Confidential manuscript submitted to Geophysical Research Letters

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Millimeter-scale tsunami detected by a wide and dense observation array in the deep ocean:2

Fault modeling of an Mw 6.0 interplate earthquake off Sanriku, NE Japan

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4

T. Kubota1, T. Saito1, and W. Suzuki1

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

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

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Key Points:lnation-wide pressure gauge array off Sanriku, Japan

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l

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Tsunami signals were identified from the pressure data adjacent to the source, whichwere contaminated by signals irrelevant to tsunamis

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Millimeter-scale tsunamis from an Mw 6.0 earthquake were captured by the S-net, a newl

We inferred the stress drop of the earthquake from the tsunami data more reliably than
could be done from seismogram analysis

1Confidential manuscript submitted to Geophysical Research Letters

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Abstract

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A new dense and widely distributed tsunami observation network installed off northeast Japan19

detected millimeter-scale tsunamis from an Mw 6.0 shallow interplate earthquake on 20 August

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2016. Based on the fault model deduced from this dataset, we obtained a stress drop of 1.5 MPa

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for this event, similar to those associated with typical interplate earthquakes. The rupture area22

was unlikely to overlap with regions where slow earthquakes occur, such as low-frequency-

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tremors and very-low-frequency-earthquakes. The results demonstrated that this new network24

has dramatically increased the detectability of millimeter-scale tsunamis. Some near-source

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stations were contaminated by large pressure offset signals irrelevant to tsunami, and we must26

therefore be careful when analyzing this data. Nonetheless, the new array enables estimations of27

the stress drops of moderate offshore earthquakes and can be used to elucidate the spatial

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variation of mechanical properties along the plate interface with much higher resolution than

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previously possible.

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Plain Language Summary

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Tsunamis are generated when an earthquake occurs beneath the seafloor. Far fewer tsunami

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observations have been recorded from moderate earthquakes than large to giant earthquakes

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because tsunamis created by moderate earthquakes have been too small to be observed. On 20

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August 2016, a moderate earthquake occurred off Sanriku, in northeastern Japan, and a tsunami

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with a height of less than one centimeter was recorded by a new seafloor tsunami observation

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network. This network has many tsunami sensors distributed much closer to each other and over38

a much wider area than any other previous network in the world. Using this data, this study2

Confidential manuscript submitted to Geophysical Research Letters39

estimated the source location and size, and the slip amount of the 2016 earthquake with higher

40

accuracy, which was impossible to achieve from past observations because they were too far

41away from the earthquake and the signals were too small. Using this source information, we

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could estimate the stress drop associated with the earthquake, which is important because the43stress drop information deepens our understanding of how and why earthquakes happen.

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Keywords

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millimeter-scale tsunami

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fault modeling48

interplate earthquake

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Sanriku

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S-net

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Confidential manuscript submitted to Geophysical Research Letters

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1. Introduction
To understand the mechanics of earthquake faulting, the earthquake source process and52
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mechanical properties in and around the rupture area must be identified and understood. An

54important parameter in these investigations is the stress drop, the average shear stress reduction

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on the fault due to the earthquake. It has been commonly thought the stress drops show no56

systematic change from smaller to larger earthquakes (e.g., Kanamori & Anderson, 1975),

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suggesting a universal mechanism of earthquake faulting irrespective of size. However, recent

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studies have reported that the estimated stress drops change depending on the frictional

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properties along the fault and/or the background stress level (e.g., Lay et al., 2012; Yoshida et al.

602017).

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Finite fault modeling using teleseismic data is one of the most common approaches to62

estimating the stress drops for major (Mw >~7) earthquakes (e.g., Ye et al. 2016). Regional

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onshore seismograms have also been widely used to measure the corner frequencies and estimate

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stress drops for minor (Mw <~5) earthquakes (e.g., Uchide et al., 2014; Yamada et al. 2017;65

Yamashita et al., 2004). However, accurately constraining stress drops for moderate (Mw ~6)66

offshore earthquakes remains difficult because of the uncertainties attributed to the low signal-to-67

noise-ratio in these datasets. In fault modeling with seismic waves, a tradeoff between rupture

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area and rupture velocity may cause considerable uncertainties in the stress drop estimation.

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For major offshore earthquakes, tsunami data recorded by ocean-bottom pressure gauges

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can be used to construct the fault models (e.g., Gusman et al. 2015; Heidarzadeh et al. 2016;

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Newman et al., 2011; Satake et al. 2013; Williamson et al., 2017; Saito & Kubota, 2020). Given72

the much slower propagation velocity of tsunamis, tsunamis are much less affected by the4Confidential manuscript submitted to Geophysical Research Letters73

rupture propagation than seismic waves, which contributes to more robust constraints on the74

earthquake’s horizontal location and fault dimensions, and thus on the earthquake stress drop

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(e.g., Kubota, Saito et al., 2018; Saito & Kubota, 2020). However, few observations of tsunamis

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excited by Mw ~6 earthquakes have been reported (Hino et al., 2001), because the typical77

offshore stations are too few (only one or two stations) and remote from the earthquake (> ~10078km); challenging the capture of tsunamis of reasonable and sufficient quality. Therefore, to79

constrain the fault models based on tsunamis requires more stations located closer to the focal

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area with better station coverage.

