Journal of Natural Disaster Science, Volume 34, Number 1, 2012, pp59-78

Relationship between Building Damage Ratios and Ground Motion
Characteristics during the 2011 Tohoku Earthquake
Hao WU*
Kazuaki MASAKI**
Kojiro IRIKURA***
Koichiro SAGUCHI****
Susumu KURAHASHI***Xin WANG****Graduate School of Engineering, Aichi Institute of Technology**Department of Urban Environment, Aichi Institute of Technology***Disaster Prevention Research Center, Aichi Institute of Technology****Department of Environmental Science and Technology,
Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology(Received May 1, 2012 Accepted October 1, 2012)
ABSTRACT
Fragility curves, the relationships between three kinds of building damage ratios, i.e.,
total collapse ratio (TCR), collapse ratio (CR) and damage ratio (DR), as well as groundmotion characteristics, i.e., peak ground acceleration (PGA), peak ground velocity (PGV),
Japan Meteorological Agency instrumental seismic intensity (IJMA) and spectral intensity(SI), were studied for the 2011 Tohoku Earthquake. It was found that the DR was related
better to ground motion characteristics than the TCR and CR during this earthquake, andthe correlation between the DR and any one of the PGV, IJMA or SI indices was almost
the same. The DR during the 2011 Tohoku Earthquake reached almost the same level asthat during the Kobe Earthquake for the same level of ground motions. There were some
districts where the DRs did not always correspond to reasonable levels of ground motion
characteristics. One reason for this was considered to be the representativeness of theground motions over each district. Thus, one method of estimating ground motions atdamaged sites was proposed by using the underground velocity structures identified fromthe H/V spectral ratios of microtremors, after we confirmed the consistency of the H/
V spectral ratios between earthquakes and microtremors. It is expected to be used for theconstruction of fragility curves with greater accuracy.
Keyword: building damage ratio, ground motion characteristics, underground velocity
structure, H/V spectral ratio.

1. INTRODUCTION
The 2011 Tohoku Earthquake on March, 11,2011 of Mw9.0 was one of the most disastrous mega-thrust earthquakes in the history of Japan. The rupture
was initiated approximately 100 km offshore of Miyagi Prefecture and extended about 450 km in length59

H. WU, K. MASAKI, K. IRIKURA, K. SAGUCHI, S. KURAHASHI, X. WANG

structures beneath the damaged sites and the observed
ground motions at strong-motion stations near thesesites. Fragility curves with greater accuracy are expected to be constructed with the building damage
ratios and estimated ground motion characteristics atdamaged sites within each stricken district, as long as
the ground motions can be estimated correctly.

and about 200 km in width. During this earthquake,tsunami caused tremendous damage to infrastructures, lifelines, and buildings in the districts along thecoastline of the East Tohoku and East Kanto region,and ground shaking also caused significant damage tobuildings in the inland districts. According to the Fireand Disaster Management Agency (FDMA, 2012),
more than one million buildings were damaged, including those totally collapsed, half-collapsed, andpartially damaged due to ground shaking and tsunami
as of March 13, 2012. Previous studies (e.g., Miyakoshi et al. 1997; Sakai et al. 2001; Midorikawa
et al. 2011; Wang et al. 2011) on the relationshipbetween building damage ratios and ground motion
characteristics at stricken districts have been carriedout for previous destructive earthquakes. Estimationof ground motions in stricken districts has also been
extensively conducted. Take the Kobe Earthquake,for example. Midorikawa and Fujimoto (1996) studied the distribution of the peak ground velocities(PGVs) in and around Kobe City from the overturning of tombstones. Hayashi et al. (1997) evaluated the
PGVs from the damage ratios of low-rise buildings.
Yamaguchi and Yamazaki (1999) constructed fragility curves based on the relationship between building
damage ratios and ground motion characteristics andthen estimated the distribution of ground motions atdamaged sites with their fragility curves. However,concerning the 2011 Tohoku Earthquake, the relationship between the building damage ratios and groundmotion characteristics has not yet been clarified, andestimation of ground motions especially at damagedsites has not been sufficiently investigated.
In this paper, first, fragility curves during thisearthquake are constructed based on the relationships
between three kinds of building damage ratios, i.e.,
total collapse ratio (TCR), collapse ratio (CR), anddamage ratio (DR), as well as ground motion characteristics, i.e., peak ground acceleration (PGA), peakground velocity (PGV), Japan Meteorological Agency
instrumental seismic intensity (I JMA) and spectral
intensity (SI) in the stricken districts. Next, the relationship between the building damage ratios andground motion characteristics during the 2011 Tohoku
Earthquake is compared with that during the Kobe
Earthquake. Then, we propose a method of estimating ground motions at damaged sites during the 2011
Tohoku Earthquake using the underground velocity

2. DATA SOURCE
2.1 Damage Data
During this earthquake, buildings in coastal
districts were mainly damaged by tsunami over the
Tohoku and Kanto areas. At the same time, in theinland districts, numerous buildings were damagedby ground shaking. The building damage statistics,
i.e., the numbers of totally collapsed, half-collapsed,and partially damaged buildings in the stricken districts, are obtained from the FDMA (2012). The total
numbers of buildings in stricken districts are obtained
from the Statistics Bureau and Director-General for
Policy Planning of Japan (STAT, 2008). The administrative unit of the stricken districts is city, town, or
village (shi, cho, or mura in Japanese). According to
the FDMA, total collapse denotes buildings whosebasic functions have been lost for the residents, i.e.,the buildings are totally collapsed, washed away,
or buried, or the damage to the buildings cannot berecovered through repair. Half collapse denotes buildings whose basic functions for residents have been
partly lost for the residents, i.e., the buildings can berecovered through repair. Partial damage means thatthe damage to buildings is not heavier than total andhalf collapse, but that the buildings need repair. Slightdamage such as cracks on several panes of glass is notclassified as partial damage. On the other hand, because our objective is to elucidate damage by groundshaking, districts damaged by tsunami were excluded
from the inundation maps provided by the Geospatial
Information Authority of Japan (GSI, 2011). At thesame time, according to a liquefaction survey reportfrom the Ministry of Land, Infrastructure, Transport
and Tourism and the Japanese Geotechnical Society(2011), districts such as Urayasu City, Chiba City and
Katori City are significantly affected by liquefaction.
They are also excluded. On the other hand, somestricken districts in which strong-motion stations
have not been installed are included as long as they60

RELATIONSHIP BETWEEN BUILDING DAMAGE RATIOS AND GROUND MOTION CHARACTERISTICS DURING THE 2011 TOHOKU EARTHQUAKE

satisfy two conditions (a) and (b): (a) the geology ofthe stricken districts to be included is similar to thatof adjacent stricken districts in which strong-motion
stations have been installed; (b) the distance between
the building-concentrated street in the district to be
included and the strong-motion station in the adjacentstricken district is less than 10 km.
Fig. 1 shows all the stricken districts in the six
prefectures along the Pacific east coast. The yellow districts are the stricken ones in which a coupleof strong-motion stations are installed. The green
districts are those included under the above two conditions. The gray districts are excluded as they aremainly damaged by tsunami. The red districts are also
excluded as they are significantly affected by liquefaction. The shadowed districts with slashes are thoselacking damage statistics.

