1

Coseismic slip model of offshore moderate interplate earthquakes on March 9,22011 in Tohoku using tsunami waveforms

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Tatsuya Kubotaa*Ryota Hinoa, Daisuke Inazub1, Yoshihiro Itoc, Takeshi Iinumad,

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Yusaku Ohtaa, Syuichi Suzukia, Kensuke Suzukid

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a

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Sendai 980-8578, Japan.

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b

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c

9

d

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

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1Present address: Department of Ocean Sciences, Tokyo University of Marine Science

11and Technology, Tokyo, Japan.

Graduate School of Science, Tohoku University, 6-6, Aza-Aoba, Aramaki, Aoba-ku,

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

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

1213E-mail addresses:

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Tatsuya Kubota: tatsuya.kubota.r6@dc.tohoku.ac.jp

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Ryota Hino: hino@m.tohoku.ac.jp

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Daisuke Inazu: inazud@oa.u-tokyo.ac.jp

17(Present e-mail address: inazud@m.kaiyodai.ac.jp)

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Yoshihiro Ito: ito.yoshihiro.4w@kyoto-u.ac.jp

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Takeshi Iinuma: iinuma@jamstec.go.jp

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Yusaku Ohta: yusaku.ohta.d2@tohoku.ac.jp

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Syuichi Suzuki: syuichi.suzuki.a1@tohoku.ac.jp

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Kensuke Suzuki: kensukes@jamstec.go.jp

23*

Corresponding author E-mail: tatsuya.kubota.r6@dc.tohoku.ac.jp

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Abstract

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We estimated the coseismic slip distribution associated with the Mw 7.2 and 6.5

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foreshocks of the 2011 Tohoku-Oki earthquake based on analysis of the tsunami

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waveform records obtained just above their focal areas. The results show that the main29

rupture areas of each of the foreshocks do not overlap with each other, and show a30

distribution that is complementary to the postseismic slip area of the first Mw 7.2

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foreshock as well as to the epicenters of smaller earthquakes during foreshock activity.

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After the second largest foreshock, seismicity increased in the area between the rupture

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area of the second largest foreshock and the mainshock epicenter, suggesting34

propagation of aseismic slip towards the mainshock epicenter. The calculated stress35

drop of the second largest foreshock was smaller than the largest one, implying strength36

reduction during the postseismic period of the largest foreshock. Based on a comparison

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of coastal tsunami records, it is suggested that the asperity ruptured in the M 7.0

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earthquake in 1981 ruptured again during the largest foreshock in 2011, but it expanded

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to the updip side of the 1981 rupture area and became larger in magnitude, exemplifying

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the irregularity of earthquake recurrence in the area.

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Keywords: 2011 Tohoku-Oki earthquake, foreshock, tsunami, subduction zone,

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seafloor observations

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Highlights

46lFinite fault models of two large 2011 Tohoku earthquake foreshocks are presented

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Nearest-field tsunami data inversion revealed coseismic slip of the foreshocks

48lSouth-migrating seismicity suggests aseismic slip triggered the Tohoku earthquake

49lForeshock coseismic and postseismic slip areas show complementary distributions

50l

A 1981 M7 earthquake asperity ruptured during the largest foreshock in 2011

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l

1. Introduction

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The 2011 Tohoku-Oki earthquake occurred at 5:46 UTC on March 11, 201154

(hereafter, the mainshock). The mainshock was preceded by intensive foreshock activity,

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including the largest foreshock (Mw 7.3, Global CMT, http://www.globalcmt.org) and56

the second largest foreshock (Mw 6.5, Global CMT) that occurred at 2:45 and 21:24,

57

respectively, on March 9, 2011. Hereafter, we refer to the largest foreshock as foreshock58#1 and the second largest foreshock as foreshock #2. The location of the epicenters and59

focal mechanisms of the mainshock and the two major foreshocks are shown in Figure 1.

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The epicenters of foreshock #1 and foreshock #2 were located ~50 km northeast and61~20 km northeast of the mainshock epicenter, respectively. The focal mechanism

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solutions of the two foreshocks closely resemble each other, indicating that the two

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events can be regarded as failures of a plate boundary fault with the same slip direction.

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Although a number of finite source models of the mainshock have been presented

65(e.g., Ide et al., 2011; Ozawa et al., 2011; Saito et al., 2011; Simons et al., 2011; Iinuma

66

et al., 2012; Satake et al., 2013), few studies have attempted to show the source model

67

of foreshock #1. Shao et al. (2011) estimated the coseismic slip distribution of68

foreshock #1 based on joint inversion of seismic and GNSS data, and Gusman et al.

69(2013) analyzed offshore tsunami waveform records associated with foreshock #1 to70

obtain its finite fault model. Ohta et al. (2012) modeled the geodetic records of onshore

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GNSS stations and ocean bottom pressure gauges (OBPG) to derive the coseismic fault

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model of foreshock #1, as well as its postseismic slip distribution. The estimated73

postseismic slip occurred on the plate boundary where a sudden increase in seismicity

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was observed, regarded as the aftershocks of foreshock #1. Ando and Imanishi (2011)75

found that the seismicity expanded from the source area of foreshock #1 and the76

mainshock rupture was initiated when it reached the mainshock hypocenter. Kato et al.

77(2012) pointed out that the southward migration of the aseismic slip occurred just after

78

foreshock #1 and initiated rupture of the mainshock. All these studies suggested that79

there was a chain-reaction interplay between the aseismic slip and the small earthquakes

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emerging after foreshock #1 in the surrounding region, and that the activity facilitated81

rupture initiation of the Mw 9 mainshock.

82

Foreshock #2, which occurred between the epicenters of foreshock #1 and the83

mainshock (Figure 1), can be regarded as the largest aftershock of foreshock #1 and84

could have been triggered by its aseismic afterslip. Therefore, the rupture process of85

foreshock #2 will provide additional information for characterizing the dynamic

86

processes preceding the 2011 Tohoku-Oki earthquake around its epicenter. However,87

little is known about foreshock #2 because of its size, which is too small for finite

88

source modeling using available onshore seismic, geodetic, and coastal tsunami data.