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A new, wide and densely-distributed seafloor pressure gauge network called the Seafloor

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Observation Network for Earthquakes and Tsunamis along the Japan Trench (S-net) was recently

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constructed by the National Research Institute for Earth Science and Disaster Resilience (NIED),

84(Kanazawa et al., 2016; Mochizuki et al., 2016; Uehira et al., 2016, Figure 1). This network

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observed tsunamis with amplitudes of less than one cm (hereafter termed millimeter-scale

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tsunamis) associated with a moderate earthquake off Sanriku, in northeastern Japan, on August

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20, 2016 (Figure 1, Mw 6.0, Ekström et al., 2012; http://globalcmt.org). This event was located88

near the up-dip ends of the rupture areas of the 1968 (Mw 8.0, Satake, 1989) and the 1994

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Sanriku earthquakes (Mw 7.7, Tanioka et al., 1996), and at the northern edge of the rupture area

90of the 1896 Mw 8.1 Sanriku tsunami earthquake (Kanamori, 1972; Satake et al., 2017; Tanioka

91& Satake, 1996). Low-frequency-tremors with a dominant frequency of a few Hz and very-low-

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frequency-earthquakes with periods of 10–20 s have also been observed around this region

93(Asano et al., 2008; Matsuzawa et al., 2015; Nishikawa et al., 2019; Tanaka et al., 2019).

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Because the rupture areas of these slow earthquake phenomena and those of regular earthquakes

5Confidential manuscript submitted to Geophysical Research Letters95

are thought not to overlap each other (e.g., Nishikawa et al., 2019), the differences between the96

regular and slow earthquake source processes and their relation to mechanical properties along97

the plate interface are of interest.

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This study used the S-net tsunami records to estimate the finite fault model and the stress99

drop for the 2016 Sanriku earthquake and then examine its relationship with other interplate

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events, including slow earthquakes and past earthquakes. In Section 2, we describe the101characteristics of the S-net pressure data from the 2016 event and Section 3 discriminates the102

tsunami signals from the data, which were contaminated by noise. Section 4 then infers the finite

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fault model and the stress drop of the 2016 event and gives the estimation uncertainties. We

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finally discuss the relationship with the other phenomena such as slow earthquakes and the 1896

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tsunami earthquake.

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Confidential manuscript submitted to Geophysical Research Letters141˚ 142˚
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Figure 1. (a) Tectonic setting off northeastern Japan. White stars and red hemispheres indicate

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the Japan Meteorological Agency (JMA)’s epicenter and the global centroid moment tensor

110solution of the 2016 Mw 6.0 earthquake, respectively. Fault models of the 1896 (Mw 8.1, Satake

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et al., 2017), 1968 (Mw 8.0 Satake, 1989), and 1994 earthquakes (Mw 7.7, Tanioka et al., 1996)112

are shown. Green and light blue circles denote very-low-frequency-earthquakes (Matsuzawa et113al., 2015; Nishikawa et al., 2019) and low-frequency-tremors (Tanaka et al., 2019), respectively.

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Small gray circles indicate regular earthquakes with thrust-faulting mechanisms (Fukuyama et al.

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Confidential manuscript submitted to Geophysical Research Letters

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1998, Mw ≥ 3.5, strike: 170–210°, dip: 0–40°, rake: 45–135°). Black arrows indicate the116

direction of the plate motion (DeMets et al., 2010). Pink dashed lines in the inset show iso-depth

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contours of the plate interface (Iwasaki et al., 2015) at 20-km intervals. (b) Locations of the118

pressure gauges. Circles denote the S-net stations (colors denote groups of observation nodes).

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Blue and pink triangles denote the Off-Kushiro (KPG) and Deep-Ocean Assessment and120

Reporting of Tsunamis (DART) stations, respectively. (c) Vertical profile along the A-B line.

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Red and black lines show the plate boundary and the seafloor.

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2. Tsunami Data
To identify tsunami, an acausal band-pass filter with a passband of 100–1000 s was

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applied to the S-net pressure records (Figure S1). It seems very difficult to recognize the126

tsunamis if only from a few stations, given the background pressure changes are almost ~1 cm at127

the stations near the epicenter (Figure S1). However, the westward propagation of tsunamis with

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amplitudes of a few cm could be recognized when the traces were aligned according to the129

station locations (Figures S1 and S2). Some pressure records showed small subsequent phases

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after the main tsunami pulses (Figure S2), due to dispersive tsunami associated with the short-131

wavelength components (e.g., Kirby et al. 2013; Saito & Furumura 2009; Saito et al. 2010).

