manuscript submitted to Earth and Space Science

1

Ultra-broadband seismic and tsunami wave observation of high-sampling2

ocean-bottom pressure gauge covering periods from seconds to hours

3
4

T. Kubota1, T. Saito1, N. Y. Chikasada1, and W. Suzuki1

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

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7Corresponding author: Tatsuya Kubota (kubotatsu@bosai.go.jp)

8910

Key points:•

Rayleigh waves and tsunamis and their dispersive feature

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12

•

15
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Theoretical relation between pressure and vertical acceleration (p = ρwΗ0az) is valid for along time (~3h for the 2010 Chile earthquake)13
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High-sampling rate is important for pressure gauges to record seismic body waves,•

A relationship between pressure and vertical velocity (p = ρwc0vz) holds only at the first P
wave arrival, but not for later phasesmanuscript submitted to Earth and Space Science17
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Abstract
Recent developments of ocean-bottom pressure gauges (PG) have enabled us to observe

19

various waves including seismic and tsunami waves covering periods of T ~100–103 s. To

20

investigate the quality for broadband observation, this study examined the broadband PG records

21(sampling rate of 1 Hz) around Japan associated with the 2010 Chile earthquake. We identified

22

three distinct wave trains, attributed to seismic body waves, Rayleigh waves and tsunamis. Clear

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dispersive features in the Rayleigh waves and tsunamis were explained by theories of elastic

24

waves and gravity waves. Quantitative comparison between pressure change and nearby

25

seismograms demonstrated the validity of the theoretical relation between pressure p and vertical26

acceleration az for ~3h from the origin time. We also found a relationship between p and vertical27

velocity vz holds only at the first P wave arrival, but not for later arrivals. Similar results were28

confirmed for various earthquakes with different source-station distances and magnitudes,

29

suggesting the robustness of these relations. The results demonstrate that the high-sampling rate30(≥ 1 Hz) is necessary to observe seismic-wave dispersion and PG can record both seismic waves

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and tsunamis with reasonable quality for waveform analyses, whereas conventional onshore and32

offshore seismometers or tide gauges can observe either of seismic waves and tsunamis.

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Utilizing the high-sampling PG in combination with the seismic and tsunami propagation theory

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for estimating earthquake source process or analyzing wave propagation processes in the ocean,

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will deepen our geophysical understanding of the solid-fluid coupled system in the earth and36

contribute towards disaster mitigation.

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Plain Language Summary

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Recent developments of offshore ocean-bottom observation networks have enabled us to40

use high-sampling (1 or more samples per second) seafloor pressure gauge (PG) data. This study

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investigated PG records with broadband period range (seconds to hours) around Japan during the42

2010 Chile earthquake. We identified a seismic P wave train arriving ~20–30 min after the focal

43

time. Another seismic wave train due to the surface Rayleigh wave during ~70–110 min and44

tsunamis during ~24–72 h were also confirmed, which showed a dispersive feature; long-period45

waves arrive earlier than short-period waves. The dispersion theories obtained from the elastic

46

and fluid dynamics thoroughly explained these features. We also compared wave amplitudes

47

between the PG and nearby ocean-bottom seismometer, and confirmed the validity of themanuscript submitted to Earth and Space Science48

relationship between pressure and vertical acceleration, and between pressure and vertical49

velocity. This study demonstrates PG can record both seismic and tsunami signals clearly with50

reasonable quality, while conventional seismometers or tide gauges can either. Ultra-broadband

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observation of PG plays an important role in deepening our understanding of geophysical wave

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propagation processes in the solid-fluid coupled system in the ocean, and enables delivery of53

essential information for earthquake early warning and disaster mitigation.

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manuscript submitted to Earth and Space Science55

1 Introduction

56

Ocean-bottom pressure gauges (PGs) have recently been developed worldwide for57

tsunami observations (e.g., Titov et al. 2005; Mungov et al. 2013; Tsushima & Ohta, 2014;

58

Rabinovich & Eblé 2015). Compared with tsunami observation using the conventional tide59

gauges, PGs are advantageous as they are less affected by complex coastal site effects (e.g.,

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Kubota et al., 2018). Owing to this advantage, PGs have significantly contributed to our61

understanding of tsunami generation and propagation processes derived from solid and fluid

62

dynamics (e.g., Satake et al., 2005; Saito et al., 2010; Inazu & Saito, 2013; Maeda et al., 2013;

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Rabinovich et al., 2013; Allgeyer & Cummins, 2014; Watada et al., 2014; Lay et al., 2016;

64

Poupardin et al., 2018; Sandanbata et al., 2018; Kubota et al., 2020; and references therein). PGs

65have further been utilized for observing much longer time-scale phenomena, such as infragravity

66

waves (e.g., Tonegawa et al., 2018) and oceanographic and geodetic phenomena (e.g., Baba et67al., 2006; Inazu et al., 2012; Wallace et al., 2016; Fukao et al., 2019).

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In addition recent studies have reported that the PG observations can record other69

geophysical waves, including ocean-acoustic and seismic waves (e.g., Nosov & Kolesov, 2007;70

Levin & Nosov 2009; Bolshakova et al., 2011; Matsumoto et al., 2012; Webb & Nooner, 2016).

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Dynamic pressure changes associated with the coseismic seafloor vertical accelerations,72

recognized as a reaction force to the seafloor lifting up the water column, can also be observed

73(e.g., Filoux, 1982; Nosov & Kolesov, 2007; An et al., 2017; Saito, 2019; Ito et al., 2020). This74

indicates the ability for PGs to be utilized as vertical accelerometers for the sea-bottom motions

75(An et al., 2017; Kubota et al., 2017). One strong advantage for using PGs in seismic wave

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observation is that the signal never saturates, unlike high-sensitivity ocean-bottom seismometers.

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The recent development of seafloor pressure observations with a sampling rate exceeding 1 Hz

78

(hereafter, high-sampling rate) in comparison with the low sampling rate of the conventional PG

79(e.g., the DART system,1/15 Hz, e.g., see Rabinobich & Eble, 2015) has contributed extensively

80

to our understanding of ocean-acoustic waves and seismic waves. Given the PG observations of81

various geophysical waves, PG could be utilized for ultra-broadband geophysical observation,

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including both seismic and tsunami waves, which will be useful to extract earthquake source

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information and the ocean’s ultra-broadband wave propagation process. However, PG records

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have primarily been utilized for analyzing tsunamis, and not extensively for seismic wave

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signals. Recent studies have discussed PG quality and performance in tsunami observation,manuscript submitted to Earth and Space Science

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which featured a period range of ~102–103 s (e.g., Saito et al., 2010; Tsushima & Ohta, 2014;

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Rabinovich & Eblé 2015), whereas those in seismic waves have not been examined in detail.

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In the present study, we examine the high-sampling PG record featuring a period range

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of ~100–103 s, with particular focus on the seismic wave signals. Section 2 describes the PG and90

additional datasets used and the method conducted for the analyses. Section 3 outlines the91

results. Section 4 interprets the results by examining the origins of the identified PG signals

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based on both the propagation theories of seismic waves and tsunamis and the comparison with

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other nearby instruments. Section 5 compares the PG waveform with nearby ocean-bottom

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seismometers (OBS) to discuss the quantitative relationship between pressure change and95

seismic waves. Section 6 examines the quality of the PG observation by comparing the spectral

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amplitudes and the background noises to discuss the performance and limitations of the high-97

sampling PG observation. Finally, Section 7 discusses future potential of the high-sampling PG

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for furthering our geophysical understanding and for contribution to practical disaster mitigation.

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The conclusion is summarized in Section 8.

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2 Data and method

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2.1 Data

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We examined the records of onshore and offshore instruments in northern Japan104(Figure 1) during some moderate local to regional earthquakes and major regional to global

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earthquakes. We here primarily focused on the 2010 Chile earthquake (Mw 8.8, Duptel et al.,1062012) because of its large magnitude and ideal source-station distance (Figure 1, the other107

examples are discussed in Section 5). The approximate distance along the great circle path from108

Chile to Japan is 17,000 km (angular distance of 150°). Station information is listed in Table S1.

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We use PGs at KPG1 and KPG2 (dark blue inverted triangles in Figure 1b) and three-component

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acceleration records from a OBS at KOBS1 (red circle) of the Off-Kushiro cabled-observatory,

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operated by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC,

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Kawaguchi et al., 2000; Hirata et al., 2002). A coastal tide gauge at Hanasaki Port operated by

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the Japan Meteorological Agency (JMA, blue diamond), and a Streckensen STS-2 onshore

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broadband seismometer at Kushiro (KSRF, green triangle) and a nearshore tiltmeter at Samani

115(SAMH, orange square) operated by National Research Institute for Earth Science and Disaster

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Resilience [NIED] (Okada et al., 2004; NIED, 2019) were also utilized. The detailed

manuscript submitted to Earth and Space Science117

specification of the instruments is described in Text S1. The velocity records from the onshore118

seismometer are converted to accelerograms. The horizontal components of the original119

seismograms and tilt records are along the north-south and east-west directions, which are120

rotated to the radial (R) and transverse (T) directions along the great circle path (Figure 1). We

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re-sampled all of these datasets with 1 Hz. Note that the instrument response at the onshore and122

offshore seismometers were not removed. We also examine the PGs of the Deep-ocean

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Assessment and Reporting of Tsunamis (DART) system deployed by the National Oceanic and124

Atmospheric Administration (NOAA) in the Pacific Ocean (Titov et al., 2005; Mungov et al.,125

2013, black inverted triangles in Figure 1). Refer to Table S2 for information on the DART

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stations.

