Bulletin of the Seismological Society of America, Vol. 88, No. 2, pp. 357-367, April 1998

A Technique for Simulating Strong Ground Motion
Using Hybrid Green's Functionb y Katsuhiro K a m a e , Kojiro Irikura, and Arben Pitarka

Abstract A method for simulating strong ground motion for a large earthquake
based on synthetic Green's function is presented. We use the synthetic motions of asmall event as Green' s functions instead of observed records of small events. Groundmotions from small events are calculated using a hybrid scheme combining deterministic and stochastic approaches. The long-period motions from the small eventsare deterministically calculated using the 3D finite-difference method, whereas thehigh-frequency motions from them are stochastically simulated using Boore's
method. The small-event motions are synthesized summing the long-period andshort-period motions after passing them through a pair of matched filters to follow
the omega-squared source model. We call the resultant time series "hybrid Green's
functions" (HGF). Ground motions from a large earthquake are simulated by following the empirical Green's function (EGF) method. We demonstrate the effectivenessof the method at simulating ground motion from the 1995 Hyogo-ken Nanbu earthquake ( M w 6.9).

Introduction
Studies of the ground motion from the 1994 Northridge,
Califomia, earthquake and the 1995 Hyogo-ken Nanbu, Japan, earthquake have shown that the combined effects of thesource process and wave propagation path may cause largeamplitude ground motions at particular areas that cannot be
predicted by simplified 1D or purely stochastic modelingtechniques (e.g., Graves, 1995; Pitarka and Irikura, 1996;
Hartzell et al., 1996; Kawase, 1996; Motosaka and Nagano,
1996; Pitarka et al., 1997, 1998). The empirical Green's
function (EGF) method, originally proposed by Hartzell(1978) and then developed by many researchers (e.g., Irikura, 1986), is one of the simplest techniques that accounts
for such effects. Compared with other deterministic techniques, it has the advantage of not requiring to compute numerically the propagation and local site effects (Kamae etal., 1998; Kamae and Irikura, 1998). Its main limitation isthat it can be applied only in cases where appropriate recordsof small events in the source area, which are considered asGreen's functions, are available. Unfortunately, it is rare tohave good records of such small events, especially in thesource area of a future large earthquake.
As an alternative way to avoid this limitation, we propose the use of synthetic Green's functions that are calculated based on a hybrid scheme that combines different
methods for calculating the low- and high-frequency part of
the Green's functions. The low-frequency part (in general,
less than 1 Hz) is calculated by a 3D finite-difference method
assuming a point source located in the source area and using

a velocity model of the irregular geological structure. The
high-frequency part (in general, higher than 1 Hz) is calculated using the stochastic simulation technique of Boore(1983). The low- and the high-frequency motions are corrected for the effect of the surface layers not included ineach motion. The synthetic Green's function is then calculated by combining the low- and high-frequency part of the
motion, as explained in the following section. We call thisthe resultant "hybrid Green's function" (HGF). Finally,strong ground motions from a large earthquake are obtainedby the summation of the HGFs following the EGF method.
Our hybrid scheme is different from the ones proposed by
Heaton et al. (1995) and Saikia (1993), which are based on
adopted empirical high-frequency Green's functions. We
have checked the capability of the proposed method by simulating the near-source ground motions from the 1995 Hyogo-ken Nanbu earthquake ( M w 6.9).

MethodThe flow chart of the HGF method is presented in Figure
1. First, we simulate high-frequency ground motion (f > 1Hz) from a hypothetical small event located in the fault planeof the target earthquake using the stochastic simulation technique of Boore (1983), assuming a point source. We canapply his method to the simulation of ground motion fromthe small event because the source size of the event is smallenough to neglect the rupture propagation effect. By using
357

358

K. Kamae, K. Irikura, and A. Pitarka

Stochastically simulated
Green's function
by Boore (1983)
Effective frequency range(feee > 1Hz)

Theoretically simulated
Green's functionby 3-D Finite Difference Modeling
Effective frequency range(~rf ~ 1 Hz)++

Effect of surface layers not included in each Green's function
Hybrid Green's function• Matched pair of f i l t e r s• Addition of both Green's functions
in time domain
Synthesis of strong ground motion
using hybrid Green's function[

I

Figure 1. Flow chart ofsirnulationme~odology ofsffong ground mofions using a
hybrid Green's function.