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Step-like signals were also observed at several stations near the source. At the station

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S4N10, closest to the epicenter (~10 km), a large and abrupt pressure step of ~20 hPa was134

observed (Figure S3). Similar steps were observed by the pressure gauges located just above the135

focal area during the 2016 Off-Mie earthquake (Mw 6.0), off southwest Japan (Kubota, Suzuki et136al., 2018; Wallace et al., 2016). Pressure offset changes are often recognized as vertical seafloor

8Confidential manuscript submitted to Geophysical Research Letters137

deformation (Saito & Tsushima, 2016; Tsushima et al. 2012), although in other cases, such

138

changes have been attributed not to the vertical deformation but to the strong shaking of the139

seafloor (e.g., Hayashimoto et al. 2015; Nakamura & Hayashimoto, 2019). Takagi et al. (2019)140

examined records from the co-located accelerometer at S4N10 during this earthquake and found141

the sensor at S4N10 was rolled with a rotation angle of 5.72° (see Figure 3a in Takagi et al.,1422019). It has been reported that outputs of pressure sensors identical to those in the S-net

143(Paroscientific Digiquartz sensors) strongly depend on the sensor rotation (Chadwick et al.,144

2006; the rotation angles of 5° corresponds to pressure changes of ~5 hPa). Therefore, careful

145

analysis is required to determine whether or not the step-like signals are caused by tsunami.

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We also used four other pressure gauges, more than 150 km away from the source

147(Figure 1b). Two of them are located off Kushiro, northern Japan (Hirata et al., 2002; hereafter

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KPG) and the other two, from the Deep-Ocean Assessment and Reporting of Tsunamis (DART)

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system (Bernard et al., 2014), are located outside of the Japan Trench. Although fluctuations

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with amplitudes of < 1 cm are seen (at ~10–20 min from the focal time), these fluctuations are

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comparable to the noise (Figure S1). We also observed large pressure changes due to the seismic152

waves (e.g., An et al., 2017; Kubota et al., 2017) soon after the focal time, which further makes it

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difficult to identify tsunamis.

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3. Preparatory Analysis: Tsunami Forward Simulation
Before estimating the finite fault model of the 2016 event, we conducted several

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preparatory analyses. We fist simulated tsunamis to identify tsunami signals in the pressure

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change based on the GCMT solution. Using the GCMT seismic moment M0 = 1.31 × 1018 Nm
9Confidential manuscript submitted to Geophysical Research Letters

159(Mw 6.0) and the scaling law of Blaser et al. (2010), we obtain the fault length L = 8.3 km and160

width W = 8.2 km. We also assumed the uniform slip amount of D = Mo/μLW = 48.2 cm (rigidity161

μ = 40GPa was assumed). Horizontal location of the fault center and the strike, dip, and rake

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angles were fixed to the GCMT centroid, which were consistent with the subducting plate

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interface (Iwasaki et al., 2015) and the direction of the plate convergence (DeMets et al., 2010).

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The spatial distribution of the seafloor vertical displacement was calculated assuming elastic half165

space (Okada, 1992). Then the seafloor displacement was converted to the sea-surface elevation

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considering the spatial smoothing effect due to the deep seawater (e.g., Kajiura, 1963; Saito,

1672019) (seawater depth of H0 = 4 km was assumed). The rectangular fault model and the sea-

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surface displacement are shown in Figure S4a. Using the sea-surface elevation as the initial169

condition, we simulated tsunami by numerically solving the linear dispersive wave equation in170

the Cartesian coordinates (e.g., Saito, 2019). We used JTOPO30v2 bathymetry data with 30

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arcsec spatial resolution, provided by Japan Hydrographic Association's Marine Information

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Research Center (http://www.mirc.jha.jp/en/), interpolating the grid interval of 2 km. The time

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step interval was 1 s. After the calculation, we applied the same band-pass filter to the174

numerically calculated waveforms as applied to the observed waveforms.

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Although the tsunami signals in the S-net pressure records could be distinguished by the176

simulated waveforms, the step-like signals just after the focal time were not reproduced at all

177(Figure S4b), indicating the step-like signals were related to neither the tsunami nor the seafloor

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deformation. The apparent pressure changes due to the seismic motion irrelevant to tsunami can

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be seen only in a few stations closest to the focal area. On the other hand, the simulated pressure

180change shows a systematic spatial and temporal evolution across the stations. Therefore, we can10Confidential manuscript submitted to Geophysical Research Letters

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distinguish the tsunami signals in the observed records by using the array observation data of the

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S-net that captures a systematic spatial and temporal tsunami propagation. However, if there

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were one or a few stations, it would be difficult to distinguish noises from the pressure records.

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We also found that at some stations, the simulated tsunamis were slightly delayed and185

were elongated in time compared to the observation. This implies that the actual fault location

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should be horizontally shifted from the GCMT centroid. The S-net pressure records were187

expected to improve the constraint for the fault location, whereas estimating the epicenter based

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on seismic waves can produce non-negligible errors, as pointed out by Inazu and Saito (2014),

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Kubota, Saito et al. (2018) and Saito & Kubota (2020).

