1

Complicated rupture process of the Mw 7.0 intraslab strike-slip earthquake in2

the Tohoku region on 10 July 2011 revealed by near-field pressure records

3
4

Tatsuya Kubota1Ryota Hino1, Daisuke Inazu2, Yoshihiro Ito3, Takeshi Iinuma4

561Graduate School of Science, Tohoku University, Sendai, Japan.

7

2

UTokyo Ocean Alliance, The University of Tokyo, Tokyo, Japan.

83Disaster Prevention Research Institute, Kyoto University, Uji, Japan.

94Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan.

10
11Corresponding Author: Tatsuya Kubota, Graduate School of Science, Tohoku

12

University,

13(tatsuya.kubota.r6@dc.tohoku.ac.jp)

6-6,

Aza-Aoba,

Aramaki,1

Aoba-ku,

Sendai

980-8578,

Japan.

14

Key Points

15

An intraslab Tohoku strike-slip earthquake on July 2011 was studied with near-field16

pressure data

17

Two orthogonal faults related to the down-dip extensional stress were involved during

18

the rupture

19

Estimated stress change around the rupture area was smaller than that in the outer-rise

20

region2

21

Abstract

22

We examined fault models of the Tohoku strike-slip intraslab earthquake (Mw237.0) on 10 July 2011 using near-field tsunami data. After constraining the strike and24

location of the fault from tsunami source distribution, we investigated fault models

25

assuming simple rupture of one fault, and simultaneous rupture of two conjugate faults.

26

The estimated single fault reached >30 km down into the slab from the plate interface,27

suggesting bending stress enhancement after the 2011 Tohoku-Oki earthquake, but the28

depth extent was inconsistent with the aftershock activity. The model involving

29

conjugate faults extended ~20 km below the slab surface, and was more consistent30

with the aftershocks. We concluded that it is more plausible that this earthquake

31

involved two conjugate strike-slip faults, and the enhancement of the down-dip

32extensional stress after Tohoku-Oki earthquake was not large enough to allow rupture

33

to propagate deeply into the slab beneath the landward slope of the Japan Trench.

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34

Index Terms

35

Primary: Dynamics and mechanics of faulting (8118)

36

1: Tsunamis and storm surges (4564)

37

2: Subduction zones (7240)

38

3: Stresses: crust and lithosphere (8164)

39

4: Fractures and faults (8010)

40
41

Keywords

42

1. Fault modeling43

2. Strike-slip earthquake

44

3. Intraslab earthquake45

4. The 2011 Tohoku-Oki earthquake46

5. Tsunami

47

6.Stress state448

1. Introduction

49

The 2011 Mw 9.0 Tohoku-Oki earthquake ruptured a length of about 500 km

50

along the Japan Trench [e.g., Ide et al., 2011; Ozawa et al., 2011; Iinuma et al., 2012].

51

After this earthquake, many shallow (< ~20 km) normal-faulting aftershocks occurred52

in the up-dip portion of the subducting slab along the Japan Trench, activated by a53

tensional stress change associated with the Tohoku-Oki earthquake [e.g., Asano et al.,54

2011; Hasegawa et al., 2012; Suzuki et al., 2012]. Before the 2011 Tohoku-Oki

55

earthquake, the down-dip tensile stress field beneath the surface of the Pacific Plate

56

near the trench and in the outer-rise region was estimated to flip to the down-dip

57

compression field ~15 km below the slab surface [Gamage et al., 2009; Koga et al.,58

2012] (Figure 1). After the Tohoku-Oki earthquake, the stress regime at the depth of59

around 40 km in the outer-rise region changed from compression to tension [Obana et60al., 2012]. At the deep edge of the large coseismic slip area of the mainshock, Ohta et61

al. [2011] suggested that the stress-neutral plane of the double-plane deep seismic zone

62

[Hasegawa et al., 1978] was deepened by the stress change related to the Tohoku-Oki

63earthquake, based on the result of the coseismic fault model of the April 201164

Fukushima earthquake (M 7.1). However, the post-Tohoku-Oki-earthquake stress state65

beneath the plate surface in the inner trench area, especially around the extremely large

66(>50 m) coseismic slip area of the 2011 Tohoku-Oki earthquake, is still unclear.

