Confidential manuscript submitted to Geophysical Research Letters1

Estimation of seismic centroid moment tensor using ocean bottom pressure gauges2

as seismometers

3
4

Tatsuya Kubota1, Tatsuhiko Saito1, Wataru Suzuki1, and Ryota Hino2

51

National Research Institute for Earth Science and Disaster Resilience, Tsukuba, Japan.

62

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

78Corresponding author: Tatsuya Kubota (kubotatsu@bosai.go.jp)

9
10
11

Key Points:
•

12
13

and offshore pressure gauges
•

14
15
16
17

We estimated the CMT of offshore M ~ 7 earthquak es using onshore seismometers

The horizontal location of the centroid is well constrained by using offshore pressuregauges as seismometers•

Observed pressure-change waveforms show the theoretical predicted relationshipbetween pressure and vertical acceleration

Confidential manuscript submitted to Geophysical Research Letters

18

Abstract

19

We examined the dynamic pressure change at the seafloor to estimate the centroid moment20

tensor solutions of the largest and second largest foreshocks (Mw 7.2 and 6.5) of the 201121

Tohoku-Oki earthquake. Combination of onshore broadband seismograms and high-22frequency (~20–200 s) seafloor pressure records provided the resolution of the horizontal

23

locations of the centroids, consistent with the results of tsunami inversion using the long-24

period (> ~10 min) seafloor pressure records although the depth was not constrained well,25

whereas the source locations were poorly constrained by the onshore seismic data alone. Also,26

the waveforms synthesized from the estimated CMT solution demonstrated the validity of the27

theoretical relationship between pressure change and vertical acceleration at the seafloor. The

28

results of this study suggest that offshore pressure records can be utilized as offshore

29

seismograms, which would be greatly useful for revealing the source process of offshore

30

earthquakes.

31Confidential manuscript submitted to Geophysical Research Letters

32

1. Introduction

33

When earthquakes occur offshore, associated tsunami are observed by ocean-bottom

34

pressure gauges (OBPGs). For example, the DART (Deep-ocean Assessment and Reporting35

of Tsunamis) systems developed by NOAA (National Oceanic and Atmospheric

36

Administration) were founded on a network of widely distributed OBPGs to monitor tsunami

37

far offshore (e.g., González et al., 2005). OBPGs are considered one of the most reliable38

sensors for investigating tsunami propagation and source models because they are free from39

the strong site effects usually observed near coasts. Near-field (less then ~100 km from the40

epicenters) OBPG tsunami records enable us to obtain good spatial resolution of the source

41

models of offshore moderate (M ~ 7) earthquakes (e.g., Saito et al., 2010; Kubota et al.,42

2015; 2017). Lack of resolution for source models will be a barrier for studying the detailed

43source processes of offshore earthquakes (e.g., Heiderzadeh et al., 2017a).

44

Near-field pressure records obtained ~20 km from two local earthquakes (Mw 7.2 and45

Mw 6.5, National Research Institute for Earth Science and Disaster Resilience [NIED],

46

2011a; 2011b) (the station and earthquake locations are in Figure 1) are shown in Figure 2.

47

By applying a low-pass filter (>400 s) to the original records (gray), we obtained clear

48

tsunami signals (blue). The maximum tsunami height was ~10 cm (Figure 2b) and ~1 cm

49(Figure 2e) for the Mw 7.2 and 6.5 earthquakes, respectively. Some studies have estimated50

earthquake fault models by analyzing such tsunami signals in the OBPGs (e.g., Gusman et al.,51

2013; Heidarzadeh et al., 2017b; Kubota et al. 2017).

52

In addition to tsunami, OBPGs can observe other signals associated with earthquakes.

53

When OBPGs are installed inside the focal area, permanent seafloor vertical deformations are54

observed as the difference between the average pressure levels before and after the55

earthquake. These are often used to estimate coseismic fault models (e.g., Ito et al., 2011;56

2013; Iinuma et al., 2012; Ohta et al., 2012; Tsushima et al., 2012; Wallace et al., 2016). The

57

pressure changes associated with tsunami and permanent deformations are interpreted as the

58change in the loading due to the water column over the OBPG based on the hydrostatic

59

assumption. OBPGs also observe dynamic pressure changes associated with seismic waves

60(e.g., Filloux, 1982; Bolshakova et al., 2011; Matsumoto et al., 2012; Saito & Tsushima,612016), which are caused by seafloor seismic motions and ocean acoustic waves. In Figure 2,

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high-frequency pressure changes are evident from large amplitudes, especially after applyingConfidential manuscript submitted to Geophysical Research Letters

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a bandpass filter with a passband of 0.01–0.05 Hz (red lines). These components are usually64

removed before tsunami waveform analyses (e.g., Gusman et al., 2013; Inazu & Saito, 2014;

65

Kubota et al., 2015; 2017; Heidarzadeh et al., 2016), because they are irrelevant to the sea

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surface displacement due to tsunami.

