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TRANSCRIPT
manuscript submitted to Earth and Space Science
Ultra-broadband seismic and tsunami wave observation of high-sampling 1
ocean-bottom pressure gauge covering periods from seconds to hours 2
3
T. Kubota1, T. Saito1, N. Y. Chikasada1, and W. Suzuki1 4
1 National Research Institute for Earth Science and Disaster Resilience, Tsukuba, Ibaraki, Japan. 5
6
Corresponding author: Tatsuya Kubota ([email protected]) 7
8
Key points: 9
• High-sampling rate is important for pressure gauges to record seismic body waves, 10
Rayleigh waves and tsunamis and their dispersive feature 11
• Theoretical relation between pressure and vertical acceleration (p = ρwΗ0az) is valid for a 12
long time (~3h for the 2010 Chile earthquake) 13
• A relationship between pressure and vertical velocity (p = ρwc0vz) holds only at the first P 14
wave arrival, but not for later phases 15
16
manuscript submitted to Earth and Space Science
Abstract 17
Recent developments of ocean-bottom pressure gauges (PG) have enabled us to observe 18
various waves including seismic and tsunami waves covering periods of T ~100–103 s. To 19
investigate the quality for broadband observation, this study examined the broadband PG records 20
(sampling rate of 1 Hz) around Japan associated with the 2010 Chile earthquake. We identified 21
three distinct wave trains, attributed to seismic body waves, Rayleigh waves and tsunamis. Clear 22
dispersive features in the Rayleigh waves and tsunamis were explained by theories of elastic 23
waves and gravity waves. Quantitative comparison between pressure change and nearby 24
seismograms demonstrated the validity of the theoretical relation between pressure p and vertical 25
acceleration az for ~3h from the origin time. We also found a relationship between p and vertical 26
velocity vz holds only at the first P wave arrival, but not for later arrivals. Similar results were 27
confirmed for various earthquakes with different source-station distances and magnitudes, 28
suggesting the robustness of these relations. The results demonstrate that the high-sampling rate 29
(≥ 1 Hz) is necessary to observe seismic-wave dispersion and PG can record both seismic waves 30
and tsunamis with reasonable quality for waveform analyses, whereas conventional onshore and 31
offshore seismometers or tide gauges can observe either of seismic waves and tsunamis. 32
Utilizing the high-sampling PG in combination with the seismic and tsunami propagation theory 33
for estimating earthquake source process or analyzing wave propagation processes in the ocean, 34
will deepen our geophysical understanding of the solid-fluid coupled system in the earth and 35
contribute towards disaster mitigation. 36
37
Plain Language Summary 38
Recent developments of offshore ocean-bottom observation networks have enabled us to 39
use high-sampling (1 or more samples per second) seafloor pressure gauge (PG) data. This study 40
investigated PG records with broadband period range (seconds to hours) around Japan during the 41
2010 Chile earthquake. We identified a seismic P wave train arriving ~20–30 min after the focal 42
time. Another seismic wave train due to the surface Rayleigh wave during ~70–110 min and 43
tsunamis during ~24–72 h were also confirmed, which showed a dispersive feature; long-period 44
waves arrive earlier than short-period waves. The dispersion theories obtained from the elastic 45
and fluid dynamics thoroughly explained these features. We also compared wave amplitudes 46
between the PG and nearby ocean-bottom seismometer, and confirmed the validity of the 47
manuscript submitted to Earth and Space Science
relationship between pressure and vertical acceleration, and between pressure and vertical 48
velocity. This study demonstrates PG can record both seismic and tsunami signals clearly with 49
reasonable quality, while conventional seismometers or tide gauges can either. Ultra-broadband 50
observation of PG plays an important role in deepening our understanding of geophysical wave 51
propagation processes in the solid-fluid coupled system in the ocean, and enables delivery of 52
essential information for earthquake early warning and disaster mitigation. 53
54
manuscript submitted to Earth and Space Science
1 Introduction 55
Ocean-bottom pressure gauges (PGs) have recently been developed worldwide for 56