Boore's method, the high-frequency part of the simulated
Green's function has an acceleration amplitude spectrum
that follows the a~ -2 model with the high-frequency cutoff,
f~a~ = 15 Hz. We consider a frequency-dependent Q value,
derived from obtained ground motions, to take into accountthe effect of the wave propagation in the acceleration spectrum. Second, we calculate the low-frequency part of theGreen's function (f < 1 Hz) using the 3D finite-difference
method, assuming a point source and adopting a 3D velocity
model of the heterogeneous structure. We apply a correction
for the effect of the local surface layers not included in
Boore's method as well as the 3D calculation. After that, we
calculate the HGF by combining both the low- and highfrequency waves in the time domain. A matched pair of filters is then used to remove the low- (less than 1 Hz) andhigh-frequency content (more than 1 Hz) from the stochastically simulated motion and the finite-difference synthetic
motion, respectively. Finally, strong ground motions fromthe large earthquake are simulated by the summation of the
HGFs following the EGF method of Irikura (1986).
We simply outline the procedure of Irikura (1986) formulated to match the scaling of source spectra as well as thescaling of source parameters, in which both large and small
events follow the co-z model. The ground motions from alarge event are expressed as a superposition of the recordsof small events as follows:
NN

U(t) -~ C ~~i=1 j=l

where

r F(t - tij) * u(t),

rij

(1)

t~;i = ri/ - r o + ~/~VR'F(t) = 6(t) + I(N-l),,

[

~

~ t-

n--7 ~=1

(2)

]
(k-l)

v
(N - 1)n'(3)

and U(t) and u(t) are the ground motion for a large eventand the observed record of a small event used as the EGF,
respectively. The terms r, r o, and r o are the respective distances from the site to the hypocenter of a small event, fromthe site to the (i, j) subfault, and from the site to the starting
point of rupture on the fault plane of the large event. ~ij isthe distance between the starting point and (i, j) sub-fault, fl
is the shear-wave velocity, VR the rupture velocity, and z therise time of the large event. C is the stress drop ratio for thelarge and small events, and n' is an arbitrary integer number
to shift the artificial periodicity to a frequency higher thanthat of interest. N, a scaling parameter, is obtained fromequation (4):

( M0, / 1'3
N = \C--~0~} '(4)where Mot and M0s are the seismic moments for the large
and small events, respectively.
This formulation can be easily extended to cases where
the target event consists of multiple shocks, each of which
follows the co-2 model. The omega-squared model used heremeans that the source displacement spectrum has a fiat levelat low frequencies and an omega-squared decay at high frequencies beyond a corner frequency but not always a con-

359

A Technique for Simulating Strong Ground Motion Using Hybrid Green's Function

134" 48'135" 00'

135" 12'135" 24'

N~:14" 48'

34" 48'\34"36''A~no~,.uomrls:35~

f ......, /

r"

1,o

/

134.'48'

136" 00'

2*

34"36"

135" 24''DIP90*_.

/135" 12'_

DIPBS*': : -- :
.

.

!"

" ~

~

1

'

.

.
.

.
.

.
.

.
.

.

~

"4

,

,

•

co

...........................

19.5kin.a_ . . . . . . . . . . . . . . . . . .

3.5kin.a. . . . . . .

A " rupture time (see)24.0km <..__
1.0m

stant stress drop between large and small events. We use
formulation (1) by replacing the records of small events as
EGFs with the calculated HGFs.
Application to Modeling Ground Motion f r o m the1995 H y o g o - k e n N a n b u Earthquake
The 1995 Hyogo-ken Nanbu earthquake is one of themost destructive earthquakes of the twentieth century in Japan. The heavily damaged zone in the Kobe area extends
along a narrow belt approximately 30 km long and 1 km
wide, offset by about 1 km southeast of the causative faults.
Based on 3D simulations of the near-fault ground motion,
Pitarka et al. (1998) concluded that such damaged band area
was caused by the amplification of the ground motion due
to the coupling of the forward rupture directivity effect andthe basin edge effects. Their simulation of long-period
ground motions ( > 1 sec) uses a simplified velocity model

Figure 2. Source model consisting of threeasperities (subevents) estimated from forward
modeling using the empirical Green' s function
method (Kamae and Irikura, 1998). Our model(hatched) is superimposed on the model of
Sekiguchi et aL (1996) in lower figure. Source
parameters for each subevent are summarizedin Table 1. We assumed that ground motions
are generated only from the hatched zone on
the fault plane. The respective number of subfaults (N) calculated from equation (4) according to the source parameters of each subevent and M 4.7 small event is 5 for subevents
1 and 3, and 9 for subevent 2.