2.2 Strong-motion Data
The strong-motion records at the K-NET and
KiK-net stations were open to the public soon after
this earthquake. In this study, the observation records
in 72 K-NET stations and 25 KiK-net stations areused to analyze ground motion characteristics. The
locations of the K-NET or KiK-net stations in thestricken districts are shown in Fig. 1. The solid triangles represent K-NET stations and the solid circles
represent KiK-net stations. For those districts inwhich there is more than one strong-motion station,
the average observed ground motion characteristics
at all of the strong-motion stations are taken as theground motion characteristics for the entire district.
In addition, the ground motion record at the Tsukidate
station in Kurihara City is not included in the following analysis, because the partial uplifting of the(a) Iwate Prefecture(b) Miyagi Prefecture(c) Tochigi Prefecture(d) Fukushima Prefecture(e) Chiba Prefecture(f) Ibaraki Prefecture

Fig. 1 Stricken districts in the six prefectures studied in this paper. The districts colored yellow are our target
areas; the gray districts mainly damaged by tsunami are excluded; the red districts affected by liquefaction are also excluded; the green districts are included as they are close to a strong-motion station; the blue
areas are lakes; the shadowed districts with slashes are those lacking damage statistics; the marks ▲ and● denote the positions of K-NET stations and KiK-net stations, respectively. This figure is plotted by thesoftware, KenMap (2011).
61

H. WU, K. MASAKI, K. IRIKURA, K. SAGUCHI, S. KURAHASHI, X. WANG

instrumental foundation might cause extremely large
motion, just as noted by Motosaka et al. (2011). On
the other hand, those stations that are installed onrock and far from densely building-concentrated sites
are also excluded regarding the representativeness ofground motions.
3. RELATIONSHIP BETWEEN BUILDINGDAMAGE RATIOS AND GROUND MOTIONCHARACTERISTICS
3.

3.1 DefinitionsBETWEEN
of Three Kinds
of Building DAMAGE
RELATIONSHIPBUILDING

Damage Ratios
CHARACTERISTICS(1)

CR= (A+B)/Dൈ100%,(2)

DR= (A+B+C)/Dൈ100%,

(3)

AND

GROUNDMOTION

Fig. 2 Relationship between the number of buildings
and the number of households.

The building damage ratios are composed of thefollowing three indicators: total collapse ratio (TCR),
3.1 Definitions of Three Kinds of Building Damage Ratios
collapse ratio (CR), and damage ratio (DR). Each ofthem is defined as the ratio of damaged buildings tototal buildings in stricken districts. Detailed definitions are given as follows.
TCR= A/Dൈ100%,RATIOS

10,000.
3.2 Representativeness of Ground Motions in
Stricken Districts
As the administrative unit of a stricken district iscity, town, or village (shi, cho, or mura in Japanese),it might be reasonable to use the median ground motions in the entire district rather than the ground motions observed at the strong-motion stations. In Japan,
the amplification factor for peak ground velocity(PGV) at a given site can be obtained from the J-SHIS
website operated by the National Research Institutefor Earth Science and Disaster Prevention (NIED,2012). This suggests that the peak ground velocity on
engineering bedrock, PGVb, where the S-wave velocity is 400 m/s~600 m/s (NIED, 2009), can be obtained
from the peak ground velocity on the ground surface,
PGVs, by dividing this factor at a given site. For an
administrative unit, PGVb can be assumed to be thesame. Then, the median PGV on the ground surface
for the entire district can be calculated mechanicallyfrom the PGVb by multiplying the median amplification factor, as is expressed in the following equation.

Here, A, B, and C are the numbers of totally collapsed, half-collapsed, and partially damaged buildings in a district, respectively. D is the total numberof buildings regardless of damage and non-damage ina district. In this paper, the damage data are obtained
from the FDMA which publishes the damage data by
the number of buildings. Therefore, denominator-D in
Eq. (1) to Eq. (3) should also be the total number ofbuildings that can be obtained from the Statistics Bureau and Director-General for Policy Planning of Japan. However, the total numbers of buildings in somesmall districts cannot be obtained from the Statistics
Bureau, but the total numbers of households in such
districts can be easily found from the homepages of
local governments and are taken as the total numbersof buildings. Fig. 2 shows the relationship between
the total numbers of buildings and the total numbers
PGVo
of households in the stricken districts where both sets
PGVm = PGVb × AVRm =× AVRm , (4)AVRoof data are available. It can be seen that the total number of households has a good correlation with the total
Here, AVR is the amplification factor, the subnumber of buildings for each district, and the former
script“m” is the median value for the entire district,
3.2 Representativeness of Ground Motions in Stricken Districts
is almost the same as the latter. This indicates that theand the subscript “o” is the observed value obtained
total numbers of buildings can be replaced with thefrom strong-motion data. Take Date City for example.
total numbers of households in those small districts
Fig. 3 shows the distribution of amplification factors
in which the total number of households is fewer thanin Date City, Fukushima Prefecture. It can be seen
62

RELATIONSHIP BETWEEN BUILDING DAMAGE RATIOS AND GROUND MOTION CHARACTERISTICS DURING THE 2011 TOHOKU EARTHQUAKE

ARV䣈䣍䣕䢲䢲䢴

0.000000
0.000001 - 0.500000
0.500001 - 0.600000
Ÿ

0.600001 - 0.800000
0.800001 - 1.000000
1.000001 - 1.200000
1.200001 - 1.400000

Ÿ

1.400001 - 1.600000
1.600001 - 2.000000
2.000001 - 2.500000
Ÿ

2.500001 - 3.800000

Fig. 3 Distribution of amplification factors in Date City. The triangle denotes the strong-motion station (FKS002).
The median amplification factor of Date City is 0.669, while the amplification factor at FKS002 is 1.997.