tsunami observations (e.g., Titov et al. 2005; Mungov et al. 2013; Tsushima & Ohta, 2014; 57
Rabinovich & Eblé 2015). Compared with tsunami observation using the conventional tide 58
gauges, PGs are advantageous as they are less affected by complex coastal site effects (e.g., 59
Kubota et al., 2018). Owing to this advantage, PGs have significantly contributed to our 60
understanding of tsunami generation and propagation processes derived from solid and fluid 61
dynamics (e.g., Satake et al., 2005; Saito et al., 2010; Inazu & Saito, 2013; Maeda et al., 2013; 62
Rabinovich et al., 2013; Allgeyer & Cummins, 2014; Watada et al., 2014; Lay et al., 2016; 63
Poupardin et al., 2018; Sandanbata et al., 2018; Kubota et al., 2020; and references therein). PGs 64
have further been utilized for observing much longer time-scale phenomena, such as infragravity 65
waves (e.g., Tonegawa et al., 2018) and oceanographic and geodetic phenomena (e.g., Baba et 66
al., 2006; Inazu et al., 2012; Wallace et al., 2016; Fukao et al., 2019). 67
In addition recent studies have reported that the PG observations can record other 68
geophysical waves, including ocean-acoustic and seismic waves (e.g., Nosov & Kolesov, 2007; 69
Levin & Nosov 2009; Bolshakova et al., 2011; Matsumoto et al., 2012; Webb & Nooner, 2016). 70
Dynamic pressure changes associated with the coseismic seafloor vertical accelerations, 71
recognized as a reaction force to the seafloor lifting up the water column, can also be observed 72
(e.g., Filoux, 1982; Nosov & Kolesov, 2007; An et al., 2017; Saito, 2019; Ito et al., 2020). This 73
indicates the ability for PGs to be utilized as vertical accelerometers for the sea-bottom motions 74
(An et al., 2017; Kubota et al., 2017). One strong advantage for using PGs in seismic wave 75
observation is that the signal never saturates, unlike high-sensitivity ocean-bottom seismometers. 76
The recent development of seafloor pressure observations with a sampling rate exceeding 1 Hz 77
(hereafter, high-sampling rate) in comparison with the low sampling rate of the conventional PG 78
(e.g., the DART system,1/15 Hz, e.g., see Rabinobich & Eble, 2015) has contributed extensively 79
to our understanding of ocean-acoustic waves and seismic waves. Given the PG observations of 80
various geophysical waves, PG could be utilized for ultra-broadband geophysical observation, 81
including both seismic and tsunami waves, which will be useful to extract earthquake source 82
information and the ocean’s ultra-broadband wave propagation process. However, PG records 83
have primarily been utilized for analyzing tsunamis, and not extensively for seismic wave 84
signals. Recent studies have discussed PG quality and performance in tsunami observation, 85
manuscript submitted to Earth and Space Science
which featured a period range of ~102–103 s (e.g., Saito et al., 2010; Tsushima & Ohta, 2014; 86
Rabinovich & Eblé 2015), whereas those in seismic waves have not been examined in detail. 87
In the present study, we examine the high-sampling PG record featuring a period range 88
of ~100–103 s, with particular focus on the seismic wave signals. Section 2 describes the PG and 89
additional datasets used and the method conducted for the analyses. Section 3 outlines the 90
results. Section 4 interprets the results by examining the origins of the identified PG signals 91
based on both the propagation theories of seismic waves and tsunamis and the comparison with 92
other nearby instruments. Section 5 compares the PG waveform with nearby ocean-bottom 93
seismometers (OBS) to discuss the quantitative relationship between pressure change and 94
seismic waves. Section 6 examines the quality of the PG observation by comparing the spectral 95
amplitudes and the background noises to discuss the performance and limitations of the high-96
sampling PG observation. Finally, Section 7 discusses future potential of the high-sampling PG 97
for furthering our geophysical understanding and for contribution to practical disaster mitigation. 98
The conclusion is summarized in Section 8. 99
100
2 Data and method 101
2.1 Data 102
We examined the records of onshore and offshore instruments in northern Japan 103
(Figure 1) during some moderate local to regional earthquakes and major regional to global 104
earthquakes. We here primarily focused on the 2010 Chile earthquake (Mw 8.8, Duptel et al., 105
2012) because of its large magnitude and ideal source-station distance (Figure 1, the other 106