67

The dynamic pressure change associated with seismic motion has been previously

68

studied (e.g., Filloux, 1982; Nosov & Kolesov, 2007; Bolshakova et al., 2011; Matsumoto et69

al., 2012; Saito, 2013). The pressure changes can be interpreted based on two different

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relationships according to their frequency range, defined by the fundamental acoustic

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resonant frequency f0 = c0/4h0 (h0 is the water depth and c0 is the velocity of the ocean

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acoustic wave). When the frequency of the seafloor motion is sufficiently low compared to73

the fundamental acoustic resonant frequency f0 (f < f0), the seafloor pressure change can be74

approximated as:

75
76
77

! = #$ ℎ$ &' ,(1)

and when the frequency is high (f > f0) as:! = #$ ($ )' ,

(2)

78

where ρ0 is seawater density and az and vz are the vertical acceleration and velocity of the79

seafloor motion (hereafter, pressure–acceleration relationship and pressure–velocity

80

relationship), respectively (e.g., Bolshakova et al., 2011; Matsumoto et al., 2012). Numerical81

simulation is useful for investigating these relationships (e.g., Maeda et al., 2013; Kozdon &82

Dunham, 2014; Saito & Tsushima, 2016; Saito, 2017). Saito and Tsushima (2016) tried to83

reproduce the dynamic pressure change associated with the 2011 Tohoku-Oki earthquake by84

numerical simulation, assuming a uniform slip fault model. The simple model roughly85

reproduced the dynamic pressure changes, but not completely. Using the seismic equations

86

considering a compressible sea and elastic crust, Saito (2017) numerically simulated the87vertical acceleration and pressure at the seafloor, and found that the pressure–acceleration

88

relationship (equation (1)) works well, whereas the pressure–velocity relationship (equation89(2)) works only for the first motion of the pressure change.

90

Although many previous studies have investigated the pressure–acceleration

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relationship (equation (1)) based on theoretical studies or numerical simulations, there are92

few studies based on real observations. Matsumoto et al. (2012) showed the pressure–Confidential manuscript submitted to Geophysical Research Letters93

acceleration relationship works reasonably well in the frequency domain by comparing

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records of the Tohoku-Oki earthquake observed ~400 km away from the focal area. Nosov

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and Kolesov (2007) also investigated pressure records of the 2003 Tokachi-Oki earthquake96(Mw 8.0), but only in the frequency domain. Those studies did not compare records in the

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time domain. Hence, it is not confirmed whether the phases are in agreement or have some98

shift in the time domain. If the pressure–acceleration relationship works well in the time99

domain, we could estimate various earthquake parameters by applying seismological analyses

100

to the pressure data.

101

The purpose of this study is to clarify whether the pressure–acceleration relationship102

holds in observed records through a centroid moment tensor (CMT) analysis of offshore

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earthquakes. Moreover, we demonstrate that the use of offshore OBPG records improves the104

centroid horizontal locations of the offshore earthquakes.

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2. Ocean Bottom Pressure Data107

We used pressure data associated with the Mw 7.2 and 6.5 interplate earthquakes off

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northeastern Japan on 9 March, 2011, which were the largest and second largest events

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preceding the 2011 Tohoku-Oki earthquake (Ohta et al., 2012; Gusman et al., 2013; Kubota

110

et al., 2017) (hereafter foreshock #1, foreshock #2, and the mainshock, respectively). Since111

the magnitudes of the two foreshocks were large enough to show good signal-to-noise ratios,112

the source processes are relatively simple compared to the mainshock, and we can expect to113

obtain a reasonable CMT solution with a point-source assumption. Also, the rupture areas of114

these earthquakes have been estimated from tsunami data by Kubota et al. (2017) (colored115

rectangles in Figure 1), and those estimates can be used as a reference for validating the116

centroid location.

117

We used 1 Hz sampled pressure data. Seven offline autonomous OBPGs with pop-up

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recovery were deployed within ~70 km of the epicenters (Figure 1). Details are given in Hino

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et al. (2014). Real-time cabled OBPGs of the Earthquake Research Institute of the University

120

of Tokyo (Kanazawa & Hasegawa, 1997), TM1 and TM2, were also in operation more than

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100 km away from the epicenters (Figure 1).

