to the poor spatial coverage of the observation sites.
After estimating the approximate location of each SMGA by the back-propagation method, we
calculate ground motions from the SMGA assuming its area (length x width) and initiation point. Then
we obtain the final solutions for the area and initiation point by comparing the observed seismogramsof each wave-packet and the synthetic ones at many stations using a trial and error approach. The
fitting function is adopted to minimize the sum of residuals for acceleration envelopes and velocity
waveforms between the observed and synthetic ones.
Characterized source model and ground motion simulation
To calculate ground motions from each SMGA, the area of the SMGA is divided into equal-sizedsquare subfaults, the area of which is set to be the same as the small event area. The rise time andrupture velocity inside each SMGA are given to be Ws/4Vr ((Ws: width of the SMGA and Vr: rupture
velocity) following empirical relations by Kataoka et al. (2003). The average S wave velocity is given
to be 3.5 km/s from Ts-p time versus arrival time at observed stations. The rupture velocities outside of
the SMGAs are estimated by the back-propagation method. The total ground motion response at eachstation is calculated by summing the contributions from the SMGAs with the arrival times from theinitiation points of the SMGAs to the station.
The small events’ records used as empirical Green’s functions (EGFs) have to share thepropagation-path and site effects as well as the radiation characteristic from the source. Therefore, therecords from the small events (closed star marks in Fig. 4) occurring near the SMGAs are adopted as
the EGFs. The records from Event A are used as the EGFs for SMGA 1, SMGA 2, and SMGA 3
because those SMGAs are located close to each other on the preliminary analysis. Those from Event B
and Event C are used for SMGA 4 and SMGA 5 offshore Fukushima prefecture and offshore Ibaragi
prefecture, respectively. The source information of the mainshock and the small events for the EGFs islisted in Table 1.
Table 1. The source parameters of the mainshock and small events A, B, and C.

The characterized source model consisting of five SMGAs is obtained by minimizing the fitting
function as described in the previous section. The area and initiation of each SMGA are shown in Fig.
4 by a rectangle and closed circle mark, respectively. The source parameters of the final source model,such as the length, width, seismic moment, stress drop and delay time from the origin time of each
SMGA are listed in Table 2. The observed and synthetic ground motions at IWTH27 and MYGH04,
from the final source model are shown in Fig. 5. The agreement between the observed and synthetic
ones is satisfactory at almost all of stations, although the comparison was shown at only two stations.
SMGA 1 is located in the source region of Southern Sanriku-oki west of the hypocenter and
SMGA 2 in that of the Middle Sanriku-oki north of the hypocenter. SMGA3 is located in the source

13

region of the Miyagi-oki, SMGA 4 is located in that of Fukushima-oki and SMGA 5 is located in thatof Ibaraki-oki. SMGA 1, SMGA 2, SMGA 3, SMGA 4, and SMGA 5 initiated to rupture 15.6 sec, 66.4
sec, 68.4 sec, 109.7 sec, and 118.2 sec after the rupture originated at the hypocenter. The probabilitiesof earthquake occurrence in these source regions including the five SMGAs have been estimated by
the ERC at less than 7 % to 99 % with magnitude about 6.9 to 7.5, separately.

Fig.3. Left: Map showing the location of observed stations. Right: Acceleration seismograms at stations
along a line from north to south. The colored thin solid lines indicate the travel times of S waves
generated from five strong-motion-generation-areas. Red, sky-blue, blue, green and pink are for the S
waves propagating from SMGA 1, SMGA 2, SMGA 3, SMGA 4 and SMGA 5 to the stations,
respectively.

Fig.4. Source model consisting of five SMGAs.
The five SMGAs are superposed on the
distribution of peak moment-rate inverted using
strong motions data by Yoshida et.al. (2011). The
initiation point at each SMGA is roughly
estimated by the back-propagating method. The
area, stress drop and initiation point of each
SMGA are estimated from the forward modelingcomparing the observed and synthetics ones using
the empirical Green’s function method. The open
star and closed stars show the epicenters of themainshock and small events A, B, and C,
respectively. The small rectangles and closed
circles inside them show the SMGAs and theirinitiation points. The closed red triangles indicate
the KiK-net stations used for analysis.