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When the two foreshocks occurred, nine ocean bottom pressure gauges (OBPGs) were90

deployed just above the focal area (Figure 1, Table 1) and they recorded clear pressure

91

changes associated with sea surface motions due to tsunamis as well as coseismic static

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displacement of the seafloor (Figure S1) during the two foreshocks. In this study, we

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analyze the OBPG data to obtain finite source models for the two major foreshocks.

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Tsunami data are often used to estimate the initial tsunami height distribution and95

source models of tsunami-generating earthquakes (e.g., Saito et al., 2011; Tsushima et96al., 2012; Satake et al., 2013; Inazu and Saito, 2014; Kubota et al., 2015). Among a5

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number of approaches for obtaining earthquake source models, tsunami waveform98

inversions have an advantage over inversions using seismic data because the spatial

99

distribution of tsunami propagation speed is much better known than that of seismic100

waves. Accurate models of tsunami wave propagation allow us to make more reliable101

waveform calculations and to increase the robustness of obtained source models. When

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tsunami waveforms are obtained far offshore, the inversion results will be more reliable

103

compared to those using coastal tsunami data because offshore waveforms are almost

104

free from the nonlinear and complex behaviors due to coastal interaction. Several

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previous studies have demonstrated that finite source models of moderate earthquakes

106(Mw ~ 7 or smaller) could be derived from offshore tsunami data (e.g., Hino et al.,107

2001; Tanioka et al., 2007; Saito et al., 2010). We use offshore near field tsunami

108

records obtained by OBPG that are more reliable than coastal records to inspect the109

source processes of the two foreshocks.

110

The purpose of this study is to obtain fault models of foreshocks #1 and #2 of the111

2011 Tohoku-Oki earthquake using OBPG records, and to discuss the spatio-temporal

112

evolution of foreshock activity driven by aseismic slip thought to trigger the Mw 9113

mainshock.

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2. Ocean Bottom Pressure Data

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Seven offshore OBPGs were deployed around the foreshock activity zone by117

Tohoku University and were in operation in March 2011 (Figure 1 and Table 1). Those

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OBPGs were offline autonomous instruments with pop-up recovery. We deployed the119

instruments at stations GJT3, P02, P03, P06, P07, P08, and P09, located within ~70 km

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of the epicenters of the foreshocks. Detailed descriptions of the instruments are given in

121

Hino et al. (2014). Although the tsunamis associated with the foreshocks were also

122

observed at TM1 and TM2, pressure-recording nodes of real-time cabled observation

123

systems operated by the Earthquake Research Institute of the University of Tokyo

124(Kanazawa and Hasegawa, 1997) (Figure 1 and Table 1), we did not use them to125

estimate the fault models of the foreshocks. This is because they were located more than126

100 km away from the epicenters.

127

Figures 2 and 3 show the pressure records obtained after the following data

128

processing. First, pressure changes caused by ocean-tides were removed from the129

observed time series. Ocean-tide variations were computed using a theoretical tide130

model, NAO.99Jb, developed by Matsumoto et al. (2000), assuming that a 1 cm water131

height anomaly was equivalent to 1 hPa of pressure change. After the de-tiding process,132

we took the moving average with a 60 s time window, then applied a low-pass filter

133(Saito, 1978) with a cutoff frequency of 2.5 mHz (=1/400 Hz) in order to remove high134

frequency components associated with elastic waves both in the seawater and beneath135

the seafloor generated by earthquakes. Examples of the observed and processed136

waveforms are shown in Figure S1

137

The observed tsunami waveforms associated with foreshock #1 are very clear and138

simple, composed of a pair of up-motion and subsequent down-motion waveforms

139(Figure 2). The width of the up-motion pulse is ~8 min. The highest water level exceeds

140

20 cm (corresponding to a 20 hPa pressure increase) at station P06. On pressure records

141of several stations, clear permanent steps associated with vertical seafloor displacement142

can be identified. The records at P02 and P06 show pressure increases of ~10 hPa,

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indicating ~10 cm of subsidence, whereas a pressure decrease of ~10 hPa,

144

corresponding to uplift of ~10 cm, was observed at P09.

145

The tsunami from foreshock #2 (Figure 3) has a much smaller amplitude than that146

of foreshock #1. The tallest height was ~3 cm, observed at P02 and P03. The waveforms

147

also appear simple, although the low signal-to-noise ratio makes it difficult to inspect

148

the waveform characteristics in detail. The duration of the up-motion pulse was ~5 min.

149

Evident coseismic uplift, as large as 4 cm, was recorded at P09 as a pressure reduction

150

of ~4 hPa, larger than the previously reported noise level (Inazu and Hino, 2011) of the151

seafloor pressure records obtained by pressure sensors with the same performance as

152

those of the OBPGs used in the present study. However, the smaller (<1 hPa) offset

153changes in other records could be apparent because of long-period noise.

154

The durations of the up-motion part of the observed tsunami waveforms enable us

155

to guess approximate source sizes based on the propagation speed at the source region.

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Based on linear long-wave theory, the tsunami wave speed v is expressed as v = gH ,157

where g is the gravity acceleration constant (=9.8 m/s2) and H is the water depth (e.g.,

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Satake, 2002). Water depth in the source region is ~2,000 m so the tsunami wave speed

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can be approximated as ~140 m/s. From the observed pulse widths, the spatial

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dimensions of the uplift area can be roughly estimated as ~60 km for foreshock #1 and161~40 km for foreshock #2.

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3. Methods

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In order to obtain the coseismic slip distribution, we carried out a tsunami

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waveform inversion using the OBPG records. We used the 1-Hz sampled pressure time

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series with a time window of 20 min from the origin time, as determined by Suzuki et al.