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To further discuss the importance of the near-field tsunami data to resolve the fault

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model, we additionally inverted the tsunami waveforms to estimate the initial sea-surface height192(i.e., tsunami source) distribution and evaluated the spatial resolution of the analysis (the details

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are in Text S1, Figures S5 to S7). As a result, the tsunami source had a spatial extent of ~40 km

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and was located ~10 km to the west of the GCMT solution. In addition, when using only the195

KPG and DART data, the horizontal location was similar; however, the spatial distribution was

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broader and the total volume of the displaced seawater was almost twice as large as that197

estimated using the S-net data. This suggests the horizontal location could be reasonably

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constrained only from the remote stations but the near-field S-net tsunami data is essential to199

obtain the higher-resolution fault models.

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4 Grid-Search for Optimum Fault Model

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We then estimated the fault model that could best explain the observations, using a two-203

step grid-search approach. First, fixing the fault dimension, the horizontal location of the fault

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was constrained. Second, we searched for the fault dimensions that best matched the observation

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data by fixing the fault’s horizontal location.

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To constrain the horizontal location of the fault in the first step, we assumed a

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rectangular fault identical to that used in the forward simulation based on a scaling law proposed

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by Blaser et al. (2010). The fault center was constrained to coincide with the depth of the plate

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interface.The suitability of each fault model candidate was assessed based on the similarity of the210

tsunami waveforms, in terms of the variance reduction (VR):

211
3

212

𝑉𝑅 = $1 −+,∑4.)*/01 2*56()*+,∑4*56 )*

3

7,

(1)

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214

where xiobs and xical are the observed and calculated tsunami waveforms of the ith data sample,

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respectively (N is the total number of data samples). We used the main tsunami phases (thick216

black lines in Figure S8b) to calculate the VR.

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The fault location that produced best the pressure records was located ~10 km west from218

the GCMT centroid, and was consistent with the tsunami source estimated by the inversion (VR219= 55%, Figure S8). The uncertainty of the horizontal location was assessed based on the220

simulation by shifting the centroid location (Figure S9). When shifting the centroid location by 5

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km from the best-matched location in the east-west direction, the peak timings of the simulated

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waveforms at S4N12 (~100 km west of the centroid) did not explain the observation (temporal

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differences of ~ 0.5 min, Figure S9a), although a simulation that shifted the centroid by 1 km

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explained the observations reasonably well. A similar tendency was seen at the station S4N09

225(~50 km northeast of the source), when the centroid location was shifted in the north-south

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direction (Figure S9b). Based on these experiments, we concluded that the horizontal location of227

the earthquake was identified with a resolution of ~5 km.

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We then estimated the fault dimensions that best explained the observations by changing

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the fault length and width. The centroid location (longitude, latitude, and depth) was fixed to that

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obtained by the grid-search for the fault’s horizontal location. The slip amount was also

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estimated, such that VR was maximized.

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As a result, we obtained L = 17 km, W = 5 km, and D = 40.5 cm (Figure 2). The seismic

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moment Mo = 1.37 × 1018 Nm (μ = 40 GPa, Mw 6.0) was comparable to the GCMT solution. The

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best-matched model explained the observations as well as the inversion result (VR = 57%;

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Figure 3). We calculated the average stress drop on the fault using the following equation (e.g.,

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Kanamori & Anderson, 1975; Madariaga, 1977):

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=

C

Δ𝜎: = 𝑐𝜇 (?@)6/3 = 𝑐 (?@)+D/3 ,

(3)

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240

where c is a constant (= 8/3π, assuming Poisson’s ratio of 0.25, Kanamori & Anderson, 1975).

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We thus obtained the stress drop of Δσs=1.5 MPa.

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Figure 2. Result of the grid-search for the fault dimensions that best matched the observation

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data. Pink circles denote the stations used for the analysis. Small green and light blue circles

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denote very-low-frequency-earthquakes (Matsuzawa et al., 2015; Nishikawa et al., 2019) and248

low-frequency-tremors (Tanaka et al., 2019), respectively. Small open circles indicate thrust

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fault earthquakes (Fukuyama et al., 1998).

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Figure 3. Comparison of the observed (gray) and synthesized waveforms from the results of the253

grid-search for the fault dimension (red). The observed waveforms indicated by thick black lines

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were used for the analysis.

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We evaluated the uncertainties of the fault dimensions based on the tsunami simulation.

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Fixing the fault center location and the seismic moment Mo, we changed the fault length and258

width (Figure 4 for the stations S4N09 and S4N12, and Figures S10 and S11 for the other259

stations). At the station S4N12, when assuming the larger fault width (W ≥ 10 km), the first up-

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motion wave (~7 min) was reasonably captured by the simulation, whereas the first down-motion

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wave (~8 min) and the secondary up-motion waves (~9.5 min) were delayed and their amplitudes

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were small compared to the observation (Figure 4a). This tendency was also seen when assuming

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the larger fault length (L ≥ 25 km, Figure 4b). One reason why the larger fault dimension could

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not explain the later phases was the differences between the horizontal locations of the uplift and265

subsidence peak. Furthermore, when assuming the smaller fault length (L ≤ 10 km), the266

amplitudes of the secondary up-motion waves at the station S4N09 were larger than the267

observation (Figure 4b). This was probably due to the tsunami dispersion, because shorter