that there are warm-colored areas with large amplification factors in the northwest part of Date City. The
strong-motion station, FKS002, indicated by a solid
triangle, is situated just in this area. This suggests thatthe representative ground motions in Date City might
be overestimated if the observed PGV at FKS002
is used. By finding the medianfactor,3.3amplification
Fragility Curves
AVRm, of this city and the amplification factor, AVRo,at FKS002, the median PGV can be obtained fromthe observed PGV at FKS002 by multiplying the ratioof AVRm to AVRo. Here, AVRm/AVRo is 0.669/1.997.
That is, the representative PGV in Date City is about
one-third of the observed PGV at FKS002. All theground motions in the stricken districts should be revised as the median ground motions in the same way.
However, it is advisable to use the median amplification factor only at sites where buildings are distributed. Unfortunately, this seems impossible as the exact
distribution of buildings within a district is unknown.
Generally, many buildings are concentrated in basins,or the warm-colored areas, with high amplification,and there are few buildings in hills, or the cold colored areas, with low amplification. Therefore, therepresentative ground motions for an entire district
might be underestimated if they are revised in the way
mentioned above. Eventually, the observed groundmotions are assumed to be representative for an entire
stricken district, as long as the strong-motion stations
are not located on the rock. In Chapter 4, the effectof velocity structures on ground motions will be dis-cussed in detail so as to understand ground motions atdamaged sites.
3.3 Fragility Curves
Fragility curves are constructed to examine therelationships between three kinds of building damage
ratios as well as the ground motion characteristics,
which are peak ground acceleration (PGA), peakground velocity (PGV), Japan Meteorological Agency
instrumental seismic intensity (IJMA), and spectral intensity (SI). The cumulative probability of building
damage, P(x), is assumed to be the normal cumulative
distribution function.

P ( x ) = Φ (( x − λ ) / ζ 

(5)Here, Фis the standard normal cumulative distribution function. x is a variable with respect to groundmotion indices, such as I JMA, natural logarithm of
PGA, natural logarithm of PGV, or natural logarithmof SI. λ and ζ are the mean and standard deviation ofx, and are determined by geometric mean regression
with a normal probability plot. SI is defined as theintegration of the velocity response spectrum with adamping coefficient of 0.20 averaged over a period of
0.1 s~2.5 s, as is shown in Eq. (6). IJMA is calculated
based on the manual issued by the Japan Meteorological Agency (1996). In addition, PGA, PGV, and SI
are adopted to be the larger value between the NS and
EW components.

63

H. WU, K. MASAKI, K. IRIKURA, K. SAGUCHI, S. KURAHASHI, X. WANG

SI =

2.5
1
SV (T )dT ,³
2.5 − 0.1 0.1

tween the DR and the PGA or PGV. From the valuesof ζ, it can be seen that the variability between the DR
and PGA is the largest. Combined with the above twocoefficients, it can be seen that the correlation of the
DR with the ground motion indices is approximately
the same as one another, except with the PGA. However, variability generally arises between the DR andeach of the four ground motion indices. One of thereasons for this is that the damage data are not classified by the building construction date and structural
type in each stricken district. The different constitutive proportions of the building construction date or
structural type in each stricken district can contributeto this variability. Furthermore, the damage data insome districts may include the numbers of damagedbuildings not directly caused by ground shaking, suchas landslide. However, the variability caused by thesefactors cannot be resolved until detailed damage data
are obtained. Another reason may be that the groundmotions at the strong-motion station are not appropriate for representing the ground motions for an entire(6)Here, SV is the velocity response spectrum with
damping coefficient h=0.20.
Fig. 4 shows the fragility curves between threekinds of building damage ratios, i.e., TCR, CR, andDR, as well as the ground motion indices, i.e., PGA,
PGV, IJMA, and SI. The coefficients of λ and ζ, andthe determination coefficient R2 used to assess the
goodness of fit, are given in Table 1. It can be seenthat standard deviationζbetween the DR and any oneof the ground motion indices is the smallest, and that
corresponding determination coefficient R2 is the largest among the three kinds of building damage ratios.
This suggests that the correlation of ground motion
indices with the DR is the best. Therefore, the relationship between the DR and the ground motion indices should be emphasized in the following analysis.
From the values of R2, it is implied that the correlation
between the DR and IJMA or SI is better than that be-

Fig. 4 Fragility curves of the three kinds of building damage ratios versus PGA, PGV, IJMA and SI. The green
marks correspond to three kinds of building damage ratios in Yabuki Town, which will be discussed in
Chapter 4.
64

RELATIONSHIP BETWEEN BUILDING DAMAGE RATIOS AND GROUND MOTION CHARACTERISTICS DURING THE 2011 TOHOKU EARTHQUAKE

Rank
TCR
CR
DR

PGA (gal)λζ
R2
8.680 0.843 0.146
7.718 0.686 0.269
6.738 0.638 0.478

Table 1 Coefficients of the fragility curves.
PGV (cm/s)
IJMA
2
λ
ζ
R
λ
ζ
R2
5.613 0.674 0.352 7.499 0.651 0.281
4.673 0.465 0.359 6.665 0.490 0.381
4.009 0.432 0.420 5.971 0.464 0.543

stricken district. For example, if the strong-motion
station is far away from the damaged sites, the groundmotions for the entire district might be underestimated. The problem can be solved by the proposition
introduced in Chapter 4. Additionally, the variability
between the DR and PGA is larger than that between
the DR and any of other three ground motion indices,which agrees with the conclusion of Midorikawa etal. (2011). This can be attributed to the sensitivityof PGA to the short-period characteristics of groundmotions. Fig. 5 shows the damage data categorized
by predominant period determined from the velocity
response spectra. It can be seen that damage data ofa short period of less than 0.4 s are mostly distributed beneath the fragility curve, i.e., large PGA witha short period of less than 0.4 s will not cause muchdamage to buildings. In contrast, the PGV seems to beinsensitive to short periods of less than 0.4 s. Besides,
both the PGA and PGV are not sensitive to longer periods of over 2.0 s which will not cause much damage
to buildings, either. This suggests that PGA is not agood ground motion index for constructing a fragility
curve.

SI (cm/s)λζ
R2
5.869 0.728 0.292
4.901 0.529 0.391
4.153 0.502 0.509

3.4 Comparison of the 2011 Tohoku
Earthquake with the Kobe Earthquake
Fig. 6 compares the 2011 Tohoku Earthquakewith the Kobe Earthquake regarding four relationships: between DR and PGA, between DR and PGV,
between DR and IJMA, and between DR and SI. It canbe seen that the DR in the 2011 Tohoku Earthquake
reaches almost the same level as that in the Kobe
Earthquake in terms of IJMA, PGA ≦ 800 gal, PGV ≦100 cm/s, and SI ≦ 100 cm/s. Fig. 7 compares the2011 Tohoku Earthquake with the Kobe Earthquake
regarding the relationships between TCR and PGA,
and between TCR and PGV. It can be seen that theTCRs for PGA ≦ 800 gal and PGV ≦ 100 cm/s during the 2011 Tohoku Earthquake are smaller thanthose during the Kobe Earthquake. This can be attributed to the different units used for the stricken
districts. That is, the unit of stricken districts is “street”
for the Kobe Earthquake, while the unit of stricken
districts is “city,” “town,” or “village,” which areunits much larger than “street,” for the 2011 Earthquake. As the number of totally collapsed buildings
are very limited, the TCR calculated in a large district
is naturally smaller than that calculated in a small district. It can also be seen that the TCRs for PGA>800
gal are close to zero. This might be caused by theFig. 5 Classification of the damage data in the stricken districts by the predominant periods of velocity response
spectra.
65

H. WU, K. MASAKI, K. IRIKURA, K. SAGUCHI, S. KURAHASHI, X. WANG

Fig. 6 Comparison of damage data for DR between the Tohoku Earthquake and Kobe Earthquake. The damage
data in the 17 stricken districts in the Kobe Earthquake are obtained from the paper of Yamaguchi and
Yamazaki (1999).