14

FEATURES OF STRONG GROUND MOTIONS

Fig. 5. Comparison of the observed (black lines) and synthetic (red lines) seismograms by the empiricalGreen’s function method at IWTH27 and MYGH04.The acceleration (upper) and velocity (lower) at eachstation are compared.

FEATURES OF STRONG GROUND MOTIONSThe horizontal components of peak ground velocity (PGV) and those of peak groundacceleration (PGA) observed during this earthquake were compared with empiricalattenuation relationships (i.e. strong motion prediction equation) for Mw 7 to Mw 9 by Si andMidorikawa (1999) as shown in Fig. 6. Very limited data of PGV and PGA for earthquakes
with more than Mw 8 and no data for Mw 9 earthquake were used to make the empiricalequation by them. Therefore, the attenuation relationship for Mw 9 is just extrapolation of
the equation by Si and Midorikawa (1999).
We found that the attenuation-distance relationship of the peak ground velocity (PGV)
from this earthquake was virtually equivalent to the empirical one from an earthquake of Mw
8.0. On the other hand, peak ground acceleration (PGA) was also virtually equivalent to theempirical one from Mw 8.0 in the distance over 100 km, but clearly larger than that from Mw
8.0 near the source fault.
High Accelerations were mainly caused by two different mechanisms.
A: Ground motions with extremely high acceleration more than 1000 gals were recorded at
soft grounds formed by the Quaternary deposits. Extremely high accelerations weregenerated by large amplifications due to surface geology with decreased S wave velocities(nonlinear soil behavior).

15

B: Ground motions with relatively high acceleration caused by source characteristics, such as
rupture directivity effects, heterogeneous slip velocity inside the strong motion generation
areas and so on.

Fig. 6. Comparison of Observed Data of PGA and PGV from the 2011 Tohoku earthquake (Mw 9.0) withand the empirical attenuation-distance relationships for Mw 7.0 to Mw 9.0 by Si and Midorikawa (1999).
Right is for PGA and left is for PGV.

On a map in the left of Fig. 7, stations are shown where high accelerations caused by A
were recorded. The observed accelerations there seem to be remarkably deviated from theattenuation-distance curves as shown in the right figure of Fig. 7. We found those stations
were put on soft grounds formed by the Quaternary deposits grounds. Examples ofacceleration waveforms at those stations are shown in Figure 8. Their waveforms present
clear cyclic mobility.
We examined site responses at the K-NET Tsukidate (MYG004) where the largest PGA,
2933 gals, was recorded. H/V spectral ratio during the mainshock is compared with that for
weak motions as shown in Fig. 9. The site response for weak motions is taken as average ofthe H/V during small earthquakes. The predominant period of the site responses at Tsukidate
during the mainshock is clearly shifting to longer than that during weak motions, showing
reduction of S wave velocity in near-surface layers. However, there was very little damage
during this earthquake in the vicinity of the Tsukidate station. It is caused by the
predominant period of ground shaking shorter than 0.5 second, although accelerations wereso high.
We found that spectral characteristics of ground motions have predominant periods
shorter than 0.5 at most of places where high accelerations were recorded. It might be
explained by predominant periods shorter than 1 sec that there were relatively small damageof houses and buildings due to ground shakings.
Ground motions with relatively high acceleration caused by source characteristics, i.e. B,
are simulated assuming a source model with heterogeneous slip velocity inside a SMGA. Thismodel is similar to super-asperity model proposed by Matsushima and Kawase (2006) andfrequency-dependent asperity model by Miyake and Koketsu (2010). Ground motions at
ONG128 (Onagawa NPP), one of nearest station to the source fault, were simulated, using the
new model with heterogeneous slip velocity inside SMGA3. We can see that simulated
acceleration and velocity waveforms by the new model agree well with observed waveforms,
compared with simulated ones by conventional model as shown in Fig. 10.

