Bulletin of the Seismological Society of America, 90, 1, pp. 117–133, February 2000

Fault Geometry at the Rupture Termination of the 1995
Hyogo-ken Nanbu Earthquake
by Haruko Sekiguchi, Kojiro Irikura, and Tomotaka Iwata

Abstract The source geometry and slip distribution at rupture termination of the
1995 Hyogo-ken Nanbu earthquake were investigated using waveform inversion on
the assumption of fault branching in the northeastern part of the rupture model.
Possible branching of the Okamoto fault is suggested both by the static-displacement
distribution and damage extension east of Kobe (Nishinomiya area). To exclude datacontaminated by the basin-edge-diffracted wave in the waveform-inversion process,we examined the spatio-temporal variation of its influence and from a comparison
with a flat model, we determined windows appropriate for the data. Three subeventswere identified, as was reported in previous works. The largest was in the shallow
part on the Awaji side, whereas the smaller two occurred at great depths (⬎7km) on
the Kobe side. We found a smaller subevent in the deep part of the branch. Total
variance reduction was larger, and the ABIC value was smaller when we assumed
the branch than when we did not, which shows the superiority of the branching fault
model. Resolution checks showed that the slips on proposed branched portions are
physical and not caused by random-data noise or systematic errors in Green’s functions that arise from misestimation of velocity structures. Calculation of the relative
static displacement between two leveling observation stations near the branchingfault also showed the greater utility of the branching fault model. The effect of slipon the branched fault has been shown in near-source ground-motion simulation using
the 3D finite-difference method (Iwata et al., 1999). The characteristic distributionof ground motion in the near-source region indicated by the damage distribution iswell reproduced by the modeling of both the source process and wave propagationin the realistic 3D velocity structure. Slip on the branched fault affected the groundmotion in eastern Kobe (Nada and Higashi-Nada wards), Ashiya, and Nishinomiya
cities, but its contribution is not dominant even in those regions; about 30 to 50%
maximum velocity in the frequency range of 0.1 to 1.0 Hz.
We conclude that branching rupture of the Okamoto fault during the Hyogo-ken
Nanbu earthquake is the preferable interpretation on the source process of this earthquake. This supports the idea of a geometrical barrier suggested by geological observations.
Introduction
area. To assess their combined effects, total simulations ofnear-source ground motions that took into account the rupture process and 3D velocity structure were made (Kawase
et al., 1997; Pitarka et al., 1998; Furumura and Koketsu,
1998). Furumura and Koketsu (1998) and Pitarka et al.
(1998) simulated near-source ground motion in the complex
basin-edge structure using the 3D finite-difference method
and the source models of Yoshida et al. (1996) and Sekiguchi et al. (1996b), respectively. They obtained a beltshaped, high-ground-velocity zone similar to the damage
belt distribution (Fig. 1), but their highest ground-velocity

Various aspects of the Hyogo-ken Nanbu (Kobe), Japan,
earthquake (MJMA ⳱ 7.2, 05:46:51.5 JST, 17 January 1995)
has been analyzed by many researchers. The goal has been
to answer the haunting question “how was such a huge disaster generated?” In particular, the mechanism that caused
the concentrated damage distribution, the so-called damage
belt, has been intensively discussed. From analyses ofstrong-motion data, we have learned that the rupture directivity constituting the source process and the local surface
geology, including the basement topography, were importantin the generation of strong ground motion in the near-source
117

118

H. Sekiguchi, K. Irikura, and T. Iwata

Figure 1.

Damage belt in the Kobe area isindicated by light gray zone. The digitizeddamage belt location data by Koketsu (1998).
Black and gray lines show the active fault
traces found by Ishihara et al. (1991). The
black lines indicate ones estimated to be causative faults in this study. The dashed line
shows the boundary of the basin’s edge (Iwata
et al., 1999).

zone stops at the eastern ends of Higashi-Nada Ward,
whereas the actual damage belt extends much further to theeast.
From Suma to Nada Ward, causative faults estimatedfrom the aftershock hypocenter distribution (Nemoto et al.,1996) run along the basin edge, and the damage belt wasformed at about a 1-km offset (Fig. 1). East of Nada Ward,
the causative faults estimated from the aftershock distribution have strikes departing from the basin edge. In contrast,
the damage belt extends along the basin edge. The Okamoto
fault, which begins near the junction of the Suwayama andGosukebashi faults (active structures considered to be partof the causative fault system) and parallels the edge of thebasin east of Nada Ward (Kobe City and Institute of Construction Engineering, 1998), was then suspected to haveruptured. Additional slip on the Okamoto fault was expected
to better explain the strong ground motion distribution in
Ashiya and Nishinomiya City. The Okamoto fault is beyond
the dense aftershock zone, but several aftershocks occurredalong it just after the mainshock (Nemoto et al., 1996). Observations of static displacements, the asymmetry of horizontal static-displacement vectors on both sides of the Gosukebashi fault from triangulation observations (Hashimoto
et al., 1996), and the irregular fringes on the SAR interferogram around the Okamoto fault (Fig. 2) (Murakami et al.,1995) also support the possibility of slip on the Okamoto
fault. Geological observations (e.g., King, 1986; Nakata etal., 1998) have shown that the irregularity of the rupturing
surface, such as fault bends and branching, works as a geometric barrier that impedes or terminates rupture extension.
Kame and Yamashita (1999) used numerical calculation to
study rupture extension without specifying the next rupturing surface. They found that the rupture surface tends tobend after reaching a certain level of rupture-propagation
velocity and terminate itself. At a certain rupture-propaga-tion velocity, the surface of the peak shear stress splits in
two, and when the rupture was permitted to branch, thebranch in the low normal stress area quickly bent and its
stretch became short, whereas the other branch in the highnormal stress area slowly extended and its stretch became
long. This feature closely resembles the configurations of
the Suwayama, Gosukebashi and Okamoto faults. The calculation was for virgin rock, but the essential mechanism inwhich the rupture surface bends and then terminates isthought to be valid even for rupture on a weak zone such as
pre-existing faults.
We considered it worthwhile to investigate the possibility of rupture on the Okamoto fault. Koketsu (1998) examined the possibility of slip on the Okamoto fault (designated as part of the Ashiya fault in his article) by comparing
waveform inversion results from fault-plane models withand without the Okamoto fault. He concluded that there issome possibility of slip on the Okamoto fault because thevariance reduction of the waveform inversion with the Okamoto fault is better than without, but not quantitatively so.
We here propose another fault-plane model with a branchedsegment—the Okamoto fault. At the other end of the fault
in this earthquake (the southwest end of the Nojima fault),
branching of the surface traces has been observed (Awata
and Mizuno, 1998). Observation stations in this area, however, are very few, and it is impossible to examine fault
branching at depth using the ground-motion records for thissouthern end.
To investigate detailed rupture geometry with improved
reliability, we gathered a new data set, adding strong-motion
records not previously used, and verified all the elements ofinversion. This article consists of six parts: (1) fault model,
parameterization, and methodology; (2) Data selection andexamination of the applicability of a 1D approximation of
the 3D velocity structure to compute synthetic waveforms;