167(2012), who relocated the foreshock and mainshock hypocenters using ocean bottom

168

seismograph data deployed in the source area. The observation equation in our inversion

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is expressed as:170⎛ obs ⎞ ⎛ G ⎞⎜⎜ d⎟⎟ = ⎜⎟a ,0⎝⎠ ⎝ αS ⎠(1)

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where d obs is the vector of the observed tsunami waveforms, G is a matrix composed

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of the tsunami Green’s functions, S is a matrix representing the smoothing constraint,

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and a is the vector of unknown parameters describing the amount of slip on the fault,

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which is being estimated. In this study, the goodness of the waveform fitting can be

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measured by a variance reduction (VR), defined as:

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N
⎛
⎞
obs
calc 2⎜ ∑ ( dk − dk ) ⎟⎟ ×100 (%)
VR = ⎜1− k=1 N⎜⎟
2,∑(dkobs ) ⎟
⎜
⎝
⎠
k=1

(2)

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where dkobs and dkcalc are the k-th data of observed and calculated waveforms,

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respectively, and N is the number of data used for the inversion. In the inversion, we

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applied a non-negative least squares inversion (Lawson and Hanson, 1978) because

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negative (normal-faulting) slips are unlikely to happen on the fault during the two

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foreshocks. We empirically determined the weight of the smoothing constraint as α = 10

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by inspecting the trade-off curve between α and the VR (Figure S2) to avoid both

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excessive fitting and over-smoothing due to small and large α, respectively.

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The tsunami Green’s functions were calculated as waveforms caused by vertical

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seafloor displacement associated with the rupture of a small subfault placed along the

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plate boundary fault. Seafloor displacement was calculated using the equation by Okada

187(1992). The initial sea-surface height distribution was obtained by applying the depth

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filter, introduced by Saito and Furumura (2009), to the seafloor vertical deformation,

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which spatially smooths seafloor deformation. For the filtering, we assumed a constant190

water depth of 2 km, which is equal to the depth around the epicenters.

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Tsunami waveforms were calculated based on a linear long-wave equation

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expressed in the local Cartesian coordinate system (e.g., Satake, 2002; Saito et al.,193

2014). In the calculation, we assumed that the slip of all the subfaults began at the same

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time and the slip duration was 10 s based on the GCMT solution. As bathymetry data,

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we resampled ETOPO1 (Amante and Eakins, 2009) into 2 km × 2 km gridded data. The

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time step interval of the calculation was 1 s. The pressure offset due to seafloor vertical

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deformation was taken into account according to a method devised by Tsushima et al.

198(2012) by subtracting the calculated vertical seafloor deformation from the calculated

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sea surface fluctuation at the point of the OBPG stations. After the tsunami calculation,

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we took the 60 s moving average and applied the low-pass filter, as for the observed

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pressure data.

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One of the inputs to the model is the geometry of the plate boundary fault on which203

the two foreshocks ruptured. We assumed that the plate boundary fault can be204

approximated by a planar fault and took the dip and strike angles of the Global Centroid

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Moment Tensor (GCMT) solution for foreshock #1 (dip = 12° and strike = 189°) as

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those of the planar plate boundary fault. The assumed dip angle is consistent with the207plate boundary model presented by Ito et al. (2005) based on active seismic exploration.

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Because the assumed strike direction matches that of the trench axis in this region, it is a

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good approximation of the local strike of the fault. We set the fault depth by referring to210

the model by Ito et al. (2005). Subfaults 20 km × 20 km in the dip and strike directions

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were distributed along the modeled plate boundary fault in the range spanning the area212

covering the epicenters of the relevant earthquakes and OBPG stations (120 km × 120

213km, Figures 2 and 3).

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In the inversion, we assumed the rake angle of slip on the subfault as a given

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constant from the GCMT solution for foreshock #1 (78°), for both foreshocks #1 and #2,

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after inspecting if the given rake angle is representative of those of interplate217

earthquakes in this area. We chose 65 interplate earthquakes (Mw > 6.0) having a strike218

of 170–210°, a dip of 0–45°, and a rake of 40–120°, according to the GCMT catalogue219

from 1 Jan. 2000 to 31 Dec. 2015, located in the region (37.5–39.5°N and 142–144°E).

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The average of their rake angles was 79.2 ± 2.0°, which is consistent with that of the221

GMT solution for foreshock #1 (78°).

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4. Results

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Figure 2 shows the result of the coseismic slip inversion for foreshock #1. The

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maximum slip is 1.23 m at the subfault marked by a thick green square in Figure 2a.

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The slip amounts in three subfaults adjacent to the maximum slip subfault are almost as

227large as the peak slip, that is 1.0, 0.96, and 0.95 m. Of the total slip, 74% is concentrated

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on these four subfaults, forming an area 40 km × 40 km northwest of the epicenter (the229four subfaults are marked by a solid square in Figure 2a). The next two largest slips are

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0.40 and 0.39 m, less than half the maximum slip, which are located north of the231

subfault with the largest slip and beneath P09, respectively. The spatial extent of the

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uplifted area of the initial sea-surface height expected from the fault slip model is233

consistent with the estimated source dimension based on the duration of tsunami pulses

234(~60 km). The obtained slip model explains the observed waveforms very well, and we

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obtained a VR of 86% for the foreshock #1 model.

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Figure 3 shows the result of the coseismic slip inversion for foreshock #2. Large237

slip was concentrated on the two subfaults to the north and northwest of the epicenter

238(marked by solid rectangle in Figure 3a). The largest slip, 0.27 m, was obtained for the239

subfault beneath P09 (marked by a thick green square) and the second largest slip (0.17240m) was obtained for the subfault beneath P08. The slip amount on these two subfaults

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constitutes 57% of the total slip. The next largest slip amounts of 0.09, 0.07, and 0.05 m,

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less than half of that on the two subfaults, were estimated at three subfaults near the two243large-slip subfaults; two were located to the south and one to the northeast. The spatial

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extent of the initial sea surface uplifted area expected from the fault slip model is almost

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consistent with the source size estimated from the tsunami pulse width, ~40 km. The

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calculated waveforms explain the observed waveforms well, and the VR was 76%.

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Although we did not include the records obtained at TM1 and TM2 in the inversion,248

it would be worthwhile to see if the source models are consistent with these records. In

249both foreshocks, the coseismic slip models mostly explain the arrival times and peak

250

amplitudes (Figure S3). It appears that a long-term drift remaining in the observed

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records accounts for the waveform misfits. Static offsets of ~5 hPa can be identified in252

the data of foreshock #1, but the seafloor vertical displacement of ~5 cm at the sites

253~100 km away from the source is not probable. The amounts of the apparent offsets are

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comparable to the expected noise level in the records of TM1 and TM2 reported by

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Inazu and Hino (2010). The higher noise level is another reason we did not include

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these data in the fault modeling.

