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Ground-Motion Prediction Equations for Subduction Slab Earthquakes in
Japan Using Site Class and Simple Geometric Attenuation Functions
by John X. Zhao, Fei Jiang, Pan Shi, Hao Xing, Haifeng Huang, Ruibin Hou,
Yingbin Zhang, Pengcheng Yu, Xiaowen Lan, David A. Rhoades, Paul G.
Somerville, Kojiro Irikura, and Yoshimitsu Fukushima
Abstract The frequency content of strong ground motions from subduction slab
earthquakes differs significantly from that of ground motions produced by other cat-
egories (tectonic locations: shallow crustal, upper mantle, and subduction interface) of
earthquakes in subduction zones. In the last two decades, a large number of records
from subduction slab events have been obtained in Japan. We present a ground-motion
prediction equation (GMPE) for this category of earthquakes. We used a large dataset
from reliably identified slab events up to the end of 2012. The GMPEs were based on
a set of simple geometric attenuation functions, site classes were used as site terms,
and nonlinear site amplification ratios were adopted. A bilinear magnitude-scaling
function was adopted for large earthquakes with moment magnitude Mw≥7:1, with
the scaling rates for large events being much smaller than for the smaller events. A
magnitude-squared term was used for events with Mw<7:1as well as the bilinear
magnitude-scaling function. We also modeled the effect of volcanic zones using an
anelastic attenuation coefficient applied to a horizontal portion of the seismic-wave
travel distance within possible volcanic zones. We found that excluding the records from
sites with inferred site classes improved the model goodness of fit. The within-event
residuals were approximately separated into within-site and between-site residuals, and
the corresponding standard deviations were calculated using a random effects model.
The separation of within-event residuals into within-site and between-site components
allows for the possibility of adopting different standard deviations for different site
classes in a probabilistic seismic-hazard analysis if desired.
Online Material: Figures showing the distribution of between-event residuals with
respect to magnitude and fault-top depth and the distribution of within-event residuals
with respect to magnitude and source distance.
Introduction
In the last decade, many modern ground-motion predic-
tion equations (GMPEs) have been published. These include
the Next Generation Attenuation models, which are mainly
based on strong-motion records from California but supple-
mented by shallow crustal records from Taiwan, Japan, and
Turkey, including Abrahamson and Silva (2008),Boore and
Atkinson (2008),Campbell and Bozorgnia (2008),andChiou
and Youngs (2008). For subduction zones, the tectonic set-
tings are complex and a relatively small number of modern
GMPEs have been developed, for example, Atkinson and
Boore (2003),Kanno et al. (2006),McVerry et al. (2006),
Zhao, Zhang, et al. (2006),andGhofrani and Atkinson
(2014). The models by Zhao, Zhang, et al. (2006) and Kanno
et al. (2006) were based on strong-motion records from Japan,
and nonlinear site terms were not used. The Zhao, Zhang, et al.
(2006) model used site class based on site period as the site
term, because many strong-motion recording stations had no
site information. For most stations in Japan, the site class was
inferred by Zhao, Irikura, et al. (2006) using response spectral
ratios of the horizontal and vertical components (H/V). The
site classes are defined in Table 1together with the approxi-
mate National Earthquake Hazards Reduction Program
(NEHRP) site classes (Building Seismic Safety Council
[BSSC], 2000). The use of site classes by Zhao, Irikura, et al.
(2006) produced consistent site amplification ratios for three
soil site classes (SC II, III, and IV) with respect to SC I sites.
BSSA Early Edition / 1
Bulletin of the Seismological Society of America, Vol. 106, No. 4, pp. –, August 2016, doi: 10.1785/0120150056
The Zhao, Zhang, et al. (2006) model used strong-motion re-
cords up to the end of 2003, and since then many more strong-
motion records have been obtained by the K-NETand KiK-net
strong-motion networks in Japan. In the past, subduction inter-
face and slab earthquakes were grouped together (Youngs
et al., 1997), and usually a constant in the GMPE was used to
describe the different attenuation characteristics. Zhao, Zhang,
et al. (2006) used common site terms for all three categories of
earthquakes: shallow crustal, subduction interface, and subduc-
tion slab categories. The subduction slab events have an addi-
tional geometric attenuation term. When the three categories of
events are combined, between- and within-event standard de-
viations are the same for all three earthquake categories.
The reasonably large number of records in each earth-
quake category allowed Zhao and Rhoades (2014) to develop
separate GMPEs for the three categories of events. The first
model was for the shallow crustal and upper-mantle events,
the second model is for subduction interface events, and the
third model is for subduction slab events. Deriving separate
GMPEs has an important advantage: separate within-event
and between-event standard deviations can be obtained. Be-
cause of the different frequency content in the strong-motion
records from different event categories, the standard devia-
tions may differ statistically. This may be significant for a
probabilistic seismic-hazard analysis in subduction zones. For
example, the standard deviations for subduction slab events
may be larger than those for shallow crustal earthquakes (Zhao
and Rhoades, 2014). If the same model standard deviation is
used, the hazard from subduction slab events would be under-
estimated whereas the hazards from the other two types of
earthquakes are overestimated.
Another advantage of deriving three separate models is
to differentiate the site terms among the three event groups.
Zhao et al. (2009) and Zhao and Zhang (2010) suggested that
site amplification ratios may depend on the frequency con-
tent and thus may depend on earthquake categories. There-
fore, it may be more appropriate to use different site terms
derived from separate GMPEs than using the same site terms
for all event categories. We derive site terms in this study that
differ from those in the Zhao, Liang, et al., 2016 study for
shallow crustal and upper-mantle events and the Zhao, Zhou,
et al. (2016) study for subduction interface events.
Zhao and Lu (2011) and Zhao and Xu (2012) investi-
gated the magnitude-scaling rates for large earthquakes with
moment magnitude Mw>7:0, using strong-motion data
from worldwide crustal earthquakes and from large subduc-
tion interface earthquakes in Japan. Their studies showed that
the magnitude-scaling rates were very small, varying in a
range of 0.0–0.3, for large crustal earthquakes. For large sub-
duction interface earthquakes (Mw>7:0), Zhao (2014) and
Zhao and Rhoades (2014) showed that the magnitude-scaling
rate was also much smaller than that for smaller events. In the
present study, a magnitude-squared term and a bilinear mag-
nitude-scaling function hinged at Mw7.1 from the Zhao and
Rhoades (2014) study was used.
Zhao and Rhoades (2014) and Zhao, Zhou, et al. (2015)
examined the earthquake locations reported in the catalogs
of the Japan Meteorological Agency, an Engdahl–van der
Hilst–Buland group in the catalogs from the International
Seismological Centre, and the U.S. Geological Survey Na-
tional Earthquake Information Center catalog. They assigned
earthquake categories for 312 events, among which are the
records from the subduction slab events used in this study.
In the present study, we use site classes as defined in
Table 1. Even though site classes do not provide a continuous
predicted response spectrum across all sites, they are still
useful for some design codes, such as the New Zealand de-
sign code NZS1170.5:2004 (Standards New Zealand, 2004),
and for some engineering sites that may have a site class but
no accurate site period or VS30 (the travel-time averaged
shear-wave velocity in the top 30 m).
Zhao, Zhou, et al. (2016) presented the site information
quality effect, that is, the change in the goodness-of-fit
parameters for GMPEs with or without the strong-motion
records from sites with an inferred site class, using H/V spec-
tral ratios (Zhao, Irikura, et al. 2006) or geological descrip-
tions of the surface soils. In the present study, we also
investigated this aspect for subduction slab records.
We used the maximum log likelihood (MLL), rather than
the model standard deviation, as the indicator of goodness of
fit for a GMPE, as described by Zhao and Rhoades (2014).
We found that the MLL was a good way to identify an ap-
parently biased distribution of residuals with a parameter that
is strongly influenced by an outlier in the dataset. In this case,
when an additional term is used to correct this type of biased
residual distribution, the MLL does not change, meaning the
correction is not statistically necessary.