Fig. 7 Comparison of damage data for CR between the 2011 Tohoku Earthquake and Kobe Earthquake.

four levels, i.e., 0% ≦ DR<20%, 20% ≦ DR<40%,40% ≦ DR<60%, and 60% ≦ DR ≦ 80%. It can beseen that the equivalent predominant period of mostdamage data ranges from 0.2 s to 1.0 s. In particular,
the equivalent predominant period of the damage datafor 60% ≦ DR ≦ 80% is around 0.5 s, and the corresponding PGA ≧ 450 gal, as well as PGV ≧ 35 cm/

short-period characteristics of ground motions.
Fig. 8 shows the relationship between PGA,
PGV, and DR. PGA and PGV are the maximum valuesof vector summation in three components in this figure. The straight solid line is plotted according to thedifferent equivalent predominant period, Teq, which
is defined as Teq=2πPGV/PGA. DR is divided into
66

RELATIONSHIP BETWEEN BUILDING DAMAGE RATIOS AND GROUND MOTION CHARACTERISTICS DURING THE 2011 TOHOKU EARTHQUAKE

Fig. 8 Relationship between PGA, PGV and DR. The solid lines show the equivalent predominant periods(Teq=2πPGV/PGA; Teq=0.2s, 0.5s, 1.0s, 2.0s). The dotted lines are the thresholds of PGA and PGV for
60% ≦ DRs ≦ 80%. Note that PGA and PGV are the maximum values of vector summation in three components. The PGA and PGV in the stricken districts of Kobe Earthquake are obtained from the paper ofKawase (1998).

s. Fig. 8 also shows the stricken districts in the Kobe
Earthquake, i.e., JR-Takatori (DR=95.3%), JMA
Kobe (DR=71.0%), and Fukiai (DR=48.7%). It canbe seen that the equivalent predominant period during
the 2011 Earthquake is shorter than that during theKobe Earthquake. On the other hand, the largest PGA
among the stricken districts used in this paper during
the 2011 Tohoku Earthquake is larger than that during
the Kobe Earthquake, yet the largest PGV among thestricken districts used in this paper during the 2011
Tohoku Earthquake is smaller than that during theKobe Earthquake.

Town shown with the green marks in Fig. 4 is notvery high, but the DR is rather large. Muraibo et al.
(2011) conducted a building damage survey in Yabuki
Town and published the numbers of damaged buildings in the villages within Yabuki Town on November, 2011, as shown in Table 2. Obviously, the DR
at Ippongi Village where the strong-motion station
FKSH11 is installed is the smallest among all the villages in Yabuki Town. Therefore, the ground motions
at FKSH11 are not appropriate for representing the
ground motions for entire Yabuki Town. It is desirable to construct fragility curves based on a smaller
administrative unit, such as “street”. Therefore, it isimportant to find a way to estimate ground motions atsites where ground motion records during the mainshock were not obtained. In this section, a method of
estimating ground motions is proposed. To constructfragility curves with greater accuracy, the ground motions at damaged sites should be estimated based on
the information on velocity structures under the sites.

4. ESTIMATION OF GROUND MOTIONS ATDAMAGED SITES
From the fragility curves, we found there aresome sites where the level of ground motion characteristics does not correspond to the DRs, such as
Yabuki Town. The level of ground motions in Yabuki

Name
Tatesaza
OhmachiMotomachi
Nakamachi
Shimachi
Yamatouchi
Ippongi

Table 2 Numbers of damaged buildings in each village of Yabuki Town.
No
SlightMinor
Moderate
Heavy
Collapse Unknown
damagedamagedamagedamagedamage
22
16
12
0
4
0
0
40
38
20
3
3
0
1
101
73
27
16
14
2
9
100
142
58
56
40
4
17
96
86
17
6
6
3
1
21
15
16
4
14
1
0
37
32
1
0
0
0
0
67

DR
(%)
59.3
61.0
54.5
71.9
54.9
70.4
47.1

H. WU, K. MASAKI, K. IRIKURA, K. SAGUCHI, S. KURAHASHI, X. WANG

between the surface and the borehole sensors can beobtained either directly from the PS-logging data or
indirectly from the spectral ratios between the surface
and the borehole sensors. For other sites where there
4.1 Methodology for Estimating Groundare neither strong-motion data nor PS-logging data,
Motions at Damaged Sites
velocity structures can be identified from the microIn general, ground motion spectrum Oi(f) on thesurface at the ith site can be expressed as the producttremor H/V spectral ratio, such as conducted by AraiofsourcespectrumSi (f), path spectrum P i (f), and
4.1 Methodology for Estimating Ground Motions at Damaged Sites and Tokimatsu (2004). They estimated the S-wave
transfer function Gi(f), as is expressed in Eq.(7). Bevelocity structures by assuming that microtremors
cause input motion spectrum Bi(f) can be defined as
are dominantly composed of surface waves. On thethe product of source spectrum Si(f) and path specother hand, Sánchez-Sesma et al. (2011) noted that
4.1 Methodology
forPEstimating
GroundMotions
at Damaged
motionspectrumOi(f) is Sites
also
trum
the microtremor H/V spectral ratio can be expressedi(f), the ground
expressed by Eq.(8).
as the square root of the ratio of the corresponding
imaginary parts of Green’s tensor components in three(7)
Oi(f)=Si(f)͌Pi(f)͌Gi(f),dimensions by assuming that the seismic field of mi(8)Oi(f)=Bi(f)͌Gi(f),crotremors is diffusive. They succeeded in interpret4.1 Methodology for Estimating Ground Motions at Damaged Sites
Transfer function Gi(f) is defined as the surface
ing the microtremor H/V spectral ratio recorded at a
response to input motion from a common basement.
site close to Mexico City with this theory. Kawase etHere, the common basement suggests that the velocal. (2011) applied this theory to the analysis of earthity structures under the basement are almost the same
quake ground motions and found that the imaginary
at the sites. Following Eq. (8), the input motion specpart of Green’s function for plane waves at the freetrum can be calculated from the ground motion specsurface is proportional to the square of the absolute
trum divided by the transfer function, as is expressedvalue of the corresponding transfer function. Theyin Eq. (9).
further ,noted that the H/V spectral ratio of earthquake
ground motions can be theoretically calculated as(9)Bi(f)=Oi(f)Gi(f),the amplitude ratio between transfer functions for SSupposing that the strong-motion station (i=0)
wave and P-wave based on diffuse-field theory, both,and the surrounding damaged site (i=1) are not far
calculated
at the strong-motion station with a coeffifrom each other compared with the distance between
cient depending on the bedrock. They also suggested
the site and the source, e.g., less than 10 km, the inputthat the earthquake H/V spectral ratio can be used tomotion can be assumed to be the same, i.e., B0(f)=identify the velocity structures. Following Kawase’s
B1(f), as long as a common basement exists. Then,viewpoint, we attempt to examine whether the H/,
ground motion spectrum E1(f) at the damaged site canV spectral ratio of microtremors can also be used to
be expressed as a product of input motion spectrum
identify the velocity structures, after confirming theB0(f) at the strong-motion station and transfer funcconsistency of H/V spectral ratios between microtion G1(f) at the damaged site.
tremors and earthquake ground motions.
Before applying our method, the effectiveness(10)
E1(f)= B0(f)͌G1(f)= O0(f)G0(f)͌G1(f),of Kawase’s proposition is verified by the following
Because ground motion spectrum O0(f) is known
procedures.
at any strong-motion station, the ground motion spec(a) Identifying the S- and P-wave velocity structrum E1(f) at the damaged site close to the strong-motures between the surface and borehole sention station can be obtained if the transfer functions
sors from the spectral ratios of small earthboth at the strong-motion station and at the damaged
quakes (M ≦ 5.0; PGA<100 gal) at KiK-net
site are estimated.
stations.
As the transfer functions depend on the under(b) Confirming that the H/V spectral ratio ofground velocity structures, it is essential to obtain
earthquake ground motions is consistent withreliable S- and P-wave velocity structures. For athe theoretical H/V spectral ratio calculated
KiK-net station, the underground velocity structureswith identified velocity structures and velociAs a case study, the ground motions at Yamatouchi in
Yabuki Town are estimated.