Fault Geometry at the Rupture Termination of the 1995 Hyogo-ken Nanbu Earthquake

119

Figure 2. (Left) SAR (Synthetic Aperture Radar) interferogram made by comparing
two SAR images before and after the Hyogo-ken Nanbu earthquake (Murakami et al.,1995). Japanese words in the original figure has been translated into English, andseveral marks added with the author’s permission. The detected crustal deformation
shown by SAR interferometry represents ground displacements parallel to the satellite
line of the site. (right) Active fault systems in the source region of the Hyogo-ken
Nanbu earthquake (Ishihara et al., 1991). The scale of this map is the same as that in
the left hand side. Dense fringes are present along the main line of the estimatedcausative faults; the Nojima, Suwayama, Suma, and Gosukebashi faults. Some irregularfringes are present around the surface trace of the Okamoto fault (indicated by thearrow in the right figure). (See Fig. 1 for locations of the named active faults.)(3) waveform inversion; (4) Examination of the likehood of
the inversion result using numerical resolution tests; (5) contribution of the branching fault to static displacement, and(6) contribution of the branching fault to near-source groundmotion.

Fault Model, Parameterization, andInversion Methodology
Fault ModelA new fault plane model is proposed (Fig. 3, Table 1).
The main part of the fault model is located taking into account the results of many detailed studies done after theearthquake: the relocated mainshock and aftershock hypocenters reported by Nemoto et al. (1996, 1997), the static
displacements of triangulation points of Hashimoto et al.
(1996), the geodetic inversion results of Ozawa et al. (1997),

and the constraints on the location of the intersection of thecausative fault planes and the earth surface in the Kobe City
area obtained by Sekiguchi et al. (1996a,b). The fault model
is divided into four main segments, A, B, C, and D (respectively corresponding to the Nojima, Suma, Suwayama, andGosukebashi faults), and a branch segment, E, corresponding to the Okamoto fault. We performed the waveform inversion with ABCDD⬘ in order to examine the effect of segment E on the inversion results. Segment D⬘ was introduced
to keep the same number of parameters in the waveform
inversions with the two different fault models.
Representation and Discretization of Faulting
Faulting is represented as moment-release vectors onplanar surfaces. According to Aki and Richards (1980), theobservation equation of ground motion at position x due
to a displacement discontinuity across the faulting surface,
R, is

120

H. Sekiguchi, K. Irikura, and T. Iwata

135˚ 00'

135˚ 30'

D’

Fault Model

D
E
C

B
A
0km

10km

20km

34˚ 30'34˚ 30'135˚ 00'

135˚ 30'

Figure 3.

Fault-plane model (with segments A, B, C, D, and E). Black and graylines show the active-fault traces reported by Ishihara et al. (1991). The black lines arethose estimated to be causative faults in this study. Vectors show static displacements
during 1984 and 1995 after the earthquake, as determined by Hashimoto et al. (1996)
from GPS data. Epicenters of the mainshock and aftershocks during the day of themainshock are those determined by Nemoto et al. (1996, 1997). Dots are epicenters ofaftershocks that occurred within 18 hours after the mainshock. The fault plane modelwith segments A, B, C, D, and D⬘ was the reference model used to examine the effectof segment E.

Table 1
Fault Model Parameters
Segment

Corresponding Active Fault

Strike (deg)Dip (deg)

Length (km)

A
B
C
D
E

NojimaSuma
Suwayama
Gosukebashi
Okamoto

45.0
50.0
233.0
218.0
268.0

78.0
90.0
82.0
82.0
82.0

20.5
14.35
10.25
12.3
6.15

u̇n(x, t) ⳱冮冮 m (n, s)* G˙
pqnp,q (x, t; n, s)dR

(1)

R

with
mpq ⬅ [ui]tjcijpq(2)

where mpq is the moment-density tensor corresponding to
the slip distribution [ui]; Gnp,q (x, t; v, s) is the spatial derivative of Green’s tensor expressing the nth component of thedisplacement response at point x to a point dislocation in thep-direction on a plane normal to the q-direction at positionv; v is the vector normal to R; and cijpq is the elastic constanttensor of Hooke’s law. A dot denotes differentiation in time.
To obtain the spatio-temporal rupture history (mpq in rightside of equation 1), we numerically inverted the groundmotion data (left side of equation 1) using the multitime
window linear-waveform-inversion procedure of Hartzell
and Heaton (1983) in which the moment-release distribution
is discretized both in space and time. Discretization of the
moment release in time is obtained by putting a finite numberof temporally localized basis functions u(t) at certain timeintervals. We adopted the smoothed ramp function as thebasis function. Discretization in space was done by dividing
the model fault planes into small subfaults. Arbitrary-directed moment release on the fault plane model was realized
by combining two orthonormal unit vectors. Convolution of
the unit moment function, u(t), with the temporal and spatial
derivative of Green’s function representing the jth component of the synthetic-velocity waveform from the ith direction of the moment release on the lth subfault, gjil (x, t0 Ⳮ
hDt, l, s), gave a matrix, A, of element waveforms,Amn ⳱

冮g (x, tjil0Ⳮ hDt; l, s)* u(s ⳮ (kⳮ1)Dtw Ⳮ trupl )ds
with

(3)

121

Fault Geometry at the Rupture Termination of the 1995 Hyogo-ken Nanbu EarthquakeJⳮ1m⳱兺j Hj Ⳮ (h ⳮ 1),Yn ⳱ (k ⳮ 1)IL Ⳮ (i ⳮ 1)L Ⳮ l,(i ⳱ 1, . . . I, k ⳱ 1, . . . , K, l ⳱ 1, . . . , L)
where t0 is the initial time in the time range of the data used
for analysis; t0 Ⳮ hDt refers to discretized time with theincrement Dt; trupl is the time the rupture front arrives at thelth subfault; and Dtw the interval between adjacent time windows. I, J, K, L, and Hj respectively are the total number ofmoment release directions, data components, basis functions, subfaults, and data points of the jth component. The
problem is determining which weights should be assigned
to each element slip discretized into space, time, and two
slip directions.
The discretized observation equation in vector form
becomesd ⳱ Am