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Concentration of large, more than a half of the peak value, slips within small areas258

adjacent to the epicenter is a common feature of the obtained source models. In order to259

confirm the reliability of those large slips and also the significance of the smaller slips

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surrounding them, we carried out a test by performing different sets of inversion

261

analyses. In the trial inversions, we used a larger model space along the trench (160 km

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instead of 120 km) and a longer time window (30 min instead of 20 min). Inversions

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with TM1 and TM2 data were also made. Further, inversions without a non-negative264

constraint were performed. In total, we carried out sixteen sets of inversions for each265

foreshock. The results of the test inversions are shown in Figures S4 and S5. The

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locations of large slip patches near the epicenters were consistently estimated267

throughout the different trials. However, the slip distributions in the margins are268

considerably different from one another, indicating less reliability of the solution there.

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To identify the region of reliable slip amount, we calculated the average and standard

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deviation of the slip amounts on subfaults from the results of additional inversions

271(Figure S6). Note that the averages and standard deviations for the 12 subfaults in the272

northern part of the model space are obtained from the results with larger model space,273

but those in the other subfaults are from all the inversion results. From this test, it is274

concluded that the characteristics of the source models explained earlier in this section275

is robustly estimated.

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It is possible that slip over a small area has spread to a larger area because of277

smearing by the smoothing constraint imposed in the slip inversion. By taking these

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spreading effects into account, the subfaults with significant amounts of slip can be

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interpreted as the main rupture areas of the two foreshocks. In order to assess the spatial

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resolution of the inversion analysis, especially in the possible coseismic slip areas, we

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performed a recovery test (Figure S7). In the test, we gave slips of 1 m to subfaults

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where the large slip amounts were estimated, then the tsunami waveforms calculated

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from the given slip models were inverted for slip distributions. All the settings of the284

inversion analysis were the same as those in the inversion of the observation data. The

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test results demonstrate how well the amount of slip in the given rupture zone is286

recovered and how much slip leaks into the surrounding cells. The slip patterns of the287

test results (Figure S7) closely resemble those inverted from the observed data (Figures288

2 and 3) and those of the averaged slip distribution (Figures S4 and S5). The results of289

the recovery test show that more than ~70% of the given slip was recovered.

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We also attempted to confirm whether only the significant slip could explain the291

observed tsunami waveforms. First, we calculated tsunamis only from the outstanding

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slip area, keeping the amount of slip at subfaults the same as that estimated by the293

inversion analyses (Figure 4, blue traces). Although the arrival times and the pulse

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width of the tsunamis are well reproduced, the amplitudes and offset amounts are295

significantly smaller than those of the observed waveforms, producing smaller VR

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values, 66% and 72% for foreshocks #1 and #2, respectively. Then, we corrected the297

slip amounts in the main rupture areas, taking into account the slip reduction rates

298

obtained by the recovery tests, in order to recalculate tsunami waveforms (Figure 4, red

299

traces). The corrected slip amount Dcorrected is expressed as:

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Dcorrected = D estimaed ×

SgivenSrecovered

,

(3)

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where Destimated denotes the estimated slip amount in the inversion, and Sgiven and302

Srecovered are the given slip amount (=1 m) and recovered slip amount on each subfault in303

the recovery test, respectively. The VRs are improved to 80% and 76% for foreshocks

304#1 and #2, respectively. Most of the characteristics of the observed waveforms are well305

modeled.

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Based on these assessments, we define the subfaults with slips larger than half of307

the maximum slip as the main rupture area. The main rupture area of foreshock #1 is a308

square 40 km × 40 km located northwest of the epicenter, and that of foreshock #2 is a309

rectangular area 20 km long by 40 km wide. After correction with the recovery rates,

310

the amounts of maximum slip are 1.3 m and 0.3 m, average slip of the main rupture

311

areas are 1.2 m and 0.3 m, and seismic moments released from the main rupture areas312

are 7.6 × 1019 Nm (Mw 7.2) and 9.0 × 1018 Nm (Mw 6.6) for foreshocks #1 and #2,

313

respectively, assuming a rigidity of 40 GPa. The good agreement between waveforms

314

calculated from the single main rupture models indicates that the estimated location and315

spatial extent of the main rupture areas are reasonably constrained.

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5. Discussion

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5.1 Comparison with previous studies on foreshock sequence319

We compare the main rupture areas of foreshocks #1 and #2 with the coseismic and320

postseismic slip distributions of foreshock #1 by Ohta et al. (2011) in Figure 5. The

321

location and spatial extent of the main rupture area of foreshock #1 estimated in this

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study (red rectangle) agrees well with the coseismic slip distribution in Ohta et al.

323(2012) (yellow contours). Shao et al. (2011) and Gusman et al. (2012) also indicated324that the coseismic slip of foreshock #1 is concentrated on the fault northwest of its

325

epicenter, although the estimated sizes of the rupture area are wider than our results,

326

possibly because of the spatial resolution limitation in the data they used. The near-field

327

tsunami records used in this study significantly improved the source model, enabling a

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more detailed discussion of the relationship between the slip regions of other major

329

events, the postseismic slip of foreshock #1, and the coseismic slip of foreshock #2.

330

The main rupture area of foreshock #2 (blue rectangle) does not overlap with that of331

foreshock #1, and is located between foreshock #1 and the mainshock epicenters. The

332

postseismic slip area estimated by Ohta et al. (2012) is located southeast of the main333

rupture area of foreshock #1 and east of that of foreshock #2 (blue contours). The main334

rupture area of foreshock #1 does not overlap with the peak of the postseismic slip area,

335

whereas that of foreshock #2 partially overlaps. Although Ohta et al. (2012) removed336

the clear coseismic displacement from the P09 data, they could not distinguish the337

coseismic deformation associated with foreshock #2 from that due to postseismic slip.

338This could explain the partial overlap between the main rupture area of foreshock #2

339

and the area of aseismic slip after foreshock #1.