68RELATIONSHIP BETWEEN BUILDING DAMAGE RATIOS AND GROUND MOTION CHARACTERISTICS DURING THE 2011 TOHOKU EARTHQUAKE

ty structures under a common basement. Thisin turn suggests that the underground velocity structures can be identified from the H/Vspectral ratio of earthquake ground motions,which agrees with Kawase’s proposition. At
the same time, the transfer function between
the surface and basement can be obtained atstrong-motion stations.
Then, the consistency of H/V spectral ratios between earthquake ground motions and microtremors
is examined at the strong-motion stations. If they arealmost identical to each other, the underground velocity structures at damaged sites close to strong-motion
stations can be identified from the H/V spectral ratiosof microtremors by assuming that the H/V spectral
ratios of microtremors would also be consistent withthose of earthquake ground motions at damaged sites.
After that, the transfer function at damaged sites
can be obtained with identified velocity structures andthe velocity structures under a common basement.
Finally, the ground motions can be estimated throughEq. (10) in the case of linear behavior. Nonlinear behavior of soil will be discussed later.

At FKSH11, the KiK-net station in Yabuki
Town, ground motions from nine small earthquakes
are selected for calculating the spectral ratios listed inTable 3. The S-wave parts with a duration of 20.48 s
measured from the onset time (the duration of all the
waveforms is 120 s) are analyzed. The initial velocity
structure model is obtained from the PS-logging dataof the National Research Institute for Earthquake Science and Disaster Prevention (NIED). Quality factor
Qs is taken as Q0*fn. Qp is assumed to be simply Qs/2
(Yoshida and Kobayashi, 2002). Initial Q0 is taken as
one-twentieth of the S-wave logging velocity. First,
the S-wave velocity structures including the S-wave
velocity, Q0, and exponent n in each layer are identified
with the simulated annealing algorithm (e.g., Ingber,
1989; Saguchi, et al., 2009). Then, the P-wave velocity in each layer is identified assuming that Qp=Qs/2.
After that, the velocity structures under a common
basement are assumed, as there is not sufficient information about them, but they are indispensable forinterpreting the H/V spectral ratio on the surface.
Table 4 lists the initial velocity structures, i.e.,
the PS-logging data, between the surface and theborehole sensors (−115.2 m) and the identified velocity structures, as well as the velocity structures
under a common basement at FKSH11. Fig. 9 shows
the observed spectral ratios between surface and borehole sensors for small earthquakes and the theoretical spectral ratios calculated with identified velocity
structures for horizontal components and those forvertical components, respectively. By matching theobserved horizontal and vertical spectral ratios withthe theoretical ratios, the optimum S- and P-wave velocity structures are obtained, respectively, as shownin Fig. 10. It can be seen from Fig. 9 (a) that the peakvalue at 0.7 s of the theoretical spectral ratio for the S-

4.2 Case study at a Damaged Site
4.2.1 Verification of Kawase’s proposition at
KiK-net stations
As there are two seismographs both on the surface and the bottom of the borehole at KiK-net stations, the underground velocity structures between
surface and borehole sensors can be identified fromthe observed spectral ratios between surface and borehole sensors. To avoid the nonlinear effect on groundmotions during a mainshock, small earthquakes
should be considered in the calculation of spectral ratios.

Table 3 Source information about small earthquakes used in the analysis for FKSH11.
Date
Origin time
Latitude (N) Longitude (E)Depth (km)M
PGA (gal)(yy/mm/dd)
11/10/26
2:08:52
36.96
141.1530
5.0
17.8
11/08/22
21:21:23
37.18
141.2231
4.1
12.1
11/05/17
0:53:33
37.38
141.3035
4.6
13.4
11/05/01
11:48:46
37.42
141.21
29
4.6
13.1
11/04/30
14:46:59
37.34
141.2933
4.5
9.5
11/04/18
0:47:2937.00
141.2829
4.8
15.6
11/04/11
13:51:45
37.47
141.3229
5.0
12.2
11/04/01
2:21:3636.96
141.2234
4.4
6.8
11/03/21
4:54:2037.30
141.20
30
4.7
11.2
69

H. WU, K. MASAKI, K. IRIKURA, K. SAGUCHI, S. KURAHASHI, X. WANG

Table 4 Initial and identified velocity structures at FKSH11.
Density (g/cm3)
Vp0 (m/s)* Vs0 (m/s)*
Vp (m/s)Vs (m/s) Thickness (m)
1.7
200
110
109
33
1
1.9
1600
250
1168
153
3
1.9
1600
250
1054
191
7.5
1.9
1600
250
1255
192
7.5
1.9
1600
250
1503
240
7.5
1.9
1600
250
1498
300
7.5
2.1
2200
1200
1777
847
11
2.1
2200
1200
2122
1059
11
2.0
1700
490
1500
851
15
2.0
1700
490
1532
882
15
2.2
1900
700
2410
1208
14.6
2.2
1900
700
2481
1260
14.6
2.3
3120
1800
100
2.4
4330
2500
100
2.5
5900
3400
∞
* The PS-logging data obtained from the NIED are used as the initial model.