4.5km

45km
Ry

4km
1.8km

X

Zs
18km

(4)

where d is the observation velocity data vector and m themodel parameter vector. Observation equations in the same
form as equation (4) with the same discretized source representation can be constructed for other sites. Combining
these sets for sufficient number and azimuthal coverage of
observation stations gives a large, overdetermined, and simultaneous equation system.
How to choose subfault size is a problem for which noclear criteria have been established. To extract detailed information on the source process, it is preferable to take thesmallest possible subfaults, but spatial changes finer than thesmallest wavelength for analysis within a certain frequency
range cannot be constrained by data. On the other hand, thespatial periodicity arising from discretization of the fault islikely to generate spurious synthetic waves predominant in
the corresponding frequency. We therefore set the pointsource intervals such that the dominant frequency caused by
the spatial periodicity was well outside the frequency rangeof our analysis.
We put point-source grids on the fault segment planes
at 2.05 km intervals, and the expected predominant frequency became slightly higher than the frequency range ofthe present study; 0.1–1.0 Hz. The number of subfaults (L)turned out to be 310. The moment-release time history wasmodeled using six time windows (K), each 0.5 sec apart.
The slip in each time window was represented by a smoothed
ramp function with an 0.8 sec rise time in pure strike andpure dipping directions (l ⳱ 2). Rupture velocity was fixed
at 3.1 km/sec for the first time window. Data of three components data (J ⳱ 3) were used when possible, but one of
the components was not available at several stations.
Constraints
Although the discretized observation (equation 4) is an
overdetermined system (after combining equations for a suf-

22km

Z

Figure 4. Model space for the 3D FDM wavefield
simulation to investigate applicability of the 1D approximation of the 3D velocity structure. Part of abasin is modeled, and its edge is along the Y-axis.
The thickness of the sediments is 1.8 km, a typicalvalue estimated along the shoreline in the Kobe area.
The point source is located 0.5 km from the edge ofthe hard rock region at a certain depth (Zs). Ry is the
distance from the source to a site on the Y-axis.
Waveforms were calculated over the shaded area.
Simulation also was done with a flat layer model that
had a flat sediment layer with the same thickness andmaterial parameters.

Table 2Model Parameters of an Underground Structure for Simulationof Basin-Edge-Diffracted Waves

Sediment 1
Sediment 2
1st rock
2nd rock
Half space

VP(km/sec)

VS(km/sec)q(g/cm3)

QP ⳱ QS

Depth (km)

2.0
2.2
5.5
6.0
6.7

0.6
1.1
3.2
3.5
3.9

2.1
2.1
2.4
2.7
2.8

80
80
300
400
500

0.85 (inside basin)
1.8 (inside basin)
4.0
17.8
—

ficient number of observation stations), the solution is unstable because the system includes underdetermined model
parameters. Stabilization techniques therefore are necessary.
Non-negative constraints to limit the rake-angle variation are
required to suppress destructive interferences between adjacent subfaults. The non-negative least-squares problem issolved by using the routine NNLS of Lawson and Hanson(1974).

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H. Sekiguchi, K. Irikura, and T. Iwata

Waveforms generated from a source at Zs ⳱ 10 km deep for the sites Ry
⳱ 12 km in the model space shown in Fig. 4. Solid lines are synthetic waveforms forthe basin-edge structure, dotted lines for the flat layer structure. FN and FP correspondto the X- and Y-axis directions in Fig. 4. Crosses (x) indicate the times at which thedifference in the two waveforms exceeds 20% of the maximum amplitude of the two
traces. The vertical measure shows the distance from the basin’s edge to the sites.

Figure 5.

Smoothing constraint is assigned to reduce instability or
too much complexity beyond the resolvability of the data
based on inspection that slips close together in space and intime should be similar. Different measures of roughness
have been proposed to smooth-model parameters, most ofwhich are based on the first and second derivatives of themodel parameters with respect to spatial or temporal coordinates. Here, we propose the following smoothing constraints.
We assign smoothing to every pair of unknown parameters n and n⬘ whose subfaults are in the same segment withstrength normal to the inverse of the spatio-temporal distance between them;rnn⬘ ⳱ 㛳{trupl ⳮ trupl⬘Ⳮ (k ⳮ k⬘)Dtw}Vs㛳 Ⳮ 㛳rspacell⬘㛳,(5)where |*| means the first norm. We gather the smoothing
equations related to a given model parameter. The smoothing equation for the nth parameter is1

兺 rnn⬘n⬘冦 冧rnn⬘ ⱕ

Vs
fh

1

mn ⳮ

兺 rnn⬘ mn⬘ ⳱ 0,n⬘rnn⬘ ⱕ

Vs
fh(6)

where rspacell⬘ is the distance between the lth and l⬘th subfaults in space, Vs the S-wave velocity at lth subfaults, andn⬘ ⳱ (k⬘ ⳮ l) IL Ⳮ (i⬘ ⳮ l) L Ⳮ l⬘. The distance thatsmoothing reaches should be limited to the length traveledby the S wave in the period corresponding to the high frequency limit (fh) of the analysis.
A smoothing matrix, S, is constructed by combiningFault Geometry at the Rupture Termination of the 1995 Hyogo-ken Nanbu Earthquake

Figure 6.

Supposing a certain position inside the basin at a certain location against
the Hyogo-ken Nanbu earthquake (i.e., the distance from the basin’s edge and the
hypocenter distance), all the waveforms calculated in the 3D FD model space (Fig. 4)
at that constant basin-edge-distance (5km in this figure) were gathered and plottedtaking into account the time shifts corresponding to the rupture propagation from the
hypocenter to the sources. The time when the 1-D approximates of the 3-D velocity
structure near the basin edge can be estimated (before the time denoted by the dashedlines). The rupture velocity assumed here is 3.1 km/sec, the same as that assumed in
the waveform inversion.

123

124

H. Sekiguchi, K. Irikura, and T. Iwata

equation 6 for all the model parameters. The system under
scrutiny then becomes

冤kSA 冥m ⳱ 冤d0冥,(7)

where k is a parameter to control the strength of thesmoothing.
ABIC for Selecting Appropriate Smoothing Strength

Figure 7.

The 25 stations used in the waveform
inversion. The collection agency for each record islisted in Table 3.