Table 1
Site Class Definitions Used in the Present Study and the Approximately Corresponding
NEHRP Site Classes (BSSC, 2000)
Site Class Description Natural Period VS30 Calculated from Site Period NEHRP Site Classes
SC I Rock T<0:2sVS30 >600 A+B+C
SC II Hard soil 0:2≤T<0:4s300 <V
S30 ≤600 C
SC III Medium soil 0:4≤T<0:6s200 <V
S30 ≤300 D
SC IV Soft soil T≥0:6sVS30 ≤200 E+F
NEHRP, National Earthquake Hazards Reduction Program.
2J. X. Zhao, et al.
BSSA Early Edition
We adopted the site terms accounting for soil nonlinear
response derived by Zhao, Hu, et al. (2015) and extended by
Zhao, Zhou, et al. (2016). The number of strong-motion re-
cords from subduction slab events in Japan with significant
nonlinear soil response is still small, because subduction
events are usually deep and distant from the land in Japan.
The Zhao, Hu, et al. (2015) and Zhao, Zhou, et al. (2016)
models were derived from 1D models based on the shear-
wave velocity profiles from a number of selected KiK-net
stations. The model parameters that were controlled by weak
motions were separated from the crossover rock spectrum
that distinguishes amplification from deamplification ranges
of a rock spectrum, as described by Zhao, Hu, et al. (2015).
The parameters controlled by weak motions were determined
from GMPE amplification ratios, whereas the crossover rock
spectrum and the slope of the attenuation in the amplification
ratios for a very high rock-site spectrum were determined
from 1D model analyses.
Strong-Motion Dataset
We constructed two datasets, as in the study by Zhao,
Liang, et al., 2016 for shallow crustal and upper-mantle
events. The first dataset includes records from all earth-
quakes since 1968, with 98 earthquakes having reverse-
faulting mechanisms, 13 strike-slip, and 25 normal-faulting
mechanisms, as listed in Table 2. In the first dataset, 2031
records are from SC I sites, 1354 from SC II sites, 443 from
SC III sites, and 882 from SC IV sites, with a total of 4710
records, as listed in Table 3. Seven earthquakes have a mag-
nitude greater than 7.0, with the largest magnitude being
8.25, and 539 records are from large events with Mw≥7:1
in the first dataset.
For the records from earthquakes before 1996 and some
records from a number of K-NET stations, the site class was
inferred from response spectral ratios of H/V components. In
the second dataset, the exclusion of sites with an inferred site
class leads to the removal of 11 events and 155 records, in-
cluding 29 SC I records, 62 SC II records, 29 SC III records,
and 35 SC IV records. In the second dataset, 125 events were
used, and the number of records in each site class is pre-
sented in Table 3. We used the first dataset to derive the
magnitude-scaling rate for large events. Then we derived the
subduction slab model from the second dataset, using the
fixed magnitude-scaling rate for large events with Mw≥7:1
derived from the first dataset. Figure 1a shows the distribu-
tion of earthquakes with respect to fault-top depth and mag-
nitude, and Figure 1b shows the distribution of records with
respect to source distance and magnitude for the second data-
set. The maximum magnitude in the second dataset is 7.92,
as shown in Figure 1.
We have fault-rupture models for a number of earth-
quakes. The references for these models can be found in the
electronic supplement of Zhao, Liang, et al., 2016.
Model Function Forms
In this study, we employed the following functions to
model the source effect, that is, the magnitude and fault depth
for subduction slab events:
Table 2
Number of Events in Each Focal Mechanism Group
Focal Mechanism
Dataset
Number Reverse
Strike
Slip Normal
Total in Each
Earthquake Category
1 98 13 25 136
2 95 10 20 125
Table 3
Number of Records in Each Site Class
Dataset Number SC I SC II SC III SC IV Total
1 2031 1354 443 882 4710
2 2002 1292 414 847 4555
Figure 1. (a) The distribution of earthquakes used in the present
study with respect to fault depth and moment magnitude and (b) the
distribution of strong-motion records with respect to source distance
and magnitude.
GMPEs for Subduction Slab Earthquakes in Japan 3
BSSA Early Edition
EQ-TARGET;temp:intralink-;df1;55;449fmSLmi;hibSLhi
cSL1micSL2mi−msc2if mi≤mc
cSL1mccSL2mc−msc2dSL mi−mcif mi>mc
;
1
in which SL indicates that the term is associated with subduc-
tion slab earthquakes, bSL is the coefficient for the fault-top
depth term, and cSL1and cSL2are the coefficients for the linear
magnitude and the magnitude-squared terms, respectively, for
events with a moment magnitude miless than or equal to mc.
The magnitude-squared term with a positive value was found
statistically significant with msc 6:3selected and msc is a
magnitude constant. In the Zhao, Zhang, et al. (2006) model, a
positive magnitude-squared term was used, and this term leads
to an unrealistically large short-period spectrum for large
events. Coefficient dSL is the magnitude term for large events.
In the present study, we selected mc7:1based on the results
of Zhao and Lu (2011),Zhao and Xu (2012),Zhao (2014),
and Zhao and Rhoades (2014).
The GMPE in the present study is
EQ-TARGET;temp:intralink-;df2a;55;204
logeyi;jfmSL gSL logeri;j gSLL logexi;j 200:0
eSLxi:j qSLH xi:j ev
SLxv
i;j γSL
logeAξi;j ηi;2a
and
EQ-TARGET;temp:intralink-;df2b;55;125 logeμi;j
yi;jξi;j ηi:2b
Var i a bl e yis for peak ground acceleration (PGA) or the 5%
damped response spectrum in units of the acceleration due
to gravity, and μdenotes the recorded PGA or spectrum.
Var i a bl e edenotes the anelastic attenuation rate; xdenotes
the shortest distance from a recording station to the fault
plane if a fault model is available and otherwise is the hy-
pocentral distance; γSL is a constant; and gSL denotes the
geometric attenuation rate. The term gSLL is a large-distance
geometric attenuation rate. The superscript vindicates as-
sociation with the volcanic path. The anelastic attenuation
rate ev
SL is applied to the horizontal distance passing
through volcanic zones, denoted by xvand illustrated in
Figure 2.ASL is the site amplification ratio for slab events
and contains both linear and nonlinear site terms. The sub-
script iindicates the ith event in the dataset, and jindicates
the jth record in the ith event. The random variable ξis the
within-event residual with an average value of 0.0 and a
standard deviation of σ(i.e., the within-event standard devia-
tion). Random variable ηiis the between-event residual with
an average value of 0.0 and a standard deviation τ(i.e., the
between-event standard deviation). The distance used for geo-
metric spreading is defined by
EQ-TARGET;temp:intralink-;df3;313;492ri;j xi;j expc1c2Cm;3
and
EQ-TARGET;temp:intralink-;df4;313;447Cmmiif mi≤Cmax
Cmax if mi>Cmax
:4
We used a maximum magnitude Cmax mcin equation (4)
as described by Zhao, Zhou, et al. (2016). Coefficient
c21:151 was selected and justified by the relationship
of magnitude and fault length relations (see Zhao, Zhou,
et al., 2016).
The anelastic attenuation term qSLH is defined by
EQ-TARGET;temp:intralink-;df5;313;325qSLH eSLH0if h<50
0:02h−1:0if h≥50 :5
The fault-top depth is denoted by hin equation (5) for the
depth-dependent anelastic attenuation rate. For slab events,
equation (5) does not appear to be reasonable because we
would expect that the seismic waves from a deep slab event
would have a long travel path within the subducting slab that
has high-Qvalues. From this simple reasoning the anelastic
attenuation rate for deep slab events should be inversely pro-
portional to the fault depth, as shown by Eberhart-Phillips
and McVerry (2003). We attempted to use an anelastic at-
tenuation rate inversely proportional to the fault depth. How-
ever, this term is not statistically significant, while the term
qSLH in equation (5) leads to a sizable increase in the MLL.