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128
129

Figure 1. Location map of this study. (a) The 2010 Chile earthquake (Duptel et al., 2012)130

and great circle paths to the stations (yellow lines). DART tsunami stations are shown by

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inverted triangles. (b) Enlarged view around northern Japan. Dark blue inverted triangles are132

the PGs, the blue diamond is the coastal tide gauge, the green triangle is the onshore

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broadband seismometer, the red circle is the OBS, and the orange rectangle is the nearshore

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tiltmeter.

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Figure 2a shows the time series after the Chile earthquake from the PGs (dark blue),137

tide gauge (blue), onshore seismometer (green), OBS (red), and tiltmeter (orange). The

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waveforms from DART records are shown in Figure S1. Tidal variations are observed by themanuscript submitted to Earth and Space Science139

PGs and tide gauge. We also confirm small tidal fluctuations in the tiltmeter. Figure 2b shows140

the highpass filtered records with a cutoff period of 10800 s (3 h, ~0.1 mHz). Seismic waves are

141

clearly observed, except with the tide gauge. Figure 2c depicts the bandpass filtered records

142(passbands of 30–10800 s, ~0.1–33 mHz). Tsunamis are clearly detected by the PGs and the143

coastal tide gauge. A pressure change of Δp = 1 hPa corresponds to a sea-surface height change

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of Δη = 1 cm (Δp = ρwg0Δη, ρw ~ 1.03 g/cm3: seawater density, g0 = 9.8 m/s2: gravitational

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acceleration), therefore the tsunami amplitudes in PGs and tide gauges are comparable. Tsunami-146

related tilt changes are also recorded with the coastal tiltmeter (e.g., Kimura et al., 2013; Nishida147

et al. 2019). The amplitudes of seismic waves and tsunamis in the PGs are almost comparable,

148

whereas tsunamis recorded in the tiltmeter (orange trace in Figure 2c) have much smaller

149

amplitudes than the seismic waves, by magnitudes of 102.

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Figure 2. Time series at onshore and offshore sensors associated with the 2010 Chile

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earthquake. (a) Raw data. (b) Highpass filtered data (cutoff period of 10800 s). The

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waveform around the first P wave arrival is enlarged in Figure 2b’. (c) Bandpass filtered154

data (30–10800 s). Note that the scales are different in each panel and U, R, and T denote155

the vertical, radial and transverse component, respectively.

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157
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2.2 Spectrogram analysis
We examine the features of the high-sampling PG data based on the spectrogram

159

analysis which calculates the Fourier transform with a moving time window. In this study, we

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applied Aki and Richards (1980)’s definition of the Fourier transform, as:manuscript submitted to Earth and Space Science

161
$ /&

𝑋(𝜔) = ∫'$! /& 𝑥(𝑡)𝑒 !"# 𝑑𝑡,

162

!

(1)

163
164

where TL is the time window length of each bin and ω is the angular frequency (=2πf, f is165

frequency). Here, the spectrogram 𝐴(𝑡, 𝜔) is defined as:

166
$ /&

𝐴(𝑡, 𝜔) = -∫'$! /& 𝑥(𝑡 + 𝜏)𝑒 !"( 𝑑𝜏-.

167

!

(2)

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169

For the calculation of the spectrogram we adopt the Fourier amplitude spectra, but not power

170

spectra. In order to examine the spectral features of the seismic waves, we set the time window

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length of each bin (TL) at 512 s and the time shift (ΔT) at 60 s (i.e., t = nΔT, n is an integer

172

number). We also investigate tsunamis based on the spectrogram with TL = 8192 s and ΔT =173

1800 s. We further examined the spectral features with broadband period ranges including both174

seismic waves and tsunamis, using TL = 1024 s with ΔT = 60 s. Prior to calculating the Fourier

175

transform of each bin, we removed the mean value and applied a Hanning taper (Blackman &176

Turkey, 1958) with a length of 0.05TL to both edges of the window.

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3 Results

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The spectrograms for the PGs at KPG1 and KPG2 are shown in Figure 3. The

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spectrograms during the first three hours from the origin time are illustrated in Figures 3a and181

3b (TL = 512 s). The spectrogram confirms two distinct seismic wave trains during the seismic

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wave arrival at ~20 min (periods of T ~3–20 s, ~50–300 mHz) and ~70 min (T ~10–200 s, ~5–183

100 mHz) (black and red arrows in Figures 3a and 3b, respectively). The second wave train at

184~70 min displays a clear dispersive feature (i.e., long-wavelength waves arrive earlier than185

short-wavelength waves). Figures 3c and 3d depict the spectrogram for 120 hours after the186

origin time (TL = 8192 s). A tsunami-attributed wave train, showing a clear dispersion (T ~60–

1871000 s, ~1–20 mHz) can be confirmed in the spectrograms at ~24 h (blue arrow in Figures 3c

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and 3d). The arrival timing and duration of seismic waves and tsunamis are significantly

189

different; hence, it is difficult to display both in one figure. In order to display both wave

manuscript submitted to Earth and Space Science190

signals, we show the spectrograms using the logarithmic scale for the elapsed time in Figures 3e191

and 3f (TL = 1024 s).

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193

manuscript submitted to Earth and Space Science

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Figure 3. Spectrograms for PGs at (a, c, e) KPG1 and (b, d, f) KPG2. (a, b) Spectrograms

195

for seismic waves. (c, d) Spectrograms for tsunamis. (e, f) Spectrograms for both seismic

196

and tsunami waves with a logarithmic scale on the horizontal axes. The highpass (Figures197

3a, 3b, 3e, and 3f) and bandpass (Figures 3c and 3d) filtered waveforms are also shown.

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Distinct wave train arrivals are denoted by the colored arrows (black: seismic P waves, red

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Rayleigh waves, pink: Rayleigh waves from the opposite direction to the first Rayleigh200

wave, blue: tsunamis).

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202

We also calculate the spectrograms for other onshore and offshore instruments to203

compare with the PG spectrograms (Figure 4, see Figures S2 and S3 for the spectrograms with204

linear scale for the elapsed time). The seismic wave trains at ~20 min and ~70 min are detected

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by the tiltmeter, onshore seismometer, and OBS, but not by the coastal tide gauge, which is206

similar to the PG spectrogram. Another distinct wave train can also be confirmed at ~40–45 min

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in the horizontal components of the seismometers (e.g., black arrow in Figure 4e). We also

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identify an additional seismic wave train in the transverse component at the station KSRF at

209~70 min (e.g., green arrow in Figure 4f), but this is not observed in the PG spectrogram. We

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recognize small amplitude increases associated with tsunamis in the tiltmeter spectrogram at

211~24 h (blue arrows in Figures 4a, 4b, and 4c), but the dispersive feature cannot be observed.

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manuscript submitted to Earth and Space Science

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214

Figure 4. Spectrograms for (a) tide gauge at Hanasaki, (b, c) tiltmeter at SAMH, (d, e, f)

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onshore seismometer at KSRF, and (g, h, i) ocean-bottom seismometer at KOBS1. The

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horizontal axes are displayed on a logarithmic scale. The Love wave train arrival is denoted217

by the green arrow. See the caption in Figure 3 for the other description.

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219

4 Interpretation on results of spectrogram analysis

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4.1 Seismic wave trains

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We interpret the wave trains in the PG and the other instruments identified by the222

spectrogram analysis based on the theory of seismic waves and tsunamis. The onset timing of the223

first waves in the pressure records (~20 min) is identical to the onshore seismometer (Figure 2).

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We calculate the theoretical travel time of the core phases such as the PKP phase, the P wave

225

penetrating into the outer core, at KSRF using the global earth structure model AK135 (Kennett

226

et al., 1995, Figure S4). We obtain a travel time of PKP phase of 1193.74 s (~19.8 min), whichmanuscript submitted to Earth and Space Science227

accurately reproduced the observed arrival time (Figure S4). Thus, we conclude that this wave

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train is the seismic body P-waves including PKP, and PKIKP, PKiKP, PKPab, and PKPbc

229

phases (e.g., Blom et al., 2015). Furthermore, the theoretical travel time of the SS phases, free-230

surface reflected S waves leaving a source downward, at KSRF, is 2570.55 s (~42.7 min, Figure

231

S4). This also corresponds with the onset of the waves confirmed in the horizontal seismograms

232

at ~40–45 min (Figure 4e), and also indicates the body wave. The direct S waves do not arrive at

233

the stations off Hokkaido because they do not propagate into the fluid outer core (e.g., Shearer,2342009).

