Earth Planets Space, 55, 000–000, 2003

Joint Inversion of Strong Motion and Geodetic Data for the Source Process ofthe 2003 Tokachi-oki, Hokkaido, Earthquake
Kazuki Koketsu , Kazuhito Hikima , Shin’ichi Miyazaki



 

and Satoshi Ide

Earthquake
Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan.
Department of Geophysics, Stanford University, 397 Panama Mall, Standford, CA 94305, USA.
Department of Earth and Planetary Sciences, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
(Received January 6, 2004; Revised March 2, 2004; Accepted March 2, 2004)

The strong motion and geodetic data are individually inverted for the source process of the 2003 Tokachi-oki,
Hokkaido, earthquake with a hypocenter 25 km deep and a fault plane above the subducting Pacific slab. Both theresults show a simple slip distribution with a single major asperity, but the strong motion inversion may include a
trade-off between slip location and rupture time and the geodetic inversion does not have sufficient resolution forfar slips. We then carry out a joint inversion of the two datasets in order to overcome these weaknesses of the single
dataset inversions. The resultant slip distribution still keeps the simple pattern and has a seismic moment of 2.2

10 N m (8.2). The asperity, with a peak slip of 7.1 m, is located in the center of the fault plane 50 km
away from the hypocenter in the down-dip direction. The slip rate functions on subfaults around the hypocenterand asperity indicate that the rupture propagates with a supershear speed on the upper part of the fault plane andslows down to 100-90% of the S-wave velocity on the middle and lower parts. These simple slip patterns andnear-supershear rupture may imply the maturity of the Hokkaido subduction zone around the source region.
Key words: Source process, joint inversion, strong motion data, geodetic data

1.

Introduction

46˚N



) of
A great earthquake with a JMA magnitude (8.0 occurred at 4:50 a.m. on September 26, 2003 (JST =UT + 9 hours) off the Tokachi district of Hokkaido, northern Japan (JMA: Japan Meteorological Agency, 2003). This
Tokachi-oki earthquake is the largest event around the Japanislands after the
8.2 Hokkaido Toho-oki earthquake in
1994. JMA (2003) located its epicenter above the subducting Pacific slab (41  46.78’N, 144  4.71’E; Fig. 1). The focal
mechanism determined by Yamanaka and Kikuchi (2003) indicates low-angle reverse faulting in the direction of subduction, therefore the earthquake is an event thrusting along theupper boundary of the Pacific slab.
Yamanaka and Kikuchi (2003) also carried out a waveform inversion of teleseismic data and obtained the best fit
with a hypocentral depth of 25 km. This depth is consistent
with the slab surface (Katsumata et al., 2004; Earthquake
Research Committee, 2003) at the JMA epicenter as shownin Fig 1, so that we will use it as the depth of the rupture
initiation point. We will also adopt the strike (230  fromthe north) and dip angle (20  ) in the above-mentioned focal
solution, for the geometry of a fault plane.

2.

44˚N

Hokkaido
160
140
120
100
80
60
50
40
30
20

42˚N
10
0 km

140˚E

142˚E

144˚E

146˚E

Fig. 1. The epicenter of the 2003 Tokachi-oki earthquake determined by
JMA (solid star). The dashed depth contours in km represent the upperboundary of the Pacific slab subducting under Hokkaido (Katsumata etal., 2004; Earthquake Research Committee, 2003).

Data and Method

Among several nation-wide seismic arrays, KiK-net (Aoiet al., 2000) is the best for our study, since it consists of bore- that seismograms are influenced little by shallow soil condihole instruments as well as surface ones at all of the stations. tions. Fig. 2 compares the borehole and surface seismograms
The former is installed in a borehole 100 m or more deep, so at the station HDKH04. The bottom trace was observed ata station of K-NET (Kinoshita, 1998) close to HDKH04.