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wavelength tsunami components are strongly affected by dispersion (e.g., Saito et al., 2010). We

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should note that the simulated waveforms showed no difference in the remote stations (e.g., the270

DART or KPG records, Figure S9 and S10), indicating that the remote stations cannot resolve271

the fault dimension and stress drop well, and we need to use the near-field records to precisely

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constrain the fault dimension and stress drop (similar discussion is also made by Kubota et al.,2732019).
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Taking this result into account, we concluded that the uncertainties of the fault length275

and width were within the ranges of 15 ≤ L ≤ 20 km and W ≤ 7 km. Given the largest plausible

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fault dimensions (20 km × 7 km) and the seismic moment of the best-matched solution, the stress277

drop of this event was expected to be larger than ~0.7 MPa. Even if we suppose the fault depth is278

shallower or deeper than ~5 km than the plate boundary (Iwasaki et al., 2015), the plausible

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maximum fault dimension and minimum stress drop was L = 20 km and W = 10 km, and Δσs ~280

0.5 MPa (see Text S2 and Figures S12 and S13 for the detail). Furthermore, in order to discuss281

the plausible maximum stress drop, we investigated the fault parameters and the VR values for282

all model candidates in Figure S14 (detail is described in Text S2). Taking a trade-off between

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each of the model parameters on the fault model candidates into account, the upper limit of the284

plausible stress drop range could be estimated at ~5 MPa (Figure S14).

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Figure 4. Comparison of the observed (gray) and simulated (red) waveforms at (a) S4N12 with288

the width changed and (b) S4N09 with the length changed. The timings of the maximum and289

minimum peaks are denoted by the red arrows. The fault locations are shown in the insets.

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5 Discussions and Conclusions
On 20 August 2016, a Mw 6.0 earthquake occurred off Sanriku and a millimeter-scale

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tsunami was observed by a dense offshore pressure gauge network called S-net. We first294

identified tsunami signals from the S-net data based on the forward tsunami simulation. The

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inversion of the tsunami data for the tsunami source showed that the horizontal location was ~10296

km west of the GCMT solution. An additional inversion without the S-net data showed that the297

S-net records were essential to constrain the high-resolution source model. We then conducted18

Confidential manuscript submitted to Geophysical Research Letters298

the grid-search analyses to constrain the centroid location and fault dimensions. This grid-search299

showed the uncertainty in the horizontal location was < ± 5 km. We obtained the fault

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parameters of L = 17 km, W = 5 km, and D = 40.5 cm (Mw 6.0), and Δσs =1.5 MPa. Based on301

the uncertainty evaluation, the possible range of the model parameters are 15 ≤ L ≤ 20 km and W302≤ 7 km, and Δσs ~0.7–5 MPa.

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The 2016 event occurred at the northern edge of the rupture area of the 1896 Sanriku

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tsunami earthquake (Satake et al. 2017; Tanioka & Satake, 1996). Tsunami earthquakes are305

defined as earthquakes that generate much larger tsunami than expected from the surface wave

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magnitudes and radiate less energy compared to typical interplate earthquakes (e.g., Kanamori,307

1972; Newman & Okal, 1998; Ye et al., 2016). Tsunami earthquakes are commonly thought to308

have smaller stress drops of less than 1 MPa (e.g., Kanamori and Anderson, 1975; Ye et al.,309

2016). Bilek et al. (2016) reported that the mean stress drops associated with minor earthquakes

310(M < ~4–5) within the 1992 Nicaragua tsunami earthquake rupture area were significantly

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smaller than those outside of the rupture area. However, in this study, the stress drop of the 2016

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event (1.5 MPa) was not as small as expected in tsunami earthquakes. Our result was rather

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consistent with the stress drops of small earthquakes around this area determined from the corner314

frequencies of onshore seismometers (Yamashita et al., 2004; Uchide et al., 2014; Yamada et al.,3152017); however they did not show systematic differences of the stress drops between inside and316

outside of the 1896 rupture area. Conventional stress drop estimations based on onshore317

seismograms can contain significant errors originating from the unreliable estimation of the318

corner frequency. Therefore, although one plausible interpretation for typical stress drop in the3192016 earthquake is this earthquake was located outside of the 1896 rupture area, we must19

Confidential manuscript submitted to Geophysical Research Letters320

investigate additional examples of stress drops of moderate earthquakes to quantify the spatial

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relationship between moderate earthquakes and the 1896 earthquake with greater confidence.

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Low-frequency-tremors and very-low-frequency-earthquakes were also detected in this323

region (Matsuzawa et al., 2015; Nishikawa et al., 2019; Tanaka et al., 2019). Based on our fault

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model, the rupture area of the 2016 event was isolated from the low-frequency-tremor and very-325

low-frequency-earthquakes region. This spatial isolation may reflect a spatial difference in the326

frictional properties along the plate boundary (e.g., Nishikawa et al. 2019). Therefore,

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investigating further examples of stress drops of moderate earthquakes in this region would be328

useful to construct a model of the heterogeneous frictional property along the plate interface.