235

The dispersion is detected in the second seismic wave train at ~70 min. To identify the236

origin of this wave, we examine the particle motion of the seismometers at KSRF and KOBS1

237(Figure 5). The pressure waveform at KPG1 is depicted in Figure 5 (red trace). The particle

238

motions in both OBS and onshore seismometer records demonstrate retrograde motion during the239

arrival of this wave at 4200–4800 s (black arrow in Figure 5). This indicates a seismic surface

240

wave (Rayleigh wave). For the time window during 100–110 min (6000–6600 s) from the origin

241time, we confirm another retrograde particle motion with the rotation direction opposite to the242

first Rayleigh wave (gray arrow in Figure 5). A corresponding spectral amplitude increase is also

243

confirmed (pink arrow in Figure 3). These comparisons suggest another Rayleigh wave train

244

from the opposite direction to the first Rayleigh wave arrival, and delayed by ~30 min. It is also

245

worth pointing out that the Rayleigh wave arrivals at 5-10 mHz is slightly delayed compared to246

those at 20-50 mHz (Figures 3a and 3b). This observation has an opposite sense to typical

247

understanding of surface dispersion that the longer-period waves arrive earlier (e.g., Shearer,

2482009). A similar dispersion pattern also appears in the KOBS1 record, in particular the vertical249

component (Figure 4g).

manuscript submitted to Earth and Space Science

250
251

Figure 5. Particle motions and displacement waveforms of (a) onshore seismometer at KSRF

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and (b) OBS at KOBS1. Particle motions during 3600–4200 s, 4200–4800 s, 4800–6000 s, 6000–

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6600 s, and 6600–7200 s from the origin time are shown at the top panels. White and black stars

254

indicate the start and end locations of the particle motion in each period, respectively. Black and255

gray arrows denote the rotation direction of the particle motion. Displacement waveforms are

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shown in the bottom. Vertical displacement expected at KPG1, obtained by the time-double-

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integration of pressure (based on p = ρH0az) is shown by pink trace. Pressure waveform at KPG1

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(dark red trace) and pressure expected from the vertical acceleration and the dynamic pressure259

relation (black) are also shown.

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261

Examining the particle motion of the seismometers suggests that the wave train

262

arriving to the PG at ~70 min is the Rayleigh wave. We further examine the dispersive feature of263

the Rayleigh wave train recorded by the PGs based on the elastic wave propagation theory. We

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calculate the theoretical group velocity dispersion of the Rayleigh wave based on the AK135

265

global structure model (Kennett et al., 1995) incorporating a seawater layer with a thickness of266

4.5 km. The velocity structure and the dispersion relationship is depicted in Figure S5. Figure 6

manuscript submitted to Earth and Space Science

267

shows the comparison between the theoretical arrival time of the Rayleigh wave and the268

spectrograms. The theoretical Rayleigh wave arrivals at each period are consistent with the269

spectral amplitude peak in the spectrograms (red lines in Figure 6). In addition, the onset of the270

delayed Rayleigh wave train is also explained (pink lines) when considering a path along the271

opposite direction of the great circle path on the earth (~23,000 km). This suggests that the272

delayed wave train is also due to the Rayleigh wave, but radiated to the opposite direction of the273

first Rayleigh wave train.

274

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276

Figure 6. Comparison of theoretical arrival times of the seismic and tsunami waves and the277

spectrograms for (a) KPG1, (b) Tide gauge at Hanasaki, (c–e) onshore seismometer at KSRF,

278

and (f–h) OBS at KOBS1. Theoretical arrival times of P and SS waves (black), the surface waves

279(red and pink: Rayleigh, green: Love waves), and tsunamis (blue). The pink line is the arrival of280

the Rayleigh wave along the opposite direction of the great circle path on the earth.

manuscript submitted to Earth and Space Science

281
282

We also calculate the theoretical dispersion relationship using different structure

283

models to compare with the observed seismograms. We reveal that a model excluding the284

seawater layer from the AK135 structure model (Figure S6) cannot explain the short-period285

Rayleigh waves (>~50 mHz, Figure S7). We also compare the theoretical arrival time based on286

the PREM global structure model (Dziewonski & Anderson, 1981), which includes a seawater287

layer (Figure S8). The observed dispersive features in the Rayleigh waves are reasonably288

reproduced by the PREM model, although the theoretical arrival time is slightly delayed by ~10–289

20 min in periods at ~10–50 s (~10–100 mHz, Figures S9 and S10). This result demonstrates that290

the earth structure model is important for reproducing the dispersive feature, which suggests

291

Rayleigh wave dispersion recorded by the PG record can be useful to constrain the subseafloor

292

structure, as well as the ocean bottom seismometers.

293

In the particle motion of the onshore seismometer, a particle motion along the294transverse direction is also confirmed during 3600–4200 s (Figure 5). This indicates the Love295

wave is also observed in the horizontal components of the seismometers. In order to examine the296

Love wave train in the PGs, we calculate the group velocity and theoretical arrival times of the297

Love wave (green line in Figure 6). The spectral amplitude increase due to the Love wave cannot

298

be confirmed in the KPG1 spectrograms, while the corresponding signal is recognized in the299transverse component of the seismometer at KSRF (green arrow in Figure 4f). This result is

300

expected given the transverse motion of Love waves (e.g., Shearer, 2009) while the pressure

301

changes due to the seafloor motion are primarily caused by the seafloor vertical accelerations

302(e.g., Saito, 2019).

303
304

4.2 Tsunami wave trains

305

The wave train arriving at ~24 h which was attributed to a tsunami, also demonstrated306

the dispersion. Based on the gravity wave theory (e.g., Pedlosky, 2013; Saito, 2019), the tsunami

307

phase velocity c and group velocity U are given as:

308
309
310

&)

"

𝑐 = *$ = * ,(3)manuscript submitted to Earth and Space Science

+

&*,

"
𝑈 = & 21 + -./0(&*,
4,
)

311

"

(4)

312
313

where k is wavenumber (=2π/λ; λ is wavelength), T is period, and ω is angular frequency. The

314

angular frequency ω follows the dispersion relation:315

𝜔& = 𝑔3 𝑘 tanh(𝑘𝐻3 ),

316

(5)

317
318

where g0 is the gravitational acceleration and H0 is the water depth. We calculate the theoretical319

arrival time of the tsunami energy using the group velocity at each period (blue line in Figure320

S5b and S5c). The theoretical arrival time explains the spectral peak in the PG (Figure 6a). The

321

tide gauge spectrogram, meanwhile, did not show clear tsunami dispersion (Figure 6b). The main322

cause for this is its low sampling rate (1/60 Hz). However, the complex coastal site effect323

associated with local bathymetry might be another possible cause (e.g., Geist, 2018; Tanioka et324al., 2019). The dispersive feature was also not clearly recognized in the tiltmeter spectrogram

325(Figures 4b and 4c).

326

We investigated the spectral feature of the PGs of the DART stations (Titov et al.,327

2005; Mungov et al. 2013, black inverted triangles in Figure 1). The information of the DART

328

stations is listed in Table S2, the waveforms are depicted in Figure S1 and the spectrogram of the329

DART data is in Figure 7. The dispersive feature can also be confirmed, even in the spectrogram330

of the DART station 32412, closest to the epicenter (~2,400 km from the source, Figure 7a),331

although the temporal delay of the shorter period components is too large for other distant DART

332

stations (Figures 7b to 7e) and KPG stations (Figure 4). We can also recognize the dispersive

333

Rayleigh wave signals in these DART records. However, because the sampling rate of these

334

DART systems is low (≤ 1/15 Hz), it is difficult to recognize the dispersive feature from the335

spectrograms.

336

manuscript submitted to Earth and Space Science

337
338

Figure 7. Spectrograms for the DART records in the Pacific Ocean. The horizontal axes are339

displayed on a logarithmic scale. The time window length of each bin (TL) of 1024 s and the340time shift (ΔT) of 60 s were used in this calculation. Red and blue lines are the theoretical341

arrival times of the Rayleigh waves and tsunamis. See the caption in Figures 3 for the other342

description.

343
344

In the KPG1 and KPG2 spectrograms (Figures 3c and 3d), after the tsunami arrival345

at 24 h, the amplitudes at periods of 50–500 s (20–200 mHz) increase between 24–36 h.

346This feature is also confirmed in the DART spectrograms (Figure 7). We also verify

347

amplitude variations above 20 mHz following tsunami arrival in the onshore seismometer at

348

KSRF (Figures S3f and S3g) and nearshore tiltmeter at SAMH (Figure S3k and S3l). No

349

local earthquakes or aftershocks occurred during the tsunami arrivals, so this may suggest

350

that these shorter-period tsunamis are generated by long-period ones with the effects of351

reflections and scattering by local bathymetry.