102

Horizontal component

102

101

100

10-1
0.01

0.1

Period(s)

1

n
0.41
1
1
0.21
0.8
1
0.99
1
0.47
0.03
0.71
0.71
1
1
1

Vertical component
Spectral ratios of earthquakes
Spectral ratio for initial model
Spectral ratio for identified model

Specrtral ratio

Spectral ratio

Spectral ratios of earthquakes
Spectral ratio for initial model
Spectral ratio for identified model

Q0
6.3
22.4
22.5
4.0
10.24
22.48
35.62
42.0
5.0
19.0
47.0
47.0
50.0
50.0
50.0

101

100

10-1
0.01

10

(a) Spectral ratios in the horizontal component

0.1

Period(s)110(b) Spectral ratios in the vertical components

Fig. 9 Observed spectral ratios (gray) between surface and borehole sensors for small earthquakes and theoretical
spectral ratios calculated with the initial (blue) and identified (red) S- and P-wave velocity structures.
wave and the curve shape are similar to the observed
spectral ratios for small earthquakes in the horizontal
component. It can also be seen from Fig. 9 (b) thatthe theoretical spectral ratio for the P-wave is in good
agreement with the observed ratios in the verticalcomponent.
Fig. 11 shows four different H/V spectral ratios,
the observed ones for S-wave motions and coda motions, and the theoretical ones for S- and P-waves andRayleigh waves. It can be seen that the theoretical H/
V spectral ratio for S- and P-waves using the identified S- and P-wave velocity structures and the common basement velocity structures matches well withthe average H/V spectral ratios for the observed S-

wave motions and coda motions (duration of 20.48s) from small earthquakes. It can be seen that they fit
well with one another, especially for the peak value atabout 0.12 s and 0.70 s. This in turn suggests that theunderground velocity structures can be obtained fromthe H/V spectral ratio of small earthquakes, which
agrees with Kawase’s proposition. In addition, thepredominant periods of the ellipticity of the Rayleighwaves at about 0.12 s and 0.70 s are consistent withthose of the theoretical H/V spectral ratio for the Sand P-wave. This indicates that the velocity structures
between the surface and −115.2 m identified fromthe spectral ratios are valid and reliable.
Verification should be conducted at any one of70

RELATIONSHIP BETWEEN BUILDING DAMAGE RATIOS AND GROUND MOTION CHARACTERISTICS DURING THE 2011 TOHOKU EARTHQUAKE

Velocity(m/s)
0

0

1000

2000

10

3000

2

FKSH11
20

H/V Spectral Ratio
FKSH11101

Depth(m)

40

100
60

10-1
0.01

80

100

10

(a)H/V of S-wave motions(b)H/V of Coda motions(c)H/V of Microtremors(d)Theoretical H/V for S- and P-waves(e)Ellipticity of Rayleigh waves

115.2
Initial Vs
Initial Vp

0.1
1
Period(s)Identified Vs
Identified Vp

Fig. 10 Profiles of initial (broken line) and identified (solid line) velocity structures between
surface and borehole sensors (−115.2 m) at
FKSH11.

Fig. 11 Comparison of the following four ratios: average H/V spectral ratios of S-wave motions (a)and coda motions (b) for small earthquakes,
theoretical H/V spectral ratio (c) for S- and Pwaves calculated with the identified S- and Pwave velocity structures at FKSH11, and theellipticity of the Rayleigh waves (d).

the KiK-net stations in the same way. Fig. 12 gives
another example at IBRH16 in Hitachiomiya City,
Ibaraki Prefecture.

surface layers and the deeper layers. Fig. 14 shows
the velocity structures obtained from the PS-logging
data, NIED. It can be seen that the velocity contrast is
not very large, compared with the velocity structuresat FKSH11 or IBRH16. At MYG013, Sendai City,
neither the fundamental mode nor the amplitude of
the H/V spectral ratio of microtremors is consistent
with that of the H/V spectral ratio of earthquakes. The
irregular underground velocity structures are considered to be one of the reasons, except the small velocity contrast in the surface layers. If the consistency of
the H/V spectral ratios between earthquake groundmotions and microtremors cannot be confirmed, how
to apply the H/V spectral ratio of microtremors to theestimation of ground motions will be a subject of our
future study.

4.2.2 Consistency of H/V Spectral Ratios
between Earthquake Ground Motions
and Microtremors
Fig.13 shows a comparison of the observed H/
V spectral ratios between earthquake ground motions and microtremors. It can be seen that the H/
V spectral ratio of microtremors is highly consistent
with that of earthquake ground motions at FKSH11
of Yabuki Town and IBRH16 of Hitachiomiya City,
not only the spectral shape but also the amplitude. At
TCGH10 in Otahara City, it can be seen that the fundamental mode of H/V spectral ratios of microtremors
and earthquake ground motions is almost the same,but that the amplitude is different, i.e., the amplitudeof the H/V spectral ratio of microtremors is lower
than that of earthquake ground motions. This may
be caused by the small velocity contrast between the

4.2.3 Identification of velocity structures andestimation of ground motions at thedamaged site
Yamatouchi is one of the damaged sites in Ya71

H. WU, K. MASAKI, K. IRIKURA, K. SAGUCHI, S. KURAHASHI, X. WANG

Horizontal component

101

100
InitialObserved
Identified

10-1
0.01

0.1

1

Vertical component

102

101

Spectral ratio

Spectral Ratio

102

100

10-1
0.01

10

InitialObserved
Identified
0.1

1

10

Period(s)Period(s)Velocity(m/s)
0

H/V spectral ratio-IBRH16
S waveCoda
Microtremor
Theoretical
Ellipticity

101

1000 2000 3000 4000 5000 6000

100
200

Depth(m)

10

2

0

100

300
400
500

Initial Vs
Identified Vs
Initial Vp
Identified Vp

600
-1

10
0.01

0.1

Period(s)

1

10

700

Fig. 12 Identification of velocity structures at IBRH16, Hitachiomiya City, Ibaraki Prefecture. The theoretical H/
V ratio for S- and P-waves calculated with the identified velocity structures and the basement velocity
structures agrees well with the observed H/V spectral ratios of both microtremors and earthquake groundmotions. The consistency of the fundamental mode of the ellipticity of Rayleigh waves with those of theoretical H/V spectral ratios for S- and P-waves suggests that the identified velocity structures are valid.
buki Town. Fig. 15 is a snapshot trimmed from theSeamless Geological Map of Japan (2012). The distance between FKSH11 and Yamatouchi is about 3
km. The geologic time and rock type of the surface
geology at both sites are almost the same. As the H/
V spectral ratios of the microtremors and earthquake
ground motions are consistent with each other at
FKSH11, it is reasonable to assume that the consistency is invariable at Yamatouchi close to FKSH11
and that these two sites share a common basement.
Then, the underground velocity structures at Yamatouchi in Yabuki Town can be identified from the