that does not account for the soft surface-layer effect. Consequently, the peak amplitude of the simulated ground motion is lower than the recorded one at sites within the Osakabasin. Synthetic Green's function calculated with the proposed hybrid scheme can better represent the effect of thesurface layers and consequently improve the result obtainedby a purely deterministic approach. In this study, we simulate near-source ground motions using the HGF method andcompare them with ground-motion records at several stations TKT (Nakamura et aL, 1996), KOB, KBU, MOT (Kagawa et aL, 1996), FKI, and ASY in the Kobe area shown in
Figure 2.
Source M o d e lMany researchers have determined the rupture model ofthe 1995 Hyogo-ken Nanbu earthquake (e.g., Sekiguchi etal., 1996; Wald, 1996; Yoshida et al., 1996; Ide and Takeo,

360

K. Karnae, K. Irikura, and A. Pitarka

1996; Horikawa et aL, 1996). All these models have beenobtained by inverting long-period ground-motion data
and/or geodetic data. Consequently, they are not always appropriate for estimating high-frequency near-source strong
ground motions. Kamae and Irikura (1998) proposed asource model, in which the slip was concentrated within
three regions on the fault to represent the main asperities
found by source inversion analysis. The stress drop is assumed to be constant within the asperities and zero in theother regions on the fault. Based on the source model, they
simulated the broadband-frequency ground motions from themainshock using the EGF method. In this study, we use thesame source representation (Fig. 2). The source parameters
for each subevent are summarized in Table 1.

Table 1
Source Parameters for Three Subevents

Subevent 1
Subevent 2
Subevent 3

M0
(N'm)

L× W
(km × kin)Aa(bars)

Depth of Top(kin)

3.4 X 10 TM
1.0 ;< 1019
1.8 × 1018

8 × 8
11 × 16
8 × 8

163
86
86

8
0
5

Table 2
Source Parameters for M 4.7 Small Event
Seismic moment (N'm)
Comer frequency (Hz)Fault area (km2)
Stress drop (bars)
Rise time (sec)

H y b r i d G r e e n ' s Function Calculation

7.1 X 1015
1.5
2.4
46
0.12

Low-Frequency Motion
Hybrid Green's functions are calculated for three point
sources located at the center of the three asperities on thefault assuming a magnitude 4.7 for each of them. This magnitude is the same as the one adopted for the aftershoek usedin another simulation of strong ground motion in Kobe thatwas based on the EGF method (Kamae and Irikura, 1998).
We used a bell-shaped source-time function, S(t) = [1.0cos(2zct/To)]/2To, with a duration To = 0.12 sec, and thesource parameters summarized in Table 2. For each point
source, we assumed a pure right-lateral strike-slip mechanism with the strike and dip corresponding to each subfault.
The basin velocity model used in the 3D finite-difference
calculations includes a single sedimentary layer with theshear-wave velocity Vs = 0.8 km/sec, compressional wave
velocity Vp = 1.6 km/sec, density p = 2.1 g/cm 3, constantattenuation factor Q = 80, and a background 1D velocity
model (Table 3). Figure 3 shows the region considered inthe 3D modeling including the Kobe city area and a part of
Awaji Island, and the fault trace. The underground bedrock
topography is depicted in Figure 4. The Green's functions
are ,calculated at sites shown in Figure 3 and Table 4. The
selected sites are stations that recorded the near-fault groundmotion from the mainshock except for FKI and ASY. These
two temporary stations were installed after the mainshock
during an array observation of ground-motion amplificationin the heavily damaged zone. Aftershock ground motions
recorded during the observation suggest a large amplification due to the basin edge and local site effects, especiallyat FKI and ASY (Iwata et al., 1996; Pitarka et al., 1996,1997). As shown later, we use these two sites to compare
the results obtained by the new technique and the EGF
method that has been done in Kamae and Irikura (1998).
Figure 5 shows the finite-difference velocity ground motions
at periods of i sec and longer for the first, second, and third
small event, respectively. The waveforms at KBU, which isa softrock site outside the basin, are very simple. They represent mainly the source process. In comparison to the wave-

Table 3Background Velocity Model
Depth
(kin)

S-WaveVelocity(km/sec)

P-WaveVelocity(km/sec)

Density(gm/cm3)

Q value

4.0

3.2
3.46

5.5
6.0

2.6
2.7

300
400

Table 4
Station Locations
Station
Name

Lat.
(deg)

Long.
(deg)