352

In addition, the delayed shorter-period tsunamis (T < ~100 s) at > ~30–40 h are not353

recognized in the DART spectrograms. The static pressure change at seafloor 𝑝 due to sea-

354

surface height change (i.e., tsunami) can be expressed as follows (e.g., Saito, 2019):

355
356

4 , 5

" " "
𝑝 = 67-0(*,
,
)
"

(6)

manuscript submitted to Earth and Space Science

357
358

where 𝑘 is the wavenumber, 𝜌3 is the seawater density, 𝐻3 is the water depth, and 𝜂3 is the359

sea-surface height change. Tsunami amplitude decay in the seafloor pressure gauge is360

expressed by the factor 1/cosh(kH0). Figure S11a shows this decay factor as a function of361

kH0 (also shown in Saito, 2019) and Figure S11b is the decay factor as a function of362

frequency assuming a constant seawater depth, which is obtained from the tsunami

363

dispersion relation (equation (5)). At a depth of > 3,000 m, the ocean bottom pressure364change due to shorter-period tsunami has an amplitude less than ~0.5 times of the sea-365

surface tsunami, suggesting that the shorter period tsunamis do not reach the seafloor, and366

thus are not recorded by the DART stations.

367
368
369

5 Quantitative relation between pressure and vertical seismogram
In section 4.1, we verify that the PG clearly observed the Rayleigh wave signal. The

370

current section compares the quantitative relationship between the pressure change and the371seafloor seismic vertical motion in detail. When the period is longer than the resonant period of372

the acoustic fundamental mode, T0 = 4H0/c0 ~6 s (c0 ~ 1.5 km/s: the velocity of the ocean

373

acoustic waves, H0 ~2200 m: seawater depth in this region), the relation between the pressure374change p(t) and vertical acceleration az(t) can be expressed as (e.g., Filloux, 1982; Nosov &375

Kolesov, 2007; An et al., 2017; Saito, 2019):

376
377

𝑝(𝑡) = 𝜌8 𝐻3 𝑎9 (𝑡),

(7)

378
379

where ρw is the seawater density. Hereafter, we refer to this relationship as dynamic relation.

380

Using the dynamic relation, we examine the quantitative relationship between the pressure

381

change at KPG1 and vertical acceleration at KOBS1. We focus on the period bands of 10–200 s

382(5–100 mHz), in which Rayleigh waves are the most dominant signal in the records. The

383

amplitudes and phases of the pressure change (p) and pressure-converted acceleration (ρwH0az)

384

are very similar (Figure 8a). The vertical displacement expected at KPG1 obtained from equation385(7) is similar to the vertical displacement at KOBS1 as well (pink trace in Figure 5). We assess386

the similarity of the pressure change and vertical acceleration based on the correlation387

coefficients (CC), which is defined as:manuscript submitted to Earth and Space Science

388
$ /&

𝐶𝐶(𝑡) =

389∫'$! /& ;(#<()=# (#<()>(

!
$! /&
$ /&
?∫'$ /& ;(#<()& >( ∫'$! /& =# (#<()& >(
!
!

,

(8)

390
391

where TL is the length of the time window. We use the two time window lengths for the CC392

calculation; TL = 60 s (gray line in the middle panel in Figure 8a) and TL = 300 s (black line). We

393

obtain CC ~1 during the dominant Rayleigh wave arrival (~70 min) and also other seismic waves394(~1–3 h). Recent studies have reported the validity of equation (6) in the time domain in the395

coseismic dataset of a few minutes from the origin time (An et al., 2017; Kubota et al., 2017).

396

Since the signal-to-noise (SN) ratios in the KPGs are so high, they had good agreement with397

seismograms for a much longer duration than the results from previous studies. We further

398

compare the pressure change at KPG1 and the vertical acceleration at KOBS1 for other local to399

regional moderate earthquakes and regional or global major earthquakes; the 2006 Kuril

400

earthquake (Mw 8.3, epicentral distance ~890 km, Figure 8b), the 2007 Kuril earthquake

401(Mw8.1, 950 km, Figure 8c), the largest foreshock of the 2011 Tohoku earthquake (Mw 7.3,

402~390 km, Figure 8d), the 2011 Tohoku earthquake (Mw 9.0, 420 km, Figure 8e), the 2012

403

Sumatra earthquake (Mw 8.6, ~6700 km, Figure 8f), and the 2018 Hokkaido Iburi Eastern

404

earthquake (Mw 6.6, 230 km, Figure 8g). We obtain similar results regardless of their very

405

different source-station distances and magnitude, which suggests the robustness of the observed

406

relation.

407

manuscript submitted to Earth and Space Science

408
409

Figure 8. Comparison of the pressure and vertical acceleration for (a) the 2010 Chile earthquake,

410(b) the Kuril earthquake, (c) the 2007 Kuril earthquake, (d) the 2011 Off-Miyagi earthquake (e)411

the 2011 Tohoku earthquake, (f) the 2012 Sumatra earthquake, and (g) the 2018 Hokkaido

412

earthquake. Magnitudes and epicentral distances are shown in each panel. Blue and red traces are413

pressure change at KPG1 and vertical acceleration at KOBS1 converted to apparent pressure

414change using the relation p=ρwH0az, respectively. Bandpass filter with passband of 10–200 s is415

applied. Correlation coefficient between pressure and acceleration is also shown (gray: TL = 60 s,

416

black: TL = 300 s). Coherency and phase difference between two waveforms are shown in the417bottom two figures. In the phase difference, the region where the coherency is less than 0.9 is418

masked.

419
420

We calculate the temporal variation of the coherency and phase difference between

421

two waveforms in the frequency domain. The procedure to calculate the coherency and phase422

difference is summarized in Text S2. Our results confirm the high coherency (> ~0.9) and zero-423

phase-difference at periods of ~10–50 s (~20–100 mHz, Figures 8d and 8e) during the Rayleigh424

wave arrival. We further assess the correlation between the pressure and vertical acceleration

manuscript submitted to Earth and Space Science425

with different dominant periods (Figure 9). The correlation between the pressure and426

acceleration is low in the shortest period bands (T < 10 s). This is due to the dynamic relation

427

being derived under the assumption that the wave period is longer than the resonant period of the428

acoustic fundamental mode T0 = 4H0/c0 ~6 s. We also find that the correlation between the429

pressure and acceleration is very high in periods of T ~10–50 s (Figures 9c and 9d), which infers

430

that the dynamic relation holds well at the period bands of ~10–50 s. Conversely, at longer

431

periods (T > 50 s) the correlation is not as high and unstable (Figures 9e to 9h). The low

432

correlation at the longer period is caused by the noises attributed to the seafloor vertical433

displacement due to the long-period ambient oceanographic water waves. This is referred to as434

the compliance noise (e.g., Crawford et al., 1991; 1998; Webb, 1998; Webb & Crawford, 1999;

435

An et al., 2020). However, we detected relatively high correlation during the Rayleigh wave

436

arrival (~70–100 min) even at the longer periods up to T ~400 s (~2.5 mHz, bottom panels in437

Figures 9e to 9g). This indicates that the PGs can observe the Rayleigh wave signals up to the438

periods of ~ 400s where the Rayleigh wave signals are larger than these compliance noises.

439

manuscript submitted to Earth and Space Science

440
441

Figure 9. Comparison of the pressure and vertical acceleration at period bands of (a) 4–6 s, (b)442

6–10s, (c) 10–20 s, (d) 20–50 s, (e) 50–100 s, (f) 100–200 s, (g) 200–400 s, and (h) 400–800 s.

443

See Figure 8 for the other description.

444
445

In contrast to the dynamic pressure relation (equation (7)), a relationship between the446pressure change and vertical velocity vz(t) is proposed in several previous studies (e.g., Nosov et447al., 2007; Bolshakova et al., 2011; Matsumoto et al., 2012):

448
449
450

𝑝(𝑡) = 𝜌@ 𝑐3 𝑣9 (𝑡).

(9)manuscript submitted to Earth and Space Science451

We also compare the pressure change at KPG1 and the vertical velocity at KOBS1, with periods

452

shorter than the acoustic resonant period T0 ~ 6 s. As a result, we can recognize high correlation

453(~1) during the theoretical P wave arrival in this period band (Figure 10a). The comparisons454

between pressure change at KPG1 and the vertical velocity at KOBS1 for other moderate to455

major earthquakes confirm that this tendency is robust (Table S3, Figures 10b–10g).

456

If we carefully review the P-wave arrivals, we find that the amplitude of the pressure

457

change p(t) does not agree with ρwc0vz(t), although the phases agree with each other. The

458

amplitude ratio between p and ρwc0vz in the first arrival of the seismic waves differs for each459

event (see Figure 10). This tendency is most evident in the 2011 Tohoku-Oki earthquake (Figure

460

10e). The local site effect due to the station location difference might be the possible cause.

461

However this seems implausible because the station difference between KPG1 and KOBS is only462

~ 4 km, and any systematic relation in the amplitude ratio among these events cannot be463

identified.