H/V spectral ratio of microtremors. The method of
identifying the velocity structures at Yamatouchi isalmost the same as that at FKSH11, but the target isreplaced with the H/V spectral ratio of microtremors.
The initial model at Yamatouchi is assumed to be thesame as the identified one at FKSH11 except the firstlayer because the identified velocities of the first layer
at FKSH11 are too slow. The initial model of the firstlayer at Yamatouchi is assumed to be the PS-logging
data of FKSH11. Table 5 lists the initial and identified
S- and P-wave velocity structures and those underlain
by a common basement. The profile of the identified
72

RELATIONSHIP BETWEEN BUILDING DAMAGE RATIOS AND GROUND MOTION CHARACTERISTICS DURING THE 2011 TOHOKU EARTHQUAKE

H/V Spectral Ratio-FKSH11

102

102

S-wave motions
Coda motions
Microtremors

101

H/V spectral ratio-IBRH16

101

S waveCoda
Microtremor

100

100
10-1
0.01

102

0.1
1
Period(s)

10-1
0.01

10

10

H/V Spectral Ratio-MYG013
102

H/V spectral ratio-TCGH10
S waveCoda
Microtremor

101

101

100

100

10-1
0.01

10-1
0.01

0.1
1
Period(s)0.11Period(s)10

S-waveCoda
Microtrmor

0.1
1
Period(s)10Fig. 13 Comparison of H/V spectral ratios between earthquake ground motions and microtremors.

Vs(m/s)0Depth(m)10

0 200 400 600 8001000

MYG0132030

TCGH1040
50
60
Fig. 15 Snapshot trimmed from the Seamless Geological Map of Japan. The geologic time is Late
Pleistocene to Holocene, and the lithology ismarine and non-marine sediments at FKSH11.
The geologic time is Late Pleistocene, and thelithology is middle terrace at Yamatouchi.

Fig. 14 Profiles of S-wave velocities at TCGH10(black) and MYG013 (red) obtained from PSlogging data.

73

H. WU, K. MASAKI, K. IRIKURA, K. SAGUCHI, S. KURAHASHI, X. WANG

Table 5 Identified velocity structures at Yamatouchi.
Density (g/cm3)
Vp0 (m/s)* Vs0 (m/s)*
Vp (m/s)Vs (m/s) Thickness (m)
Q0
n
1.7
200*
110*
434
139
1
7.9
0.96
1.9
1168
153
1382
159
3
6.4
0.33
1.9
1054
191
820
211
7.5
9.9
0.15
1.9
1255
192
2038
150
7.5
6.7
0.07
1.9
1503
240
2417
221
7.5
6.8
0.52
1.9
1498
300
946
198
7.5
6.4
0.00
2.1
1777
847
2692
1485
11
74.5
0.96
2.1
2122
1059
1868
1007
11
51.0
0.70
2.0
1500
851
2484
654
15
8.7
0.13
2.0
1532
882
2317
549
15
9.1
0.18
2.2
2410
1208
2779
576
14.6
16.3
0.26
2.2
2481
1260
2721
1099
14.6
85.3
0.37
2.3
3120
1800
3120
1800
100
50.0
0.50
2.4
4330
2500
4330
2500
100
50.0
0.50
2.5
5900
3400
5900
3400
∞
50.0
0.50
* The initial model at Yamatouchi is assumed to be the same as the identified model of FKSH11 except the firstlayer (PS-logging data at FKSH11 are used)velocity structures between the surface to −115.2 m
is also shown in Fig. 16. Fig. 17 shows a comparison
between the H/V spectral ratio of microtremors andthe theoretical H/V spectral ratio for S- and P-wave
calculated with the underground velocity structures at
Yamatouchi. The good fitting between the observed

Velocity(m/s)
0

0

1000

2000

102

3000

H/V Spectral Ratio

Yamatouchi
20

Depth(m)40

60

Damaged site (Yamatouchi)

101

100

10-1
0.01

80

0.1

1

10

Period(s)H/V of microtremors
Theoretical H/V
Initial H/V
Ellipticity

100
115.2
Initial Vs
Initial Vp

Fig. 17 Comparison of the H/V spectral ratio of microtremors, the theoretical H/V spectral ratio
calculated with identified velocity structures,and velocity structures underlain by a common basement at Yamatouchi, the theoretical
H/V spectral ratio calculated with initial velocity structures, and the ellipticity of Rayleigh waves.

Identified Vs
Identified Vp

Fig. 16 Profiles of initial (broken line) and identified(solid line) velocity structures between thesurface and −115.2 m at Yamatouchi.

74

RELATIONSHIP BETWEEN BUILDING DAMAGE RATIOS AND GROUND MOTION CHARACTERISTICS DURING THE 2011 TOHOKU EARTHQUAKE

H/V spectral ratio and the theoretical H/V spectral
ratio, especially the peak value at about 0.90 s and thespectral shape around the predominant period, suggests that the identified velocity structures are reliable
at Yamatouchi. Fig. 17 also shows the ellipticity of theRayleigh waves. It can be found that the fundamental
mode of the ellipticity is highly consistent with thatof other H/V spectral ratios. This indicates that themethod of identifying velocity structures from the H/

V spectral ratio of microtremors is valid and reliable.
Based on the underground velocity structures at
FKSH11 and Yamatouchi, the transfer functions canbe obtained. Fig. 18 shows the transfer functions bothat FKSH11 and Yamatouchi. It can be seen that thetransfer function at FKSH11 is much larger than thatat Yamatouchi in the short-period range, i.e., less than
0.3 s, but it is smaller at about 1.0 s. Then, groundmotions at Yamatouchi are estimated from the transfer
functions at FKSH11 and Yamatouchi and the groundmotions at FKSH11. Fig. 19 compares the estimatedvelocity waveforms in three components at Yamatouchi with the observed velocity waveforms at FKSH11.
Table 6 compares the estimated ground motion indices of Yamatouchi with those of FKSH11. It can beseen that the ground motion indices at Yamatouchi arelarger than those at FKSH11, except the PGA, which
may be caused by the smaller transfer function in the
short-period range. Fig. 20 shows the pseudo-velocity
response spectra (pSv) at Yamatouchi and FKSH11. It
can be seen that Yamatouchi has a larger pSv of about
400 cm/s around the 1.0 s period than the pSv ofabout 200 cm/s at FKSH11. This can be explained by
the larger transfer function at about 1.0 s for Yamatouchi. The larger ground motion indices except PGA
and the larger pSv at Yamatouchi agree with the DR
as high as 70%. Therefore, the proposition of identifying the velocity structures from the H/V spectral
ratio of earthquake ground motions by Kawase et al.