67

On 10 July 2011, an Mw 7.0 intraslab earthquake with a focal depth of 17.5 km

68

occurred ~50 km east of the epicenter of the Tohoku-Oki earthquake, close to the large

69

coseismic slip area. The earthquake had a strike-slip focal mechanism with the T-axis

70in the down-dip direction (Global CMT, http://www.globalcmt.org) (Table 1). Since it5

71is expected that this earthquake was induced by the stress enhancement of down-dip

72extension associated with the Tohoku-Oki earthquake, the intraslab stress state should73

be well represented in its rupture process. Obana et al. [2013] determined the location74of the aftershocks of this strike-slip earthquake using the records of ocean bottom

75

seismometers (OBSs), and found that the aftershock distribution formed two

76

orthogonal lineations. The strikes of the lineations correspond to those of the two nodal

77

planes of the focal mechanism, and it is suggested that two conjugate faults could be78

involved in the Mw 7.0 earthquake and its aftershock sequence. However, most of the79

relocated aftershock hypocenters were concentrated along the slab surface, so it is80

difficult to estimate the depth extent of the ruptured faults. Therefore, the finite source

81

model of the M 7 strike-slip earthquake should provide important constraints on the82

post-2011 stress state, if it can be estimated.

83

When this event occurred, six ocean bottom pressure recorders (OBPRs) were84

deployed near the epicenter, and they observed a tsunami and static seafloor vertical85

deformation (Figures 1 and 2). The use of such near-field OBPR data will be helpful86

to estimate the source models and reveal the source processes of the offshore

87

earthquakes, which are difficult to investigate using only onshore data (e.g., GPS,88

seismometers, strainmeters). For instance, Saito et al. [2010] demonstrated that high-89

quality tsunami waveform records obtained at offshore stations could help to resolve90

the detailed picture of the fault model for the 2004 off the Kii Peninsula earthquake91(Mw 7.4). The purposes of this study are to estimate the source model of the 2011 Mw

92

7.0 intraslab event using near-field OBPR data and to discuss the stress state beneath93

the plate surface in the inner trench area.

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94
95

2. Data96

The OBPRs, which measure high-frequency quartz oscillations associated with97

both pressure and temperature, are identical to those used in the study of the crustal

98

deformation associated with the Tohoku-Oki earthquake [Hino et al., 2014]. The

99

recorded oscillation frequencies of quartz sensors were converted to absolute pressure

100

on the seafloor [e.g., Matsumoto et al., 2012] and 1-s averages of them were taken.

101

From the pressure records, we estimated and removed ocean tide components

102

using the tidal analysis program BAYTAP-G [Tamura et al., 1991]. Then, we applied103

a digital recursive low-pass filter [Saito, 1978] to reduce high-frequency fluctuations

104

associated with the seismic and hydroacoustic waves of large amplitudes. The

105

optimum filter cutoff frequency was determined by minimizing the filtering effect on

106

the tsunami signals and by suppressing the high-frequency components sufficiently

107(Figure S1). We adopted 10 mHz as an appropriate cutoff frequency for the present

108

OBPR waveforms. The maximum amplitudes of the tsunami reached about 7 cm, and109

static seafloor vertical deformation of about 3 cm was also recorded at the nearest (~30110km) station, GJT3 (Figure 2). The travel time of the tsunami was less than 15 min for111

all the stations, and the duration times of the main tsunami pulses were about 4 min.

112
113

3. Tsunami Waveform Inversion

114

We first estimated the initial sea-surface height distribution by applying tsunami

115

waveform inversion, because the geometry of the source fault is unclear based on only116

the seismic wave analysis of inland stations. The tsunami Green’s functions were

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117

calculated by solving the linear dispersive tsunami equation using a finite difference118

approximation in local Cartesian coordinates [e.g., Saito et al., 2010; Saito et al., 2014].