When a smoothing constraint is used, the resulting inversion solution depends on the value of k, the trade-off
parameter controlling the strength of the smoothing constraint. The smaller k becomes, the better the fit between theobserved and synthesized waveforms. The moment release
distribution, however, is too complicated because of overinterpretation of the data, and the solution is unstable due tonoise in the data and/or synthetic Green’s functions. To determine the proper value of k, we used Akaike’s Bayesian
information criterion (ABIC) (Akaike, 1980). Yoshida(1989) and Ide et al. (1996) introduced ABIC into source
modeling.
When the above system (equation 7) is solved using theleast-square-inversion method, Gaussian distributions of error are automatically assumed for synthetic data and estimated parameters, and likehood functions are assumed;

冤

M

P(d|m, r) ⳱ (2pr2)ⳮ 2 exp ⳮ
Table 3Observed Seismograms Used
StationLatitudeLongitude

Organization

AMC
CHY
KBU
MOT
TDO
TOY
AID
AIO
AWA
HEG
KOB
KOY
MRT
OKA
OSA
WAC
NKY
SOK
KMT
ABU
KN1
NRT

34.7180
34.439034.7250
34.7250
34.4800
34.801034.94033.79234.33634.65334.69
34.21833.2483
34.6583
34.678335.28334.9667
34.7431
34.38334.8600
34.85534.234135.4080
135.6590
135.2400
135.2810
135.4080
135.5010
134.168
134.452134.908
135.685
135.18135.593134.1800
133.9183
135.5217
135.402135.6222
135.4417
135.35135.5735
135.217134.641

TZK

34.8083

135.3437

RKI
KPI

34.6883
34.670135.2728
135.208

CEORKACEORKACEORKACEORKACEORKACEORKA
JMA
JMA
JMA
JMA
JMA
JMA
JMA
JMA
JMA
JMA
Kansai Electric Power Co. Inc.
Kansai Electric Power Co. Inc.
RRI, Kyoto Univ.
RCEP DPRI, Kyoto Univ.
Matsumuragumi Co. Inc.
Honshu-Shikoku Bridge Public
Corporation
Railway Technical ResearchInstitute
Sekisui House Co. Inc.
Kobe City㛳d ⳮ Gm㛳2
2r2

冥

(8)

for data distribution, andMs

冤P(m, r⬘) ⳱ (2pr⬘2)ⳮ 2 exp ⳮ

㛳Sm㛳2
2r⬘2

冥

(9)

for prior distribution of the parameters, that is, smooth distribution of slip in space and in time is given as a priori
information for the parameter distribution. M and Ms, respectively, are number of data and the smoothing equations.
The ratio r/r⬘ turns out to be k. Based on the idea of ABIC,a set of parameters that have the largest values in the integration of the product of the above two distributions withrespect to the model parameter gives the largest entropy, andrealization of such parameter set should occur most frequently extracting the largest amount of information included in the simultaneous equations. The ABIC value isdefined as follows (Akaike, 1980):

冮

ABIC ⳱ ⳮ2log| P(d|m, r)P(m, r⬘)dm| Ⳮ 2Nhp
⳱ (M Ⳮ Ms ⳮ N)log 2p Ⳮ (M Ⳮ Ms ⳮ N)log(㛳d ⳮ Am㛳2 Ⳮ k2㛳Sm㛳2) ⳮ 2Ms log kⳭ 2(M Ⳮ Ms ⳮ N)log(M Ⳮ Ms ⳮ N)
Ⳮ log㛳ATA Ⳮ k2STS㛳 Ⳮ (M Ⳮ Ms ⳮ N) Ⳮ 2Nhp

(10)

125

Fault Geometry at the Rupture Termination of the 1995 Hyogo-ken Nanbu Earthquake

Figure 8.

(left) Six different inversion results found with the same fault model, data set,
Green’s functions, and rake angle variation
constraints, and with different smoothing
strengths. (right) Variation in ABIC, misfit, andtotal moment due to the smoothing constraint
strength, k.

where N is the total number of model parameters, Nhp thenumber of hyperparameters; 2 (r and k or r⬘) in our system.
A solution is most appropriate in our system when the
ABIC value is smallest. The ABIC value depends on unknown parameters {m} and the strength parameter ofsmoothing, k. This value can be calculated only after aninversion result has been obtained. Several waveform inversions with different smoothing strengths, k, are performed
and the ABIC value for each inversion calculated to find thebest parameters set and smoothing strength.

Examination of the 1-D Approximation for the 3-D
Velocity Structure and Data Selection
To obtain improved resolution in the rupture distribution, we used near-source seismograms recorded in the
Osaka sedimentary basin. As has been pointed out, the waveforms there, especially in the Kobe City area, are strongly

affected by diffraction from the northern edge of the Osakabasin (Kawase 1996; Motosaka and Nagano, 1996; Pitarka
et al., 1998). The synthetics used in the waveform inversion,
however, are calculated on the assumption of a flat layeredvelocity structure because of computational limitations andthe lack of detailed underground structure information. Because the basin-edge-diffracted wave produces a remarkable
phase, use of records affected by the basin-edge wave maylead to a wrong slip distribution. Expected errors in the synthetics must be evaluated when the 3D structure is approximated using the 1D (flat layer) structure in this area to avoid
including them in the waveform inversion.
The effect of the basin edge-diffracted wave differs depending on hypocenter depth and the relative location of thesite with respect to the source. To gauge spatial variation inits effect, we simulated the wave field in this 3D model space(Fig. 4, Table 2) using the 3D finite-difference method (Pitarka et al., 1998). Figure 5 shows the synthesized wave-

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H. Sekiguchi, K. Irikura, and T. Iwata

in the Kobe downtown area (inside of the basin in the Kobe
City) are strongly affected almost from the beginning of the
S wave; (3) the KPI and RKI (Figure 7) waveforms, however, are not contaminated by the diffracted wave for the
first few seconds after the S arrival; (4) at the KOB and MOT
stations, several hundred meters from the basin edge, thebasin-edge-diffracted wave is not yet expected to have developed as clearly shown in Figure 5, and Moya and Irikura(1998) showed that the site response in the low-frequency
range (⬍1Hz) at MOT is similar to that of a hard rock site,
although more than a 700 m depth of alluvium layer is estimated there from reflection survey analysis (e.g., Huzita,
1996).
Data Selection
This earthquake provided much strong ground motion
data in the source region, particularly east of the hypocenter.
The quality and quantity of this waveform data excels thoseof other earthquakes. The plentitude of valuable data madeit possible to investigate complex-fault configuration.
For the simple examination of the 1D approximation forthe 3D velocity structure, we selected 25 records (Fig. 7 andTable 3), most being within the epicentral distance of 100
km. The original seismograms at stations KBU and MOT
were clipped on some components. Kagawa et al. (1996)
restored these seismograms on the basis of the saturation
characteristics of servovelocity-type seismographs.
Velocity Structure Models

Figure 9.