The physical cause behind equation (5) is probably related to
the geometry of the subduction interface and the location of
the strong-motion recording stations relative to the subduc-
tion trench, as shown in Figure 3. For the North Island of
New Zealand, the onshore depth of the interface is relatively
Figure 2. (a) The definition of volcanic path for four cases and
(b) the horizontal and slant volcanic distance. The color version of
this figure is available only in the electronic edition.
4J. X. Zhao, et al.
BSSA Early Edition
small (starting from about 20 km), and the trench formed by
the subducting slab is also relatively close to the shoreline.
For many slab earthquakes, a large portion of the travel path
for the seismic waves recorded by New Zealand onshore
stations lies in the subduction slab, as illustrated by the seis-
mic-wavetravelpathtotherecordingstationontheright
side of Figure 3. Therefore, the length of the travel path
within the high-Qslab increases with increasing earthquake
depth. This travel path leads to an anelastic attenuation co-
efficient inversely proportional to the fault depth. For Japan,
the subduction trench is usually far offshore, and the seis-
mic waves reaching the recording stations travel in the slab
and also through the upper mantle and crust that have
smaller Qvalues than the subducting slab. We expect that
the Qvalue in the upper mantle is likely to be smaller than
the Qvalue within the subducting slab. The travel path
within the mantle would increase with increasing depth, and
therefore the apparent anelastic attenuation rate may in-
crease with increasing depth, as shown in equation (5).
Zhao (2010) showed that, if the constructive interference
between the seismic waves traveling along the direct path
and the waves traveling along a refracted path through the
slab were modeled by depth-scaled geometric attenuation
functions, the apparent anelastic attenuation rate for the slab
events would decrease.
We adopted the method of modeling volcanic path
attenuation from Zhao, Zhou, et al. (2016), using the sum
of the horizontal portions of the path (along a straight line be-
tween a station and the fault plane) that pass through volcanic
zones xvas the measure of volcanic path. An anelastic attenu-
ation rate ev
SL was applied to the volcanic path. We adopted
the minimum and the maximum values for xvas 12 and
80 km, respectively. For example, when 0:0<x
v≤12:0km,
xv12:0km, and when xv≥80:0km, xv80:0km, as
suggested by Zhao and Rhoades (2014) and Zhao, Zhou, et al.
(2016).
Following Zhao, Zhou, et al. (2016), the random vari-
able ξcan be divided into a within-site component ξSand a
between-site component ηS, using the algorithm of Abra-
hamson and Youngs (1992). We fit the following random
effects model to the within-event residuals:
EQ-TARGET;temp:intralink-;df6;313;673ξk;n ξs
k;n ηs
k;6
in which kstands for the site number and ndenotes the nth
record from the kth site. The within-site component ξs
k;n has
a zero mean and a within-site standard deviation of σS. The
between-site component ηs
khas a zero mean and a between-
site standard deviation of τS. The between-site standard
deviation is an indicator of how well the site effects are mod-
eled. The within-event residuals contain the random errors
associated with path effects, as well as any other effects that
are not modeled.
The total site standard deviation can be calculated by
EQ-TARGET;temp:intralink-;df7;313;513σSTk
σ2
Sk τ2
Sk
q;7
in which kdenotes the site class number.
SC I sites are neither rock nor engineering bedrock sites.
Many SC I sites have a layer of stiff soil with a thickness up
to 24 m and a shear-wave velocity as small as 200 m=s for
some sites with a thin surface soil layer. The average imped-
ance ratio (defined by Zhao, Hu, et al., 2015) is 3.7, and
many sites have an impedance ratio between 4 and 8. The
sites with a thin soil layer usually have a small average shear-
wave velocity and a large impedance ratio. The sites with a
thick soil layer usually have a large average shear-wave
velocity and a relatively small impedance ratio for a given
site period. These characteristics of the SC I sites lead to
small nonlinear soil response, even when subjected to strong
rock motions, because the shear stress from the inertial force
in the thin soil layer can be smaller than the soil yield stress.
Also the definition for rock sites, with a shear-wave velocity
of 760 m=s or larger at the ground surface, means that the
VS30 for these sites could be over 1000 m=s and the site could
be classified as A or B in the NEHRP (BSSC, 2000).
Because the amplification ratio of the nonlinear site model
in Zhao, Hu, et al. (2015) and Zhao, Zhou, et al. (2016) is
the spectral ratio for all sites over the rock sites, we need to
estimate the amplification ratio for SC I sites relative to the
rock sites.
We used the following method to determine the ampli-
fication ratios for SC I sites or deamplification ratios for rock
sites. We examined the within-event residuals of the SC I
sites and fitted a linear function of site periods to the SC I
within-event residuals from all three GMPEs (one for shallow
crustal and upper-mantle events presented by Zhao, Zhou,
et al., 2016, one for subduction slab events presented in this
study, and one for subduction interface events by Zhao,
Liang, et al., 2016). We combined the residuals from three
Figure 3. Different seismic-wave propagation paths from a
deep subduction slab event to a recording station in Japan (left)
and a recording station in New Zealand (right). The Japanese islands
are much further from the subduction trench than is the North Island
of New Zealand. The color version of this figure is available only in
the electronic edition.
GMPEs for Subduction Slab Earthquakes in Japan 5
BSSA Early Edition
GMPEs in order to have a large number of records. Figure 4
shows the distribution of within-event residuals with respect
to site period, and the distributions are clearly biased. The
solid trend lines represent the average within-event resid-
uals, and the negative value of the average residuals at zero
site period is then defined as S1N, the negative intercept of
the linear trend line. We used linear functions for all spectral
periods.
Figure 5a shows the smoothed deamplification ratios
for rock sites with respect to SC I sites (or the average am-
plification ratios for SC I sites with respect to rock sites).
At short spectral periods, the deamplification ratios vary
between 1.2 at 0.1 s spectral period and 2.05 at 0.3 s, and
then decrease with increasing spectral periods down to 1.27
at 5.0 s. The PGA deamplification ratio is 1.38. These deam-
plification ratios are surprisingly large and may be caused
by large impedance ratios for SC I sites. We referred to S1N
as the hard-rock-site term. Figure 5b shows an example SC I
spectrum and the rock-site spectrum derived by dividing the
SC I site spectrum by the deamplification ratio presented in
Figure 5a. The spectral period at the peak spectrum for rock
sites is close to 0.05 s, shifted slightly from that of the SC I
spectrum, as it should be. This method does not require
iterations because very few records from SC I sites contain
the effect of significant soil nonlinear response. Table 4
presents the rock-site factor AmSC I expS1N. The maxi-
mum site amplification ratio is defined by
EQ-TARGET;temp:intralink-;df8a;313;271ANmax kAmSC I for SC I sites k1;8a
and
EQ-TARGET;temp:intralink-;df8b;313;222ANmax kAmSC I expSk
for SC II;III;IV sites k2;3;4:8b
Dropping kfor simplicity, the nonlinear amplification ratio
is given by
EQ-TARGET;temp:intralink-;df9;313;142
logeA
logeANmax−logeAmaxlogeSα
MR β−logeβ
logeSα
ReffCβ−logeβ;
9
Figure 4. Distribution of within-event residuals for site class
(SC I) sites with respect to site period for (a) peak ground accel-
eration (PGA), (b) 0.5 s, and (c) 2.0 s spectral periods. The color
version of this figure is available only in the electronic edition.
Figure 5. (a) Smoothed deamplification ratio for a rock-site
spectrum with respect to SC I sites and (b) an example SC I and rock
spectrum. The rock-site spectrum equals the SC I spectrum divided
by the deamplification ratio presented in (a). Rock sites have a surface
shear-wave velocity of 760 m=s or larger. The color version of this
figure is available only in the electronic edition.
6J. X. Zhao, et al.