Confidential manuscript submitted to Geophysical Research Letters

122

Figure 3 shows the original and bandpass-filtered pressure records. We applied the123

Butterworth-type bandpass filter in both the forward and reverse directions. The passband

124

was determined according to the fundamental resonant frequency f0 and the frequency range

125

used in the F-net Moment Tensor (MT) analysis by the National Research Institute for Earth126

Science and Disaster Resilience (NIED, 2011a; 2011b). Supposing the acoustic wave velocity

127(0 = 1.5 km/s and the water depth h0 = 1.5 km (average depth of the focal area), the128

fundamental resonant frequency (f0 = c0/4h0) is ~0.25 Hz (4 s). If the sea depth is 3.2 km

129(corresponding to the depth of the deepest OBPG, GJT3), f0 is ~0.12 Hz (8.5 s). Since the130

pressure–acceleration relationship holds when the dominant frequency is lower than the131

acoustic resonant frequency (f < f0), the high-frequency component (f > ~0.1 Hz) should be

132

suppressed. As for the low-frequency cutoff, tsunami components (T > ~400 s, f < ~0.0025

133Hz) should be reduced. The F-net MT analysis adopted a passband of 0.005–0.02 Hz (50–200

134s) for foreshock #1, and 0.01–0.05 Hz (20–100 s) for foreshock #2 (NIED, 2011a; 2011b).

135

Considering the factors above, we took the passband to be 0.005–0.02 Hz for foreshock #1,

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and 0.01–0.05 Hz for foreshock #2.

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138

3. Methodology and Results: Centroid Moment Tensor Inversion using Dynamic

139

Pressure Records

140

We estimated the centroid moment tensors, centroid times, and centroid locations of141

the two earthquakes by analyzing onshore seismic and offshore dynamic pressure data. The

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procedure for the CMT inversion followed the grid-search approach of Ito et al. (2006),

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which uses five independent basis MT components (Kikuchi & Kanamori, 1991) (details of144

the calculation of Green’s functions and the CMT inversion are given in Text S1). In the145

analysis, the seafloor vertical acceleration is calculated using a conventional elasto-dynamic

146

equation using the discrete wavenumber method (e.g., Saikia, 1994) with the 1-D subsurface

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structure model of Kubo et al. (2002), and is converted to the dynamic pressure change using148

the pressure–acceleration relationship (equation (1)), where the water density ρ0 is set as 1.03

149

g/cm3. The sea depths h0 of the OBPGs are summarized in Table S1. The same bandpass

150

filter used for the observation is applied to the calculated waveforms. As a measure of151

waveform reproducibility, we used variance reduction (VR):Confidential manuscript submitted to Geophysical Research Letters152*+ = ,1 −

456
89:8
∑=
;
2>?012 32 712 32456∑=
2>?@12 32 A<<

B × 100 (%)

(3)

153

where IJKLM and IJNOPN are the k-th data of observed and calculated waveforms, respectively,

154

and N denotes the number of data used for inversion. Note that the onshore seismometers and155

offshore OBPGs have different dimensions. To reduce the bias caused by the difference in156

the inversion analysis, we introduced the weight value, QJ , as the inverse of the maximum

157

amplitude of each waveform:
S

158

QJ = TUV@3 (X)A,

159

where di(t) is the time series of the i-th station including the k-th datum. With respect to the160

grid search, we sought the horizontal and vertical locations of the centroid at 0.1° intervals in161

the horizontal and 2 km in the vertical. The interval of the temporal grids is 1 s.

W

(4)

162

In the analysis, we used two types of datasets, as follows. One of the datasets consists

163

only of the onshore seismograms (dataset 1). Three (radial, transverse, and vertical) velocity

164

components were obtained by the F-net stations (e.g., Okada et al., 2004). We analyzed the165same datasets used in the F-net MT solution: the F-net stations NOP, WJM, and WTR for

166

foreshock #1 (NIED, 2011a, red triangles in Figure 1) and IMG, KZK, and SGN for

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foreshock #2 (NIED, 2011b, blue triangles). We prepared another dataset (dataset 2) by

168

adding the pressure data obtained at GJT3, which is located on the offshore side of the169

epicenters, to dataset 1, in order to improve the station coverage.

170

The estimated CMT solutions of foreshock #1 are shown in Figure 4. Using only the171

onshore seismograms (dataset 1), the centroid of foreshock #1 was estimated at 143.2°E,

172

38.4°E, and 30 km with a VR of 66.1% (gray CMT solution in Figure 4a). The strike, dip,173

and rake were 171.2°, 21.2°, and 52.0°, respectively, and the seismic moment Mo was 5.5 ×

1741019 Nm (Mw 7.1). This solution was close to the F-net solution in location and mechanism

175(143.2798°E, 38.3285°E, 23 km, and 8.9 × 1019 Nm; black CMT solution in Figure 4a)

176(NIED, 2011a). The centroid was not located inside the rupture area estimated by the tsunami

177

waveform analysis (Kubota et al., 2017) (red rectangle in Figure 4b).