Time progression of rupture in terms ofthe moment release density at 1 sec intervals.

forms at stations Ry ⳱ 12km from the source at Zs ⳱ 10km
depth. Solid lines correspond to the basin-edge-structure
model, and dashed lines correspond to the flat layered model.
Crosses (x) in each seismogram indicate times when the difference in the two waveforms exceeds 20% of the maximum
amplitude of both traces. These differences are caused by
the basin-edge-diffracted waves that propagate at a lower
velocity than the apparent velocity of the direct S wave. They
affect therefore the direct S-wave portion in the near-edge
area but separate clearly from it in the off-edge area. Figure
6 shows synthesized waveforms from sources in various Ry
and Zs for a site 5 km from the edge of the basin.
We found that (1) more than 10 km from the basin’sedge, the entire direct S-wave portion escapes being overlapped by the basin-edge-diffracted wave; (2) most records

Velocity structure modeling was done as follows. Starting models of the underground-velocity structure first wereconstructed based on geological information obtained fromreflection or refraction surveys and from logging records.
The parameters of the underground structures then weretuned by trial-and-error to explain the P- and S-wave travel
times for the mainshock and specific phases in the aftershocks.
Models for sites inside the Osaka basin were based on
the results of extensive reflection surveys (e.g., Huzita,
1996) made after this earthquake to determine the depth of
bedrock near the basin’s edge in Kobe. Velocities and densities of the sedimentary layers were modeled according to
Kagawa et al. (1993). Structures of the rock sites at the KOB
and MOT stations were assumed.
Green’s Functions
The discrete-wavenumber method (Bouchon, 1981) together with the reflection-transmission method (Kennett and
Kerry, 1979) was used to calculate the point-source Green’s
functions in laterally homogeneous (1D) velocity structures.
Velocity synthetics were calculated. The observed records
were integrated into velocity when the original records werein acceleration. All the observed and point source synthetics
were bandpass filtered from 0.1 to 1.0 Hz and resampled at
5.0 Hz.

Fault Geometry at the Rupture Termination of the 1995 Hyogo-ken Nanbu Earthquake

Figure 10.

Observed velocity waveforms (solid lines) and synthetics (dotted lines).

127

128

H. Sekiguchi, K. Irikura, and T. Iwata

(a)

A

B

C

D

E

A

B

C

D

D’

10 15 20
X(km)

25 30

35 40

z(km)

5
10
15
20

(b)

*1010(N/m)

z(km)

5
10
15

Figure 11.

Observed (bold line) and synthetic(thin line) waveforms at KBU station. From the top:
observed, synthetics for all 5 segments (ABCDE), andsynthetics from segment A, B, C, D, and E.

Inversion Results
Rupture Process for the Branching Fault Model
Six different source models that use identical fault models, data sets, Green’s functions, and rake angle variation
constraints with different smoothing strengths are shown in
Figure 8. A k value of 0.05 gave the smallest ABIC values
among the inversions performed. So this was adopted as thesource model. The misfit value increases markedly when k
exceeds 0.05, and the total moment release varies greatly
due to the smoothing strength. Because the total-moment
release varies with the amount of destructive interference
suppressed by the smoothing constraint, and the total moment release values inverted for a large number of model
parameters do not have high reliability.
The time progression for inverted rupture and the waveforms calculated for the ABCDE fault model when the ABIC
value is smallest are shown in Figures 9 and 10. As in previous source inversion studies (Horikawa et al., 1996; Ide etal., 1996; Sekiguchi et al., 1996b; Wald, 1996; Yoshida andKoketsu, 1996), rupture progressed upward on the Awaji
side and went into the deeper part on the Kobe side. Spatial
distribution is more complicated as compared with previous
findings (Sekiguchi et al., 1996b) perhaps because velocity
waveforms and smaller grid spacing were used in the inversion. The three areas that had a relatively large moment release (subevents) were confirmed on segments A, B, and C
in agreement with a previous report (Sekiguchi et al.,1996b). We found a subevent smaller than those three at thebottom of segment E. Significant contribution (remarkable
phase that contributes to marked variance reduction) of segment E is seen only at stations near this segment, the second
pulse in the waveforms being strengthened by the waves
from the slip on segment E (Fig. 11). This kind of slip thatappears at the very edge of an assumed fault plane often issuspected to be caused by random noise contained in thedata, errors in Green’s functions due to misestimation ofshallow-velocity structures, or the need for extension of themodel-fault plane. To examine its reliability, we performed

20-20 -15 -10 -5

0

5

14
12
10
8
6
4
2
0

Figure 12. Final moment release distribution (a)for the ABCDE fault model with segments A, B, C,
D, and E, and (b) for the ABCDD⬘ fault model.
another waveform inversion with the ABCDD⬘ model andmade numerical resolution checks (see subsegment sections).
The UD components of synthesized waveforms at stations
near the fault are very small compared to the observed records. We considered the following reasons: the model fault
planes are assumed by several planar, nearly vertical surfaces,
and the slips on the fault planes are dominant in strike slip
component. Because the angle formed by the fault plane anda line between a point on the fault planes and a nearby station
generally is very small, the synthetics for those stations become dominant in the horizontal component. In contrast, real
fault planes have not flat but rough and/or curved surfaces
and should generate more UD component waves than themodel fault. Small-scale heterogeneity of the crust, which is
not considered in the theoretical Green’s function calculation, also may give more UD components.
Rupture Process for a Fault Model without Branching
Waveform inversion was performed with the ABCDD⬘
model (without the Okamoto fault) (Fig. 11), the source
model with the minimum ABIC value was obtained, and results were compared with those of the ABCDE model. The
final moment release distribution for this fault model isshown in Figure 12b. The overall rupture distribution characteristics are similar. No large moment releases were seenin the northeastern part of the fault. Variance reduction wasslightly higher (2%), and the ABIC value was smaller for the
ABCDE model as compared with the ABCDD⬘ model. Variance reduction was much higher when branching was assumed at stations near the branch.

Numerical Resolution Check
Examination of the Effect of Random
Noise on Inversion Results
We examined whether random noise in the data would
generate a ghost subevent on the Okamoto fault. Again, aFault Geometry at the Rupture Termination of the 1995 Hyogo-ken Nanbu Earthquake

Figure 13. Distribution of the final moment release and slip of the assumed (left)
and inverted (right) source models for the resolution check used to examine the effectof random noise on the waveform inversion result. In case 1 (upper), five subevents
are assumed, and in case 2, four subevents are assumed.

Figure 14. Distributions of final-moment release and slip of the assumed (left) andinverted (right) source models for the resolution check on the effect of misestimationof the velocity structure on the waveform inversion result. In case 1 (upper), five
subevents are assumed, and in case 2, four subevents.