119

In the calculation, the water height anomaly was transformed to bottom pressure,120

assuming that 1 cm of water height is equivalent to 1 hPa of bottom pressure. The

121

spatial grid interval and time step interval of the calculation were 2 km and 1 s,

122

respectively. As the bathymetry data, we interpolated ETOPO1 [Amante and Eakins,1232009]. The rupture duration T was assumed to be 0 s. The static offsets in the pressure

124

records related to the vertical seafloor deformation were corrected using the method

125

proposed by Tsushima et al. [2012]. In this study, we distributed pyramid-like-shaped

126

unit sources of the sea surface displacement with the size of 20 km × 20 km in the area

127

180 km in the EW direction and 170 km NS around the hypocenter (rectangular area

128

shown in Figure 1). Each unit source is located with an interval of 10 km and overlaps

129

with next ones (Text S1 and Figure S2). The same low-pass filter that was applied to130

the observed records was also applied to the Green’s functions. In the inversion, we

131

calculated waveform residuals in a time window of 20 minutes from the origin time

132

(white back ground area in Figure 2). We applied a smoothing constraint in the133

inversion by adjusting its weight based on inspecting the trade-off relationship134

between the weight and RMS misfit (Figure S3).

135

The obtained initial sea surface height distribution is shown in Figure 1. The

136

diameter of the major uplift zone was about 50 km, and the peak uplift and subsidence137

were 4.9 cm and 3.9 cm, respectively. The spatial pattern of the seafloor deformation138

was consistent with the focal mechanism estimated from seismological data. The

139

locations and strikes of the hinge lines between the uplift/subsidence areas

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140

corresponded well to the aftershock lineations [Obana et al., 2013]. Tsunami

141

waveforms calculated from the model were in good agreement with the observation

142(Figure 2).

143
144

4. Fault Modeling with Grid-search Methods

145

We sought an optimum finite fault with uniform slip of the strike-slip earthquake

146

using a grid-search method. We assumed that the location and strike of the fault were147

well constrained by the aftershock distribution, because of good consistency between

148

the epicenter distribution and the initial sea surface height distribution inverted from149

the tsunami waveforms, as shown in the previous section. The strike angle is assumed

150

to be 65°or 330° according to the nodal planes of the GCMT solution. Note that these151

directions match those of the aftershock lineations very well. The unknown parameters152

we searched for were the dip and rake angles, the locations of both ends of the fault

153

along strike, and the depths of the top and bottom of the fault. The locations of these154

four ends of the fault were defined by distances from a reference point on the fault

155(Figure S4). We regarded a fault model with a strike of 65° (EW model) to be156

preferable because the mainshock hypocenter was located along the aftershock157

lineation with this strike. In the EW model, the hypocenter was used as the origin of158

the fault. However, we also tried to seek another model, assuming a fault with a strike159

of 330° (NS model), even though the hypocenter was not located on the aftershock160

lineation with this strike. In the analysis assuming the NS model, we set the reference161

point at the location of the GCMT centroid, since it is located near the intersection of162

the aftershock lineaments. The slip amount was adjusted so that the resultant seismic

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163

moment Mo is consistent with the Global CMT solution (3.96 × 1020 Nm) with a164

rigidity of 40 GPa.

165

The seafloor displacement field was calculated using Okada’s [1992] equations,166

and converted to the initial sea surface displacement by applying the depth filter [Saito

167

and Furumura, 2009]. In the depth filtering, we assumed a constant seafloor depth of168

3.5 km, the average water depth in the source area. Tsunami waveforms were169

calculated by superposition of the Green’s functions prepared for the inversion for the170

initial sea surface height. The search range of the grid-search is shown in Table S1.

171

The results are shown in Table 1 and Figures 3 and S5.