340

In Figure 5, the epicenters of foreshocks relocated by Suzuki et al. (2012) are also341

plotted. The epicenters of earthquakes occurring immediately after foreshock #1 and342

before foreshock #2, and those after foreshock #2 until the mainshock on March 11 are

343

plotted with open and solid symbols, respectively. We can point out that most foreshock344

epicenters, regardless of their timing, are distributed outside of the main rupture area of

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foreshock #1. If we regard the intense seismicity after foreshock #1 as aftershocks, this346

complementary relationship is the same as that between the mainshock rupture zone and347

the aftershock distribution commonly found for many large earthquakes (e.g., Hartzell,348

1989; Hirata et al., 1996; Shinohara et al., 2004). We further note that the seismicity is349

concentrated along the updip and southern sides of the main rupture zone of foreshock350#1, but not on the downdip and northern sides. In the southern part of the main rupture

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area of foreshock #1, most of the earthquakes occurred after foreshock #2 (solid circles).

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Notably, no aftershocks are identified before foreshock #2 to the south of the main353

rupture area of foreshock #2, suggesting that secondary aftershocks migrated further

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south after foreshock #2.

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We interpret the spatio-temporal relationship between the obtained source models

356

and foreshock activity based on the idea suggested by previous studies (e.g. Ando and357

Imanishi, 2011; Kato et al. 2012; Ohta et al., 2012), in which the series of foreshock358

activity is interpreted as the consequence of propagating aseismic slip, as follows.

359

Following foreshock #1, its postseismic slip migrated to the east and south, causing360

intense seismicity. Foreshock #2, one of the earthquakes triggered by aseismic slip that361

propagated southward from foreshock #1, advanced the propagation of aseismic slip

362

further to the south, becoming postseismic slip, causing the increasing seismicity along363

the southern rim of the foreshock #2 rupture. This aseismic slip could have triggered the364

initial rupture of the mainshock.

365
366
367

5.2 Stress drops of the two foreshocks
We calculated the stress drop Δσ associated with the two foreshocks from the

17

368

source areas and slip amounts estimated here, based on the conventional relationship369(e.g., Kanamori and Anderson, 1975) expressed as:

370

Δσ = c µ D

S,

(4)

371

where c is constant and µ, D, and S are the shear modulus (=40 GPa), average slip, and372

size of the rupture area, respectively. In this calculation, Poisson’s ratio is assumed to be

373

0.25, and we obtain c = 8/3π from Kanamori and Anderson (1975). In the calculation,374

we used the average slip amounts of the modified main rupture model (1.2 m and 0.3 m

375

for foreshocks #1 and #2, respectively). The fault sizes are 1600 km2 for foreshock #1

376

and 800 km2 for foreshock #2, which are also taken from the size of the main rupture

377

area.

378

The obtained stress drop is Δσ =1.0 MPa for foreshock #1 and 0.3 MPa for379

foreshock #2. For foreshock #1, this is comparable to that estimated by Shao et al.

380(2011). Shao et al. (2011) suggested that foreshock #1 is a typical M~7 earthquake in381

terms of the stress drop calculation. The expected size of the main slip area of typical382

Mw 7.2 earthquakes is ~1400 km2, if we apply the scaling relationship proposed by

383

Blaser et al. (2010). This is similar to that of the main rupture area of foreshock #1 in384

our model. Nevertheless, the scaling relationship predicts a fault area of ~330 km2 for a385

Mw 6.6 earthquake, which is smaller than that of our rupture model for foreshock #2.

386

Therefore, it appears that foreshock #2 has a disproportionally larger rupture area than387

typical earthquakes, and this large rupture size is the reason for its small stress drop.

388

However, it could be of concern whether or not the grid size and layout of our389

inversion are appropriate for correctly estimating the rupture size of the smaller390

foreshock #2. Here, we carried out a test to confirm whether the size of the main rupture

18

391

area of foreshock #2 is significantly larger than the typical rupture size. In the test, we

392

assumed that the rupture of foreshock #2 could be expressed as one subfault (400 km2),

393

which is similar to the typical fault size expected from the scaling relationship. The slip

394

amount was assumed to be 0.5 m, so that the seismic moment was equivalent to that of395

the preferred model. This trial model yields a stress drop of ~0.90 MPa, which is almost

396

identical to that of foreshock #1.

397

As the first trial, we set the fault so that its center matched that of our preferred398

model (blue hatched area in Figure 6a) and calculated the tsunami waveforms to399

compare with the observed waveforms (model A, blue square in Figure 6a). The

400

calculated pressure offset change at P09 is much larger than the observed one (blue401

traces in Figure 6b) and the VR is very low (24%). Next, the fault was shifted by 10 km

402

to the south along the strike (model B, red square in Figure 6a). This model mostly

403

explains the characteristics of the observed waveforms (red traces in Figure 6b), but the404

duration of the main tsunami pulses is shorter than the observations, as clearly seen in405

the waveforms at P02 and P06. The calculated VR is 70%, which is smaller than that406

obtained from the preferred model (76%). After the test, it is probable that the observed

407

tsunami waveforms do not conform with the fault rupture according to a stress drop

408

comparable to that of foreshock #1.

409

Some studies reported that the stress drops of aftershocks are smaller than their410

mainshocks (Somei et al., 2014; Nakano et al., 2015). Although no specific physical411

reasons have been given, the stress drop difference between foreshocks #1 and #2 may

412

be a manifestation of the proposed mainshock–aftershock relationship. A possible

413

reason is the stress evolution or strength reduction associated with processes causing

19

414

aftershocks. If the process after foreshock #1 involves pore fluid diffusion, it could

415

reduce the strength along the plate boundary fault surrounding the ruptured area (e.g.,416

Nur and Booker, 1972; Bell and Nur, 1978; Bosl and Nur, 2002). Frictional strength on417

the fault can be reduced under the high loading rate (e.g., Cao and Aki, 1986; Karner418

and Marone, 2000). Since it is expected that aseismic slip after foreshock #1 increased419

the loading rate to the locked patch of foreshock #2, it is probable that the smaller stress420

drop of foreshock #2 reflects the strength reduction caused by the postseismic slip

421

following foreshock #1. However, it also has to be pointed out that the strength can vary422

spatially along the fault, and the stress drop difference might be simply a consequence423

of the inhomogeneous distribution of strength.