129

130

H. Sekiguchi, K. Irikura, and T. Iwata

Figure 15. Relative static displacement vectors
between the leveling observation stations near the
branching fault. The station on the northwest side ofsegment D segment is fixed, whereas the relative
static displacements of the two stations on the southeast side are calculated. Open arrows indicate the observed static displacements, gray ones synthetics fromthe ABCDE-model, and black ones synthetics fromthe ABCDD⬘-model.
homogeneous pure strike slip was assumed on areas surrounded by the bold line (Fig. 13), and target waveforms
were generated for two conditions. In case 1, five subeventswere assumed, and in case 2, four subevents. Gaussian noise
was added to the target waveforms. The standard deviationof noise was 20% of the peak amplitude of the target waveforms. The noise level was deduced from the misfitting of
the target and inverted waveforms for available aftershocks,
using the velocity structure models in the present waveform
inversion (Bouchon et al., 1998). In this test, the smoothing
strength parameter was fixed at the same value found as themost appropriate value in the inversion of the real data. Because of noise and smoothing constraints in the waveform
inversion, moment release appears even beyond the assumed
subevent areas, and especially around the subevents. In case
1, an assumed subevent at the bottom of the Okamoto fault
was recovered. In case 2, no remarkable ghost subevent was
found there. This means that a subevent like the one obtainedat the bottom of the Okamoto fault in the real-data inversion
can not be generated, even assuming there is as much as
20% random noise.
Examination of Misestimation of the Velocity
Structure on Inversion Results
Next, we examined whether the effect of misestimating
the velocity structure can generate a ghost subevent on the
Okamoto fault. Such misestimation is thought to induce systematic errors in the Green’s functions for the inversion. As
explained earlier, the velocity-structure models were tuned

by trial and error to obtain the P-arrival, S-arrival, or P-Stime in the observations. Tuning, however, was not complete. Moreover, the lateral heterogeneity of the velocity
structure, which was not considered in our calculations, generates errors in the Green’s functions. These errors are characterized by amplitude and phase misestimation, and arrivaltime differences, the latter being more severe in the
waveform inversion. The average error of the S-arrival timesof the Green’s functions, calculated between the hypocenter
subfault and observation stations for which absolute time
information is available, was about 3.5% of the S-wave
travel time. It turns out that in our study the average seismic
wave velocity in the medium has about 3.5% error. A set ofelement waveforms was generated, and time shifts were
given corresponding to the misestimation of the average velocity that had a deviation range that followed a Gaussian
distribution with a standard deviation of 3.5% of the averagevelocity of each station’s structure model. Of course, all theelement waveforms shifted in time for the structure modelmisestimation and were time-shifted again so that the S arrival from the hypocenter subfault would meet the S-arrivalof the observation, a usual procedure in waveform inversion.
Target waveforms were calculated assuming five subeventsin case 1 and four in case 2, using no time-shifted element
waveforms (Fig. 14).
Recovery of the moment-release distribution was not
good, even with only 3.5% misestimation of the average
seismic-wave velocity, indicative that misestimation of thevelocity structure causes large errors in the resulting solution
and of the importance of constructing reliable velocity structure models for waveform inversion. Even so, an assumed
subevent at the bottom of the Okamoto fault was recoveredin case 1, but not in case 2. This means that a subevent likethat we obtained at the bottom of the Okamoto fault in thereal data inversion can not be generated by 3.5% misestimation of the average velocity of the seismic wave in thecrust.

Contribution of the Branching Segment
to Static Displacement
Static displacements were computed at leveling observation stations near the branching fault to determine the contribution of the branching fault (Fig. 15), using the methodof Hernandez et al. (1997). The same lateral homogeneous
velocity structure as for the KBU station in the waveform
inversion was assumed, and the static on the synthetics far
after the arrival of the slowest waves was measured. As theleveling observation stations are close to the model fault
planes, the Green’s functions from distributed point sources
on a subfault too close to a station to be represented by asingle-point source were calculated. The density of the distributed point sources on the subfault was determined fromthe relative distance between the subfault and the station.
Clearly, the direction of the synthetic-static displacement at
the southernmost station of the two better agrees with that

Fault Geometry at the Rupture Termination of the 1995 Hyogo-ken Nanbu Earthquake

131

Figure 16. Bird’s eye view of the sediment-bedrock interface topography of themodel space for 3D FDM wave-field modeling (Iwata et al., 1999). The space stretches
58 km in the direction N58⬚E, 13.6 km in the direction of N148⬚E, and 23 km in deep.

Table 4Model Parameters of an Underground Structure for 3D
Simulation (after Iwata et al., 1999)

Sediment 1
Sediment 2
1st rock
2nd rock
Half space

VP (km/sec)

VS (km/sec)

q (g/cm3)

QP ⳱ QS

Depth (km)

2.0
2.2
5.5
6.0
6.7

0.6
1.1
3.2
3.5
3.9

2.1
2.1
2.4
2.7
2.8

80
80
300
400
500

Irregular
Irregular
4.0
17.8
—

of the observation of the slip distribution of the ABCDE
model, rather than the ABCDD⬘ model is assumed. At thenorthernmost station the difference caused by the two source
models is negligible.

Contribution of the Branching Segment to the
Near-Source Ground Motion
Near-source ground motion was simulated using 3-D
FDM (Pitarka et al., 1998) to gauge the effect of slip on the

branched fault (Iwata et al., 1999). The heterogeneous structure model was selected based on the results of extensive
reflection surveys (e.g., Huzita, 1996) made after this earthquake and on findings of Kagawa et al. (1993, 1998). A
bird’s eye view of the sediment-bedrock-interface topography in the model space is shown in Fig. 16. The model
parameters of the underground structure are given in Table
4. The fourth and bottom windows of Figure 17 (after Iwata
et al., 1999, but recalculated using the source model of thepresent study) respectively show the distribution of maximum horizontal ground velocity when whole moment release (inside the model space) is introduced and when moment release on only the branched fault is assumed.
Characteristic distribution of ground motion in the nearsource region, indicated by the damage distribution (Fig. 1),
is well reproduced by the modeling of both the source process and wave propagation in the realistic 3D velocity struc-

Figure 17. Distribution of the maximum-horizontal velocity from each segment of the source (after
Iwata et al., 1999, but recalculated using the source
model of the present study.) From top to bottom: distributions of maximum horizontal velocities causedby slip on Segments B, C, D, E and on the entire
source area.

ture. The slip on the branched fault affected the ground motion in the eastern part of Kobe (Nada and Higashi-Nada
wards), Ashiya, and Nishinomiya cities. But its contribution
was not dominant, even in those regions.