Copy right c The Society of Geomagnetism and Earth, Planetary and Space Sciences High-frequency reverberation in the soil contaminates the(SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan;
surface motions at both the KiK-net and K-NET stations, but
The Geodetic Society of Japan; The Japanese Society for Planetary Sciences.
the borehole seismogram is almost free from this contami1

2

K. KOKETSU ET AL.: JOINT INVERSION FOR THE SOURCE PROCESS OF THE 2003 TOKACHI-OKI EARTHQUAKE

nation. Therefore, we use three-component borehole seismograms at the eleven KiK-net stations plotted with solid
triangles in Fig. 3. The seismograms were recorded by accelerometers and so they were numerically integrated to obtain velocity waveforms. The resultant velocities are filteredout with a pass band of 0.05 – 0.2 Hz, and re-sampled withan interval of 0.5 s.
  

the 15 time windows. Since Yamanaka and Kikuchi (2003)
already found the slip orientation to be of reverse faultingwith a rake angle of 109  , the slip vector on a subfault isrepresented by a linear combination of two components inthe directions of 90 H 45  . We stabilize the inversion by
imposing smoothness constraints for the discrete Laplacianin space and time:I-/. -1032465879: 4;9< 4*JLKNMOQPRJLKTSVRJLK[Z


! "

J

 # 
 

-=. -1032465>?@: A B@C4


! "
!# 
!$ 
 # 
 

-10(DFE8G


! "
!# 

 

# 

$ 

%

&'

&( 

8U

& # *) +,Fig. 2. Borehole and surface velocity seismograms at HDKH04 of KiK-net.
The seismogram observed at a K-NET station close to HDKH04 is also
shown for comparison.

Miyazaki and Kato (2003) derived coseismic displacements from GPS data at the stations of GEONET (Geographical Survey Institute, 1998) in Fig. 3. They calculated theaverage coordinates for September 2 to 24 and those for one
hour between the mainshock and largest aftershock. The difference between these coordinates will be used as horizontal
displacements due only to the mainshock.

8U

GPS (GEONET)

ABSH04

44˚N

TKCH10

KSRH05

KSRH10

KSRH09
TKCH11
TKCH07
HDKH04
HDKH06

TKCH08

HDKH07

42˚N

140˚E

142˚E

144˚E

146˚E

Fig. 3. KiK-net stations (solid triangles) and GEONET stations (crosses)
where the used data were observed.

OWVXJLKUMUOWV\J]K

MS
U
U

M^Z

8U
U

OYVXJLKOYV\J]K

M
U
U

OS

M

U
U

O Z


`_ba

JLK
U

M

(1)
U

O

KNMO

where
isJ theonJ theK M slipOgS
K M ceO d -th J subfault
K M O"Z in the
M O
J K f -thU U
 _U U andU U
 _U Utime window.
in (1) perform temporal smoothing and relax the overparameterization, which may arise from an inversion with somany time functions as in this study. We determine the appropriate weights of the constraints relative to the data misfits referring to the Akaike Bayesian information criterion(Akaike, 1980).
We use the reflectivity method of Kohketsu (1985) withthe velocity structure in Table 1 for the Green’s functions,and extend it to buried receivers to calculate synthetic borehole seismograms. We here represent the elements of the
propagator matrix product for the part of the structure above
the receiver as h  , h " , h i , h j . We can now relate theFourier-Bessel transforms of radial k , tangential l and vertical motions m at the receiver to the transformed surface
motions kon , lpn and mLn asPklmstrong motion (KiK-net)Mj k nhPPhhq j l n
 k n

V

V

h

  m
n

h

 m

nsr

(2)

where hut'v with or without a prime denotes an element for the
SH wavefield or the P-SV wavefield. Equation (2) enables us
to calculate borehole motions from surface motions by theoriginal method.
This method works only for one-dimensionally stratified
structures, but the stations are located in various site conditions. Therefore, we use a set of velocity structures introducing a common part below a depth of 1.5 km as shownin Table 1. This part is determined based on Iwasaki et al.
(1989), and the varying shallower part is modeled by using
the results of velocity logging at the KiK-net stations andothers. To reduce possible artifacts due to the incompleteness of the velocity structure, scalar time shifts are added to
the Green’s functions, and their values are also determinedby the inversion. For geodetic Green’s functions we assume
a semi-infinite medium with a Poisson ratio of 1/4, since
the velocity structure does not affect static displacements somuch as shown in e.g. Koketsu et al. (2003).

3.