Geological
Condition

TKT
KOB
KBU
MOT
FKI
ASY

34.64934.68834.72534.72534.71834.724135.138
135.180135.240135.281135.281135.309

Alluvium
Diluvium
Soft rock
Alluvium
Alluvium
Alluviumforms at KBU, the ground motions simulated at the sedimentary sites are characterized by complex waveforms
influenced by the basin edge effects.
In order to check the quality of the calculated low-frequency Green's functions, we computed long-period groundmotion obtained by the summation of the synthetic Green's
function for the source model (Fig. 2) by Kamae and Irikura(1998) and compared it with recorded mainshock groundmotion, bandpass filtered at 0.2 to 1.0 Hz. Figure 6 shows
the comparison at KBU, KOB, and MOT. The original velocity seismograms at MOT were clipped in amplitudes larger
than 40 cm/sec. Therefore, we used the restored seismograms based on the saturation characteristics of the sensor(Kagawa et al., 1996). The synthetic motion agrees well withthe observed one at KBU. The peak amplitude of the synthetics is underestimated at KOB and MOT by a factor of 2.
This discrepancy might be caused by the adopted 3D veloc-

A Technique for Simulating Strong Ground Motion Using Hybrid Green's Function

135" (~0'361135" 30'135" 15'" Epicenter• : of"Subevents•O......

StationAreaoflatensity VII (JMA-scale)
BasinEdge
Fault

34" 45'Osaka

Akashi Strait

0

Bay

1Okra

34°3~

Awaji Is.
135" 00'

135' 15']35" 30'

Figure 3. Map of the Kobe area and station locations. The rectangle shows the aerial
extention of the basin model used in this study. Also shown are the locations of theheavily damaged zone [intensity 7, JMA scale, digitized data from Koketsu (1997)],
and the epicenters of three hypothetical M 4.7 small events (star symbol). Solid triangles
indicate the location of mainshock observation stations (TKT, KOB, KBU, and MOT)
and aftershock observation stations (FKI and ASY). Solid lines show the surface intersections of the causative faults determined by the strong-motion data (Sekiguchi et aL,
1996).

r--S:~

Figure 4. The bedrock topography in the
Kobe area used in the 3D finite-difference
modeling (Pitarka et al., 1997b).

ity model that does not include the soft surface layers in thebasin. To include the amplification due to the surface sedimentary layers into the Green's function, we correct themusing the spectral ratio between the transfer function calculated for the one-dimensional velocity model (Table 5) of

the structure beneath each station and the one for the corresponding one-dimensional profile of the 3D velocity
model, assuming a vertical incidence of S waves. Figure 7
shows the comparison between the synthetic velocity seismograms using low-frequency Green's functions, corrected

362

K. Kamae, K. Irikura, and A. Pitarka

Fault Normal(a)

TKT ~ ~

' ~K

Bo.,, ~

0.43,

.

o.=~

o.=,s

o.5ol

--~,~'~--~----

o.,6

o.o~=

o.o,

o.1.

o.o~

o.lo3

o,,,

o,,

FKI
AS Y

-

-

-

~

/

~

I

I

1

I

I

I

1

l

1

o.,-

1

I

I

I

1

I

I

I

I

I

~

I

I

i

I

3

6

9

12 15 18 21 24 27 0

3

6

9

12 15 18 21 24 27 0

3

6

9

12 15 18 21 24 27

see

I

,

0

sec

TKT - - - - ~ V V I / U V ~0.3.

0.439 -

KOB ~.... 3

0.250

o,=,

oo4~

o.o7~

,).or,,

o.113

0.063

KBU

(b)

Up-Downo.~,,O

KBU "-

Fault Parallel

~

~

MOT

- ~ J ~

FKI

I

I

I

l

I

0

3

6

9

12 15 18 21

I

I

I

I

I

I

I

I

0 3 6 9

sec

I

I

I

-

I

I

sec

I

I

|

I

:!!
0.3aO

I

I

I

I

I

12 15 18 21

sac

TKT ~

o.337 ~

o....

o.~n

FKI

ozTo

o.ls,,

0.4,

(c)
'

I

I

I

I

0 3 6 9

I

--I

1

1

i

12 15 18 21 24

sec

I

I

I

I

0 3 6 9

I

I

I

I

I

12 15 18 21 24

sec

I

I

!

!

sec

~

0 3 6 912 15 18 21

1I

0 3 6 9

I

I

I

I

I

12 15 18 21 24

sec

Figure 5. Finite-difference velocity seismograms from three hypothetical M 4.7
small events: (a) number 1 small event, (b) number 2 small event, and (c) number 3
small event.

A Technique for Simulating Strong Ground Motion Using Hybrid Green's Function

KBU (normal)363
MOT (normal)

KOB (normal)o-'x- "'.

~

u&l:.~.s7

SYNTHETIC

MAX.