178

On the other hand, using dataset 2 (pressure data from GJT3 included), the centroid179

was estimated at 142.9°E, 38.5°E, and 30 km (red CMT solution in Figure 4b) with a VR of

Confidential manuscript submitted to Geophysical Research Letters

180

61.9%; the strike, dip, and rake were 164.1°, 23.2°, and 44.1°, respectively, and Mo = 5.1 ×

181

1019 Nm (MW 7.1). The centroid was located almost at the center of the rupture area obtained

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from tsunami waveform inversion (Kubota et al., 2017).

183

We conducted forward simulations of OBPG waveforms not used for the inversion, to184

examine the agreement with and observation. Both CMT solutions estimated from dataset 1

185

and dataset 2 reproduced the seismograms of the F-net stations nicely (Figure 4c), suggesting186

that the difference in the centroid horizontal locations cannot be resolved using only the187

seismograms of onshore stations. In contrast, we recognize the difference in the pressure

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waveforms recorded at offshore stations. The waveforms obtained from dataset 2 (red lines in

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Figure 4d) reproduce the observations (black) better than those from dataset 1 (gray). Note

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that we used only GJT3 in the inversion analysis, but we also see this improvement in other191

pressure records. For example, if we evaluate the VR of P09 (VRP09) using the same time

192

window used for inversion (white background area in Figure 4d), we obtained 2.5% for the193

CMT solution from dataset 1 and 70.6% for the solution of dataset 2.

194

We obtained similar results for foreshock #2. The centroid location of foreshock #2

195

obtained from dataset 1 was 143.2°E, 38.2°E, and 26 km with a VR of 80.1% (gray CMT

196

solution in Figure 5a), and the strike, dip, and rake were 194.0°, 19.1°, and 77.3°,

197

respectively (Mo = 4.2 × 1018 Nm, Mw 6.4). These are similar to the F-net solution (black) of

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143.0448°E, 38.1722°E, and 20 km (Mo = 5.51 × 1018 Nm) (NIED, 2011b). When GJT3 was

199

included (dataset 2), the centroid was at 142.9°E, 38.3°E, and 32 km with a VR of 68.8%,200

and the strike, dip and rake were 144.1°, 39.2°, and 21.1°, respectively (Mo = 4.2 × 1019 Nm,

201

Mw 6.4) (Figure 5b). We found that the centroid estimated from dataset 2 was closer to the202

center of the fault model than that from dataset 1. Also, the CMT solution estimated using203

dataset 2 reproduced the OBPG records better: the values of VRP09 were −13.6% (dataset 1)

204

and 48.0% (dataset 2).

205

To evaluate the resolution and accuracy of the centroid horizontal location, we

206

calculated the area where the VR exceeds 90% of the best-fit VR in each result. The high-VR

207

area (>90%) is surrounded by gray lines in Figures 4a, 4b, 5a, and 5b. For both foreshocks #1

208

and #2, the high-VR area extended in the ENE–WSW direction when pressure records from

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GJT3 were not used for the inversion (dataset 1) by ~100 km and ~50 km, respectively

210(Figures 4a and 5a), suggesting the horizontal location of the centroid is not well constrained.

Confidential manuscript submitted to Geophysical Research Letters

211

On the other hand, the high-VR area obtained from dataset 2 was much smaller and the EW

212

extent of the high-VR area became by half (by ~50 km for foreshock #1 and ~25 km for213

foreshock #2), and mostly confined within the spatial extent of the finite fault models derived

214

by the tsunami inversion (Figures 4b and 5b). Since the station coverage was improved by215

adding the dynamic pressure obtained at GJT3, located on the offshore side of the focal area

216

(Figure 1), the resolution of the centroid horizontal location was significantly improved.

217

The obtained centroid depths (~30 km) are systematically deeper than the plate

218

boundary depth obtained by the seismic survey (Ito et al., 2005). To discuss the depth219

resolution, we examined the vertical VR distribution at the horizontal point where the best-fit

220

CMT is obtained (Figures S1 and S2). When the centroid depth is less than ~10 km, the VR

221

is smaller than 90% of the maximum VR, suggesting that the centroid depth is deeper than 10

222

km. However, the vertical range where the VR exceeds 90% of the best value (gray lines in223

Figures S1 and S2) is widely distributed, suggesting the centroid depths are not well224

constrained. We also point out that that the centroid depths and the centroid time delay have a

225

trade-off relationship.