132

H. Sekiguchi, K. Irikura, and T. Iwata

Conclusions
Waveform inversion for the source process of the 1995
Hyogo-ken Nanbu earthquake was performed, focusing on
the fault geometry and slip distribution at rupture termination. Fault branching in the northeastern part of the faultplane model was assumed because it was suggested by static
displacements (Murakami et al., 1995; Hashimoto et al.,1996) and damage extension east of Kobe (the Ashiya andNishinomiya areas). Three main subevents were recovered
as in a previous study (Sekiguchi et al., 1996b). Moreover,a subevent smaller than these three subevents was found at
the bottom of the assumed branching E segment. A significant contribution of the E segment was seen only at stations
near this segment at which the second pulse in the waveforms was strengthened by waves from slips on the E segment. Relatively large slips were found in the deep part ofthe branch. Total-variance reduction was larger and the ABIC
value was smaller when this branch was assumed, which isindicative of the superiority of the branching fault model.
Resolution checks showed that the slip on the branched segment was caused neither by the random noise contained in
the data nor by synthetic errors in the Green’s functions due
to misestimation of shallow-velocity structures. Slip distribution obtained with the ABCDE model (with the branch)produced a synthetic-static-displacement vector that better
agreed with that of the actual record at the leveling observation station closest to the branching fault than did the slip
distribution of ABCDD⬘ model (without the branch).
We conclude that a scenario in which there was thepossibility that the causative fault branched and rupture advanced to the bottom of the Okamoto fault should be thepreferred interpretation for this earthquake. We carefully
eliminated records contaminated by strong-diffraction waves
generated by the 3D bedrock topography near the basin’sedge, and after obtaining the inversion result, ruled out thepossibility that the result was caused by random noise or themisestimation of the shallow-velocity structure.
This finding agrees with Koketsu’s (1998) report. He
performed joint inversion of near- and far-field waveforms
and geodetic data using fault models with and without the
Okamoto fault branch (referred to as the Ashiya fault in his
analysis) and obtained slightly better fitting to the data when
he used the branching model.
As briefly noted in the introduction, the static displacements and the SAR interferograms around the Okamoto fault
indicate the possibility of dislocation on that fault. No
strong, conclusive evidence has been found, but there ismuch evidence providing positive support for rupture
branching in the northeastern part of the source fault.
The fact that earthquake termination with fault branching was found using the waveform inversion of strong
ground motion records supports the idea of a geometricalbarrier suggested by geological observations (e.g., King,
1986; Nakata et al., 1998). The concept of such a barrier is

expected to provide useful information for predicting in advance the source areas of future earthquakes.
The effect of slip on the branched fault has been shownin a near-source ground-motion simulation using the 3D
FDM (Iwata et al., 1999). The characteristic distribution ofground motion in the near-source region, indicated by thedamage distribution, is well reproduced by the modeling ofboth the source process and wave propagation in the realistic
3D velocity structure. The slip on the branched fault affected
the ground motion in eastern Kobe (Nada and Higashi-Nada
wards), Ashiya, and Nishinomiya, but its contribution was
not dominant, even in those regions, being about 30 to 50%
the maximum velocity at 0.1 to 1.0 Hz.

Acknowledgments
We thank the organizations who provided the recordings: the Committee of Earthquake Observation and Research in the Kansai Area
(CEORKA); Japan Meteorological Agency (JMA); Kansai Electric PowerCo. Inc.; Port and Harbor Research Institute; Research Center of Earthquake Prediction of Disaster Prevention Research Institute, Kyoto University (RCEP of DPRI, Kyoto Univ.); Research Reactor Institute, Kyoto Univ.
(RRI, Kyoto Univ.); Public Works Research Institute (Public Works Research Institute, 1995); Kobe City; Sekisui House Co. Inc.; Matsumuragumi
Co. Inc.; and the Railway Technical Research Institute (Nakamura et al.,1996) (serial no. 032). We also are grateful to Takao Kagawa for providing
the restored recordings for the KBU and MOT stations, Olivier Coutant
who originally coded the program used to calculate Green’s functions forlayered media, Arben Pitarka for his 3D finite-difference code and instruction on its use, and Francisco J. Sanchez-Sesma, Hiroshi Kawase, and Andreas Rietbrock for their helpful advice. GMT (Genetic Mapping Tools,
Version 3.0, Wessel and Smith, 1991) was used to make the figures. The
discussion in this article was significantly improved by the efforts of theassociate editor, David Wald, and two anonymous referees. This study waspartially supported by Grant-In-Aide for Scientific Research, No. 08248111
and No. 11209201, from the Ministry of Education, Science, Sports, andCulture, Japan.

References
Akaike, H. (1980). Likelihood and the Bayes procedure, in Bayesian Statics, J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M.
Smith (Editors), University Press, Valencia, Spain, 143–166.
Aki, K., and P. G. Richards (1980). Quantitative Seismology, W. H. Freeman, San Francisco, 932 pp.
Awata, Y., and K. Mizuno (1998). Explanatory text of the strip map of thesurface fault ruptures associated with the 1995 Hyogo-ken Nanbu
earthquake, central Japan: The Nojima, Ogura and Nadagawa earthquake faults, Geological Survey of Japan, Tsukuba, Tectonic map
series 12, 74 pp, scale 1:10,000, (in Japanese).
Bouchon, M. (1981). A simple method to calculate Green’s function forelastic layered media, Bull. Seism. Soc. Am. 71, 959–971.
Bouchon, M., H. Sekiguchi, K. Irikura, and T. Iwata (1998). Some characteristics of the stress field of the 1995 Hyogo-ken Nanbu (Kobe)
earthquake, J. Geophys. Res. 103, B10, 24271–24282.
Furumura, T., and K. Koketsu (1998). Specific distribution of ground motion during the 1995 Kobe earthquake and its generation mechanism,
Geophys. Res. Lett. 25, 785–788.
Hartzell, S. H., and T. H. Heaton (1983). Inversion of strong ground motion
and teleseismic waveform data for the fault rupture history of the 1979
Imperial Valley, California, earthquake, Bull. Seism. Soc. Am. 73,
1553–1583.