52.S

38.0

MAX:

SYNTHETIC ~

6

~o

~

~5

io

sec

CM/SEC )

10 s

is

~o

6

h---0.0S

10 2

10 3

~_
I

0.1

i

,111.

i

i

1.0

0,1

io

CM/SEC )is
h=O,0S

~o

6

~

10

1.0

1.0

F
o.1

PERIOD (SEC)iii [ iiii

i

i

i

1.0

Illl

io

is

~o

h=O.OS

0.1
10

PERIOD (SEC)~s

CM/SEC )

10 s

10

10

~o

sec

10 2

o.1

,llll

~5

sec

10 2

--\

10
1.0

~o

~

1.0

0,1

10

P E R I O D (SEC)

Figure 6. Comparison between the fault normal synthetic velocity seismogram using a low-frequency Green's function and the observed one from the mainshock at
KBU, KOB, and MOT. Each lower panel shows the corresponding pseudo-velocity response spectra (5% damping). The heavy solid lines are observed spectra, and the lightsolid lines are the synthetics. The seismograms are bandpass filtered between 0.2 and
1.0 Hz.

Table 5
One-Dimensional Velocity Models
Site: TKT
Depth
(m)
24.0
34.0
54.0
150.0
350.0
1250.0Site: FKI,ASY(m/sec)Density(g/cra3)

Os

200
300
350
500
650
1100
3200

1.8
1.9
1.9
2.0
2.0
2.2
2.5

30
50
50
80
80
170
300

Vs

Depth
(rn)
10.0
45.0
100.0
250.0
550.0
1150.0Site: KOB
10.0
60.0
200.0
400.0
600.0

300
450
550
650
1100
3200

H i g h - F r e q u e n c y Motion(m/sec)Density(g/crn3)

Qs

150
300
450
550
650
1100
3200

1.8
1.9
1.9
2.0
2.0
2.2
2.5

10
50
80
80
80
170
300

1.8
1.9
1.9
2.0
2.0
2.2
2.5

30
50
80
80
80
170
300

Vs

Site: MOT
1.8
1.9
2.0
2.0
2.2
2.5

30
80
80
80
170
300

10.0
35.0
50.0
150.0
300.0
600.0

240
300
450
500
650
1100
3200

for the surface layer effect, and the observed ones (0.2 to
1.0 Hz) at KOB and MOT. The good fit between the synthetic
and the observed long-period ground motion suggests thatthe adopted source model and the calculated low-frequency
Green's functions can be used to simulate the long period
from the mainshock ground motion at other sites in the basin.
The slight discrepancy at 1 to 2 sec shows the necessity of
improvement of the adopted 3D basin velocity model.

Next, we simulate the high-frequency part of Green's
functions based on the stochastic simulation technique proposed by Boore (1983). The magnitude and the source parameters of the corresponding small event are the same as
the ones for the low-frequency Green's function previously
described (see Table 2). To take into consideration the propagation path effect, we use a frequency-dependent Q value(Qs = 33f °85) estimated by Tai et al. (1996) using aftershock records at sites in our target area. We generated 20
high-frequency Green's functions using a pseudo-random
generator of white noise. The Green's functions were corrected for the local site effect by using the 1D transfer functions at each sediment site. The 1D velocity models are
based on the available geotechnical information and shallow
bore-hole data (Table 5).

Simulation o f Near-Source Ground Motion
f r o m the M a i n s h o c k
We followed the proposed procedure to calculate HGFs
for the three subevents of the mainshock. The entire procedure for estimating the acceleration of HGF is schematicallyshown in Figure 8. The synthetic ground motions from themainshock are generated at each site by summing the HGF
for each subevent assuming that their source spectrum obeys
the omega-square model (Irikura, 1986). For each station, in
Figure 9, we show the comparison between the observed and364

K. Kamae, K. Irikura, and A. Pitarkaoo

KOB (normal)

MOT (normal)
MAX. IS.t

MAC. 7~7

6~~o~,s ~o~s ~osec( CM/SEC )

10 s

6

10

~
.~0 3

...o.u

~s

~o

sec

( CM/SEC )~5~oFigure 7. Comparison between the faultnormal synthetic velocity seismogram using
corrected low-frequency Green's function andthe observed one from the mainshock at KOB
and MOT stations. Each lower panel shows thecorresponding pseudo-velocity response spectra (5% damping). The heavy solid lines areobserved spectra, and the light solid lines are
the synthetics. The seismograms are bandpass
filtered between 0.2 and 1.0 Hz.