226
227

4. Discussion

228

4.1. Checking the validity of the pressure–acceleration relationship

229

Past studies have found that the seismograms and pressure records in the Fourier

230

amplitude are consistent with the theoretical relationship given by equation (1) (e.g.,

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Matsumoto et al., 2012). However, equation (1) suggests not only an agreement in the232

Fourier amplitude but also in the time series of the accelerograms and pressure records. It is233

important to confirm the agreement in the waveforms by observations. Our results confirmed

234

equation (1) by indirect comparison of the waveforms: the observed pressure records and235

theoretically calculated accelerograms. In Figures 4d and 5d, we compare the observed236

pressure records and pressure changes converted from the calculated accelerograms based on237

equation (1). The theoretically predicted pressure changes (red and blue lines) agree well238

with the observations (gray lines) at stations P02, P06, and P09, although those data were not239

used in the inversion analysis. Hence, the agreement found in those waveforms strongly

240

supports the validity of equation (1) in time domain. Disagreement at station P08 may beConfidential manuscript submitted to Geophysical Research Letters241

caused by insufficient modeling using the point-source approximation near the finite-fault

242

source.

243244

4.2. Importance of offshore dynamic pressure change for source estimation

245

Our results show that OBPGs are very useful in constraining centroid horizontal

246

locations. This is mainly because of the improvement in station coverage achieved by using247

the pressure data as offshore seismograms. A high sampling rate (1 Hz) also contributes to248

obtaining the CMT solution. Filloux (1982) has already suggested the applicability of249

seafloor pressure data as seismometers, but the sampling rate in his analysis was very low (28250s). If the sampling rate is low, aliasing due to the higher-frequency ocean acoustic wave (with251

a dominant period of ~5–10 s) may prevent us from obtaining high-quality bandpass filtered252

waveforms. The use of 1-Hz-sampling pressure data enabled us to use high-quality

253

seismograms for CMT analysis. The dynamic pressure records, free from amplitude

254

saturation, can be treated as on-scale near-field seismic records of offshore large earthquakes,

255

as demonstrated here. As mentioned by Heidarzadeh et al. (2017a), lack of resolution for256

source models of offshore moderate earthquakes will make it difficult to investigate the257

detailed source processes. It is expected that broadband seismograms provided by OBPGs

258

will contribute to estimating earthquake source processes in future studies, such as the finite

259

fault model or source duration. The source duration would be useful for identifying tsunami

260

earthquakes. The investigation of more examples would be necessary to confirm the261

applicability of OBPGs as the broadband seismometer in more detail (e.g., lower limit of the262

analyzable magnitude range).

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5. Conclusions

265

Using the dynamic pressure data observed by OBPGs deployed near the focal area

266

together with onshore seismograms, we estimated CMT solutions for two moderate (M ~ 7)267

offshore interplate earthquakes, and evaluated the robustness of the estimation of the268

horizontal centroid location. When offshore OBPG data were excluded, the horizontal

269

location of the centroid was not well resolved, and the best-fit centroid was estimated outside

270of the rupture areas obtained by a previous study. Meanwhile, the centroid locations wereConfidential manuscript submitted to Geophysical Research Letters271

well resolved and reasonably constrained inside the rupture area when we used both onshore272

seismograms and offshore OBPGs, although the depth resolution were not so good in the273

present study. The extent of the area where relatively high VRs were obtained (i.e.,274

estimation error) became around half by adding offshore OBPG record. Also, by using the275

estimated CMT solution, we successfully simulated the actual observed ocean-bottom276

pressure change records, except for a few stations near the source. The results of our study

277

indicate that the theoretical relationship of equation (1) is valid for actual observations, and278

we can improve the source estimation of offshore earthquakes using OBPGs based on279

equation (1).

280

Confidential manuscript submitted to Geophysical Research Letters

281

Acknowledgments, Samples, and Data

282

The authors are grateful to Earthquake Research Institute, the University of Tokyo and283

Earthquake and Volcano Hazards Observation and Research Program, the Ministry of284

Education, Culture, Sports, Science and Technology (MEXT) of Japan for providing seafloor

285

pressure data. This study was supported by the research project “Research concerning

286

Interaction between the Tokai, Tonankai, and Nankai Earthquakes” of MEXT, and by JSPS

287

KAKENHI Grant Numbers JP20244070, JP26000002, and JP15K17752. The authors declare288

that they have ho competing interests. The figures in this paper were prepared using Generic

289

Mapping Tools (GMT) (Wessel & Smith, 1998). The authors thank the editor Andrew V.