examples are discussed in Section 5). The approximate distance along the great circle path from 107
Chile to Japan is 17,000 km (angular distance of 150°). Station information is listed in Table S1. 108
We use PGs at KPG1 and KPG2 (dark blue inverted triangles in Figure 1b) and three-component 109
acceleration records from a OBS at KOBS1 (red circle) of the Off-Kushiro cabled-observatory, 110
operated by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC, 111
Kawaguchi et al., 2000; Hirata et al., 2002). A coastal tide gauge at Hanasaki Port operated by 112
the Japan Meteorological Agency (JMA, blue diamond), and a Streckensen STS-2 onshore 113
broadband seismometer at Kushiro (KSRF, green triangle) and a nearshore tiltmeter at Samani 114
(SAMH, orange square) operated by National Research Institute for Earth Science and Disaster 115
Resilience [NIED] (Okada et al., 2004; NIED, 2019) were also utilized. The detailed 116
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specification of the instruments is described in Text S1. The velocity records from the onshore 117
seismometer are converted to accelerograms. The horizontal components of the original 118
seismograms and tilt records are along the north-south and east-west directions, which are 119
rotated to the radial (R) and transverse (T) directions along the great circle path (Figure 1). We 120
re-sampled all of these datasets with 1 Hz. Note that the instrument response at the onshore and 121
offshore seismometers were not removed. We also examine the PGs of the Deep-ocean 122
Assessment and Reporting of Tsunamis (DART) system deployed by the National Oceanic and 123
Atmospheric Administration (NOAA) in the Pacific Ocean (Titov et al., 2005; Mungov et al., 124
2013, black inverted triangles in Figure 1). Refer to Table S2 for information on the DART 125
stations. 126
127
128
Figure 1. Location map of this study. (a) The 2010 Chile earthquake (Duptel et al., 2012) 129
and great circle paths to the stations (yellow lines). DART tsunami stations are shown by 130
inverted triangles. (b) Enlarged view around northern Japan. Dark blue inverted triangles are 131
the PGs, the blue diamond is the coastal tide gauge, the green triangle is the onshore 132
broadband seismometer, the red circle is the OBS, and the orange rectangle is the nearshore 133
tiltmeter. 134
135
Figure 2a shows the time series after the Chile earthquake from the PGs (dark blue), 136
tide gauge (blue), onshore seismometer (green), OBS (red), and tiltmeter (orange). The 137
waveforms from DART records are shown in Figure S1. Tidal variations are observed by the 138
manuscript submitted to Earth and Space Science
PGs and tide gauge. We also confirm small tidal fluctuations in the tiltmeter. Figure 2b shows 139
the highpass filtered records with a cutoff period of 10800 s (3 h, ~0.1 mHz). Seismic waves are 140
clearly observed, except with the tide gauge. Figure 2c depicts the bandpass filtered records 141
(passbands of 30–10800 s, ~0.1–33 mHz). Tsunamis are clearly detected by the PGs and the 142
coastal tide gauge. A pressure change of Δp = 1 hPa corresponds to a sea-surface height change 143
of Δη = 1 cm (Δp = ρwg0Δη, ρw ~ 1.03 g/cm3: seawater density, g0 = 9.8 m/s2: gravitational 144
acceleration), therefore the tsunami amplitudes in PGs and tide gauges are comparable. Tsunami-145
related tilt changes are also recorded with the coastal tiltmeter (e.g., Kimura et al., 2013; Nishida 146
et al. 2019). The amplitudes of seismic waves and tsunamis in the PGs are almost comparable, 147
whereas tsunamis recorded in the tiltmeter (orange trace in Figure 2c) have much smaller 148
amplitudes than the seismic waves, by magnitudes of 102. 149
150
Figure 2. Time series at onshore and offshore sensors associated with the 2010 Chile 151
earthquake. (a) Raw data. (b) Highpass filtered data (cutoff period of 10800 s). The 152
waveform around the first P wave arrival is enlarged in Figure 2b’. (c) Bandpass filtered 153
data (30–10800 s). Note that the scales are different in each panel and U, R, and T denote 154
the vertical, radial and transverse component, respectively. 155
156
2.2 Spectrogram analysis 157
We examine the features of the high-sampling PG data based on the spectrogram 158
analysis which calculates the Fourier transform with a moving time window. In this study, we 159