.-0~

i
10 2

10 2

10

10

1.0

\

1.0

=_
i

0.1

;

iIiflli

i

0.1

i Iiiit

1.0

0.1

i
0.1

10

i 111111

i

,

1.0

111111

10

PERIOD (SEC)PERIOD (SEC)

(b)

(a)

~
¢N

~ I

3D-sim

~3D-sim

MAX= 0.7

'.No

¢d O

STOC.-sim

MAX= 20.7

MAX= 0.5

STOC.-sim

MAX= 13.0

O O

HYBRIDHYBRID

MAX= 21.1

I

I

I

I

I

0

3

6

9

12 15
sec

I

I

I

18

21

'

24

MAX= 13.3

I

I

I

t

I

0

3

6

9

12 15
sec

I

!

I

I

18

21

24

(c)
3D-sireSTOC.-simi

HYBRID
j

68.9

k

MAX=

~

MAX= 70.5

i

i

i

i

i

0

3

6

9

12 15
sec

i

I

I

i

18

21

24

Figure 8. An example of the entire procedure used for estimating the acceleration of hybrid Green's function. (a), (b), and (c) show theGreen's functions from, respectively, number
1, 2, and 3 hypothetical small events at MOT
station. In each figure, "3D-sire" shows thecorrected low-frequency Green's function,
bandpass filtered between 0.2 and 1.0 Hz;"STOC-sim" shows the corrected high-frequency Green's function, bandpass filtered between 1.0 and 10 Hz; and "HYBRID" shows
the hybrid Green's function obtained by sumruing "3D-sire" and "STOC-sim" seismograms.

KOB (normal)

KBU (normal)i]

OBSERVED

MAX= 316.4

MAX= 849.5

oMAX= 1160.8"1MAX= 48.5

OBSERVED

MAX= 103.9

SYNTHETIC

MAX= 101,8ooMAX= 67.2
S Y K T H ~

0'

2'

I

!

I

I

i

I

10

15

20

25

30

51

0

I

I

10

15

I

20

I

25

I

30

sec

SeC

MOT (normal)

TKT (normal)
OBSERVED

MAX= 574.4

MAX= 734.3

OBSERVEDoj

MAX= 1208.1

OBSERVEDSYNTHETIC-- _MAX= 773.7~

MAX= 144.7

MAX= 77.4
Uoo

SYNTHETIG

0i

I

5

0

MAX= 182.4

t

10

I

15

sec

l

20

MAX= 82.7

i

!

25

30

I

0

51

I

10 "

I

15

I

20

I

25

!

30

sec

FKI (normal)

ASY (normal)

EGF-sy=n~oMAX= 1030.7$'OfPdE'nC

MAX= 925.5

SYNTHETIC

MAX= 120.3

g

T-

0
0

SYNTHETIC

I

51

0

Figure 9.

I

I

I

I

I

10

15

20

25

30

sec

o

10

15

sec

20

25

Comparison between the synthetic acceleration and velocity seismograms (faultnormal component) using hybrid Green's functions and the observed ones from the mainshock.
The seismograms are bandpass filtered between 0.2 and 10.0 Hz. The synthetic is the result of 1
of 20 simulations that has the peak acceleration amplitude close to the simulated mean value.

30

366

K. Kamae, K. Irikura, and A. Pitarka

KBU (normal)

KOB (normal)( CM/SEC )h---o.os

1.0( CMISEC )h=O.051,00.1[ ~ J I,Ii~
0.1

10 3

-

1.0

1.0

10

I,,=,
0.1

1.0

10

PERIOD (SEC)

M O T (normal)

FKI (normal)

ASY (normal)( CM/SEC ),=o.os( CM/SEC )h=O.OS

10 3
~

10 2

I

I ~ StillI

1.0
PERIODI

I I Ittt

J

0.1
10

(SEC)

( CM/SEC )h=O.0S

10 3
10 2

\

1.0
I

0.1

PERIOD (SEC)

_=_

0.1

'"'
0.1

10

0.1

h=O.o5

1.0

0.1

10

( CM/SEC )PERIOD (SEC)

_

10= .

1.0

TKT (normal)

i

I

I

0.1

~ Ill

i

1,0
PERIOD~I [ tlll

10
(SEC)

10

_=

1.0

_=_

0.1

L

I

I I lilt

0.1

t

I

1.0

I I~lE

10

PERIOD (SEe)Figure 10. Comparison of the synthetic pseudo-velocity response spectra (the average and the average _+ one standard deviation: light solid line) and the observed one(heavy solid line).