BSSA Early Edition
EQ-TARGET;temp:intralink-;df10;55;278
SNC
explogeANmaxlogeSα
ReffCβ−logeSFlnβ
logeAmax−β1
α;
10
EQ-TARGET;temp:intralink-;df11;55;215SMR SReff
SNC
SReffC
fSR;11
EQ-TARGET;temp:intralink-;df12;55;167SReff SRImf;12
EQ-TARGET;temp:intralink-;df13;55;131SReffCSRC Imf; 13
and
EQ-TARGET;temp:intralink-;df14;55;95SFANmax
Amax
:14
Parameters α2:0and β0:6were used for all periods,
and Amax,SRC ,andImf are the maximum amplification
ratio, crossover rock-site spectrum, and impedance ratio
factor, respectively, of the 1D models defined by Zhao and
Rhoades (2014) and Zhao, Hu, et al. (2015). All parameters
are presented in tables 4 and 5 in Zhao, Zhou, et al. (2016),
with 12 spectral periods being added and smoothed to the
model by Zhao, Hu, et al. (2015). An adjustment factor fSR
is introduced so that a broadly smoothed spectrum for non-
linear soil site can be obtained. This parameter has a value
in the 0–1.106 range, as shown in Table 5of this article. The
adjustment factor fSR is zero for spectral periods over 2.5 s,
which means that only linear amplification ratios are
necessary.
The adjustment factor fSR was determined in the follow-
ing manner:
1. Select an expected largest magnitude, such as Mw8.5 or
the magnitude of the largest event in the dataset; a
Table 4
Rock-Site Deamplification Factor AmSC I
Period
Number Period (s) AmSC I
Period
Number Period (s) AmSC I
Period
Number Period (s) AmSC I
Period
Number Period (s) AmSC I
1 PGA 1.381 11 0.1 1.231 21 0.4 2.025 31 2.0 1.574
2 0.01 1.228 12 0.12 1.334 22 0.45 1.999 32 2.5 1.500
3 0.02 1.087 13 0.14 1.448 23 0.5 1.975 33 3.0 1.439
4 0.03 1.042 14 0.15 1.510 24 0.6 1.931 34 3.5 1.387
5 0.04 1.035 15 0.16 1.573 25 0.7 1.891 35 4.0 1.341
6 0.05 1.047 16 0.18 1.707 26 0.8 1.855 36 4.5 1.301
7 0.06 1.071 17 0.2 1.833 27 0.9 1.822 37 5.0 1.265
8 0.07 1.103 18 0.25 1.954 28 1.0 1.791
9 0.08 1.141 19 0.3 2.034 29 1.25 1.724
10 0.09 1.184 20 0.35 2.052 30 1.5 1.667
PGA, peak ground acceleration.
Table 5
Adjustment Factors for Nonlinear Site Model
Site Classes Site Classes
Period Number Period (s) I II III IV Period Number Period (s) I II III IV
1 PGA 1.0 1.0 1.0 1.0 17 0.2 0.0 0.565 0.650 1.006
2 0.01 1.0 1.0 1.0 1.0 18 0.25 0.0 0.601 0.479 1.027
3 0.02 1.0 1.0 1.0 1.05 19 0.3 0.0 0.579 0.449 1.021
4 0.03 1.0 1.0 1.0 0.58 20 0.35 0.0 0.679 0.482 1.003
5 0.04 1.0 1.006 1.0 0.482 21 0.4 0.0 0.655 0.499 1.010
6 0.05 1.0 0.851 1.0 0.472 22 0.45 0.0 0.615 0.515 0.985
7 0.06 1.0 0.803 1.044 0.506 23 0.5 0.0 0.550 0.530 0.990
8 0.07 1.0 0.918 0.975 0.587 24 0.6 0.0 0.0 0.530 1.006
9 0.08 1.0 1.062 0.964 0.683 25 0.7 0.0 0.0 0.499 1.000
10 0.09 1.0 1.106 0.980 0.782 26 0.8 0.0 0.0 0.369 1.000
11 0.1 1.0 1.071 0.970 0.823 27 0.9 0.0 0.0 0.3 0.960
12 0.12 0.0 0.952 1.022 1.029 28 1.0 0.0 0.0 0.2 0.904
13 0.14 0.0 0.672 0.889 0.991 29 1.25 0.0 0.0 0.0 0.738
14 0.15 0.0 0.631 0.861 0.983 30 1.5 0.0 0.0 0.0 0.535
15 0.16 0.0 0.600 0.831 0.973 31 2.0 0.0 0.0 0.0 0.358
16 0.18 0.0 0.571 0.748 0.979 32 2.5 0.0 0.0 0.0 0.0
GMPEs for Subduction Slab Earthquakes in Japan 7
BSSA Early Edition
shortest possible source distance for most subduction
zones, such as 25 km; and a possible fault depth that is
consistent with the source distance (e.g., the distance
must be less than the fault depth).
2. Set fSR 1:0for all spectral periods for which a nonlin-
ear site term is required.
3. Fit a smoothed curve to the calculated spectrum.
4. Manually adjust fSR so that the calculated spectrum equals
the smoothed spectrum derived in the last step.
When Amax is less than 1.25, SReffCcan be calculated by
equation (13) in Zhao, Hu, et al. (2015). When ANmax is less
than 1.25, SNC can be calculated by equation (15) in Zhao,
Hu, et al. (2015).
Model Coefficients and Standard Deviations
We established two GMPEs with identical functional
forms for each dataset. The first GMPE used the strong-
motion records in the first dataset, and the second GMPE used
the second dataset, excluding those records from the sites
with an inferred site class. We used MLLs from the two mod-
els to identify the effect of excluding the sites with an in-
ferred site class. Figure 6shows the differences between the
weighted MLL (defined by Zhao, Zhou, et al., 2016) from the
second dataset and those from the first dataset. Zhao, Zhou,
et al. (2016) referred to the differences as the site information
quality effect, with a positive value suggesting that a better
model can be derived by excluding the sites with an inferred
site class. The increase varies between 18 and 75, suggesting
a better model by excluding the sites with an inferred site
class.
We used the first dataset to determine the magnitude-
scaling rate dSL for large slab events with Mw≥7:1. We then
used the second dataset to determine the other terms for the
GMPE presented in this study. Figure 7shows the values of
dSL and the ratio of dSL=cSL1. The magnitude-scaling rates
for events with Mw≥7:0are much smaller than those for the
smaller events.
The strategy of determining model parameters and
smoothing the model coefficients is presented in the Zhao,
Liang, et al. (2016) study.
Tables 6and 7present the smoothed coefficients in the
model for the GMPEs described in equations (1)–(5). Figure 8
shows the magnitude-squared term cSL2. This coefficient is
positive, varying between 0.0454 at spectral periods over
2.5 s and 0.507 at 0.07 s. The subduction slab model by
Zhao, Zhang, et al. (2006) has a magnitude-squared term for
the slab events. This term is also positive, leading to a rapid
increase in the predicted spectrum with increasing magnitude
when magnitude is large.
Figure 9compares the anelastic attenuation rate,
expressed as a percentage, with that of the depth-dependent
anelastic attenuation rate for events with a depth over
50.0 km (calculated at 150 km depth) and with the attenu-
ation rate for the volcanic path. The volcanic attenuation rate
is much larger than the other two terms for spectral periods
up to about 1.0 s. The depth-dependent anelastic attenuation
rate is not large compared with the linear anelastic attenua-
tion rate at many spectral periods.
Figure 10 shows the site class terms, which are similar to
those for the shallow crustal and upper-mantle events pre-
sented by Zhao, Zhou, et al. (2016) and to those for the sub-
duction interface model by Zhao and Rhoades (2014) and
Zhao, Liang, et al. (2016) at some spectral periods.