290

Newman and the reviewers Mohammad Heidarzadeh of Brunel University, London, and291

Yoshihiro Ito of Kyoto University, Japan, for helpful comments, which improved the292manuscript. The F-net waveform data and MT solutions are available at the website of the

293

National Research Institute for Earth Science and Disaster Resilience (NIED), Japan294(http://www.fnet.bosai.go.jp/top.php?LANG=en). The OBPG data used in this study are

295

available in the supplementary datasets S1, S2, and S3 (the description of the datasets is in

296

Text S2).

297

Confidential manuscript submitted to Geophysical Research Letters

298

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426
427

Figure 1. Location map of this study. Stars are the epicenters428

determined from ocean bottom seismographs (Suzuki et al., 2012), and429

rectangles are coseismic rupture areas from near-field tsunami analysis

430(Kubota et al., 2017) (red: foreshock #1, blue: #2). Inverted triangles

431

denote station locations (green: OBPGs, red and blue: F-net broadband

432

seismometers). F-net routine MT solutions (NIED, 2011a; 2011b) are

433

shown in black, and colored CMT solutions are those obtained jointly

434

using onshore and offshore datasets (also shown in Figures 4b and 5b).

Confidential manuscript submitted to Geophysical Research Letters

GJT3 time series (foreshock #1)

80

80
60
40
20
0

0

0

-400

-20

-1200

-60

-20

-40

-800

-80

-1600

Relative Pressure [hPa]

GJT3 time series (foreshock #1)

20

400

160

100

40

800

200

(c)

(b)

60

1200

-2000
-20

435

100

-15

(d)

-10

-5

0

5

10

Lapse Time from foreshock #1 [min]15

10

GJT3 time series (foreshock #2)

8

-15

(e)

-10

-5

-60
-80

0

5

10

Lapse Time from foreshock #1 [min]

15

20

4
2

2

40

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-2
-4

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-8

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0

5

10

Lapse Time from foreshock #2 [min]

15

-10
20
-20

(f)

6

-4

Raw
Tsunami (LP 400s-)
Dynamic (BP 20-100s)
-15

-10

-5

-6
-8

0

5

10

Lapse Time from foreshock #2 [min]

15

20

-10

Period [s]

103
102
1010
GJT3 spectrum (foreshock #1)
109
108
107
106
105
104
103
102
101
No event
100
During foreshock #1
10-1
10-3
10-2
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4

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GJT3 time series (foreshock #2)

6

120

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20
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Raw
Tsunami (LP 400s-)
Dynamic (BP 20-100s)

Power [hPa2/Hz]

1600

(a)

Power [hPa2/Hz]

Relative Pressure [hPa]

2000

102

1010
GJT3 spectrum (foreshock #2)
109
108
7
10
106
105
104
103
102
101
No event
100
During foreshock #2
10-1
-3
10
10-2

Frequency [Hz]436

Figure 2. OBPG records of local earthquakes on 9 March 2011

437

observed at station GJT3 (shown in Figure 1). (a–b) Time series438

associated with the Mw 7.2 earthquake. Gray, blue, and red lines are the439

original, low-pass (>400 s), and bandpass filtered (0.01–0.05 Hz)

440

records, respectively. (c) Power spectra during the Mw 7.2 earthquake

441(green) and calm period (black), calculated from 1024 s time windows442

marked by colored bars in Figure 2b. Passbands of the filter in Figure 2b

443

are marked by colored rectangles. (d–f) Time series and power spectra444

of the Mw 6.5 earthquake.

101

100

10-1

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101

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10-1

100

Confidential manuscript submitted to Geophysical Research Letters

120
110
100
90

Relative Pressure [hPa]

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70

Raw
0.005 - 0.02 Hz (50 - 200 s)(a) Foreshock #1

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TM2

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TM1

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90

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GJT3

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GJT3

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30

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Raw
0.01 - 0.05 Hz (20 - 100 s)(b) Foreshock #2

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180

Lapse Time from foreshock #1 [s]

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300

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-120

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0

60

120

180

Lapse Time from foreshock #2 [s]446Figure 3. Comparison of raw pressure waveforms (gray) and bandpass

447

filtered waveforms for (a) foreshocks #1 and (b) #2.

240

300

Confidential manuscript submitted to Geophysical Research Letters

448
449

Figure 4. CMT inversion of foreshock #1. (a) Result obtained from450

dataset 1, only onshore seismometers (NOP, WJM, and WTR). The

451

best-fit solution is in gray. (b) Result obtained from dataset 2, jointly

452

using onshore seismometers and OBPGs (NOP, WJM, WTR, and GJT3).