172

We inspected the top 100 solutions in terms of the variance reduction of the173

waveform fit. Figures 3b, 3c, and 3d show the top 100 fault models projected onto the174

vertical cross section, and histograms of the model parameters. From these figures, it

175

is clear that the dip and rake angles and the depth to the top of the fault (W2) are176

reasonably well constrained. Although the uncertainty of the depth of the bottom of177

the fault was large, the solutions with large fault widths tend to explain the observed

178

data better. For example, the best-fit model with an EW fault plane is 30 km in width

179

from the epicenter to the lower edge of the fault plane (W1) (Figure 3). However, the180

aftershocks are concentrated only in the shallowest part of the fault plane, and no181

aftershocks occur in the deeper part. Moreover, L/W ratios, ratios of the fault length

182(L = L2 – L1, Figure S4) to the width (W = W1 – W2, Figure S4) are less than one in183

most of the solutions (i.e., the fault width is greater than the length), as shown in Figure

184

3e. According to the empirical scaling relationship reported by Wells and Coppersmith

185[1994], a common M 7 class strike-slip earthquake has a fault width of ~15 km and an

10

186

L/W ratio of ~4. Our solution differs significantly from the standard picture, and a

187

similar discrepancy is also seen in the NS fault model (Figure S5). Therefore, we

188

conclude that the assumption of a single fault rupture caused this discrepancy.

189
190

5. Fault Modeling with Simultaneous Rupture of Conjugate Faults

191

One of the largest strike-slip intraplate earthquakes ever recorded, associated with192

a megathrust earthquake, was the 2012 Mw 8.6 Sumatra earthquake. The rupture

193

occurred on the trench outer region of the source area of the 2004 Sumatra–Andaman194

earthquake (Mw 9.1). The earthquake had a complicated rupture process, which

195

ruptured on distinct planes in an orthogonal fault system, based on seismic analyses

196[Meng et al., 2012]. In a similar way, the Tohoku strike-slip earthquake may have197

ruptured two conjugate strike-slip faults in the subducting slab simultaneously. Here,198

we try to estimate a fault model consisting of two conjugate faults that ruptured

199

simultaneously (hereafter, the conjugate model).

200

For simplicity in the modeling, Mo is divided equally between the two conjugate

201

fault planes, and the search range for the fault length and location is mostly constrained

202

based on the aftershock distribution, and the depths of the top and bottom of the two

203

fault planes are required to be equal. We did not assume any time delay between the204

two subfaults, because the observed tsunami waveforms are composed of single large

205

pulses, and it is unlikely that the tsunami data would have sufficient temporal

206

resolution to distinguish the difference between the origin times of the ruptures of the207

two conjugate faults. Other settings are all the same as for the single fault model.

208

The fault parameters obtained from the conjugate model are shown in Table 1.

11

209

The initial sea surface displacement distribution expected from the conjugate model

210(Figure 4a) is similar to that from the single fault models (Figures 3 and S5) and211

resemble that obtained from direct inversion of the tsunami records (Figure 1).

212

Tsunami waveforms synthesized from the conjugate model fit the observed ones well

213

(Figure 2).

214

The depths of the bottom of the two fault planes were constrained to 15 km

215(Figures 4b, 4c, 4d), making the fault location more consistent with the aftershock

216

distribution than the single fault models (red rectangles in Figure 3). The fault length

217

appears to fall within the range of 10–30 km for the NE-SW fault and 20–30 km for218

the NW-SE fault, which are slightly shorter than the fault lengths expected for219

earthquakes of Mw 6.8 (equivalent to half of the total moment), ~40 km according to220

the scaling relationship of Wells and Coppersmith [1994]. The solutions tend to have221

an L/W ratio of ~1.4 (Figure 4e), which is greater than the majority of solutions with222

a single fault assumption, reducing the discrepancy with the empirical relationship.

223

We assumed here that the two conjugate faults to have equal amount of seismic

224

moment, but that is not always the case. Since it required formidable computation time225

to seek a model by changing the moment ratio between the two faults, we only made226

the grid-searching with the ratio of 1:2 and 2:1 to assess the effect of the imbalance in227

the released moment. The best-fit model in the trial was that with the moment ratio of

228

2:1 between the EW and NS faults and its L/W ratio was similar to those of the best-229

fit single fault models (Figure S6). Since the single fault models can be regarded as230

the extreme case of the conjugate models with the moment ratio of 0:1 or 1:0, the result

231of the trial seems to be plausible. From this inspection, we conclude that the model

12

232

with the conjugate fault of similar moment release amount is more consistent with

233

aftershock distribution and with the empirical fault scaling relationship than any other234

models we sought so far.