ⒺFigures S1–S14, available in the electronic supple-
ment to this article, show the distribution of the between-
event and within-event residuals for PGA, 0.5, 1.0, 2.0, 3.0,
4.0, and 5.0 s spectral periods. Linear trend lines are also
presented. The slope of each trend line seems to be satisfac-
torily small. For each spectral period, we fitted a linear func-
tion of magnitude and source depth to the between-event
residuals and a linear function of magnitude and source
distance to the within-event residuals. The coefficients of the
linear functions should not differ from 0.0 at a significance
Figure 6. The effect of site information quality: the increase in
the weighted maximum log likelihood after excluding the strong-
motion records from stations with inferred site class.
Figure 7. Magnitude-scaling coefficient dSL for large subduc-
tion slab events and the ratio dSL=cSL1. The color version of this
figure is available only in the electronic edition.
8J. X. Zhao, et al.
BSSA Early Edition
level of 5%. If this criterion was not satisfied, a new regres-
sion analysis was carried out.
Figure 11 shows the variation of standard deviations
with spectral period. The largest between-event standard
deviation is 0.598 at 0.07–0.08 s. The largest within-event
standard deviation is 0.713 at 0.2 s, and the largest total stan-
dard deviation is 0.884 at spectral periods of 0.08–0.09 s. The
standard deviations are larger than those from the other cat-
egories of events (Zhao and Rhoades, 2014;Zhao, Liang,
et al., 2016;Zhao, Zhou, et al., 2016) at many spectral peri-
ods. Figure 12a compares the interevent and total standard
deviations from the present study with those from the Abra-
hamson et al. (2015) model (digitized from fig. 7 in that
study), in which the subduction interface and slab events
were combined together as a single group. The between-
event standard deviations of the two models are very similar
at many spectral periods. The total standard deviations of the
present study are larger than those of the Abrahamson et al.
(2015) study in the 0.04–2.5 s period range, with the largest
difference being about 18%. Figure 12b shows the within-
event standard deviation. The values from the present study
are considerably larger than those of the Abrahamson et al.
(2015) model; the largest difference is about 19%. However,
the standard deviations from subduction interface events in
the Zhao, Liang, et al. (2016) study are considerably smaller
than those for slab events in the present study for spectral
periods up to 2 s. This may mean that the smaller standard
deviations in the Abrahamson et al. (2015) study are caused
by the interface events, whereas the data in the present study
are all from slab events. Zhao, Liang, et al. (2016) suggested
the possibility that the use of VS30 in the Abrahamson et al.
(2015) study may lead to a reduction in within-event standard
deviations. This cannot be confirmed without comparing
between-site standard deviations from the two studies.
Table 6
Model Coefficients, Part 1
T(s) c1cSL1cSL2dSL bSL gSL gSLL eV
SL
PGA −5.30119 1.44758 0.37625 0.42646 0.01826 −1.98471 1.12071 −0.01499
0.01 −5.28844 1.45400 0.38099 0.42075 0.01826 −1.96360 1.03278 −0.01503
0.02 −5.27568 1.46625 0.39101 0.40055 0.01826 −1.91839 0.94715 −0.01517
0.03 −5.26822 1.49246 0.41976 0.36433 0.01826 −1.89271 0.93420 −0.01567
0.04 −5.26293 1.50129 0.45746 0.32072 0.01826 −1.87260 0.97168 −0.01616
0.05 −5.25882 1.51051 0.48601 0.30000 0.01826 −1.85351 1.01492 −0.01676
0.06 −5.25547 1.51380 0.50311 0.31147 0.01826 −1.83395 1.06854 −0.01722
0.07 −5.25263 1.51111 0.50704 0.32673 0.01826 −1.81345 1.13401 −0.01752
0.08 −5.25017 1.50406 0.50004 0.34289 0.01826 −1.79189 1.20364 −0.01768
0.09 −5.24801 1.49423 0.48071 0.35921 0.01826 −1.76931 1.25808 −0.01772
0.1 −5.24607 1.48300 0.45759 0.37000 0.01826 −1.74581 1.30112 −0.01768
0.12 −5.24271 1.45559 0.41355 0.40606 0.01826 −1.73746 1.39137 −0.01742
0.14 −5.23988 1.44277 0.37828 0.43450 0.01826 −1.74463 1.47084 −0.01700
0.15 −5.23861 1.43314 0.36308 0.45000 0.01826 −1.74972 1.50784 −0.01676
0.16 −5.23742 1.43253 0.34919 0.46055 0.01826 −1.76259 1.54326 −0.01649
0.18 −5.23525 1.43710 0.32464 0.48439 0.01826 −1.78989 1.60985 −0.01594
0.2 −5.23331 1.44781 0.30358 0.50900 0.01826 −1.82110 1.67146 −0.01537
0.25 −5.22921 1.48260 0.26174 0.55500 0.01826 −1.90412 1.80738 −0.01395
0.3 −5.22585 1.51881 0.23036 0.59300 0.01826 −1.98439 1.92242 −0.01261
0.35 −5.22302 1.55291 0.20580 0.62500 0.01826 −2.05756 2.02102 −0.01139
0.4 −5.22056 1.58443 0.18597 0.65200 0.01826 −2.12282 2.10642 −0.01029
0.45 −5.21839 1.61360 0.16960 0.67500 0.01826 −2.18047 2.18097 −0.00931
0.5 −5.21645 1.64075 0.15585 0.69500 0.01826 −2.23118 2.24651 −0.00843
0.6 −5.21310 1.69020 0.13405 0.72900 0.01826 −2.31475 2.35602 −0.00694
0.7 −5.21026 1.73450 0.11757 0.75600 0.01826 −2.37885 2.44331 −0.00574
0.8 −5.20781 1.77474 0.10476 0.77800 0.01826 −2.42769 2.51391 −0.00477
0.9 −5.20564 1.81162 0.09458 0.79600 0.01826 −2.46450 2.57166 −0.00398
1−5.20370 1.84561 0.08636 0.81200 0.01826 −2.49170 2.61931 −0.00333
1.25 −5.19959 1.92015 0.07173 0.84100 0.01808 −2.52758 2.70638 −0.00215
1.5 −5.19624 1.98274 0.06258 0.86100 0.01786 −2.53359 2.76244 −0.00142
2−5.19095 2.08214 0.05327 0.88400 0.01718 −2.49565 2.82205 −0.00067
2.5 −5.18684 2.15841 0.05036 0.90000 0.01628 −2.42623 2.84475 −0.00039
3−5.18349 2.22046 0.04536 0.90000 0.01549 −2.34726 2.84988 −0.00030
3.5 −5.18065 2.27406 0.04536 0.90000 0.01489 −2.27002 2.84667 −0.00026
4−5.17819 2.32307 0.04536 0.90000 0.01458 −2.19947 2.83992 −0.00021
4.5 −5.17602 2.37009 0.04536 0.90000 0.01459 −2.12528 2.82802 −0.00021
5−5.17409 2.37009 0.04536 0.90000 0.01459 −2.02646 2.82521 −0.00021
msc 6:3.