424
425

5.3 Comparison with M 7.0 event in 1981

426

In the area of foreshock activity preceding the 2011 Tohoku-Oki earthquake, an

427

earthquake of M 7.0 occurred on 19 January 1981. The 1981 earthquake was followed428

by clear aftershock seismicity, including several earthquakes of M~6, similar to the429

seismicity after foreshock #1. Ando and Imanishi (2011) pointed out a similarity

430

between the 1981 seismicity and the foreshock sequence in 2011 based on the epicenter

431

distribution. In this section, we explore the relationship between the rupture areas of the432

two M 7 class earthquakes activating the seismic sequences.

433

The finite fault model of the 1981 earthquake was derived from the terrestrial

434

strong motion seismograms by Yamanaka and Kikuchi (2004). Hatori (1981) examined435

the tsunami generated by the 1981 earthquake at coastal tide stations to estimate the436spatial extent of the tsunami source. Both results show good agreement with the rupture

20

437

area of foreshock #1 in 2011 obtained in this study (Figure 7), suggesting that foreshock438#1 was a recurrent rupture of the fault patch ruptured in 1981. However, there are439

notable discordances; a ~30 km difference in epicenter locations and the larger size of440

the 1981 source estimated by either seismographs or tsunami records, in spite of its

441

smaller magnitude. These differences could arise from the different resolutions between

442

the previous studies, using old and remote data, and this study, based on near field443

observations.

444

We examined the difference between the source models of the 1981 earthquake and445

foreshock #1 based on a comparison of coastal tsunami records, since the records are

446

supposed to be comparable in quality for both earthquakes. In the comparison, we did447

not perform a waveform inversion for the source models because of the low

448

signal-to-noise ratio of records in 1981. Instead, we compared the travel times (time449difference between the arrival times and the origin times according to the JMA

450

catalogue) and amplitudes of the first up-going tsunami wave at coastal stations,451

summarized by Hatori (1981) for the 1981 event. For foreshock #1 in 2011, we used the452

observed coastal tsunami time series provided by the Japan Meteorological Agency

453

(JMA,

454

Japanese). The result of the comparison is shown in Table 2. The amplitudes of the455

1981 event are about half those of foreshock #1, consistent with the smaller magnitude456

of the 1981 earthquake. The differences in arrival times never exceed 5 min at all

457

stations, although the travel times of the 1981 earthquake tsunami are shorter by a few

458

minutes in some stations. A few minutes difference in arrival times can be459

approximated as a distance of ~15–25 km, based on the estimated tsunami wave speed

http://www.jma.go.jp/jma/press/1103/10a/kaisetsu201103100820.pdf,

21

in

460

(~140 m/s) in this region. Based on comparisons of travel times, the location of the461

tsunami source of the 1981 event is almost identical to that of foreshock #1, but may be

462

shifted slightly landward to explain the earlier arrivals of the 1981 tsunami.

463

We carried out another evaluation based on the tsunami numerical calculations to464

discuss the difference in coastal tsunami waveforms characteristics between the 1981465

and 2011 earthquakes in more detail. We calculated the coastal tsunami waveforms

466

using the long-wave equation. For the source model, we assumed a rectangular fault on467

the plate boundary with length, width, and slip of 40 km, 20 km, and 0.7 m, respectively.

468

These values were set based on the scaling law of Blaser et al. (2010) for a typical M

469

7.0 earthquake. In Figure 8, the calculated tsunami waveforms for foreshock #1 and for470

the 1981 earthquake are compared. Taking the earlier tsunami arrivals at the coast into

471

account, we set a model composed of two subfaults corresponding to the deeper half of472

the foreshock #1 rupture area for the 1981 earthquake (orange rectangle in Figure 8a),473

whereas our preferred model for foreshock #1 in 2011 is composed of four subfaults

474(red hatched square in Figure 8a). The maximum uplift and subsidence expected from475

the 1981 fault model are 13.5 cm and 6.7 cm, respectively, which are less than half of476

those for foreshock #1.

477

We compared the travel times and amplitudes as we did for the observed records. In

478

Figures 8b and 8c, we mark, using allows, the onsets of up-going waves, defined as the479time when the uplift amplitude exceeds 1 cm,. The onset times are very close at all480

stations, but slightly earlier arrivals can be seen for the 1981 tsunami than for foreshock481#1, as we found when comparing the observed waveforms. The calculated amplitudes of482

the initial waves of the 1981 event are about half of those for foreshock #1, and we

22

483

therefore regard that the observed characteristics are well reproduced by this modeling.

484

It is notable that the epicenter of the 1981 earthquake coincides with the up-dip edge of485

the modeled fault, as for the epicenter of foreshock #1, suggesting that the rupture

486

propagated down-dip in both events.

487

We also calculated tsunamis by shifting the 1981 fault in the dip direction to488

determine how the travel time differences are sensitive to the source locations (blue and489

green rectangles in Figure 8a). The arrival times of the first up-going waves are490

significantly different from those of foreshock #1 or those of the 1981 model, assuming

491

the down-dip half of the 2011 fault. It can be concluded that the 1981 fault must overlap492

the rupture area of foreshock #1 in order to explain the observed tsunami waveforms.

493

We speculate that foreshock #1 broke the fault patch ruptured in 1981 again in 2011,494

but generated further slip on the up-dip side of the 1981 patch and therefore became a495

larger earthquake.

496

It is beyond the scope of this study to determine why the 1981 earthquake was not497

followed by a Mw 9 megathrust earthquake while foreshock #1 was, even though these498

earthquakes are considered to be ruptures of an identical fault patch. The postseismic499

deformation associated with the 1981 earthquake was observed by a tiltmeter placed at

500

station Esashi (International Latitude Observatory of Mizusawa, 1981). The observation

501

strongly suggests the 1981 earthquake was followed by substantial aseismic afterslip,

502

but the data quality does not allow quantitative comparison with the postseismic process503

following foreshock #1 in 2011. Sato et al. (2013) argued that a series of large (M > ~6)504

earthquakes near the epicenters of the 2011 mainshock or of foreshock #1 facilitated the505

occurrence of the Tohoku-Oki earthquake by weakening interplate coupling. Since the

23

506

1981 earthquake was not preceded by pronounced activity near its epicenter, the507

difference between the two earthquakes in 2011 and 1981, with or without additional508

rupture of the up-dip side, might be related to the difference in the stress condition and509

might provide clues for understanding the processes leading to generation of the very510

large 2011 earthquake.