Transfer functions

102

FKSH11
Yamatouchi

101
100
10-1
0.01

0.1
1
Period(s)10Fig. 18 Transfer functions between FKSH11(black)and Yamatouchi (red).

100
50
0
-50
-100
-150

0

NS
60cm/s

EW
62cm/sUD
17cm/s49cm/s51cm/s

18cm/s

300

600

900

1200

Time (s)Fig. 19 Velocity waveforms at Yamatouchi (top) and FKSH11 (bottom).

Yamatouchi
FKSH11

Table 6 Ground motion indices at Yamatouchi and FKSH11.
PGA (gal)
PGV (cm/s)
IJMA
440
62
6.0
492
51
5.8
75

SI (cm/s)
7761

H. WU, K. MASAKI, K. IRIKURA, K. SAGUCHI, S. KURAHASHI, X. WANG

(2011) is proved to be applicable to microtremors. It
can be applied to estimate the ground motions at damaged sites as long as the consistency of H/V spectral
ratios between microtremors and earthquake groundmotions is confirmed at strong-motion stations close
to damaged sites.

linear effect is not considered.
The objective of estimation of ground motions atdamaged sites is to reduce the variability of the current fragility curves and to construct fragility curves
with greater accuracy. In order to obtain fragility
curves with greater accuracy, damage data and thecorresponding estimated ground motions at damagedsites should be used. Unfortunately, the estimation of
the ground motions is only conducted at one damagedsite. More microtremor measurements and more estimation of the ground motions at damaged sites shouldbe the focus of our work in the near future.

5. DISCUSSION
Estimation of ground motions at damaged sites
was performed on the basis of a linear assumption
in this study, but nonlinear behavior was confirmed
at many K-NET and KiK-net stations during themainshock. Fig. 21 shows the H/V spectral ratios ofthe mainshock and small earthquakes at FKSH11 in
Yabuki Town. It can be seen that the peak of the H/
V spectral ratio shifts from about 0.12 s to 0.15 s during the mainshock, yet the peaks at 0.70 s and 1.0 s
are invariable. This suggests that the shallow surface
soil layers behave nonlinearly during the mainshock.
However, the period of the ground motions that relates with building damage is usually around 1.0 s.
Thus, the nonlinear behavior of surface soil will only
affect ground motions in the short-period range, while
this effect on ground motions might not be related tothe building damage. Therefore, the estimated groundmotions both at the basement of FKSH11 and on thesurface of Yamatouchi are reasonable even if the non-

6. CONCLUSIONS
The fragility curves are investigated based on therelationships between the building damage ratios (i.e.,
TCR, CR and DR) and ground motion characteristics
in the stricken districts in the East Tohoku and East
Kanto region during the 2011 Tohoku Earthquake.
Then the features of ground motions and damage ratios are compared with those of the Kobe Earthquake.
Finally a method of estimating the ground motions
was proposed using the velocity structures identified
from the H/V spectral ratios of microtremors at thedamaged sites. This method is expected to be used toconstruct fragility curves with greater accuracy. The
following conclusions are obtained:

Pseudo-velocity response spectra
500

300

H/V Spectral Ratio

Yamatouchi
FKSH11400

pSv (cm/s)

102

h=0.05

200
100
0

0.5

1

1.5

2

2.5

Mainshock
Small earthquakes

101
100
10-1
0.01

3

Period(s)Fig. 20 Pseudo-velocity response spectra (damping
ratio h=0.05) of the vector summation for thehorizontal component at Yamatouchi and at
FKSH11.

FKSH110.1

1Period(s)10Fig. 21 H/V spectral ratios of the mainshock andsmall earthquakes at FKSH11.

76

RELATIONSHIP BETWEEN BUILDING DAMAGE RATIOS AND GROUND MOTION CHARACTERISTICS DURING THE 2011 TOHOKU EARTHQUAKE

observation records at the K-NET and KiK-net stations, PS-logging data at KiK-net stations, and theamplification factor map.

(1) DR relates better to the ground motion indices, i.e., PGA, PGV, IJMA, and SI, than TCR or CR.
The correlations for DR versus PGV, DR versus IJMA,
and DR versus SI are almost the same as one another.
The relationship between DR and PGA has larger
variability than the relationships between DR and
PGV, between DR and IJMA, and between DR and SI,
because PGA is more sensitive to the predominantperiod. Even large PGA is not always related to highDR if the predominant period is shorter than 0.4 s.
(2) DR for the 2011 Tohoku Earthquake is almost the same as those for the Kobe Earthquake forthe same level of ground motions in terms of IJMA,PGA ≦ 800 gal, PGV ≦ 100 cm/s, and SI ≦ 100 cm/s.
(3) DRs greater than 60% occur when the equivalent predominant period is around 0.5 s and the PGV
is larger than 35 cm/s, and the PGA is larger than 450
gal in the 2011 Tohoku Earthquake.
(4) The consistency of H/V spectral ratios between microtremors and earthquake ground motions
is confirmed at some strong-motion sites where thevelocity structures have a big velocity contrast due tosoft, shallow layers.
(5) The ground motions at Yamatouchi, a damaged site, from the mainshock are well simulated using the transfer functions at Yamatouchi and FKSH11
and the observed records at FKSH11. The estimatedground motion indices at Yamatouchi agree well withthe large damage ratio. This suggests that the proposition of identifying the velocity structures from the
H/V spectral ratio of earthquake ground motions by
Kawase et al. (2011) is applicable to microtremors, aslong as the consistency of H/V spectral ratios between
earthquake ground motions and microtremors is confirmed.
(6) The peak of the H/V spectral ratio shiftingfrom about 0.12 s to 0.15 s suggests that nonlinear
behavior will only affect a short-period of the groundmotions which are not related to building damage.
Thus, a linear estimation of ground motions is reasonable even if nonlinear behavior is not considered.

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Seim. Soc. Am., Vol. 94, 53-63.
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http://www.fdma.go.jp/bn/2012/detail/691.html.
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http://www.gsi.go.jp/BOUSAI/h23_tohoku.html.
Hayashi, Y., Miyakoshi, J., Tamura, K., and Kawase, H.
1997. Peak ground velocity evaluated from damage ratio of low-rise buildings during the Hyogo-Ken Nambu
Earthquake of 1995. J. Struct. Constr. Eng., AIJ, No.
494, 59-66 (in Japanese).
Ingber, L. 1989. Very fast simulated re-annealing. Math.
Comput. Modeling, Vol. 12, No. 8, 967-973.
Japan Meteorological Agency. 1996. Understanding seismic
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