GMPEs for Subduction Slab Earthquakes in Japan 9
BSSA Early Edition
Table 7
Model Coefficients, Part 2
Period (s) eSL eSLH γS2S3S4στσ
T
PGA −0.00340 −0.00050 −9.880 0.2320 0.1437 0.1470 0.587 0.457 0.744
0.01 −0.00331 −0.00050 −9.513 0.2289 0.1398 0.1328 0.587 0.458 0.745
0.02 −0.00345 −0.00050 −9.266 0.2183 0.1260 0.1443 0.587 0.465 0.749
0.03 −0.00391 −0.00050 −9.332 0.1874 0.0616 0.0660 0.588 0.480 0.759
0.04 −0.00454 −0.00050 −9.508 0.1233 −0.0171 −0.0171 0.599 0.521 0.794
0.05 −0.00510 −0.00050 −9.729 0.0721 −0.0633 −0.0731 0.607 0.555 0.823
0.06 −0.00552 −0.00050 −9.966 0.0270 −0.1010 −0.1196 0.623 0.584 0.854
0.07 −0.00588 −0.00049 −10.226 −0.0062 −0.1468 −0.1601 0.638 0.600 0.876
0.08 −0.00615 −0.00048 −10.551 0.0157 −0.1448 −0.1243 0.651 0.598 0.884
0.09 −0.00635 −0.00048 −10.807 0.0509 −0.1267 −0.0729 0.662 0.585 0.883
0.1 −0.00652 −0.00048 −11.022 0.0956 −0.0932 −0.0146 0.674 0.567 0.881
0.12 −0.00660 −0.00049 −11.365 0.2004 −0.0088 0.0825 0.689 0.534 0.872
0.14 −0.00652 −0.00051 −11.730 0.3037 0.0893 0.1715 0.692 0.504 0.856
0.15 −0.00647 −0.00052 −11.880 0.3428 0.1360 0.2093 0.696 0.486 0.849
0.16 −0.00636 −0.00053 −12.056 0.3740 0.1775 0.2412 0.697 0.465 0.838
0.18 −0.00614 −0.00056 −12.420 0.4270 0.2531 0.2990 0.704 0.430 0.825
0.2 −0.00590 −0.00059 −12.785 0.4630 0.3201 0.3459 0.713 0.406 0.821
0.25 −0.00526 −0.00067 −13.635 0.5086 0.4530 0.4423 0.711 0.385 0.808
0.3 −0.00468 −0.00075 −14.381 0.5078 0.5488 0.5178 0.684 0.365 0.775
0.35 −0.00415 −0.00083 −15.035 0.4971 0.6171 0.5760 0.665 0.371 0.762
0.4 −0.00369 −0.00091 −15.616 0.4807 0.6663 0.6224 0.657 0.383 0.761
0.45 −0.00327 −0.00099 −16.138 0.4616 0.7011 0.6598 0.647 0.391 0.756
0.5 −0.00290 −0.00107 −16.613 0.4422 0.7256 0.6907 0.640 0.403 0.756
0.6 −0.00227 −0.00124 −17.453 0.4054 0.7529 0.7380 0.633 0.412 0.755
0.7 −0.00178 −0.00139 −18.181 0.3734 0.7625 0.7723 0.632 0.432 0.766
0.8 −0.00139 −0.00154 −18.825 0.3462 0.7612 0.7974 0.635 0.438 0.772
0.9 −0.00109 −0.00166 −19.403 0.3236 0.7538 0.8162 0.636 0.438 0.772
1−0.00086 −0.00178 −19.928 0.3048 0.7428 0.8301 0.636 0.439 0.773
1.25 −0.00052 −0.00199 −21.058 0.2703 0.7083 0.8504 0.635 0.444 0.775
1.5 −0.00043 −0.00213 −21.996 0.2483 0.6726 0.8573 0.645 0.448 0.786
2−0.00070 −0.00225 −23.488 0.2253 0.6107 0.8499 0.633 0.425 0.762
2.5 −0.00127 −0.00219 −24.647 0.2154 0.5640 0.8276 0.607 0.413 0.735
3−0.00198 −0.00207 −25.597 0.2115 0.5261 0.7991 0.582 0.407 0.710
3.5 −0.00271 −0.00193 −26.410 0.2098 0.4977 0.7678 0.562 0.395 0.687
4−0.00341 −0.00180 −27.132 0.2088 0.4769 0.7359 0.540 0.381 0.661
4.5 −0.00421 −0.00170 −27.793 0.2077 0.4622 0.7041 0.526 0.367 0.641
5−0.00500 −0.00158 −28.313 0.2067 0.4527 0.6722 0.522 0.378 0.645
Figure 8. The magnitude-squared term for slab events with a
magnitude less than 7.1. The color version of this figure is available
only in the electronic edition.
Figure 9. Comparison of anelastic attenuation rates for slab
events, the depth-dependent anelastic attenuation rate calculated
at a depth of 150 km, and the anelastic attenuation rates for volcanic
path. The color version of this figure is available only in the elec-
tronic edition.
10 J. X. Zhao, et al.
BSSA Early Edition
Table 8presents the within-site and between-site stan-
dard deviations derived from the within-event residuals using
a random effects model described in equation (6). Figure 13a
shows the between-site standard deviations, and Figure 13b
shows the within-site standard deviations. SC I sites have the
largest between-site standard deviation for spectral periods
(up to 0.16 s) compared with those for the other site classes.
The largest value is 0.643 at a spectral period of 0.08 s, which
is close to the average site period of SC I sites. SC II sites
have the second largest between-site standard deviations at
spectral periods up to 0.15 s. The largest value is 0.601 at
about 0.18–0.25 s spectral period. The between-site standard
deviations for SC III sites are similar to those of SC IV sites
up to about 0.06 s and smaller than those for SC IV sites in
the 0.07–0.3 s spectral period range. At long spectral periods
over 0.5 s, the between-site standard deviations are very sim-
ilar among all site classes. Figure 13b shows that the within-
site standard deviations among the four site classes are very
similar for all site classes. These do not vary with spectral
periods as much as the between-site standard deviations do.
In this aspect, they are similar to the within-site standard de-
viations from shallow crustal and upper-mantle events in
Zhao, Zhou, et al. (2016). Figure 14 compares the total site
standard deviations σST for all site classes with the within-
event standard deviation σ. The total site standard deviation
σST is larger than σat very short periods but is very similar to
σat spectral periods over 1.0 s. At short periods, SC I sites
have the largest total site standard deviation; the largest dif-
ference among the four site classes is close to 20%. For SC I,
II, and III sites, the total site standard deviation has the larg-
est peak value at a spectral period close to the average site
period of each site class, suggesting that site resonance
response may increase model variability.
We also evaluated whether the model standard devia-
tions depend on earthquake magnitude. We divided the
residuals into magnitude bins, each of which covers 0.5 mag-
nitude units if there is a reasonable number of events for
between-event residuals and a reasonable number of records
for within-event residuals. Then we calculated the standard
deviations of the residuals in each magnitude bin. Figure 15a
shows the standard deviations for the between-event resid-
uals in four magnitude bins, with the last bin containing all
events with Mw>6:5so as to have enough events. Clearly,
the between-event standard deviations do not decrease with
increasing magnitude in a consistent manner, as shown in
Figure 15a. Figure 15b shows that the standard deviations
Figure 10. Comparison of elastic site terms for three site
classes. The color version of this figure is available only in the elec-
tronic edition.
Figure 11. Variation of between-event standard deviation (τ),
within-event standard deviation (σ), and total standard deviation
(σT) with spectral period. The color version of this figure is avail-
able only in the electronic edition.
Figure 12. Comparison of (a) between-event and total standard
deviations and (b) within-event standard deviations from the present
study and the Abrahamson et al. (2015) study. The color version of
this figure is available only in the electronic edition.
GMPEs for Subduction Slab Earthquakes in Japan 11
BSSA Early Edition
for the within-event residuals do not decrease or increase
with magnitude either. Abrahamson et al. (2015) also used
a magnitude-independent standard deviation.
Predicted Response Spectra
Next, we present the predicted spectra for various mag-
nitude, depth, and distance ranges. The smoothing of each
model parameter with respect to the logarithm of spectral
periods does not lead to smoothed spectra at all magnitude
and distance ranges.
Figure 16 shows the rock-site spectra from events with
magnitudes of 5, 6, 7, and 8 at a source distance of 30 km and
a fault-top depth of 30 km, and the predicted PGAs are listed
in Table 9. Among the periods that have been modeled, the
peak rock-site spectrum is at a spectral period of 0.1 s. The
differences between the spectra for Mw7 and Mw6 events
are considerably larger than those between the spectra for
Mw6 and Mw5 events at spectral periods up to about 0.4 s
because of the magnitude-squared term.
Figure 17a shows the predicted spectra for SC I sites for
four magnitude units, and the peak of the SC I spectrum is at
about 0.1 s. Figure 17b presents the predicted spectrum for
SC II sites, and the peak of the spectrum for all events is at
0.15 s. Figure 18a shows that the peak of the predicted spec-
trum is at about 0.15–0.16 s for SC III sites, similar to that in
Figure 17b. Figure 18b shows the predicted spectrum for SC
IV sites. The corresponding PGAs for the predicted spectra in
Figures 17 and 18 are presented in Table 9.