the synthetic seismograms, selected among 20 simulations,that has the peak acceleration amplitude close to the simulated mean value. The standard deviation of the simulated
peak amplitude at the considered sites varies from 10 to
20%. A comparison of the pseudo-velocity response spectrais shown in Figure 10. Also shown in this figure is the variation (the mean value and the mean value plus/minus one
standard deviation) of the response amplitude in the shortperiod range. At FKI and ASY, where we do not have recordsof the mainshock ground motions, we compare synthetic
seismograms obtained with the HGF and EGF methods. Thevery good agreement between the synthetics shows that inregions where there is enough information about the deepand shallow geological structure, the HGF method performs
as well as the EGF method. The synthetic velocity seismograms are in good agreement with the observed ones in almost all the strong-motion station sites including those in
the heavily damaged area. However, at high frequencies, thesynthetic ground motions obtained by the HGF method arelarger than the observed ones. The same discrepancy wasobserved when the EGF method was used (Kamae and Irikura, 1998). The fact that the discrepancy exists even at

KBU, which is a rock site, suggests that one factor of thedifference in the high frequencies might be caused by thedifference in the fm~x of the mainshock and the small event.
The assumption of linear behavior of soils on which thetechnique is based might be another factor. Our simulationsuggests that during the mainshock, the soft soils at the considered sediment sites behaved nonlinearly. This is in agreement with the conclusion reached by Aguirre and Irikura(1995), who found evidences of nonlinear behavior of thesoft-surface sediments at some specific sites in the Kobe city.
Conclusions
We have proposed a method for simulating broadband
ground motions using HGFs. The HGF is produced by combining the finite-difference and stochastic methods that areused to calculate the low- and high-frequency content of thesynthetic Green's function, respectively. The method is effective at predicting ground motions from a large earthquake, especially for regions where the absence of smallmagnitude event records precludes the application of the
EGF method. We tested the method by comparing the syn-

A Techniquefor Simulating Strong Ground Motion Using Hybrid Green's Function
thetic with the recorded motion from the 1995 Hyogo-ken
Nanbu earthquake (Mw = 6.9). The comparison suggeststhat the HGF method is effective at simulating near-source
ground motions in a broad-frequency range of engineeringinterest.
Acknowledgments
We thank the Committee of Earthquake Observation and Research in the
Kansai Area for providing us with the velocity records. We would like tothank T. Kagawa for providing the restored velocity record at MOT station,
the Railway Technical Research Institute for the mainshock data at TKT
station (Serial Number R-032), and K. Koketsu for the digitalized data for
the JMA Intensity 7 area. Encouragements from Prof. Ralf Archuleta areappreciated. We greatly appreciate the useful review by two anonymous
reviewers. This study was partially supported by a Grant-in-Aide for Scientific Research, Number 08248111, from the Ministry of Education, Science, Sports, and Culture.

References
Aguirre, J. and K. Irikura (1995). Preliminary analysis of non-linear site
effects at Port island vertical array station during the 1995 Hyogoken Nanbu earthquake, J. Natural Disaster Sci. 16, 49-58.
Boom, D. M. (1983). Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra, Bull.
Seism. Soc. Am. 73, 1865-1894.
Graves, R. W. (1995). Preliminary analysis of long-period basin responsein the Los Angeles region from the 1994 Northridge earthquake, Geophys. Res. Lett. 22, 101-104.
Hartzell, S. H. (1978). Earthquake aftershocks as Green's functions, Geophys. Res. Lett. 5, 1-4.
Hartzell, S., A. Leeds, A. Frankel, and J. Michael (1996). Site response forurban Los Angeles using aftershocks of the Northridge earthquake,
Bull. Seism. Soc. Am. 86, S168-S192.
Heaton, T. H., J. F. Hall, D. J. Wald, and M. N. Hailing (1995). Responseof high-rise and base-isolated buildings to hypocetical Mw7.0 blind
thrust earthquake, Science 267, 206-211.
Horikawa, H., K. Hirahara, Y. Umeda, M. Hashimoto, and F. Kusano(1996). Simultaneous inversion of geodetic and strong motion data
for the source process of the Hyogo-ken Nanbu, Japan, earthquake,
Z Phys. Earth 44, 455-472.
Ide, S. and M. Takeo (1996). Source process of the 1995 Kobe earthquake:
determination of spatio-temporal slip distribution by bayesian modeling, Bull. Seism. Soc. Am. 86, 547-566.
lrikura, K. (1986). Prediction of strong acceleration motion using empiricalGreen's function, Proc. 7th Japan Earthquake Symp., 151-156.
Iwata, T., K. Hatayama, H. Kawase, and K. Irikura (1996). Site amplification of ground motions during aftershocks of the 1995 Hyogo-ken
Nanbu earthquake in severely damaged zone--array observation ofground motions at Higashinada ward, Kobe city, Japan, J. Phys. Earth44, 553-562.
Kagawa, T., K. Irikura, and I. Yokoi (1996). Restoring clipped records ofnear-field strong ground motion during the 1995 Hyogo-ken Nanbu(Kobe), Japan earthquake, J. Natural Disaster Sci. 187 43-57.
Kamae, K., P. Y. Bard, and K. Irikura (1998). Prediction of strong groundmotion in a EURO-SEISTEST using the empirical Green's function
method, J. Seism., in press.
Kamae, K. and K. Irikura (1998). Source model of the 1995 Hyogo-ken
Nanbu earthquake and simulation of near-source ground motion, Bull.
Seism. Soc. Am. 887 400-412.
Kawase, H. (1996). The cause of the damage belt in Kobe: "The basinedge effect," constructive interference of the direct S wave with thebasin-induced diffracted/rayleigh waves, Seism. Res. Lett. 67, 25-34.
Koketsu, K. (1997). Source process of the mainshock, Joint Report on Great