235
236

6. Discussion and Conclusions

237

The focal mechanism of this earthquake was consistent with the pre-2011 down-238

dip extensional stress state in the shallow part of the subducting slab [e.g., Gamage et239al., 2009; Obana et al., 2012], suggesting that the earthquake occurred in the tensional

240

stress field near the slab surface enhanced by the Tohoku-Oki earthquake. Therefore,241

the depth extent of the coseismic rupture area is an important indicator of the post-

242

Tohoku-Oki earthquake stress state in the subducting slab around the inner trench area.

243

Regardless of the strike, the single fault models derived from local tsunami

244

waveform analysis extend deep into the slab, more than ~30 km below the plate

245

interface. Before the Tohoku-Oki earthquake, the stress-neutral plane between the246

down-dip tensile field and the down-dip compression field near the surface of the slab247

was estimated to be ~15 km below the slab surface [Gamage et al., 2009; Koga et al.,2482012]. After the Tohoku-Oki earthquake, Obana et al. [2012] reported that the down-249

dip extensional earthquakes occurred deeper than 30 km below the surface of the250

incoming plate, and suggested that the Tohoku-Oki earthquake made the tensile stress251

regime extend even deeper. If we assume a single fault rupture, we can interpret that252

the deep penetrations of the rupture plane of the single fault models suggest a253

manifestation of deepening of the lower limit of the extensional stress field in the inner254

trench area, as well as beneath the outer-rise region.

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255

On the other hand, the coseismic rupture is not required to penetrate deep into the256

slab if we assume a conjugate fault model. The bottom of the fault was estimated to be257~20 km from the plate interface, which is reasonably consistent with the depth of the258

stress transition from shallow tensile to deep compressional intraslab stress before the259

Tohoku-Oki earthquake. Although it is difficult to determine which is better, the single

260

or conjugate fault model, based only on the misfit of the tsunami waveforms, we261

concluded that the conjugate fault model is more probable because of its consistency

262

with the depth distribution of the aftershocks. The disproportion of the lengths and263

widths of the single fault models is another reason we prefer the conjugate fault model.

264

Obana et al. [2013] documented the fact that the conjugate aftershock lineations are265

related to the structural features within the Pacific slab [Nakanishi et al., 1992]. If the266

strike-slip earthquake occurred as the reactivation of such pre-existing weak planes,

267

their simultaneous rupture is probable. If conjugate rupture occurred during the268earthquake, our result suggests that the enhancement of the down-dip tensile field269

associated with the 2011 Tohoku-Oki earthquake was not large enough to significantly270

deepen the extensional regime beneath the trench inner slope region, whereas

271

remarkable change was found beneath the outer-rise region [Obana et al., 2012].

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Acknowledgements

273

The authors thank Dr. Tatsuhiko Saito of the National Research Institute for Earth274

Science and Disaster Prevention (NIED), for the Fortran code to calculate the tsunami,

275

insightful discussions, and many helpful comments. Much support and advice of Dr.

276

Yusaku Ohta of Tohoku University were so invaluable. This study was supported by277

the research project “Research concerning Interaction between the Tokai, Tonankai,

278

and Nankai earthquakes” of the Ministry of Education, Culture, Sports, Science and279

Technology, and by JSPS KAKENHI (A) 20244070 and 26000002. The figures in this280

paper were prepared using Generic Mapping Tools (GMT) [Wessel and Smith, 1998].

281

The authors thank anonymous reviewers for constructive comments.

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282

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Tsushima, H., R. Hino, Y. Tanioka, F. Imamura, and H. Fujimoto (2012), Tsunami

366

waveform inversion incorporating permanent seafloor deformation and its

367

application to tsunami forecasting, J. Geophys. Res., 117, B03311, doi:368

10.1029/2011JB008877.