Single Dataset Inversions

We first carry out an inversion of the strong motion dataset
The strong motion and geodetic data mentioned above will alone. All the waveforms are equally weighted. We asbe inverted using the method of Yoshida et al. (1996) based sume the rupture to start from the hypocenter and the firston the formulation of multiple time windows (e.g.,
Olson and time window to propagate with a velocity of 3.6 km/s. This
Apsel, 1982). We assume the 120 x 100 km fault plane in propagation velocity corresponds to 82% of the S-wave veFig. 1 and divide it into 10 by 10 km subfaults with point locity (4.4 km/s) on most of the fault plane. Fig. 4 shows
slips at their centers. The time function of slip is expressed the slip distribution inferred from this strong motion inverby a superposition of ramp functions with a rise time of 1 s in sion. The synthetic seismograms for the inversion result

K. KOKETSU ET AL.: JOINT INVERSION FOR THE SOURCE PROCESS OF THE 2003 TOKACHI-OKI EARTHQUAKE

3

Table 1. Velocity structure.

thickness (km)
1.5
2.5
10
6
8
32
|

wyx

(km/s)w{z(km/s)

varying with stations
5.8
3.3
6.1
3.5
6.5
3.7
7.0
4.0
7.7
4.4
8.0
4.6

agree well with the observed ones as shown in Fig. 5. The
stations KSRH05 and HDKH04 are located in large sedimentary basins, so that well-developed surface waves contaminate the later portions of their seismograms. We notethat these portions were already removed from the dataset.
143˚

144˚

145˚

146˚

43˚

8m
8

1

j

L3(g3` g@  

6
42˚

4
2
0m

Fig. 5.
Comparison of the observed velocity waveforms (red traces)and synthetic waveforms for the solution of the strong motion inversion(black traces).

50 km

Fig. 4. Slip@ distribution recovered by the strong motion inversion ( }~ :2.5  10 N  m, } : 8.2). The arrows indicate the slip vectors of thehanging wall relative to the foot wall.

An asperity, that is a zone of large slips, is recovered with apeak slip of 6.7 m in the north-western part of the fault plane.
It is located 70 km away from the hypocenter in the dip direction.
The total seismic moment of this solution is 2.5 
i
10 N m, which corresponds to a moment magnitude ()
of 8.2. An average delay of 1.6 s is obtained for the seismograms observed at the western stations HKDH04, 06 and07, while time advances of 1.1 s and 0.7 s are recovered for
the TKC and KSR stations in the eastern Hokkaido, respectively. These time shifts are consistent with the 3-D crustal
structure in this region (Murai et al., 2003).
Next, we invert the horizontal displacements at the 127
GPS stations shown in Fig. 3. The resultant slip distribution
in Fig. 6 shows similar features to those in the strong motion
inversion. There exists one major asperity with a peak slip of
6.8 m and it is located in the dip direction from the hypocenter again. However, the GPS solution shows stronger slip on
the far parti of the fault plane and the total seismic moment(2.0  10 N m,
8.1) is a little smaller than the previous result, though the synthetic displacements agree wellwith the observations in Fig. 7. Since similar behavior of a
GPS solution is found by Jónsson et al. (2002) for the 1999
Hector Mine earthquake, these differences may be due to low
resolving power of GPS data for far slips. Nevertheless, astrong motion inversion intrinsically has a trade-off between
slip location and rupture time, and GPS data can ease it byconstraining the locations of near slips. So, finally, we carryout a joint inversion of the strong motion and GPS data in thenext section.
143˚

144˚

145˚

146˚

43˚

8m
8
6
42˚

4
2
0 m
50 km

Fig. 6.
@ Slip distribution recovered by the geodetic inversion ( }~ : 2.0 
10 N  m, }  : 8.1).

4.