453

The best-fit solution is in red. Thick gray lines and small CMTs denote454

area where the calculated VR exceeds 90% of the best-fit VR. (c)455Comparison of onshore seismograms. (d) Comparison of OBPG

456

waveforms, between observed waveforms (black), and synthesized457

waveforms calculated from the best-fit solution obtained from datasets 1458(gray) and 2 (red), respectively. A time window of 0–240 s (white459

background area) was used for inversion.

Confidential manuscript submitted to Geophysical Research Letters

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461

Figure 5. CMT inversion of foreshock #2. Symbols and colors are the462same as in Figure 4.

Geophysical Research Letters
Supporting Information for
Estimation of seismic centroid moment tensor
using ocean bottom pressure gauges as seismometers
Tatsuya Kubota1, Tatsuhiko Saito1, Wataru Suzuki1, and Ryota Hino2
1

National Research Institute for Earth Science and Disaster Resilience, Tsukuba, Japan.
2

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

Contents of this file
Text S1 to S2
Figure S1 to S2Table S1 to S2Introduction
Text S1 describes the method to estimate the centroid moment tensor by waveform inversion.
The description for the supplementary datasets (Datasets S1, S2, and S3) is in Text S2. Figure
S1 is the vertical distribution of moment tensor solutions to evaluate the resolution of thecentroid depth. Table S1 gives the locations of the OBPG stations. The seismic structure used
for calculation of the dynamic pressure is shown in Table S2.

1

Text S1.
In this study, the centroid moment tensors, centroid times, and centroid locations were
estimated using the grid-search approach of Ito et al. (2006), under the assumption that thesource can be represented by a point source. Here, the detail of the procedure is described.
By assuming the target events is represented by a pure deviatoric moment tensor (MT)without an isotropic component, the observation equation is expressed as:! " # = ! " %&,(S1)

where w is the vector representing the weight of the data, d is the data vector, G is thematrix composed of the Green’s function, and m is the model parameter vector consisting offive independent basis MT components (e.g., Kikuchi & Kanamori, 1991). Note that the onshore
seismometers and offshore OBPGs have different dimensions. To reduce the bias caused by thedifference in the inversion analysis, we introduced the weight value wk (k-th datum of theweight vector w):'( =)*+, -. /,(S2)

where di(t) is the time series of the i-th station including the k-th datum. From equation (S1),
we obtain the model parameter vector as:& = %" !! " % 0) %" !! " #.

(S3)

We used a time window of 0–240 s from the focal time determined from the ocean bottom
seismometers (Suzuki et al., 2012) for foreshock #1, and 0–180 s for foreshock #2, taking theirmagnitudes and the time windows used in the F-net MT analysis into account.
In the analysis, we calculated the Green’s function using the discrete wavenumber frequency
method with a 1-D subsurface structure (e.g., Saikia, 1994). Table S2 gives the seismic velocity,
attenuation, and density structure used for the calculation, which are the same as those used in
the F-net moment tensor calculation, and considered suitable for the 1-D structure of inland
Japan (Kubo et al., 2002). Note that we did not assume the effect of the sedimentary layer andthe topography for simplicity (i.e., OBPGs are assumed to be located on hard rock on the sea
surface). We assumed an impulsive source time function, and the bandpass filter is applied asthat used for the observation. Finally, the calculated seafloor vertical acceleration is converted
to the dynamic pressure change using the pressure–acceleration relationship p = ρ0h0az(equation (1)), assuming the water density ρ0 is 1.03 g/cm3, where az is the vertical acceleration.
The water depth (h0) of the OBPGs are summarized in Table S1. The same bandpass filters usedin the dynamic pressure records are also applied to the Green’s function. After we obtained thebest fit CMT solution, we forwardly calculated the waveforms which are not used for the
inversion analysis to compare with the observation, using the superposition of the Green’s
functions calculated from five independent basis MT components.

2

Text S2.
The 1-s sampled raw pressure data used in this study are available in supplementary
datasets S1, S2, and S3. This text describes the contents of the datasets.
Dataset S1 is the raw pressure time series for both foreshocks at GJT3, with the time windowof -20 min to 20 min from the focal time. This dataset was used to prepare Figure 2. Note thatboth datasets contain the ocean tide components, although tides were removed in the timeseries shown in Figure 2 (detail of the tide removal procedure is in Kubota et al. (2017)). The firstcolumn denotes the lapse time from the focal time (02:45:16 UTC on 9 March 2011 forforeshock #1 and 21:24:01 UTC for foreshock #2), determined by Suzuki et al. (2012). Times ofday (hour, minute, and second in UTC) for both events are also shown.
Datasets S2 and S3 are the raw pressure data for foreshocks #1 and #2, respectively. These
datasets were used to prepare Figures 3, 4, and 5. The formats of the time stamps are the sameas Dataset S1. The names of the OBPG stations are shown in the first row.
We note that the deployment and retrieval of the OBPGs at GJT3, P02, P03, P06, P07, P08,
and P09 were conducted by Tohoku University (Hino et al., 2014; Kubota et al., 2017), and thereal-time cabled OBPGs at TM1 and TM2 were operated by Earthquake Research Institute (ERI)of the University of Tokyo (Kanazawa & Hasegawa, 1998). The TM1/TM2 data were resampled
to 1 s, although the sampling rate of the original ones was 10 Hz.