369

Wells, D. L., and K. J. Coppersmith (1994), New empirical relationships among370

magnitude, rupture length, rupture width, rupture area, and surface displacement,

371

Bull. Seismol. Soc. Am., 84(4), 974–1002.

372
373

Wessel, P., and W. Smith (1998), New, improved version of generic mapping tools
released, Eos Trans. AGU, 79(47), 579, doi: 10.1029/98EO00426.

19

374

Table 1. Comparison of fault parameters
Conjugate model

Global CMT

EW

EW

EW
Model

NS modelmodel

NS fault
fault

fault

Strike [°]a

65

330

65

330

65

330

Dip [°]

85

80

90

85

74

75

Rake [°]

10

180

15

170

16

164

L1 [km]

˗5

˗5

˗ 10

˗ 10

L2 [km]

0

10

10

15

W1 [km]

˗ 30

˗ 30

˗ 15

˗ 15

W2 [km]

0

0

0

0

6.6

2.2

1.7

1.3

0.603

0.679

Slip amount[m]
RMS misfit
0.615

[cm]
375
376

a

NS fault

Strike angle is fixed at Global CMT value.

20

377

Figure Captions

378
379

Figure 1. (a) Initial sea surface height distribution derived from tsunami waveform

380

inversion. Black thin lines denote the analytical area. Uplift and subsidence areas are

381

shown in red and blue, respectively. White and black stars are epicenters of Mw 7.0

382

event and Mw 9.0 mainshock, respectively. Contour interval is 1.5 cm. Small dots

383

denote aftershocks. Red star and beach ball indicate focal mechanism. Green inverted

384

triangles denote OBPR stations. (b) Vertical profile along A–B line in Figure 1a and

21

385

schematic illustration of the stress field before the 2011 Tohoku earthquake estimated386

by Gamage et al. [2009] and Koga et al. [2012]. The down-dip tensile stress field (blue387

allows and beach ball) flips to the down-dip compression field (red) ~15 km below the388

slab surface (shown by thick green line, stress neutral zone).

389
390

Figure 2. Comparisons between observed (black lines) and calculated waveforms

391

derived from waveform inversion (blue), EW (green), NS (brown), and conjugate

392

models (red).

22

393
394

Figure 3. Grid-search results for EW model. (a) Initial sea surface height distribution

395

derived from optimum fault model (black) and inversion (blue). (b) Vertical profile

396

along A–A’ and (c) B–B’ line in Figure 3a. Red line denotes optimum fault. Black lines

397

show top 100 solutions of grid search. Thick black curved line denotes plate boundary

398[Ito et al., 2005]. (d) Histograms of model parameters. (e) Histogram of L/W ratios.

23

399
400

Figure 4. Grid-search results for conjugate model. (a) Initial sea surface height

401

distribution derived from fault model (black) and inversion (blue). (b) Vertical profile402

of A–A’ and (c) B–B’ line in Figure 4a. Red and green lines denote optimum fault.

403

Brown lines denote optimum EW model. Arrows indicate schematic image of stress404

field in shallower (blue) and deeper (red) portions of subducting slab, and the pre-2011405

stress transition zone (thick green line) between them [Koga et al., 2012]. (d)406Histograms of model parameters. Upper and lower rows denote results of fault with407

strikes of 65° and 330°, respectively. (e) Histogram of L/W ratios.

24Geophysical Research Letters
Supporting Information forComplicated rupture process of the Mw 7.0 intraslab strike-slip earthquake in the Tohoku
region on 10 July 2011 revealed by near-field pressure records
Tatsuya Kubota1Ryota Hino1, Daisuke Inazu2, Yoshihiro Ito3, Takeshi Iinuma4
1) Graduate School of Science, Tohoku University, Sendai, Japan
2) UTokyo Ocean Alliance, The University of Tokyo, Tokyo, Japan
3) Disaster Prevention Research Institute, Kyoto University, Uji, Japan4) I Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

Contents of this file
Text S1
Figures S1 to S6Table S1Introduction
Text S1 is the description of the assignment of the unit source used in the tsunami waveform
inversion. Figure S1 shows the comparisons of the low-pass filtered waveform that was used todetermine the optimum cutoff. A schematic illustration of assignment of the unit source used in
the tsunami waveform inversion is shown in Figure S2. The trade-off relationship used todetermine the smoothing weight in the tsunami source inversion is shown in Figure S3. A
schematic of the unknown parameters in the grid search is shown in Figure S4. The result of thegrid-search assuming a fault striking NW–SE (NS model) is shown in Figure S5. Figure S6 is theresult of the grid-search assuming uneven Mo between two fault planes. Table S1 shows thesearch range for the unknown parameters in the grid-search analysis.