511
512

6. Conclusion

513

Based on the analysis of tsunami waveforms observed by OBPGs deployed just514

above the focal area, we developed fault models for the largest and second largest

515

foreshocks (foreshocks #1 and #2, respectively) of the 2011 Tohoku-Oki earthquake.

516

The use of the near-field tsunami records helped us to obtain good spatial resolution of517

the source model, especially the fault model of foreshock #2, which had never been

518

obtained, because of its small size for finite source modeling. Our result showed that the519

main rupture areas of foreshocks #1 and #2 did not overlap. From comparison with the520

spatio-temporal evolution of small earthquake activity after foreshock #2, we suggest

521

that foreshock #2 was triggered by postseismic slip following foreshock #1, and522

aseismic slip propagated further south, towards the mainshock epicenter, after foreshock523#2. The stress drop of foreshock #2 seems to be smaller than that of foreshock #1,

524

which is likely associated with the strength reduction along the plate interface under525

aseismic slip with intense seismicity. Foreshock #1 is likely to have been a re-rupture of526

the fault patch ruptured during the M 7.0 earthquake in 1981, but ruptured a wider area

527

that included the up-dip side of the 1981 source.

528

24

529

Acknowledgements

530

The authors thank the Earthquake Research Institute of the University of Tokyo for531

the use of tsunami data recorded by the cabled ocean-bottom pressure sensors of the532

observatory off Kamaishi. The coastal tide waveforms used in this study were recorded533

by the Japan Meteorological Agency (JMA), the Japan Coast Guard (JCG), the Ports

534

and Harbors Bureau under the Ministry of Land, Infrastructure, Transport, and Tourism

535(MLIT), and the Port and Airport Research Institute (PARI). The authors wish to thank536

Dr. Tatsuhiko Saito of the National Research Institute for Earth Science and Disaster

537

Prevention (NIED), for the Fortran code to calculate the tsunamis, as well as helpful538

comments. The authors deeply thank two anonymous reviewers for constructive

539

comments on the manuscript. This study was supported by the research project

540“Research concerning Interaction between the Tokai, Tonankai, and Nankai

541

earthquakes” of the Ministry of Education, Culture, Sports, Science and Technology,

542

and by JSPS KAKENHI (A) 20244070 and 26000002. The figures in this paper were543

prepared using Generic Mapping Tools (GMT) (Wessel and Smith, 1998). The authors544

used the English language editing service Editage (www.editage.jp).

25

545

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Tanioka, Y., Hino, R., Hasegawa, Y., 2007. Slip distribution estimated from tsunami

692

waveforms for the 2005 Miyagi-oki earthquake occurred on August 16 (in Japanese693with English abstract). Zisin 2 59, 385-387.

694

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

695

waveform inversion incorporating permanent seafloor deformation and its

696

application to tsunami forecasting. J. Geophys. Res. 117, B03311, doi:697

10.1029/2011JB008877.

698
699

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

700

Yamanaka, Y., Kikuchi, M., 2004. Asperity map along the subduction zone in701

northeastern Japan inferred from regional seismic data. J. Geophys. Res. 109,702

B07307, doi: 10.1029/2003JB002683.

32

703
704

Table 1. Locations and observation periods of OBPGs
StationLatitude [°N]Longitude [°E]

Depth [m]Operation (Month/Year)

GJT3a38.2945

143.4814

3,293

Nov/2010–May/2011

P02a

38.5002142.5016

1,104

June/2010–May/2011

P03a38.1834

142.3998

1,052

June/2010–Sept/2011

P06a

38.6340

142.5838

1,254

June/2010–May/2011

P07a38.0003142.4488

1,059

Sept/2010–Sept/2011

P08a38.2855

142.8330

1,418

Sept/2010–Sept/2011

P09a

38.2659

143.0006

1,556

June/2010–Sept/2011

TM1b39.2330

142.7830

1,564Continuous observation

TM2b

39.2528

142.4500

954(Before March 11, 2011)

705
706

a

707

b

708

of the University of Tokyo (Kanazawa and Hasegawa, 1997)

Pop-up recovery OBPG identical to those used in Hino et al. (2014)
Real-time cabled observation systems operated by Earthquake Research Institute (ERI)

33

709
710

Table 2. Travel times and amplitudes of initial waves of tsunami observed by coastal
wave gauges.

711

1981 Off-Miyagi
StationTravel time[min]

Foreshock #1

Amplitudea[cm]

Travel time

a

[min]

Amplitude
b

[m]

b

Agencyc

Hachinohe

62

3

65

0.1

JMA

Miyako

30

8

33

0.2

JMA

Kamaishi

26

23

28

0.4

JCG

Ofunato

26

20

26

0.6

JMA

Ayukawa

33

8

33

0.5

JMA

Sendai Port

68

4

69

0.2

PARI

Souma

60

3

65

0.2

GSI

Onahama

54

3

55

0.1

JMA

712
713

a

714

b

715

JMA.

716

c

717

and Airport Research Institute, and Geospatial Information Authority of Japan,

718

respectively.

Travel time and amplitude data from Hatori (1981).
Travel time and amplitude read from waveforms of coastal wave gauges shown by

JMA, JCG, PARI, and GSI are Japan Meteorological Agency, Japan Coast Guard, Port

34

719
720

Figure Captions

721

Figure 1. Location map of this study. Green inverted triangles denote location of offline

722

OBPGs; black triangles are real-time cabled OBPGs. Stars and beach balls denote723

epicenter locations (Suzuki et al., 2012) and Global CMT mechanisms of foreshock #1

724(red) and #2 (blue), and M9 mainshock (black), respectively. Gray contour lines show725

coseismic slip distribution of mainshock derived by Iinuma et al. (2012) with 10 m

726

contour intervals. Topography data are from ETOPO-1.

727
728

Figure 2. (a) Estimated coseismic slip distribution of foreshock #1. Red and blue729

represent positive (reverse-faulting) and negative (normal-faulting) slip, respectively.