Joint Inversion

We simultaneously invert the strong motion and geodetic
data all together. The resultant slip distribution in Fig. 8
appears to be an average of the two solutions of the single
datasetinversions in Figs. 4 and 6. The seismic moment (2.2

10 N m,8.2) is also an average of those from thesingle dataset inversions. The major asperity with a peakslip of 7.1 m is now located in the center of the fault plane
50 km away from the hypocenter in the dip direction. The
synthetic seismograms are still in good agreement with theobserved seismograms as shown in Fig. 9. Fig. 10 compares

4

K. KOKETSU ET AL.: JOINT INVERSION FOR THE SOURCE PROCESS OF THE 2003 TOKACHI-OKI EARTHQUAKE

Obs
Cal
20 cm

Fig. 7. Comparison of the observed displacements (green arrows) and synthetic displacements for the solution of the geodetic inversion (blue arrows). The red box and star indicate the fault plane and rupture initiation
point, respectively.

the observed geodetic data with displacements calculated
for the joint inversion solution. The agreement is as goodas in the result of the geodetic inversion, but a match to
the displacements near the source region is a little degradedbecause of compromise in the joint inversion.
143

144

145

146

8

j

L3u33u3` 36  Fig. 9. Comparison of the observed velocity waveforms (red traces) andsynthetic waveforms for the solution of the joint inversion (black traces).

Obs

43

Cal
20 cm

8m
8
6
42

4
2
0 m
50 km

@

Fig. 8. Slip distribution recovered by the joint inversion ( } ~ : 2.2  10
N  m, }  : 8.2). The slip rate functions of the subfaults in the black
rectangle will be shown in Fig. 12.

Fig. 11 represents the growth of the rupture by showing
the slip-rate distribution at every 3 s. The major asperity
A propagates from the hypocenter to the northwest in thedip direction. In addition, we can identify two minor asperities in the snapshots. b appears on the northeastern part of
the fault plane at 21 to 36 s after the rupture initiation. Ide(2003) identified this asperity using ocean-bottom seismograms observed by JAMSTEC. The other, which is labeled
c in Fig. 11, is initiated around the center of the fault plane
after A runs through this part. It then turns to the north approaching the lowermost corner of the fault plane.
There are ten subfaults in line between the hypocenter andthe lower boundary of the fault plane. This line (black rectangle in Fig. 8) runs across the main part of the slip distribution including the major asperity, and so the slip rate

Fig. 10. Comparison of the observed displacements (green arrows) and synthetic displacements for the solution of the joint inversion (blue arrows).
The red box and star denote the fault plane and rupture initiation point,respectively.

functions (derivatives of slip histories) recovered in the subfaults along the line are displayed in Fig. 12 in order to represent the details of the rupture during the 2003 Tokachi-oki
earthquake. As mentioned earlier, the slip history in eachsubfault is modeled with ramp functions in fifteen sequential
time windows and a rise time of 1 s. The first time window isassumed to propagate with a velocity of 3.6 km/s, but the slip
rates in the first several windows are very small in the uppermost subfault of the hypocenter, so that the rupture looks toK. KOKETSU ET AL.: JOINT INVERSION FOR THE SOURCE PROCESS OF THE 2003 TOKACHI-OKI EARTHQUAKE©/ª(«=¬¯6±=ª²¯6³=¬

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% &'( )+*  
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£
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¡ ¤£
¡ ¢£

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Ä
Å
¡ ¤£ ¡ ¥£ ¡ ¦£ £¦£ ¥£

Ã

£(§ ¢
£(§ ¤
£(§ ¥
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Fig. 11. Snapshots of the source process represented by the slip-rate
distribution at every 3 s. The bottom-right panel schematically illustrates
the progress of the asperities.

ãä
â
àá
Þyß

ú ùû
÷ø

õFö



    



Fig. 13. Radial velocity seismograms observed at the stations in the northof the source region. The traces are normalized to their peak amplitudes.
The star and arrow denote the epicenter and main rupture direction,
respectively.

finally slows down to 4.0 km/s as shown in Fig. 12. The slip
rate functions in the center subfaults have two peaks, whichindicate the major asperity A and the minor asperity c.
The upper one and a half subfaults fall within the fifthlayer of the velocity structure in Table 1. As the S-wave
velocity ( l/. ) is 4.0 km/s in this layer, the rupture velocity( l/0 ) is higher than l1. . In other words, the fault rupture
propagates at a ‘supershear’ speed in the zone around the
hypocenter (Rosakis, 1999; Ide, 2003). l10 is almost equal
to l/. in the middle of the fault plane, and it is reduced to2
90% in the lower part. This supershear ( l/0
l/. ) or nearsupershear ( l 043 l . ) situation results in directivity effects
on P-waves and the near-field term, or those on S-waves,respectively. The effects are confirmed by the long-period
pulses indicated by the red and blue brackets in the velocity
seismograms at the stations in the north beyond the major
asperity (TKCH08, 11, 10 and ABSH04 in Fig. 13).
143˚