34(a) Dataset 1(b) Dataset 2
8s

6

12s
8s

8

12s
9s

10

9s

12

Depth [km]14

Plate boundary at
16 143.20°E 38.40°N
18

9s

13s

10s

14s
14s
10s
10s

24
26
28
30

143.20°E 38.40°N 30km
4050

VR [%]

Plate boundary at
142.90°E 38.50°N

14s
14s

VRmax × 0.9

VRmax × 0.9

22

34

13s

10s

20

32

13s

10s
11s
11s

15s
15s
15s

11s

15s

11s

15s

142.90°E 38.50°N 30km
60

70 40

50

VR [%]

60

70

Figure S1. Vertical distribution of VRs and moment tensors at the horizontal location of thebest-fit CMT solution for foreshock #1 (Figure 4). (a) Result from dataset consisting of only theonshore seismograms (Figure 4a). (b) Result from dataset consisting of onshore seismograms
and offshore pressure data (Figures 4b). The location of the best-fit centroid is shown in thebottom left in each figure. Horizontal and vertical axes denote VR and centroid depth,
respectively. Small numbers above each solution are the centroid time delay from the focal
time. Red lines denote plate boundary depths obtained from seismic surveys by Ito et al. (2005).

44(a) Dataset 1(b) Dataset 2
4s

6

9s
4s

8

9s
4s

10

4s

12

Depth [km]Plate boundary at
16 143.2°E 38.2°N

10s
4s

10s
4s

18

10s

4s

20

4s

24
26
28
30
143.2°E 38.2°N 26km
50

60

VR [%]

Plate boundary at
142.90°E 38.30°N
VRmax × 0.9

VRmax × 0.9

22

34

10s
4s

14

32

10s

4s
4s
4s

10s
10s
10s
10s
9s

4s

9s

4s

9s

142.90°E 38.30°N 32km
70

80 50

60

VR [%]

70

80

Figure S2. Vertical distribution of VR and moment tensors at the horizontal location of thebest-fit CMT solution for foreshock #2 (Figure 5). (a) Result from dataset consisting of only
onshore seismograms (Figure 5a). (b) Result from dataset consisting of onshore seismograms
and offshore pressure data (Figures 5b). The location of the best-fit centroid is shown in thebottom left in each figure. Horizontal and vertical axes denote VR and centroid depth,
respectively. Small numbers above each solution are the centroid time delay from the focal
time. Red lines denote plate boundary depths obtained from seismic surveys by Ito et al. (2005).

5

Table S1. Locations of OBPGs
StationLatitude [°N]Longitude [°E]

Depth [m]GJT3a38.2945

143.4814

3,293

P02a

38.5002142.5016

1,104

P03a

38.1834

142.3998

1,052

P06a

38.6340

142.5838

1,254

P07a

38.0003142.4488

1,059

P08a

38.2855

142.8330

1,418

P09a

38.2659

143.0006

1,556

TM1b

39.2330

142.7830

1,564

TM2b

39.2528

142.4500954a

Pop-up recovery OBPG identical to those used in Hino et al. (2014) and Kubota et al. (2017)
Real-time cabled observation systems operated by the Earthquake Research Institute (ERI) of
the University of Tokyo (Kanazawa & Hasegawa, 1997)b

6

Table S2. Structure model used in this studya

Depth
[km]

Thickness[km]

P-wavevelocity[km/s]

S-wavevelocity[km/s]

Density[kg/m3]

Qp

Qs

0

3

5.50

3.14

2300

600

300

3

15

6.00

3.55

2400

600

300

8

15

6.70

3.83

2800

600

300

18

67

7.80

4.46

3200

600

300

33

125

8.00

4.57

3300

600

300

100

100

8.40

4.80

3400

600

300

225

100

8.60

4.91

3500

600

300

425

—

9.30

5.31

3700

600

300

a

This structure is same as that used in the F-net MT calculation and considered to be suitable forthe one-dimensional structure of inland Japan (Kubo et al., 2002).

7