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This study demonstrated that the detectability of a millimeter-scale tsunami was

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dramatically increased by S-net’s dense and wide pressure gauge network. The ability to resolve331

the slip distribution of offshore earthquakes was limited by sparse and remote tsunami networks

332(e.g., Williamson et al., 2018). Although the horizontal location could be reasonably constrained

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using only the remote tsunami data, the resolution was insufficient to constrain the detailed fault

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model (e.g., Inazu & Saito 2014; Kubota et al. 2019). In contrast, using the new dense and335

widely distributed tsunami network significantly improved the constraints on earthquake source

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parameters: in particular, the fault dimensions and stress drops, even for the moderate

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earthquake. This would greatly contribute to the source process estimation using the seismogram

338

analysis, which is usually difficult to precisely resolve the fault dimension, especially for the339

moderate earthquakes, because of the trade-off due to the assumption of the rupture propagation

340

velocity and of the signal-to-noise ratio. Although in the onshore region the InSAR data has

341

played this important role to extract the spatial extent of the coseismic displacement and to20

Confidential manuscript submitted to Geophysical Research Letters342

precisely constrain the fault dimension of moderate earthquakes (e.g., Massonnet et al., 1993;

343

Feigl et al., 1995; Kobayashi, 2017), such observations have not been available in the ocean. The

344

near-field dense and wide tsunami network has the great advantage to estimate the initial sea-

345

surface displacement distribution and thus the fault dimension for offshore moderate

346

earthquakes, as we demonstrated. Our results promise that the tsunami records from the nearest-347

field pressure gauge array data will enable us to obtain the relation between the stress drop and348

magnitude with the wider magnitude range and spatial extent.

349

Because some stations near the epicenter can contain large pressure offset signals

350

irrelevant to tsunamis, we must be careful to analyze the signals to distinguish whether such

351

signals are the real ones or the artefacts (Kubota, Suzuki et al., 2018; Tanioka, 2018).

352

Nonetheless, the S-net data show significant promise for constraining earthquake source

353

processes and stress drops, to elucidate mechanical properties along the fault in the Tohoku

354

subduction zone.

355
356

Acknowledgments, Samples, and Data357

We thank three anonymous reviewers and the editor Gavin Hayes for their reviews and fruitful358

comments. This work was financially supported by the Sasakawa Scientific Research Grant from359

the Japan Science Society (#2019-2037), and by JSPS KAKENHI JP19K14818 from the360

Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. S-net pressure

361

data can be accessed from the NIED’s data repository (http://www.doi.org/10.17598/nied.0007;

362

http://www.seafloor.bosai.go.jp). We thank the Japan Agency for Marine-Earth Science and363

Technology (JAMSTEC) for the KPG data (http://www.jamstec.go.jp/scdc/top_e.html). The

21

Confidential manuscript submitted to Geophysical Research Letters

364

DART data was downloaded from the website of the National Data Buoy Center (NDBC) of the365

National Oceanic and Atmospheric Administration (NOAA), USA366(https://www.ndbc.noaa.gov/dart.shtml). We thank Takanori Matsuzawa for the very-low-367

frequency-earthquake catalog (also available in Nishikawa et al., 2019) and Sachiko Tanaka for368

the low-frequency-tremor catalog (Tanaka et al., 2019). The regular earthquake catalog was

369

acquired from the F-net NIED earthquake mechanism catalog

370(https://doi.org/10.17598/nied.0005; http://www.fnet.bosai.go.jp/event/search.php?LANG=en).

371

We used the JTOPO30 bathymetry model by the Marine Information Research Center of the372Japan Hydrographic Association (http://www.mirc.jha.jp/en/index.html) and the plate boundary

373

model by Iwasaki et al. (2015) (http://evrrss.eri.u-

374

tokyo.ac.jp/database/PLATEmodel/PLMDL_2016/README_en.pdf). The discussion with

375

Ryota Hino, Ryota Takagi, and Naoki Uchida and the members of the Research Center for

376

Prediction of Earthquakes and Volcanic Eruptions at Tohoku University was fruitful.

22Confidential manuscript submitted to Geophysical Research Letters

377

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Geophysical Research Letters
Supporting Information for
Millimeter-scale tsunami detected by a wide and dense observation array in the deep ocean:
Fault modeling of an Mw 6.0 interplate earthquake off Sanriku, NE JapanT. Kubota1, T. Saito1, and W. Suzuki1
1