144˚

145˚

146˚

43˚

óô
ò
ðñ
îiï

8m

Õ

ÓÔ

8

Ñ Ò çèæ éÏ Ð çèæ åÍÎ å æ éÉÊË Ì å æ å å æ å

 

6
42˚

ê æå

ëæ å

ì æå

íæ å ç´åæ å ç´êæ å ç(ëæ å
Ö1× ØyÙÛÚ ÜÝ

Fig. 12. Slip rate functions in the subfaults indicated in Fig. 8 with a black
rectangle.

be locked for about 5 s in the initial stage. The rupture propagation is then accelerated to a velocity of 4.3 km/s, and it

4
2
0 m
50 km

Fig. 14. Slip distribution by another joint inversion with ten time windows
and a rise time of 2 s.

65.

K. KOKETSU ET AL.: JOINT INVERSION FOR THE SOURCE PROCESS OF THE 2003 TOKACHI-OKI EARTHQUAKE

Discussion and Conclusions

We have inverted the strong motion and geodetic data forthe source process of the 2003 Tokachi-oki, Hokkaido, earthquake and conclude the study with the result of the joint inversion. It indicates that the fault rupture initiated on the upper tip of the 120 by 100 km fault plane and was developedin the single large asperity generating seismic pulses in the
direction of rupture propagation. The obtained slip rate functions around the hypocenter and asperity suggest supershear
or near-supershear rupture, which resulted in the distinct directivity effects on ground motions.
Such fast rupture was recovered in the faulting models
for the major strike-slip earthquakes, that are the 1979 Imperial Valley earthquake (Archuleta, 1984), the 1992 Landers earthquake (Wald and Heaton, 1994) and the 1999 Izmit
earthquake (Bouchon et al., 2000). The 2003 Tokachi-oki
earthquake should be the first thrust-faulting event foundwith this sort of rupture, though our result still includes someuncertainty because of the assumptions on the fault geometry, subfault formulation and crustal structure. Another limitation for studies of this earthquake is that there are no seismic or geodetic stations to the south of the source region.
The simple slip distribution in Fig. 8 is also somewhat
unusual for a large earthquake with a magnitude of 8 orgreater. However, Yamanaka and Kikuchi (2003) obtaina similar result using teleseismic data, so we can consider
the simple distribution with a single major asperity and few
minors as a real aspect of this earthquake. It may imply
the maturity of the subduction zone in conjunction with thesupershear rupture.
Since inverting for fifteen time windows sounds highly
over-parameterized, we have carried out another joint inversion using ten time windows and a rise time of 2 s. The
resultant slip distribution in Fig. 14 keeps similar features
to those in the previous results, though the major asperity issomewhat intensified. This similarity suggests that our formulation of fifteen time windows works well in cooperation
with the spatio-temporal constraints.
Wald and Graves (2001) pointed out the effect of thecrustal complexity on the accuracy of geodetic Green’s functions, though we assume only the uniform halfspace in thisstudy. This assumption should have introduced some limitations into our results, and so the source model will be refinedusing 3-D Green’s functions in future work.
Acknowledgments. We are grateful to the National ResearchInstitute for Earth Science and Disaster Prevention, Geographical
Survey Institute, and JMA for the KiK-net records, GPS data andhypocenter information. The manuscript was greatly improved by
the review from Dr. Wald (USGS). We appreciate suggestions by
Prof. Archuleta (UC Santa Barbara) on the rupture velocity andgeodetic inversion. Figs. 1, 3, 4, 6 and 8 were drawn using the
GMT by Drs. Wessel (Univ. Hawaii) and Smith (NOAA) and ashell script by Dr. Yagi (Build. Res. Inst.). This study was partially supported by the Special Coordination Funds for Promoting
Science and Technology.

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Kazuki Koketsu (e-mail: koketsu@eri.u-tokyo.ac.jp)