1Text S1.
In the tsunami waveform calculation, we used the pyramid-like-shaped unit source expressed by
the following form:"x − x0 % "y − y0 %η0 ( x, y) = $1−
'$1−
',
10 &#
10 &
#
x0 −10 < x < x0 +10(km) ,y0 −10 < y < y0 +10(km)where η0(x, y) denotes the displacement of each unit source at the grid point (x, y) and (x0, y0) is
the center of the unit source. The schematic illustration of the unit source is shown in Figure S3.
Each unit source has the size of 20 km × 20 km, and is distributed with an interval of 10 km.

2Figure S1. Comparison of low-pass filtered waveforms with several cutoff periods, de-tided
waveform (light gray), and 60 s moving averaged waveform (dark gray). Cutoff parameters forthe filter [Saito, 1978] were as = 5.0 and ap = 0.5, and as shown in upper right legend. In theanalysis, cutoff parameters of Tp = 100 s and Ts = 20 were used (red lines).

3

Figure S2. Schematic illustration of the unit source used in the tsunami waveform calculation.
Upper figure is the top view. Each cell is enclosed by computational grids. Numerals in cells
show the given amount of uplift. Lower figure is the side view. Each unit source overlaps withnext ones by 10 km in length.

4Figure S3. Trade-off curve between smoothing weight of initial sea surface height inversion and
RMS misfit between observed and calculated waveforms. Because of the large curvature around
100 in the smoothing weight, we used a smoothing weight of one in the tsunami waveform
inversion.

5

Figure S4. Schematic image of the unknown parameters in the grid-search. The origin of thefault lengths and widths (reference point) is defined as the epicenter for the fault model of 65°
strike, or as the location of the CMT solution for the 330° fault model. The optimum solution issought in the range of the parameters shown in Table S1.

6

Figure S5. Result of grid search assuming fault striking NW–SE (NS model). (b) Vertical profile
along A–A’ and (c) B–B’ line in Figure S4a. Red line denotes optimum fault. Black lines show top
100 solutions of grid search. Thick black curved line denotes plate boundary [Ito et al., 2005]. (d)Histograms of model parameters. (e) Histogram of L/W ratios.

7

Figure S6. Result of grid search assuming uneven moment between the two faults. The best-fit
model with moment ratio of 2:1 between the EW and NS faults. (a) Initial sea surface height
distribution. (b) Vertical profile along A–A’, and (c) B–B’ lines in (a). (d) Histograms of model
parameters. (e) Histogram of L/W ratios.

8

Table S1. Search range of the grid-search

Conjugate model
Model

Strike [°]a

EW modelNS model65

NS fault

65

330

0 – 30150 – 180

330

Dip [°]b
Rake [°]b

EW fault

60 – 90
0 – 30150 – 180

L1 [km]c,d

˗40 – 0

˗20 – 0

˗25 – ˗10

L2 [km]c,d0 – 400 – 15

5 – 15

W1 [km]c,d,e˗30 – ˗5

˗30 – ˗5

˗30 – ˗5

W2 [km]c,d,e

0–5

0–5

0–5

Slip amount [m] Adjusted to Mo = 3.96 × 1020 Nm with rigidity of 40 GPa.
aStrike angle is fixed to the Global CMT focal mechanism.
Interval of dip and rake angle parameters is 5°.
cInterval of parameters L1, L2, W1, and W2 is 5 km.
dTotal fault length L and width W are defined as L2˗L1 and W2˗W1, respectively.
e
The total width W and depth of the fault is constrained to be equal.
b9