National Research Institute for Earth Science and Disaster Resilience, Japan

Contents of this file
Text S1 to S2
Figure S1 to S14

Introduction
The procedure and result for the inversion for the initial sea-surface height is describedin Text S1. Text S2 discusses the uncertainty of the stress drop estimation attributed tothe depth uncertainty of the plate boundary model and the trade-off between each of
the fault model parameters.
Figure S1 is the filtered pressure gauge waveforms. Figure S2 shows the tsunami
dispersion captured by the S-net pressure gauges. The time series at the station S4N10,
nearest to the focal area, is shown in Figure S3. Result of the forward tsunami
simulation is shown in Figure S4. Figures S5 is the tsunami source distribution estimatedfrom all pressure data. Figure S6 is the result of the recovery test for the inversion for
the tsunami source. Figure S7 is the tsunami source distribution from only the KPG andDART data. Figure S8 shows the result of the grid-search for the fault horizontal location.
Figure S9 is the simulation result for horizontally shifting the fault location. Figures S10and S11 are the comparison of the simulated waveforms with the fault width and lengthchanged, respectively. Figures S12 and S13 are the comparison of the waveforms when
the fault is deepened and shallowed, respectively. Figure S14 shows the VR and fault
parameters searched in the grid-search for the fault dimension.

1

Text S1This text describes the detailed procedure and result of the inversion for the
spatial distribution of the initial sea-surface height (tsunami source). The procedure issimilar to that described in Kubota, Suzuki et al. (2018). Unit source elements of seafloor
vertical displacements with a dimension of 8 × 8 km were distributed with the horizontal
spacing of 4 km. The sea-surface elevation due to the unit source element wascalculated considering the spatial smoothing effect due to the deep seawater (e.g.,
Saito, 2019) (seawater depth of H0 = 4 km was assumed). The calculation scheme of thetsunami Green’s function is identical to that in the forward simulation. In the inversion,
the smoothing constraint for the initial sea-surface height distribution was imposed, andits weighting was determined by trial and error. The time-window used for the inversion
was manually determined based on the result of forward simulation as described above(thick black lines in Figure S5). After we obtained the solution, we evaluated the solution
based on the similarity of the tsunami waveforms between the observation and thesimulation from the model, in terms of the variance reduction (VR):3!" = $1 −+,∑4.)*/01 2*56()*+,∑4*56 )*

3

(S1)

7,

where xiobs and xical are the observed and calculated tsunami waveforms of the ith data
sample, respectively (N is the total number of the data samples). We did not use thepressure gauges near the epicenter which seem to be affected by the large apparent
pressure changes due to the seismic strong motion (e.g., S4N10 and S4N22).
As a result, the inversion analysis provided a distribution that paired uplift andsubsidence (Figure S5). The tsunami source had a spatial extent of ~40 km and was
located ~10 km to the west of the GCMT solution. The main features of the tsunami
waveforms were reasonably reproduced (variance reduction of 66%, Figure S5b).
In order to assess the spatial resolution of the inversion analysis, we conducted
the recovery test of the sea-surface height inversion (Figure S6). We assume the input
sea-surface displacement distribution as:
).)

F

H.H

F

89 (;, =) = ?9 exp $− ( D C2 − G D CJ 7
E

I

(S2)

where a0 is the maximum displacement (a0 = 5 cm was assumed), (x0, y0) is the center ofthe displacement (we assumed to coincide with the center of the optimum fault model),and Lx and Ly are the horizontal dimension of the source (we assumed Lx = Ly). We
inverted the simulated tsunami waveforms under the same condition as the original
source inversion. As a result, the displacement was not reconstructed when Lx = Ly = 4
km was assumed, whereas that was reconstructed well when we assume Lx = Ly ≥ 8 km.
This indicating our inversion has a spatial resolution of 8 km.
We also evaluated how better the near-field S-net tsunami data increases theresolution of the tsunami source estimation than the far-field data, based on the2

inversion using only the KPG and DART data, more than 150 km away (the otherinversion settings are identical to the original). We obtained a centroid location similar
to the original result (Figure S7). However, the distribution was spatially broader and thetotal volume of the displaced seawater (4.0 × 107 m3) was almost twice as large as thatshown when the S-net data were added (2.2 × 107 m3). Therefore, we concluded thatthe horizontal location could be reasonably constrained from the remote pressuregauges, although the spatial resolution of the tsunami source was inferior to thatobtained with the S-net data. The S-net data was essential to obtaining the higherresolution tsunami source distribution and fault dimensions.
Text S2.
In order to evaluate the uncertainty of the stress drop estimation attributed to
the fault depth uncertainty attributed to the uncertainty of the plate boundary model of
Iwasaki et al. (2015), we calculated tsunami by changing the depth of the fault of ± 5 km
from the optimum model (Figures S12 and S13). When supposing the fault deeper by 5km, the later dispersive phases could not be reproduced at all even if we suppose thesmallest fault dimension (W = 1 km). If we suppose the shallow fault by 5 km, the fault
should have a dimension of L ≤ 20 km and W ≤ 10 km to reproduce the observation,
which corresponds to the stress drop of Δσs ≥ ~0.5 MPa. This possible fault dimension
and stress drop was almost identical to the original modeling (15 ≤ L ≤ 20 km, W ≤ 7 km,
and Δσs ≥ ~0.7 MPa). This is probably because this event occurred at very shallow part ofthe plate boundary (~12 km) and the tradeoff between the fault dimension and depth
was small.
In order to discuss the upper limit of the plausible stress drop, we further
investigated the fault parameters and the VR values for all model candidates (Figure
S14, arranged in descending order in terms of VR). We found the variability of the fault
dimension parameters for the top 100 model candidates corresponded to theuncertainty of the fault dimension from the additional tsunami simulation (Figures S14d
and S14e). We also found the top 100 candidates had almost identical and relatively
high VR values (Figure S14a), which indicates that the top 100 candidates reasonably
reproduce the observed waveforms. Based on the variability of the stress drop values
within the top 100 fault model candidates, we concluded the plausible maximum stressdrop was ~ 5 MPa (Figure S14c). It seems that the uncertainties attributed to
uncertainty of the fault length or width are not so large (e.g., uncertainty of fault lengthof 10–15 km corresponds to the stress drop uncertainty of 1.0–2.0 MPa). However,
because of the trade-off between each of the model parameters, the expected
uncertainty range of the stress drop became larger.