367

Hanshin-Awaji earthquake disaster, Vol. 1, Chap. 4, Source process,
SSJ, SJCE, AIJ, JGC, and JSME, in print.
Motosaka, M. and M. Nagano (1996). Analysis of ground motion amplification characteristics in Kobe city considering a deep irregular underground structure--interpretation of Heavily damaged belt zone
during the 1995 Hyogo-ken nanbu earthquake, J. Phys. Earth 44,
577-590.
Nakamura, Y., F. Uehara, and H. Inoue (1996). Waveform and its analysisof the 1995 Hyogo-Ken-Nanbu earthquake (II), JR Earthquake Information No. 23d, Railway Technical Research Institute, March (in Japanese).
Pitarka, A. and K. Irikura (1996). Basin structure effects on long period
strong motions in the San Fernando valley and the Los Angeles Basinfrom the 1994 Northridge earthquake and an aftershock, Bull. Seism.
Soc. Am. 86, S126~S137.
Pitarka, A., K. Irikura, T. Iwata, and T. Kagawa (1996). Basin structure
effects in the Kobe area inferred from the modeling of ground motions
from two aftershocks of the January 17, 1995 Hyogoken-nanhn earthquake, J. Phys. Earth 44, 563-576.
Pitarka, A., K. Irikura, and T. Iwata (1997). Modeling of ground motion in
Higashinada (Kobe) area for an aftershock of the January 17, 1995
Hyogo-ken Nanbu, Japan, earthquake, Geophys. J. Int. 131, 231-239.
Pitarka, A., K. Irikura, T. Iwata, and H. Sekiguchi (1998). Three-dimensional simulation of the near-fault ground motion for the 1995 Hyogoken Nanbu (Kobe), Japan, earthquake, Bull. Seism. Soc. Am. 88, 428440.
Saikia, C. K. (1993). Estimated ground motions in Los Angeles due to
Mw = 7 earthquake on the Elysian thrust fault, Bull Seism. Soc. Am.
83, 780-810.
Sekiguchi, H., K. Irikura, T. Iwata, Y. Kakehi, and M. Hoshiba (1996).
Minute locating of faulting beneath Kobe and the waveform inversionof the source process during the 1995 Hyogo-ken Nanbu, Japan, earthquake using strong ground motion records, J. Phys. Earth 44, 473488.
Tai, M., Y. Iwasaki, and A. Okazaki (1996). A simulation of the 1995
Hyogo-ken nanbu earthquake using stochastic Green's function
method in consideration of site specific amplifications and phase characteristics, Proc. l l th WCEE.
Wald, D. J. (1996). Slip history of the 1995 Kobe, Japan, earthquake determined from strong motion, teleseismic, and geodetic data, J. Phys.
Earth 44, 489-504.
Yoshida, S., K. Koketsu, B. Shibazaki, T. Sagita, T. Kato, and Y. Yoshida(1996). Joint inversion of near- and far-field waveforms and geodetic
data for the rupture process of the 1995 Kobe earthquake, J. Phys.
Earth 44, 437-454.
Research Reactor InstituteKyoto University
Noda, Kumatori-cho, Sennan-gun
Osaka, 590-04, Japan
Tel: + 81-724-51-2369; Fax: + 81-724-51-2603;
E-mail: kamae @kuca.rri.kyoto-u.ac.jp(K.K.)
D.P.R.I., Kyoto University
Gokasho, Uji
Kyoto, 611, Japan
Tel/Fax: + 81-774-33-5866; E-mail: irikura@egmdpri01.dpri.kyoto-u.ac.jp(K.I.)
Woodward-Clyde Federal Services
566 E1 Dorado Street, Suite 100
Pasadena, California 91101
Tel: 818-449-7650; Fax: 818-449-3536; E-mail: axpitar0@wcc.com(A.P.)
Manuscript received 10 September 1997.