464

We also point out that the high correlation is confirmed only in the P-wave arrivals, but

465neither in the entire wave trace nor in the later arrivals such as S waves (Figures 10b–10g).The

466

pressure p tends to be larger than ρwc0vz around the P arrivals. We should note that a relation467

p=ρwc0vz can be derived assuming a P-wave propagation through fluid medium (e.g., Saito,

4682019). However, the wavefields are more complicated than a P-wave propagation through fluid469

medium, in particular, in the later wave arrivals where the waves are trapped by the reflections

470

between the sea surface and the seafloor. The previous results of numerical simulations suggest

471

this feature; the pressure changes at the seafloor due to trapped P-waves, or ocean-acoustic

472

waves exceed ρwc0vz (Bolshakova et al., 2011; Saito, 2017). Although Matsumoto et al. (2012)473

compared the Fourier amplitudes of the seismograms and pressure records and found the474

consistency with the relation p=ρwc0vz in the frequency domain, they discussed only the Fourier

475

amplitudes and not the phases. Our results show that the validity of the theoretical relationship476

between the pressure and velocity is very limited, and holds only at the first arrival of the seismic477

waves, not at the latter arrivals.

478

Notably, the time window at ~6300 s demonstrates relatively high correlation (Figure

479

10a, Figure S12a for more detail), which might be due to the P wave associated with the Mw 7.4

480

aftershock (GCMT) which occurred ~1.4 h after the Chile earthquake. We also examined themanuscript submitted to Earth and Space Science481

correlation between the pressure and vertical velocity with several different period bands (Figure482

S12), although it seems the correlation is low in longer period ranges (T > T0 ~ 6 s).

483

484
485

Figure 10. Comparisons of the pressure and vertical velocity for the multiple events. Blue and486

red traces are pressure change at KPG1 and vertical velocity at KOBS1 converted to apparent

487

pressure change using the relation p=ρwc0vz, respectively. Correlation coefficient between

488

pressure and vertical velocity is also shown (gray: TL = 60 s, black: TL = 20 s). Bandpass filter

489with passband of 4–6 s is applied. Comparisons of the pressure change and vertical velocity at490

the time window around the P wave arrival are also shown at the bottom. Theoretical arrival

491

times of the direct P and S phase are also shown.

492
493

6 Quantitative comparison in amplitudes of tsunami and seismic waves

494

We finally investigate the quantitative relationship between the spectral amplitude and495

the background noise, using the 10-Hz sampled original data. The time window of 58.25 h (=0.1496

× 222 s) is used for the Fourier transform. Figure 11 shows the spectral amplitudes of the onshoremanuscript submitted to Earth and Space Science497

and offshore records for background (gray) and coseismic (black) signals. In order to498

quantitatively compare the amplitudes between each record, the units are converted to apparent499

pressure change ([Pa·s] = [(m-1· kg1·s-2)·s]). We assume that a sea height change of 1 cm equals

500

a pressure change of 1 hPa (102 Pa) to convert to apparent pressure change for the tide gauge at

501

Hanasaki. The vertical accelerations in the OBS at KOBS1 and onshore seismometer at KSRF

502

are converted to the apparent pressure change by using equation (6), with ρw = 1.03 g/cm3 and H0503= 2218 m (water depth at KOBS1).

504

PG spectra (Figure 11a) demonstrates an amplitude increase for the period range of505~60–5000 s, which are associated with tsunamis. Conversely, in the tide gauge spectra, the506

significant increase in the tsunami amplitude is limited within the period range of ~2000–4000 s

507(~0.25–0.5 mHz, Figure 11b), which is due to the coastal site effect (e.g., Geist, 2018; Tanioka et508al., 2019). The broadband amplitude increase in the PG spectra demonstrates that PGs are509

capable of detecting the wider period range of tsunamis and are much less affected by the coastal

510

site effect than coastal tide gauges.

511

Our results further confirm that amplitude increases are related to the seismic waves in512

the spectra of the PG and seismometers (Figures 11a, 11c, and 11d). Small spectral amplitude513

increases at periods of ~5 s correspond to the body waves (marked by green arrow). In the514

periods of ~10–50 s (~20–100 mHz), where the Rayleigh wave is dominant, we verify the signals

515

amplitude increases in the PG (orange text). This Rayleigh wave-related amplitude increase can

516

also be observed in the spectra of the OBS and onshore seismometer. The background noise level517

in the frequency band of Rayleigh waves in the KPG1 is small compared to the KOBS1. This

518

suggests that the KPG1 can detect seismic Rayleigh wave signals with qualities similar to or

519

better than the KOBS1 during this event. One challenge in the seafloor seismic observation is520

that the installation environment (i.e., we cannot fix the sensor to the ground) cannot be521

controlled. This can easily be achieved in the onshore seismic observation. The lower noise level522

in the PG in this frequency band may suggest that the PG will provide good supplementary523

information for seafloor seismic observation.

524

manuscript submitted to Earth and Space Science

525
526

Figure 11. Fourier amplitude for (a) KPG1, (b) HANA, and vertical components for (c)527

KOBS1 and (d) KSRF. The gray and black lines depict the power spectra with a time528

window of ~2.5 days before and after the 2010 Chile earthquake, respectively.

529

Characteristic spectral bands of tsunami and seismic waves are shown by blue and red

530

arrows, respectively. Note that the instrumental responses are not removed.

531
532
533

7 Future applicability of the high-sampling PG
We summarize the key results of the spectral analyses in Figure 12. Five key findings534

can be drawn from our analyses:

535(1) High-sampling-rate (≥ 1 Hz) is necessary for PGs to detect the dispersive Rayleigh waves in536

broadband periods (~10–400 s, ~2.5–100 mHz) and dispersive tsunamis (~50–1000 s, ~1–20

537mHz) very clearly.

538(2) Sampling rate of the typical DART system (~1/15 Hz) is not sufficient to fully analyze the539

wave propagation processes of the seismic waves and tsunamis.

540(3) Seismometers (≥ 100 Hz sampling) can record seismic wave signals clearly but do not record

manuscript submitted to Earth and Space Science541

tsunamis, even when installed at the ocean floor.

542(4) Coastal tiltmeters observe both seismic wave and tsunami signals but do not clearly record543

the dispersion.

544(5) Tide gauges cannot clearly detect tsunami dispersion or seismic waves.

545

546
547

Figure 12. Schematic illustration of geophysical phenomena in the ocean. The geophysical548

phenomena which can be observed by the high-sampling-rate ocean bottom pressure gauges549

and other instruments are shown by colored arrows. Note that the application of PG to

550

geodetic phenomena is shown by the dashed arrow, because this time-scale range is not

551

covered in this study.

552
553

In particular, finding (1) cannot be explicitly indicated if the sampling rate of the PG is554

low (e.g., the third-generation DART system, 1/15 Hz, e.g., see Rabinobich & Eble, 2015). Our

555

result suggests that the high-sampling PG observation would be a good candidate for the556

alternative and backup tools of seismic wave observations. This corresponds with An et al.

557(2017) and Kubota et al. (2017) who also demonstrated that the seismic waves retrieved from the558

PG records greatly contribute to accurately determining the centroid moment tensor solution of559

moderate-sized offshore earthquakes. New, wide, and dense offshore observation networks

560

incorporating OBSs and PGs were recently installed in the deep-sea region (e.g., Kaneda et al.,561

2015; Kawaguchi et al., 2015; Rabinovich & Eblé 2015; Kanazawa et al., 2016; Mochizuki et al.,562

2016; Uehira et al., 2016; Howe et al., 2019). These new PG networks feature a higher samplingmanuscript submitted to Earth and Space Science563

rate (≥ 1 Hz). Furthermore, the sampling rate of the next generation DART system (DART4G)

564

will possibly be higher than the third-generation system (e.g., Rabinobich & Eblé, 2015; An et565al., 2017; Angove et al., 2019). Utilizing the array of high-sampling PGs will enable us to566

analyze the ultra-broadband geophysical wave propagation, including tsunamis and seismic567

waves. Developments of the offshore PG networks will facilitate the analysis of ultra-broadband

568

pressure signals covering periods of 100–103s. PGs can further be employed for observing much

569

longer time-scale phenomena (e.g., Baba et al., 2006; Inazu et al., 2012; Wallace et al., 2016;

570

Tonegawa et al., 2018; Fukao et al., 2019, Figure 12). Using these new PG networks will create571

new possibilities for understanding the geophysical wave propagation processes in the solid-fluid572

coupled system and the generation processes of earthquakes and tsunamis. Several studies have573

already begun to use an array of the high-sampling PGs for the broadband geophysical wave

574

propagation analyses (Fukao et al., 2018; 2019; Sandanbata et al., 2018; Mizutani & Yomogida,5752019).

576

Real-time earthquake early warnings are especially important for developing nations

577

exposed to a high tsunami risk (e.g., Mulia et al., 2019). For more reliable and early earthquake

578

warnings, it is desirable to install OBSs in these networks, despite the higher economic costs

579

associated with construction. Nevertheless, this present study demonstrates that seismic wave

580

signals can still be observed by high-sampling-rate PGs, even if they do not incorporate OBSs.