Figure 19a compares the spectra from an Mw7.0 event
with a fault depth of 30 km at a source distance of 30 km for
rock sites and four soil site classes. The PGA is 0.394gfor
rock site, 0.542gfor SC I sites, 0.651gfor SC II sites, 0.577g
for SC III sites, and 0.553gfor SC IV sites. The reduced
Table 8
Within-Site and Between-Site Standard Deviations
SC I SC II SC III SC IV
Period (s) σS1τS1σST1σS2τS2σST2σS3τS3σST 3σS4τS4σST4
PGA 0.398 0.511 0.648 0.417 0.449 0.613 0.409 0.431 0.594 0.415 0.422 0.592
0.01 0.397 0.517 0.651 0.417 0.450 0.614 0.409 0.431 0.594 0.415 0.418 0.589
0.02 0.395 0.518 0.652 0.417 0.449 0.613 0.408 0.431 0.594 0.416 0.425 0.594
0.03 0.389 0.537 0.663 0.418 0.449 0.614 0.409 0.430 0.593 0.417 0.422 0.593
0.04 0.387 0.572 0.691 0.420 0.456 0.620 0.413 0.428 0.595 0.420 0.431 0.602
0.05 0.387 0.586 0.702 0.422 0.479 0.639 0.409 0.429 0.592 0.422 0.439 0.609
0.06 0.397 0.613 0.730 0.416 0.507 0.656 0.401 0.449 0.602 0.423 0.445 0.614
0.07 0.403 0.633 0.750 0.412 0.532 0.673 0.394 0.456 0.603 0.420 0.473 0.633
0.08 0.413 0.643 0.765 0.412 0.555 0.692 0.389 0.455 0.599 0.423 0.491 0.648
0.09 0.422 0.631 0.759 0.412 0.568 0.702 0.391 0.475 0.615 0.427 0.518 0.671
0.1 0.429 0.626 0.759 0.418 0.566 0.704 0.394 0.507 0.642 0.426 0.559 0.703
0.12 0.440 0.614 0.755 0.429 0.570 0.713 0.428 0.548 0.695 0.445 0.576 0.728
0.14 0.441 0.613 0.755 0.435 0.597 0.739 0.433 0.507 0.667 0.442 0.561 0.714
0.15 0.450 0.602 0.752 0.440 0.599 0.743 0.420 0.490 0.645 0.440 0.555 0.708
0.16 0.452 0.599 0.750 0.444 0.597 0.744 0.424 0.494 0.651 0.437 0.552 0.704
0.18 0.454 0.599 0.752 0.447 0.601 0.749 0.446 0.500 0.670 0.436 0.553 0.705
0.2 0.462 0.590 0.749 0.450 0.596 0.747 0.441 0.491 0.660 0.432 0.562 0.709
0.25 0.474 0.555 0.730 0.470 0.601 0.763 0.459 0.450 0.643 0.432 0.507 0.666
0.3 0.472 0.532 0.711 0.475 0.557 0.732 0.437 0.499 0.663 0.432 0.489 0.653
0.35 0.468 0.505 0.688 0.478 0.518 0.705 0.444 0.532 0.692 0.432 0.463 0.633
0.4 0.457 0.479 0.663 0.484 0.488 0.687 0.453 0.546 0.709 0.416 0.466 0.624
0.45 0.450 0.461 0.644 0.477 0.479 0.676 0.477 0.529 0.713 0.408 0.461 0.616
0.5 0.445 0.451 0.633 0.470 0.471 0.665 0.472 0.495 0.684 0.409 0.467 0.620
0.6 0.448 0.436 0.625 0.460 0.467 0.655 0.459 0.470 0.657 0.407 0.434 0.594
0.7 0.440 0.430 0.615 0.460 0.464 0.653 0.461 0.473 0.660 0.403 0.430 0.589
0.8 0.441 0.427 0.614 0.460 0.456 0.647 0.457 0.457 0.646 0.407 0.454 0.610
0.9 0.435 0.431 0.612 0.456 0.466 0.652 0.449 0.439 0.628 0.408 0.456 0.612
1 0.427 0.440 0.613 0.448 0.466 0.647 0.442 0.442 0.625 0.408 0.462 0.616
1.25 0.413 0.440 0.603 0.442 0.476 0.649 0.428 0.432 0.608 0.412 0.444 0.606
1.5 0.416 0.449 0.612 0.448 0.473 0.651 0.418 0.461 0.622 0.418 0.443 0.609
2 0.409 0.441 0.601 0.437 0.462 0.636 0.406 0.472 0.623 0.413 0.439 0.603
2.5 0.398 0.425 0.582 0.429 0.427 0.606 0.387 0.484 0.620 0.414 0.427 0.595
3 0.390 0.396 0.556 0.423 0.407 0.587 0.369 0.447 0.580 0.412 0.431 0.596
3.5 0.386 0.386 0.545 0.410 0.401 0.574 0.376 0.434 0.574 0.402 0.413 0.576
4 0.377 0.373 0.530 0.410 0.386 0.564 0.362 0.406 0.544 0.394 0.391 0.555
4.5 0.360 0.364 0.512 0.412 0.373 0.556 0.368 0.383 0.531 0.385 0.366 0.532
5 0.361 0.359 0.509 0.447 0.322 0.551 0.381 0.316 0.495 0.380 0.324 0.499
Subscripts 1, 2, 3, and 4 with σand τdenote site classes.
12 J. X. Zhao, et al.
BSSA Early Edition
short-period spectra for SC III and SC IV sites are mainly
caused by the reduced elastic site term for these two site
classes compared with the elastic site term for SC II sites.
The nonlinear site terms for SC III and SC IV sites also lead
to the reduction in predicted spectrum at short periods.
Figure 19b compares the nonlinear soil spectrum with
the elastic spectrum for an SC IV site from an Mw8 event
with fault depth of 30 km at a source distance of 30 km. The
nonlinear soil spectrum has a PGA of 0:76g, reduced from
1:04gin the elastic spectrum. The largest reduction is at
0.16 s, and the nonlinear spectrum is 1:42g, reduced from
2:44gin the elastic spectrum.
Figure 20a shows the attenuation of PGA, and Figure 20b
shows the spectrum at 0.5 s from events with magnitudes of
Figure 15. Variation of standard deviations for (a) between-
event and (b) within-event residuals in a number of magnitude bins.
The color version of this figure is available only in the electronic
edition.
Figure 16. Predicted rock-site spectra for slab events with Mw5–8
and a depth of 30 km at a source distance of 30 km. The color version of
this figure is available only in the electronic edition.
Figure 13. Comparison of (a) between-site standard deviations
and (b) within-site standard deviations for four site classes. The
color version of this figure is available only in the electronic edition.
Figure 14. Comparison of site total standard deviations with
the within-event standard deviations. The color version of this figure
is available only in the electronic edition.
Table 9
Predicted PGA (g) for Four Magnitude Units and Five
Site Classes
Magnitude (Mw)
Site Class 5.0 6.0 7.0 8.0
Rock site 0.071 0.136 0.394 0.651
SC I 0.099 0.187 0.542 0.893
SC II 0.124 0.235 0.651 0.997
SC III 0.113 0.214 0.577 0.845
SC IV 0.114 0.213 0.553 0.760
GMPEs for Subduction Slab Earthquakes in Japan 13
BSSA Early Edition
5, 6, 7, and 8, and with a fault-top depth of 25 km for SC II
sites. The distance range is 30–320 km. These figures clearly
show the reduced scaling for events with Mw>7:0and the
increased magnitude scaling for the events with a magnitude
between 6.0 and 7.0 as a result of the magnitude-squared
term. The magnitude scaling between magnitudes 5 and 6 is
also markedly smaller than that between magnitudes 6 and 7.