133

Fault Geometry at the Rupture Termination of the 1995 Hyogo-ken Nanbu Earthquake
Hashimoto, M., T. Sagiya, H. Tsuji, Y. Hatanaka, and T. Tada (1996).
Coseismic displacements of the 1995 Kobe earthquake, J. Phys. Earth44, 255–279.
Hernandez, B., F. Cotton, M. Campillo, and D. Massonnet (1997). A comparison between short term (co-seismic) and long term (one year) slip
for the Landers earthquake: Measurements from strong motion and
SAR interferometry, Geophys. Res. Lett. 24, 1579–1582.
Horikawa, H., K. Hirahara, Y. Umeda, M. Hashimoto, F. Kusano (1996).
Simultaneous inversion of geodetic and strong motion data for thesource process of the Hyogo-ken Nanbu, Japan, earthquake, J. Phys.
Earth 44, 455–471.
Huzita, K. (1996). Survey results of active faults in the Osaka-Kobe area,
Proc. 9th Seminar on Studying Active Faults: On the Deep Structureof the Osaka Bay Area, 1–10 (in Japanese).
Ide, S., M. Takeo, and Y. Yoshida (1996). Source process of the 1995 Kobe
earthquake: Determination of spatio-temporal slip distribution by
Bayesian modeling, Bull. Seism. Soc. Am. 86, 547–566.
Ishihara, M., S. Yoshikawa, M. Mitamura, K. Mizuno, and T. Hayashi(1991). Quaternary Geological Map of Osaka and Adjacent Areas,
Kinki, Japan, scale 1:125,000, in Urban Kubota 30, Kubota Co. Ltd.
(in Japanese).
Iwata, T., H. Sekiguchi, A. Pitarka, and K. Irikura (1999). Ground motion
simulations in the Kobe area during the 1995 Hyogoken-Nanbu earthquake, in The Effects of Surface Geology on Seismic Motion, Irikura
K., K. Kudo, H. Okada, and T. Sasatani (Editors), Vol. 3, BALKEMA,
Rotterdam, 1295–1310.
Kagawa, T., S. Sawada, Y. Iwasaki, and A. Nanjo (1993). Modeling of the
deep underground structures of the Osaka basin, Proc. 22th JSCE
Earthq. Eng. Symp., 199–202 (in Japanese).
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 Disas. Sci. 18, No. 1, 43–57.
Kagawa, T., S. Sawada, Y. Iwasaki, and A. Nanjo (1998). S-wave velocity
structure model of the Osaka sedimentary basin derived from microtremor array observations, J. Seism. Soc. Jpn (Zisin) 51, 31–40 (inJapanese).
Kame, N., and T. Yamashita (1999). A new light on arresting mechanismof dynamic earthquake faulting, Geophys. Res. Lett. 26, 1997–2000.
Kawase, H. (1996). The cause of the damage belt in Kobe: The basin-edgeinduced diffracted Rayleigh waves, Seism. Res. Lett. 67, 25–34.
Kawase, H., and S. Matsushima (1998). Strong motion simulation in Kobeduring the Hyogo-ken Nanbu earthquake of 1995 based on a threedimensional basin structure, J. Struct. Constr. Eng., AIJ 514, 111–
118 (in Japanese).
Kennett, B. L. N., and N. J. Kerry (1979). Seismic waves in a stratified
half-space, Geophys. J. R. Astr. Soc. 57, 557–583.
King, G. C. P. (1986). Speculations on the geometry of the initiation andtermination process of earthquake rupture and its relation to morphology and geological structure, PAGEOPH 124, 3, 567–585.
Kobe City and Institute of Construction Engineering (1998). HanshinAwaji earthquake disaster, and geology and active faults in Kobe,
Kobe City, Kobe (in Japanese).
Koketsu, K. (1998). An overview of the rupture process, Report on the
Hanshin-Awaji Earthquake Disaster, Common Series 2, Maruzen, Tokyo, 168–175 (in Japanese).
Lawson, C. L., and R. J. Hanson (1974). Solving Least Square Problems,
Prentice-Hall, Inc., New Jersey, 340 pp.
Motosaka, M., and M. Nagano (1996). Analysis of amplification characteristics of ground motions in Kobe City taking account of deep irregular underground structure: interpretation of heavily damaged beltzone during the 1995 Hyogo-ken Nanbu earthquake, J. Struct. Constr.
Eng., AIJ 488, 39–48 (in Japanese).
Moya, C. A., and K. Irikura (1998). Seismic attenuation, kappa and site
response in the Osaka area, Japan, in Strong Motion Seismology: Lesson from the 1995 Hyogo-ken Nanbu Earthquake, Irikura K., T. Iwata,and H. Sekiguchi (Editors), Disaster Prevention Research Institute,
Kyoto University, Uji, 715–729.
Murakami, M., S. Fujiwara, and T. Saito (1995). Detection of crustal deformations associated with the 1995 Hyogoken-Nanbu earthquake byinterferometric SAR, Current News of the Geophysical Survey Institute of Japan, Tsukuba, No. 83, 24–27 (in Japanese).
Nakamura, Y., F. Uehan, and H. Inoue (1996). Waveform and its analysisof the 1995 Hyogo-ken Nanbu earthquake (II), JR Earthquake Information No. 23d, Railway Technical Research Institute, Tokyo (in Japanese).
Nakata, T., K. Shimazaki, Y. Suzuki, and E. Tsukuda (1998). Fault branching and directivity of rupture propagation, J. Geography 107, 4, 512–528 (in Japanese).
Nemoto, H., H. Katao, E. Suzuki, Y. Yoshida, and K. Irikura (1996). The
spreading of aftershocks area directly after the 1995 Hyogo-ken
Nanbu earthquake, Programme and Abstracts of Seism. Soc. Japan
1996, No. 2 (in Japanese).
Nemoto, H., H. Negishi, and K. Irikura (1997). Re-examination of the hypocenter of the Hyogo-ken Nanbu earthquake, J. Seism. Soc. Japan,
Zisin 50, 125–129 (in Japanese).
Ozawa, S., M. Murakami, S. Fujiwara, and M. Tobita (1997). Synthetic
aperture radar interferogram of the 1995 Kobe earthquake and its
geodetic inversion, Geophys. Res. Lett. 24, 2327–2330.
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, 428–
440.
Public Works Research Institute, Ministry of Construction (1995). StrongMotion Acceleration Records from Public Works in Japan (No. 21),
Technical note of public works research institute 64, Public Works
Research Institute, Ministry of Construction, Tsukuba, 265 pp.
Sekiguchi, H., K. Irikura, T. Iwata, Y. Kakehi, and M. Hoshiba (1996a).
Determination of the location of faulting beneath Kobe during the
1995 Hyogo-ken Nanbu, Japan, earthquake from near-source particle
motion, Geophys. Res. Lett. 23, 387–390.
Sekiguchi, H., K. Irikura, T. Iwata, Y. Kakehi and M. Hoshiba (1996b).
Minute locating of fault planes and source process of the 1995 Hyogoken Nanbu, Japan, earthquake from the waveform inversion of strong
ground motion, J. Phys. Earth 44, 473–487.
Wald, D. J. (1996). Slip history of the 1995 Kobe, Japan, earthquake determined from strong motion, teleseismic, and geodetic data, J. Phys.
Earth 44, 489–503.
Wessel, P., and W. H. F. Smith (1995). New version of the Genetic Mapping Tools released, EOS Trans Amer. Geophys. U. 76, 441, 445–
446.
Yoshida, S., K. Koketsu, B. Shibazaki, T. Sagiya, and Y. Yoshida (1996).
Joint inversion of near- and far-field waveforms and geodetic data forthe rupture process of the 1995 Kobe earthquake, J. Phys. Earth 44,
437–454.
Yoshida, S. (1989). Waveform inversion using ABIC for the rupture processof the 1983 Hindu Kush earthquake, Phys. Earth Planet. Inter. 56,
389–405.
Disaster Prevention Research InstituteKyoto University
Kyoto, Japan
E-mail: haru@egmdpri01.dpri.kyoto-u.ac.jp(H.S.)
Disaster Prevention Research InstituteKyoto University
Kyoto, Japan(K.I., T.I.)
Manuscript received 9 March 1999.