730

Distribution of subfaults is shown by dashed line. Contours denote expected initial731

sea-surface height distribution calculated from the slip model with 10 cm intervals

732(solid and dashed lines are uplift and subsidence, respectively). Main rupture area is733

denoted thin black line, and subfault with the largest slip is denoted by thick green line.

734(b) Comparison of observed (gray) and synthesized waveforms based on slip model

735(red). Waveforms in white background area are used in the inversion.

736
737

Figure 3. (a) Estimated coseismic slip distribution of foreshock #2. Contours are in 2

738

cm intervals. (b) Comparison between observed and synthesized waveforms. See Figure739

2 caption for detailed explanation.

740

35

741

Figure 4. Comparison of calculated tsunami waveforms assuming slip in the main742

rupture areas of (a) foreshock #1 and (b) #2. Observed waveforms are shown by gray743

line. Blue dashed lines and red solid lines show calculated waveforms with uncorrected744

and corrected slip amounts, respectively.

745
746

Figure 5. Main rupture areas of foreshock #1 and #2 and coseismic and postseismic slip

747

distribution of foreshock #1 estimated by Ohta et al. (2012). Red and blue rectangles

748

denote main rupture areas of foreshocks #1 and #2 estimated in this study, respectively.

749

Orange contours indicate coseismic slip distribution of foreshock #1 of Ohta et al.

750(2012) with 0.5 m interval. Blue contours indicate postseismic slip distribution (Ohta et751

al., 2012) with 0.1 m interval. Open circles denote epicenters of aftershocks occurring

752

between foreshocks #1 and #2; solid circles are epicenters of earthquakes occurring

753

between foreshock #2 and mainshock. Epicenter locations are determined by Suzuki et754

al. (2012).

755
756

Figure 6. Result of the numerical test to evaluate size of foreshock #2 rupture. (a) Blue757

square represents fault model A, a 20 × 20 km2 fault with a center location identical to758

main rupture area of foreshock #2, shown by blue hatched rectangle. Red square

759

represents model B, with the same fault size but shifted south by 10 km. (b) Observed

760

tsunami waveforms (gray) with calculated traces for model A (blue) and model B (red).

761
762

Figure 7. Main rupture area of foreshock #1 and source models of the 1981 Off-Miyagi

763

earthquake (M7.0). Red square is main rupture area of foreshock #1 in 2011. Black

36

764

contours show initial sea surface height distribution from foreshock #1. Yellow shading765

indicates area with coseismic slip larger than 0.3 m for the 1981 earthquake (Yamanaka

766

and Kikuchi, 2004). Green shading indicates tsunami source model of 1981 event

767(Hatori, 1981). Red and light gray stars are epicenters of foreshock #1 and mainshock,768

respectively, by Suzuki et al. (2012). Yellow star indicates epicenter of 1981 earthquake

769(JMA). Blue square indicates location of tiltmeter (Esashi) recording postseismic

770

deformation of the 1981 earthquake.

771
772

Figure 8. Calculated tsunami waveforms at coastal stations from foreshock #1 and773

source models for 1981 earthquake. (a) Three fault models with different locations for774

1981 earthquake. Orange rectangle is preferred model, corresponding to down-dip half775

of main rupture area of foreshock #1 (indicated by red hatched area). Green and blue776

rectangles are fault models located outside of rupture area of foreshock #1. Red and777orange stars are epicenters of foreshock #1 and 1981 earthquake, respectively.

778

Distribution of coastal tide stations is also shown. (b) Calculated tsunami waveforms

779

from fault model of foreshock #1 (gray) and preferred model (red). Small arrows denote

780

timings of onsets of tsunami waves. Arrow colors indicate the difference of assumed

781

fault models, gray: foreshock #1, red: preferred 1981 earthquake model, green: model

782

located landward of foreshock #1 fault, blue: model located trenchward of foreshock #1

783

fault. (c) Close-up of calculated tsunami waveform at Ofunato in time window shown784

by thick black bar in (b). Waveforms from models located landward and trenchward of785

foreshock #1 fault are shown by green and blue dashed lines, respectively. Other786

captions are the same as (b).

37

787

788
789

Figure 1

38

790

791
792

Figure 2

39

793

794
795

Figure 3

40

796
797

Figure 4

41

798

799
800

Figure 5
42

801
802

Figure 6

43

803
804

Figure 7
44

805
806

Figure 8

45

807
808

Supporting Information

809
810

Figure S1. Examples of pressure time series during foreshocks #1 and #2. Time series

811

for (a) foreshock #1 at P03, (b) foreshock #2 at P03, (c) foreshock #1 at P09, and (d)812foreshock #2 at P09. Gray, blue, and red traces denote tide-free, 60 s moving averaged

813

and low-pass filtered waveforms, respectively. Green lines denote origin time.

46

814

815
816

Figure S2. Trade-off curves of waveform inversion for foreshocks #1 (red) and #2

817(blue). Weight of smoothing α and variance reduction (VR) are shown in horizontal and818

vertical axis, respectively.

47

819
820

Figure S3. Comparison of observed (gray) and calculated waveforms obtained from inversion result (red) at stations TM1 and TM2 for

821(a) foreshocks #1 and (b) #2.
48

822

823
824

Figure S4. Results of inversions with different conditions for foreshock #1. The conditions are: number of stations (7, without TM1 and825

TM2, and 9, with TM1 and TM2), along-trench length of mode space (120 km and 160 km), time window length (20 min and 30 min),826

and inversion constraint (with and without non-negative constraint). Green squares denote subfault with slip larger than 1.0 m.
49

827

828
829

Figure S5. Same as Figure S4, but for foreshock #2. Green squares denote subfault with slip larger than 0.2 m.

50

830

831
832

Figure S6. Averaged slip amounts and standard deviations of foreshock #1 (a and c) and foreshock #2 (b and d) calculated from fault

833

models shown in Figures S4 and S5. Averages and standard deviations for 12 subfaults in northern part of model space are obtained

834

from results with a larger model space (160 km length), but those in other subfaults are from all the inversion results.
51

835
836

Figure S7. Results of recovery test, giving slips of 1 m for main rupture areas of837

foreshocks (a) #1 and (b) #2.

52