Figure 21 shows the attenuation of spectra at 1.0 s and 3.0 s
spectral periods; again, the magnitude-scaling rates for large
events are significantly less than those for events with an Mw
up to 7.1. The magnitude-scaling rate for magnitude 5 and 6
events is similar to that for magnitude 6 and 7 events because
the magnitude-squared term is small for these spectral periods.
Figure 22 shows the effect of volcanic path on the pre-
dicted response spectra for an event with Mw8.0 and a depth
of 30 km at a source distance of 65 km. The PGA is reduced
from 0:372gto 0:278gat a volcanic distance of 20 km,
0:207gat 40 km, and 0:153gat 60 km. The reduction is sig-
nificant for spectral periods up to about 0.7 s.
Conclusions
We assembled 4710 strong-motion records from sub-
duction slab events in Japan up to the end of 2012. The
large number of records allows us to develop a GMPE for
the subduction slab events as one group. We found that
the standard deviations from the present study are larger
than those from the shallow crustal and upper-mantle events
(Zhao, Zhou, et al., 2016) and the subduction interface
events (Zhao, Liang, et al., 2016). The different model stan-
dard deviations may improve the seismic-hazard estimation
for each type of earthquake.
The model in the present study adopted a bilinear
magnitude-scaling function hinged at Mw7.1, leading to
a considerably reduced magnitude scaling for events
with an Mw≥7:1. The coefficient for this magnitude term
was much smaller than that for events with Mw<7:1.
We also adopted a magnitude-squared term for events with
a magnitude up to 7.1. The effect of volcanoes on the at-
tenuation of seismic waves was modeled by applying an
anelastic attenuation term to the volcanic path, the horizon-
tal portion of a straight-line distance (the closest distance
from a station to the fault plane if available) that passes
through the assumed low-Qzones around the active volca-
noes. The absolute values of the anelastic attenuation rate
for volcanic path are much larger than the anelastic attenu-
ation rate at spectral periods up to 1.0 s. A volcanic path of
60 km can lead to nearly 60% reduction in the predicted
PGA.
Site classes based on site period were used for the site
term. We tested the effect of site information quality. The over-
Figure 18. Predicted spectra for slab events with Mw5–8 and a
depth of 30 km at a source distance of 30 km for (a) SC III sites and
(b) SC IV sites. The color version of this figure is available only in
the electronic edition.
Figure 17. Predicted spectra for slab events with Mw5–8 and a
depth of 30 km at a source distance of 30 km for (a) SC I sites and
(b) SC II sites. The color version of this figure is available only in
the electronic edition.
14 J. X. Zhao, et al.
BSSA Early Edition
all goodness offit for the attenuation models improved signifi-
cantly after records from sites with inferred site classes were
excluded. The model coefficients presented in this study were
derived based on the records from sites that have a measured
shear-wave velocity profile down to engineering bedrock.
The model standard deviations derived from the present
study are generally similar to those by Abrahamson et al.
(2015) at some periods, but the within-event standard devia-
tions are significantly larger than those from Abrahamson
et al. (2015) in the 0.2–2.5 s period range. One possible
explanation is that subduction slab events may have larger
standard deviations, because the Abrahamson et al. (2015)
model used both interface and slab events whereas the
present study is for slab events only. Compared with the re-
sults from the Zhao, Liang, et al. (2016) model for interface
events, the slab events do have substantially larger standard
deviations. Another possible explanation is that Abrahamson
et al. (2015) used VS30 as the site term, whereas site classes
are used in the present study. VS30 may lead to a reduced
within-event standard deviation compared with site classes.
However, this cannot be confirmed without comparing
between-site standard deviations.
We approximately separated the within-event residuals
into within-site and between-site residuals using a random
effects model. We found that the between-site standard
deviations are generally larger than the within-site standard
deviations for spectral periods up to 0.6 s. The between-site
standard deviations tend to vary significantly with site class
and spectral period. The values at spectral periods close to
the average site period of each site class tend to be large. The
within-site standard deviations from the four site classes are
generally similar and do not vary significantly with spectral
periods.
We investigated whether model standard deviations
depend on magnitude by comparing the standard deviations
computed from the residuals in a number of magnitude bins.
We found that these standard deviations do not depend on
magnitude, which is consistent with the Abrahamson et al.
(2015) study.
We adopted a nonlinear site model based on 1D model-
ing. The nonlinear site term reduced the elastic spectrum sig-
nificantly, up to the 0.7 s period for records from large events
at short distances.
Data and Resources
The strong-motion records are from K-NET and KiK-
net, administered by the National Research Institute for Earth
Science and Disaster Prevention of Japan. A small number of
records are from the Port and Airport (Port and Harbour) Re-
Figure 19. (a) Predicted spectra from slab events with Mw7.0
and a depth of 30 km at a source distance of 30 km for four site
classes and (b) the elastic and nonlinear spectra for SC IV sites from
an Mw8.0 event. The color version of this figure is available only in
the electronic edition.
0.0001
0.001
0.01
0.1
1
20 40 80 160 320
Acceleration spectrum (g)
Source distance (km)
Mw=5
Mw=6
Mw=7
Mw=8
(a)
PGA
Slab
SC II
0.0001
0.001
0.01
0.1
1
20 40 80 160 320
Acceleration spectrum (g)
Source distance (km)
Mw=5
Mw=6
Mw=7
Mw=8
(b)
0.5s
Slab
SC II
Figure 20. Attenuation of predicted response spectra for four
magnitude units of subduction slab events with a fault-top depth of
25 km at SC II sites for (a) PGA and (b) 0.5 s. The color version of
this figure is available only in the electronic edition.
GMPEs for Subduction Slab Earthquakes in Japan 15
BSSA Early Edition
search Institute. A number of rock-site strong-motion records
are from the Pacific Earthquake Engineering Research Center
strong-motion database (http://peer.berkeley.edu/smcat/;last
accessed August 2015).
Acknowledgments
The work reported here is partially supported by research grants from
the National Science Foundation of China (51278432) and the Southwest
Jiaotong University (SWJTU12ZT04), 973 Project from the Ministry of
Science of China (2013CB036204), and by the New Zealand Earthquake
Commission 2010 Biennial Research Grant. At an early stage (2011), sup-
port was received from the New Zealand Foundation for Research Science
and Technology, New Zealand Hazards Platform (Contract C05X0907).
The authors would like to thank Jim Cousins and Chris Van Houtte of
GNS Science for their review of this manuscript. We would like to thank
Kimiyuki Asano from Disaster Prevention Research Institute (DPRI) of
Kyoto University for supplying the fault model parameters for a number
of earthquakes. Finally, we would like to thank Eric Thompson and two
anonymous reviewers for their constructive review comments.
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School of Civil Engineering
Southwest Jiaotong University
111 1st Northern Section of Erhuan Road
Chengdu 610031
Sichuan, China
J.Zhao@gns.cri.nz
(J.X.Z., F.J., P.S., H.X., H.H., R.H., Y.Z., P.Y.)
Institute of Crustal Dynamics
China Earthquake Administration
1 Anningzhuang Road
Haidian District
Beijing 100085, China
(X.L.)
GNS Sciences
1 Fairway Drive
Avalon
Lower Hutt 5010
New Zealand
(D.A.R.)
AECOM
915 Wilshire Boulevard, 7th Floor
Los Angeles, California 90017
(P.G.S.)
Aichi Institute of Technology
Aichi Prefecture
Toyota 470-0392, Japan
(K.I.)
International Seismic Safety Centre
Division of Nuclear Installation Safety
Department of Nuclear Safety and Security
International Atomic Energy Agency
Vienna International Centre
P.O. Box 100
1400 Vienna
Austria
(Y.F.)
Manuscript received 19 February 2015;
Published Online 12 July 2016
GMPEs for Subduction Slab Earthquakes in Japan 17
BSSA Early Edition