581

Recently, Nakamura et al. (2019) estimated earthquake body-wave magnitudes based on high-582

frequency seismic wave signals in PGs for real-time data analyses. The present study

583

demonstrates the significant potential of longer and wider period seismic signals in near-field584

high-sampling PG records for real-time estimation of the moment magnitude and centroid585

moment tensor (e.g., Kubota et al., 2017). The broadband observations of high-sampling PG are

586

significantly valuable for real-time earthquake warnings and disaster mitigation.

587
588

8 Conclusions

589

We examined the performance of PGs in a wide frequency range by investigating the590

spectral features in the PG records in northern Japan associated with the 2010 Chile earthquake,591

and comparing these with nearby onshore and offshore instruments. We calculated the592

spectrograms and revealed that the PGs clearly detected the wave trains due to body waves,593

Rayleigh waves, and tsunamis. The dispersive features were visibly recognized in the Rayleighmanuscript submitted to Earth and Space Science594

wave (periods covering ~10–400 s) and tsunami (~60–5000 s) wave trains, which were explained595

by the propagation theories of seismic waves and tsunamis, respectively. The quantitative596

comparison between the pressure change and the vertical acceleration demonstrated that the597

dynamic relation holds for ~ 3h from the origin time, whereas, the relationship between the598pressure change and the vertical velocity at higher period range (< ~6 s) holds only at the first P

599

wave arrival. This validity was confirmed in time domain from the real observation. Similar

600

results seen for multiple earthquakes, regardless of their very different source-station distance601

and earthquake magnitude, suggest the robustness of the observed relation. This study602

demonstrated that high-sampling PGs can observe the broadband seismic wave and tsunami

603

signals. In particular, seismic wave signals can be detected with similar quality as the OBS. The

604

broadband geophysical wave observations of the high-sampling PG are important for furthering

605

our understanding of the geophysical analyses and developing practical disaster mitigations.

606
607

Acknowledgments, Samples, and Data608

We thank the Editor Benoît Pirenne and two anonymous reviewers for their comments. We thank609

Katsuhiko Shiomi for the information of the coastal tilt observation of NIED. This work was

610

financially supported by Sasakawa Scientific Research Grant (Grant Number 2019-2037) from611

the Japan Science Society and JSPS KAKENHI Grant Number JP19K14818 from the Japan

612

Society for the Promotion of Science. Coastal tide gauge data is available at the613

Intergovernmental Oceanographic Commission (IOC)’s website (http://www.ioc-614

sealevelmonitoring.org). PG and OBS data are acquired by JAMSTEC

615(http://www.jamstec.go.jp/scdc/top_e.html). DART tsunami data is available at the NOAA’s

616

website (https://www.ngdc.noaa.gov/hazard/dart/2010chile_dart.html). Onshore broadband

617

seismometer is available at the NIED F-net (NIED, 2019, https://doi.org/10.17598/NIED.0005).

618

Tiltmeter record used in this study, which is operated by NIED, is available in619

https://doi.org/10.17598/NIED.0018. We used TauP Toolkit (Crotwell et al., 1999) version 2.4.5

620(https://www.seis.sc.edu/taup/) to calculate the theoretical arrival times. Figures in this paper was

621

prepared using Generic Mapping Tools (GMT) software version 6.0.0 (Wessel et al., 2019). We

622

used Editage (www.editage.com) for English language editing.

manuscript submitted to Earth and Space Science

623

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Earth and Space Science
Supporting Information for
Ultra-broadband seismic and tsunami wave observation of high-sampling
ocean-bottom pressure gauge covering periods from seconds to hours
T. Kubota1, T. Saito1, N. Y. Chikasada1, and W. Suzuki1
1 National Research Institute for Earth Science and Disaster Resilience, Tsukuba, Ibaraki, Japan.

Contents of this file
Texts S1 to S2
Figures S1 to S12
Tables S1 to S3

Additional Supporting Information (Files uploaded separately)
Dataset S1 is available at https://doi.org/10.17598/NIED.0018. The Dataset file includes
tilt record at SAMH during the 2010 Chile earthquake. The .sac files are in SAC format
and .csv ascii file is also available. Time zone of the record is UTC.

Introduction
Text S1 describes the specification of the instruments used in this study. Text S2 explains theprocedure employed to calculate the coherency and phase spectra. Figure S1 shows the timeseries for the DART stations installed in the Pacific Ocean during the 2010 Chile earthquake.
Figures S2 and S3 show the spectrograms displayed with the linear scale on the elapsed time.
Figure S4 shows the comparison between the theoretical and observed arrival times of theseismic phases at KSRF. Figure S5 shows the AK135 structure model and theoretical dispersion
relation. Figures S6 and S7 show the AK135 structure model without a seawater layer and its
dispersion relation, and the comparison between the spectrograms and theoretical arrival
times. Figures S8 and S9 display the PREM structure model and its dispersion relation, and thecomparison between the spectrograms and theoretical arrival times. Figure S10 compares
theoretical arrival times of the Rayleigh waves between different structure models. Figure S11shows tsunami amplitude decay in the seafloor pressure gauge. Comparison between thepressure change and vertical velocity at varying period bands are shown in Figure S12. Tables S1and S2 are the station lists for the different instruments around northern Japan and the DART
stations in the Pacific Ocean, respectively. Table S3 is the event list investigated in this study.

1

Text S1.
This text summarizes specifications of the observation instruments used in this study.
The specification of the Off-Kushiro PG and OBS, which are maintained by the Japan
Agency for Marine-Earth Science and Technology (JAMSTEC), is described in Hirata et al. (2002)
and the website of the JAMSTEC Submarine Cable Data Center (SCDC, http://www.jamstec.
go.jp/scdc/top_e.html). The OBS uses JA-5III-A servo accelerometer developed by the Japan
Aviation Electronics Industry. The details summarized in http://www.jamstec.go.jp/scdc/
html_sysindex_e/obsdetail.html. The direction of the original X, Y, and Z components areconverted to the EW, NS, and UD components based on the procedure provided by the
JAMSTEC SCDC. The response of the OBS is flat at frequency bands of 0 to 40 Hz. The PG equips
the quartz-oscillation type pressure sensor HP2813E developed by Hewlett-Packard, Inc. (http://
www.jamstec.go.jp/scdc/html_sysindex_e/hpdetail.html).
The onshore seismometer at KSRF, which is one of the NIED (National Research Institutefor Earth Science and Disaster Resilience)’s F-net observation network, uses Streckeisen STS-2
broadband seismometer (Okada et al., 2004; NIED, 2019). The nearshore tiltmeter at SAMH uses
a high-sensitivity accelerometer JTS-3B manufactured by Mitutoyo Corporation (Okada et al.,2014).
Text S2.
This text explains the procedure to calculate the coherency and phase difference
between the pressure and vertical acceleration waveforms in Figure 8. We first calculate theFourier spectra X(ω) and Y(ω) from the time series x(t) and y(t) in every 1 s step, with a tapered
512 s time window. The cross spectra SXY(ω) is defined as:!!" (#) = 〈'(#)( ∗ (#)〉,(S1)

where ⟨⟩ denotes the ensemble average, and * is the complex conjugate. Considering the
average over time as the ensemble average, we calculate SXY(ω) using the time window of ±256s, in every 30 s step. Using the cross spectra SXY(ω) and the power spectra SXX(ω) and SXY(ω), thecoherency CohXY(ω) is calculated as:,-ℎ!" (#) =|%!" (')|)%!! ('))%"" (')

.

(S2)

In addition we also calculate the phase shift between the spectra X(ω) and Y(ω), θXY(ω), using
the phases θX(ω) and θX(ω), as:/!" (#) = /! (#) − /" (#),-./0[〈!(')〉],-./0[〈"(')〉]= tan*+ 5 50.6[〈!(')〉] 6 − tan*+ 5 50.6[〈"(')〉] 6.

(S3)

2

(a) No filter(b) Highpass 10800s

32412

5hPa
15s

32411
32412

100hPa

32411

1min

5hPa

51406

5hPa

51407

5hPa

21413

5hPa

100hPa051406

100hPa51407

100hPa3600
7200
10800 14400 18000
Elapsed time from the origin time [s](c) Bandpass 30s-10800s

32412

10hPa
15min

32411
21413

100hPa0

12 24 36 48 60 72 84 96 108 120 132 144
Elapsed time from the origin time [h]

21600

10hPa

51406

10hPa

51407

10hPa

21413

10hPa
0

12

24 36 48 60 72 84 96 108 120
Elapsed time from the origin time [h]Figure S1. DART records installed in the Pacific Ocean associated with the 2010 Chile earthquake. The sampling rate is 1/15 Hz
except for the station 32412. The sampling rate for the station 32412 is shown in Figures S1b and S1c (red: 1/15 Hz, green: 1/60 Hz,
blue: 1/900 Hz).