3

Figure S1. Pressure waveforms after the data processing. Light gray and red traces
denote the de-tided and the band-pass filtered waveforms.
4

Figure S1. (Continued)
5

Figure S1. (Continued)

6

Figure S1. (Continued)

7

Figure S1. (Continued)

8

Figure S2. The tsunami waveforms at the stations S4N11 to S4N15. The main tsunami
pulses and small subsequent dispersive waves are marked by green and gray arrows,
respectively.

9Figure S3. Time series at the station S4N10. Light gray, dark gray, and red waveforms are
the de-tided, the low-pass filtered (100 s), and the band-pass filtered (100 – 1000 s)
records, respectively.

10

Figure S4. Result of the forward tsunami simulation. (a) Spatial distribution of the initial
sea-surface height. (b) Comparison of the observed (gray) and synthesized (red)waveforms.

11

Figure S4. (Continued)
12

Figure S5. Result of the inversion for the tsunami source. (a) Spatial distribution of theinitial sea-surface height. (b) Comparison of the observed (gray) and synthesized (red)waveforms. The rectangle with dashed lines denotes the analytical area.

13

Figure S5. (Continued)
14

Figure S6. Result of the recovery test for the tsunami source inversion. Left panels are
the input displacement distributions, assuming spatial extent Lx of (top) 4 km, (center) 8
km and (bottom) 12 km (contour interval of 1 cm). Middle panels are the inverted
distributions. Small dots are the locations of center of the unit source elements and thedashed lines denote the analytical area (also shown in Figure S5). Right panels show thecomparisons of the displacement profile along y = 26 km (gray: input, blue: inverted).

15

Figure S7. Result of the inversion for the tsunami source without the S-net data. (a)Spatial distribution of the initial sea-surface height. (b) Comparison of the observed(gray) and synthesized (red) waveforms.

16

Figure S7. (Continued)
17

Figure S8. Result of the grid-search for the horizontal location. (a) Spatial distribution of
the initial sea-surface height. Blue contours are the initial sea-surface height distribution
estimated by the inversion analysis. (b) Comparison of the observed and simulated
waveforms.

18

Figure S8. (Continued)
19

Figure S9. Comparison of the observed (gray) and simulated (red) waveforms at (a) S4N12 with the centroid location shifted along the east-west
direction and (b) S4N09 with the centroid location shifted along the north-south direction. The timings of the maximum and minimum peaks were
denoted by red arrows. The centroid locations are shown in the insets.
20

Figure S10. Comparison of the observed (gray) and simulated (red) waveforms with the fault width changed. The direction and azimuth are shownin each panel. The timings of the maximum and minimum peaks were denoted by red arrows.

21

Figure S10. (Continued)

22

Figure S10. (Continued)

23

Figure S10. (Continued)

24

Figure S10. (Continued)

25

Figure S10. (Continued)

26

Figure S10. (Continued)

27

Figure S10. (Continued)

28

Figure S11 Comparison of the observed (gray) and simulated (red) waveforms with the fault length changed. The direction and azimuth are shownin each panel. The timings of the maximum and minimum peaks were denoted by red arrows.

29

Figure S11. (Continued)

30

Figure S11. (Continued)

31

Figure S11. (Continued)

32

Figure S11. (Continued)

33

Figure S11. (Continued)

34

Figure S11. (Continued)

35

Figure S11. (Continued)

36

Figure S12. Comparison of the observed (gray) and simulated (blue) waveforms assuming the fault 5 km deeper than the optimum model, at (a)S4N12 with the width changed and (b) S4N09 with the length changed. The simulated waveforms from the optimum fault without changing depth
is also shown (red).
37

Figure S13 Comparison of the observed (gray) and simulated (blue) waveforms assuming the fault 5 km shallower than the optimum model, at (a)S4N12 with the width changed and (b) S4N09 with the length changed. The simulated waveforms from the optimum fault without changing depth
is also shown (red).
38

Figure S14. VR and fault parameters for all fault models in the grid-search for the fault dimension, arranged in descending order in terms of VR. The
light green lines denote the maximum and minimum limit of the possible range of the fault dimension.
39