16

Fig. 7. Right: Stations where more than 1,000 gals recorded are shown. Left: High acceleration observations
encircled by red mark are remarkably deviated from the attenuation-distance curve. The stations shown bysmall red solid circle correspond to high acceleration observations encircled by red mark in the left figure.

Fig. 8. Closeup of acceleration
waveforms for ground motion
records with more than 1000 gals
at stations in the left figure of
Fig.7. Most of waveforms show
remarkable cycle mobility.

17

KURIHARA
H/V Spectral Ratio

10

1

Mainshock
Small earthquake

Fig. 9. Site responses at the K-NET
Tsukidate (MYG004) where the largest
PGA, 2933 gals. H/V spectral ratios during
the mainshock (red) is compared with thatfor weak motions (green). The site
response for weak motions is taken as
average of the H/V during small
earthquakes.

100

0.1

Period[s]1Fig. 10. Ground motions at ONG128 (Onagawa NPP), one of nearest station to the source fault, were
simulated, using the new model with heterogeneous slip velocity inside SMGA3.

CONCLUSIONSThe source model inverted from long period ground motion data (20 to 200 sec) by Yoshida et al.
(2012) shows that a large asperity (about 300 km × 100 km) located on the shallower part of thefault was estimated, and maximum slip is about 47 m. This source model with a shallow large asperity
is consistent with the tsunami source model (Fujii and Satake, 2011).
We find that acceleration as well as velocity motions during the 11 March 2011 off Tohoku, Japan
earthquake (Mw 9.0) are well simulated using a characterized source model consisting of five SMGAs.
SMGA 1 is located in the source region of Southern Sanriku-oki west of the hypocenter and SMGA 2
in that of the Middle Sanriku-oki north of the hypocenter. SMGA3 is located in the source region of
the Miyagi-oki, SMGA 4 is located in that of Fukushima-oki and SMGA 5 is located in that of
Ibaraki-oki. SMGA 1, SMGA 2, SMGA 3, SMGA 4, and SMGA 5 initiated to rupture 15.6 sec, 66.4
sec, 68.4 sec, 109.7 sec, and 118.2 sec after the rupture originated at the hypocenter. The probabilitiesof earthquake occurrence in these source regions including the five SMGAs have been estimated by18

the ERC at less than 7 % to 99 % with magnitude about 6.9 to 7.5, separately.
The locations of the SMGAs coincide with large peak moment-rate areas inverted from long
period ground motion data (20 – 200 sec) by Yoshida et al. (2011), particularly along the down-dip
edge of the source fault.
Attenuation-distance relationship of peak ground velocity (PGV) from this earthquake wasvirtually equivalent to the empirical one from Mw 8.0 determined by Si and Modorikawa (1999). On
the other hand, peak ground acceleration (PGA) was also virtually equivalent to the empirical one
from Mw 8.0 in the distance over 100 km, but clearly larger than that from Mw 8.0 near the source
fault.
Ground motions with extremely high-accelerations cannot be simulated near the source fault using
the source model mentioned above. Then, two different mechanisms for Group A and B are examinedfor explaining such high accelerations. A: Ground motions with extremely high acceleration more than
1000 gals were recorded at soft grounds formed by the Quaternary deposits. Extremely highaccelerations were generated by large amplifications due to surface geology with decreased S wave
velocities (nonlinear soil behavior). B: Ground motions with relatively high acceleration weregenerated by heterogeneous slip velocity inside the strong motion generation areas. That is, stressparameters are not uniform inside the strong motion generation areas.
ACKNOWLEDGMENTS
We used the wave data provided by the KiK-net of National Research Institute for Earth Science andDisaster Prevention (NIED). We also used the hypocentral information from Japan Meteorological
Agency, and the moment tensor solution from the F-net (NIED). The long-period source model wasreferred from Yoshida, Miyakoshi, and Irikura (2011).
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