1

2

3

0

1

2

Frequency [mHz](e) Onshore seismometer KSRF.U

1

2

3

0

1

2

Frequency [mHz]

102

0

1

2

3

0

0

1

2

0

0

1

2

[µrad⋅s]
101

102

3

0

1

2

3

Elapsed time [h][µm/s2⋅s]

103

3Elapsed time [h]Elapsed time [h][µm/s2⋅s]1033(l) Tiltmeter SAMH.T

2

2
5
10
20
50
100
200
500

[cm⋅s]

103

1

2
5
10
20
50
100
200
500

3

103

[µm/s2⋅s]
102

3

2

(k) Tiltmeter SAMH.T(j) OBS KOBS1.T

2

1

102

Elapsed time [h]Elapsed time [h][µm/s2⋅s]

103

3

103

1

0

Elapsed time [h](g) Onshore seismometer KSRF.T(i) OBS KOBS1.R

Elapsed time [h]3[hPa⋅s]102[µm/s2⋅s]102(h) OBS KOBS1.U

2

101

Elapsed time [h][µm/s2⋅s]

1

Elapsed time [h](f) Onshore seismometer KSRF.R

Elapsed time [h]

500
200
100
50
20
10
5
2

0

[hPa⋅s]
102

101

0

3

Elapsed time [h]Period [s]RayleighSS

1

Elapsed time [h]

2
5
10
20
50
100
200
500

Period [s]

0

500
200
100
50
20
10
5
2

(d) Tidegauge Hanasaki

Love(c) PG KPG2

Period [s](b) PG KPG1(a)P

Frequency [mHz]

500
200
100
50
20
10
5
2

[µrad⋅s]
101

102

Figure S2. Spectrograms for seismic waves. (a) Theoretical arrival time of seismic waves. (b–l) Spectrograms for onshore andoffshore instruments. See the caption in Figure 3 for a description of each panel.

1(d) Tidegauge Hanasaki

0

24

48

72

96

120

144 0

24

Elapsed time [h]

48

72

96

120

144 0

24

Elapsed time [h]

48

72

96

[hPa⋅s]Frequency [mHz]

101

500
200
100
50
20
10
5
2
1
0.5
0.2

(e) Onshore seismometer KSRF.U

0

24

48

72

96

120

144 0

24

48

72

96

Frequency [mHz]

500
200
100
50
20
10
5
2
1
0.5
0.2

102

100

(h) OBS KOBS1.U

0

24

48

72

103

120

96

120

144 0

24

48

72

120

24

102

103

48

100

144 0

24

Elapsed time [h][µm/s2⋅s]
104

96

72

96

120

48

72

102

103

103

(k) Tiltmeter SAMH.R

144 0

24

48

72

96

120

[µrad⋅s]
100

101

102

(l) Tiltmeter SAMH.T

96

2
5
10
20
50
100
200
500
1000
2000
5000
144

Elapsed time [h][µm/s2⋅s]
102

101

120

[cm⋅s]

120

144 0

24

Elapsed time [h][µm/s2⋅s]
104

72

102

(j) OBS KOBS1.T

96

48

102

Elapsed time [h][µm/s2⋅s]
102

101

24

Elapsed time [h](g) Onshore seismometer KSRF.T

144 0(i) OBS KOBS1.R

Elapsed time [h]
102

101

Elapsed time [h][µm/s2⋅s]

101

144 0

[hPa⋅s]102(f) Onshore seismometer KSRF.R

Elapsed time [h]120Elapsed time [h]

2
5
10
20
50
100
200
500
1000
2000
5000
144

Period [s](c) PG KPG2

Period [s](b) PG KPG1

48

72

96

120

2
5
10
20
50
100
200
500
1000
2000
5000
144

Period [s](a)TsunamiFrequency [mHz]

500
200
100
50
20
10
5
2
1
0.5
0.2

Elapsed time [h][µm/s2⋅s]
104[µrad⋅s]
100

101

102

Figure S3. Spectrograms for tsunamis. (a) Theoretical arrival time of tsunamis. (b–l) Spectrograms for onshore and offshore
instruments. See the caption in Figure 3 for a description of each panel.

2

KSRF (Raw)

400

U

100

R

200

R

0

T

0

T

300

SS

U

PKIKP
PKP
PKiKP
PKP

200

−100

−200
600

KSRF (BPF 4-6s)

KSRF (BPF 20-200s)

200

U

400

U

100

R

200

R

0

T

0

T

−100
1150

1200

SS

[cm/s]600

KSRF (Raw)

PKIKP
PKP
PKiKP
PKP

[cm/s]

300

1250

Elapsed time [s]−2001300 2400 2500 2600 2700 2800 2900 3000 3100 3200

Elapsed time [s]Figure S4. Theoretical arrival times of the seismic phases at KSRF calculated from the AK135 structure model, for (left) the P waves
and (right) the S-waves.

3

(a) AK135
Vel [km/s], ρ [g/cm3]
8 10

(b)
5000 20001000 500

120
140
160

5

2

Rayleigh

100
10−1
10−2

TsunamiPhase velocity
Group velocity

180
200

10

500

(c)

2

200
Velocity [km/s]

Depth [km]

100

20

Love

60
80

200 100 50

101

10−3

100
50
20
10
5
2
1

0.2 0.5 1

2

5 10 2050 100200 500

Frequency [mHz]

5
10

0.1

1

20
50

10

100

Period [s]

40

P
S
ρ

Tsunami20

Rayleigh

6

Love

4

P
SS

2

Frequency [mHz]

0
0

200
500
1000
100

Elapsed time [h]Figure S5. (a) Velocity structure model based on AK135. (b) The phase velocity (dashed lines) and group velocity (solid lines) of thefundamental mode of the Rayleigh (red) and Love (green) waves and tsunami (blue). (c) Theoretical arrival times of P and SS waves(black), the surface waves (red and pink: Rayleigh, green: Love waves), and tsunamis (blue). The pink line is the arrival of theRayleigh wave along the opposite direction of the great circle path on the earth.

4

(a) AK135 without seawater
Vel [km/s], ρ [g/cm3]
8 10

(b)

40

P
S
ρ

5000 20001000 500

120
140
160

5

2

Rayleigh

100
10−1
10−2

Phase velocity
Group velocity

180
200

10

500

(c)

2

200
Velocity [km/s]

Depth [km]

100

20

Love

60
80

200 100 50

101

10−3

100
50
20
10
5
2
1

0.2 0.5 1

2

5 10 2050 100200 500

Frequency [mHz]

5
10
20
50
100

0.1

Period [s]20Rayleigh

6

Love

4

200

P
SS

2

Frequency [mHz]

0
0

500
1000
1

10

100

Elapsed time [h]Figure S6. (a) Velocity structure model based on AK135 without seawater layer. (b) The phase velocity (dashed lines) and groupvelocity (solid lines) of the fundamental mode of the Rayleigh (red) and Love (green) waves and tsunami (blue). (c) Theoretical arrival
times of P and SS waves (black), the surface waves (red and pink: Rayleigh, green: Love waves), and tsunamis (blue). The pink line isthe arrival of the Rayleigh wave along the opposite direction of the great circle path on the earth.

5

100

0.1

1

Rayleigh(d) Onshore seismometer KSRF.R

100

0.1

100

10

100

10

0.1

100
[µm/s2⋅s]103(g) OBS KOBS1.R

Elapsed time [h]

102

103

(h) OBS KOBS1.T

1

10

100

Elapsed time [h][µm/s2⋅s]

103

1

0.1

2
5
10
20
50
100
200
500
1000

1

10

100

Elapsed time [h][µm/s2⋅s]

103

2
5
10
20
50
100
200
500
1000

Elapsed time [h][µm/s2⋅s]

102

P
1

Period [s]

0.1

SS

(f) OBS KOBS1.U

10

Love

[µm/s2⋅s]
103

102

SS
1

Elapsed time [h]Rayleigh

101

Frequency [mHz](e) Onshore seismometer KSRF.T

SS

10

Rayleigh

1

Elapsed time [h]

500
200
100
50
20
10
5
2
1
0.1

103

SS

Rayleigh[cm⋅s]
102

P

Frequency [mHz](c) Onshore seismometer KSRF.U

500
200
100
50
20
10
5
2
1
0.1

100

Period [s][hPa⋅s]
102

101

10

Elapsed time [h]Period [s]10Elapsed time [h]

Love

1

2
5
10
20
50
100
200
500
1000

TsunamiRayleigh(b) Tidegauge Hanasaki

TsunamiP

Frequency [mHz](a) PG KPG1

500
200
100
50
20
10
5
2
1
0.1

[µm/s2⋅s]
103

Figure S7. Comparison of theoretical arrival times of the seismic and tsunami waves based on the AK135 without seawater layer andthe spectrograms.

6

(a) PREM
Vel [km/s], ρ [g/cm3]
8 10

(b)

40

P
S
ρ

5000 20001000 500

120
140
160

5

2

Rayleigh

100
10−1
10−2

Phase velocity
Group velocity

180
200

10

500

(c)

2

200
Velocity [km/s]

Depth [km]

100

20

Love

60
80

200 100 50

101

10−3

100
50
20
10
5
2
1

0.2 0.5 1

2

5 10 2050 100200 500

Frequency [mHz]

5
10
20
50
100

0.1

Period [s]20Rayleigh

6

Love

4

200

P
SS

2

Frequency [mHz]

0
0

500
1000
1

10

100

Elapsed time [h]Figure S8. (a) Velocity structure model based on the PREM model. (b) The phase velocity (dashed lines) and group velocity (solidlines) of the fundamental mode of the Rayleigh (red) and Love (green) waves and tsunami (blue). (c) Theoretical arrival times of P
and SS waves (black), the surface waves (red and pink: Rayleigh, green: Love waves), and tsunamis (blue). The pink line depicts thearrival of the Rayleigh wave along the opposite direction of the great circle path on the earth.

7

100

0.1

1

Rayleigh(d) Onshore seismometer KSRF.R

100

0.1

100

10

100

10

0.1

100
[µm/s2⋅s]103(g) OBS KOBS1.R

Elapsed time [h]

102

103

(h) OBS KOBS1.T

1

10

100

Elapsed time [h][µm/s2⋅s]

103

1

0.1

2
5
10
20
50
100
200
500
1000

1

10

100

Elapsed time [h][µm/s2⋅s]

103

2
5
10
20
50
100
200
500
1000

Elapsed time [h][µm/s2⋅s]

102

P
1

Period [s]

0.1

SS

(f) OBS KOBS1.U

10

Love

[µm/s2⋅s]
103

102

SS
1

Elapsed time [h]Rayleigh

101

Frequency [mHz](e) Onshore seismometer KSRF.T

SS

10

Rayleigh

1

Elapsed time [h]

500
200
100
50
20
10
5
2
1
0.1

103

SS

Rayleigh[cm⋅s]
102

P

Frequency [mHz](c) Onshore seismometer KSRF.U

500
200
100
50
20
10
5
2
1
0.1

100

Period [s][hPa⋅s]
102

101

10

Elapsed time [h]Period [s]10Elapsed time [h]

Love

1

2
5
10
20
50
100
200
500
1000

TsunamiRayleigh(b) Tidegauge Hanasaki

TsunamiP

Frequency [mHz](a) PG KPG1

500
200
100
50
20
10
5
2
1
0.1

[µm/s2⋅s]
103

Figure S9. Comparison of theoretical arrival times of the seismic and tsunami waves based on PREM and the spectrograms.

1

(b) PG KPG1

100
50
20
10
5

5
10
20
50

Period [s]200Frequency [mHz]2

AK135 w/o water
PREM

500

100
200
500

2
0

1

2

3

4

Elapsed time [h]101102[hPa⋅s]Figure S10. Comparison of theoretical arrival times of the Rayleigh wave from different velocity structure models at KPG1. Red,
green, and blue lines denote the theoretical arrival times of the Rayleigh waves based on the AK135 model, AK135 model without
seawater layer, and the PREM model, respectively.

2

20

10
100

10−1

10−1

10−2

10−2

1/cosh(kH0)

10

6000m

(a)

10−3
0.01
0.1
1
10
100 1
Normalized Wavenumber, kH0

(b)

2

1000m
2000m

H 0=

0

1/cosh(kH0)1000 500

Period [s]200 100 50

5 10 20Frequency [mHz]10−3
50 100Figure S11. The factor of 1/cosh(kH0) as a function of (left) the wave number, k, normalized by the water depth H0 and (right) the
frequency.

3

−1
3600

7200

[Pa]

120
60
0
−60
−120

[Pa]

BPF 20-50s

120
60
0
−60
−120

CC(TL=60s)

0
−1
3600

7200

[Pa]

30
15
0
−15
−30

[Pa]

30
15
0
−15
−30

BPF 200-400s

KOBS1 ρwc0vz

BPF 200-400s

Correlation

CC(TL=60s)0−1
0

BPF 50-100s

Correlation

3600

7200

10800 14400 18000 21600

Elapsed time [s]

[Pa]
[Pa]
CC(TL=60s)

−1
3600

7200

30
15
0
−15
−30

10800 14400 18000 21600

Elapsed time [s]

(h)
30
15
0
−15
−30

KPG1 p

BPF 400-800s

KOBS1 ρwc0vz

BPF 400-800s

Correlation

1

BPF 10-20s

KOBS1 ρwc0vz

BPF 10-20s

Correlation

CC(TL=60s)0−10Elapsed time [s]KOBS1 ρwc0vz

0KPG1 p110800 14400 18000 21600

010800 14400 18000 21600

KPG1 p1

7200

BPF 50-100s

Elapsed time [s]

(g)

3600

KPG1 p

1

[Pa]

0

−1
0

Correlation

KOBS1 ρwc0vz

Correlation

CC(TL=60s)(e)
BPF 20-50s

240
120
0
−120
−240

0

10800 14400 18000 21600

KPG1 p1

Correlation

1

[Pa]

[Pa]
[Pa]

Correlation

240
120
0
−120
−240

BPF 6-10s

Elapsed time [s]

(d)
240
120
0
−120
−240

KOBS1 ρwc0vz

240
120
0
−120
−240

Correlation

0

0

Correlation

Correlation

CC(TL=60s)

BPF 6-10s

3600

7200

60
30
0
−30
−60
60
30
0
−30
−60

10800 14400 18000 21600

Elapsed time [s]

(f)

[Pa]

Correlation

1

240
120
0
−120
−240

(c)

KPG1 p[Pa]

BPF 4-6s

240
120
0
−120
−240

Correlation

KOBS1 ρwc0vz[Pa]

BPF 4-6s

[Pa]

(b)

KPG1 pCorrelation

[Pa]

240
120
0
−120
−240

Correlation

[Pa]

(a)
240
120
0
−120
−240

KPG1 p

BPF 100-200s

KOBS1 ρwc0vz

BPF 100-200s

Correlation

1

CC(TL=60s)

0
−1
0

3600

7200

10800 14400 18000 21600

Elapsed time [s]CC(TL=60s)

0
−1
0

3600

7200

10800 14400 18000 21600

Elapsed time [s]Figure S12. Comparison of the pressure and vertical velocity at period bands of (a) 4–6 s, (b) 6–10s, (c) 10–20
s, (d) 20–50 s, (e) 50–100 s, (f) 100–200 s, (g) 200–400 s, and (h) 400–800 s. See Figure 10 for the otherdescription.

1

Table S1. Summary of the records used in this study.
Latitude Longitude Altitude
StationInstrument
[°N]
[°E]
[m]

Sampling
ratea

observation# ofcomponent

KPG1

41.7040

144.4375-2218

Pressure
gauge

10 Hz

Pressure1

KPG2

42.2365

144.8454-2210

Pressure
gauge

10 Hz

Pressure

1

Hanasaki43.2833

145.5667

N/A

Tide gauge

1/30 Hz(30 s)

Sea-surface
height1

KSRF

42.9820144.4851

18

Onshoreseismometer

100 Hz

Velocityb

3

KOBS1

41.6870

144.3945-2329

Ocean-bottom
seismometer

100 HzAcceleration

3

SAMH

42.1330

142.9164-63

Tiltmeter

10 Hz

Tilt

2

a

All records are re-sampled to 1 Hz.
Velocity records are converted to accelerograms.

b

Table S2. Summary of the DART records used in this study.
LatitudeLongitude Altitude Approx. distance from
Station
[°N]
[°E]
[m]
the source [km]Sampling ratea

32412-17.9750-86.3920

-4325

2400

1/15 Hz, 1/60 Hz (1 min),or 1/900 Hz (15 min)a

32411

4.9242-90.6858

-3232

4900

1/15 Hz

51406-8.4925-125.0214

-4480

6100

1/15 Hz

51407

19.6368-156.5192

-4682

10300

1/15 Hz

21413

30.5460

152.1140

-5827

12300

1/15 Hza

Sampling rate depends on the time (see Figure S1 for details).

1

Table S3. Summary of the earthquakes analyzed in this study.aApprox.
Date
Time
Epicentral
Event nameMw
(yyyy/mm/dd) (hh:mm:ss UTC)
distance[km]

Latitude[°N]

Longitude Depth
[°E]
[km]

2010 Chile

2010/2/27

06:34:11.530

8.8

17000

-36.122-72.898

22.9

2006 Kuril

2006/11/15

11:14:13.570

8.3

890

46.592

153.266

10.0

2007 Kuril

2007/01/13

04:23:21.160

8.1

950

46.243154.524

10.0

2011 Off
Miyagi2011/03/09

02:45:20.330

7.3

390

38.435142.84232.0

2011 Tohoku

2011/03/11

05:46:24.120

9.0

420

38.297142.373

29.0

2012 Sumatra

2012/04/11

08:38:36.720

8.6

6720

2.327

93.06320.0

141.92935.0

2018
2018/09/05
18:07:59.150
6.6
230
42.686
HokkaidoJapanaSource information derived from the U.S. Geological Survey (USGS).

2