applied Aki and Richards (1980)’s definition of the Fourier transform, as: 160
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161
𝑋(𝜔) = ∫ 𝑥(𝑡)𝑒!"#𝑑𝑡$!/&'$!/&
, (1) 162
163
where TL is the time window length of each bin and ω is the angular frequency (=2πf, f is 164
frequency). Here, the spectrogram 𝐴(𝑡, 𝜔) is defined as: 165
166
𝐴(𝑡, 𝜔) = -∫ 𝑥(𝑡 + 𝜏)𝑒!"(𝑑𝜏$!/&'$!/&
-. (2) 167
168
For the calculation of the spectrogram we adopt the Fourier amplitude spectra, but not power 169
spectra. In order to examine the spectral features of the seismic waves, we set the time window 170
length of each bin (TL) at 512 s and the time shift (ΔT) at 60 s (i.e., t = nΔT, n is an integer 171
number). We also investigate tsunamis based on the spectrogram with TL = 8192 s and ΔT = 172
1800 s. We further examined the spectral features with broadband period ranges including both 173
seismic waves and tsunamis, using TL = 1024 s with ΔT = 60 s. Prior to calculating the Fourier 174
transform of each bin, we removed the mean value and applied a Hanning taper (Blackman & 175
Turkey, 1958) with a length of 0.05TL to both edges of the window. 176
177
3 Results 178
The spectrograms for the PGs at KPG1 and KPG2 are shown in Figure 3. The 179
spectrograms during the first three hours from the origin time are illustrated in Figures 3a and 180
3b (TL = 512 s). The spectrogram confirms two distinct seismic wave trains during the seismic 181
wave arrival at ~20 min (periods of T ~3–20 s, ~50–300 mHz) and ~70 min (T ~10–200 s, ~5–182
100 mHz) (black and red arrows in Figures 3a and 3b, respectively). The second wave train at 183
~70 min displays a clear dispersive feature (i.e., long-wavelength waves arrive earlier than 184
short-wavelength waves). Figures 3c and 3d depict the spectrogram for 120 hours after the 185
origin time (TL = 8192 s). A tsunami-attributed wave train, showing a clear dispersion (T ~60–186
1000 s, ~1–20 mHz) can be confirmed in the spectrograms at ~24 h (blue arrow in Figures 3c 187
and 3d). The arrival timing and duration of seismic waves and tsunamis are significantly 188
different; hence, it is difficult to display both in one figure. In order to display both wave 189
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signals, we show the spectrograms using the logarithmic scale for the elapsed time in Figures 3e 190
and 3f (TL = 1024 s). 191
192
193
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Figure 3. Spectrograms for PGs at (a, c, e) KPG1 and (b, d, f) KPG2. (a, b) Spectrograms 194
for seismic waves. (c, d) Spectrograms for tsunamis. (e, f) Spectrograms for both seismic 195
and tsunami waves with a logarithmic scale on the horizontal axes. The highpass (Figures 196
3a, 3b, 3e, and 3f) and bandpass (Figures 3c and 3d) filtered waveforms are also shown. 197
Distinct wave train arrivals are denoted by the colored arrows (black: seismic P waves, red 198
Rayleigh waves, pink: Rayleigh waves from the opposite direction to the first Rayleigh 199
wave, blue: tsunamis). 200
201
We also calculate the spectrograms for other onshore and offshore instruments to 202
compare with the PG spectrograms (Figure 4, see Figures S2 and S3 for the spectrograms with 203
linear scale for the elapsed time). The seismic wave trains at ~20 min and ~70 min are detected 204
by the tiltmeter, onshore seismometer, and OBS, but not by the coastal tide gauge, which is 205
similar to the PG spectrogram. Another distinct wave train can also be confirmed at ~40–45 min 206
in the horizontal components of the seismometers (e.g., black arrow in Figure 4e). We also 207
identify an additional seismic wave train in the transverse component at the station KSRF at 208
~70 min (e.g., green arrow in Figure 4f), but this is not observed in the PG spectrogram. We 209
recognize small amplitude increases associated with tsunamis in the tiltmeter spectrogram at 210
~24 h (blue arrows in Figures 4a, 4b, and 4c), but the dispersive feature cannot be observed. 211
212
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213
Figure 4. Spectrograms for (a) tide gauge at Hanasaki, (b, c) tiltmeter at SAMH, (d, e, f) 214
onshore seismometer at KSRF, and (g, h, i) ocean-bottom seismometer at KOBS1. The 215
horizontal axes are displayed on a logarithmic scale. The Love wave train arrival is denoted 216
by the green arrow. See the caption in Figure 3 for the other description. 217
218
4 Interpretation on results of spectrogram analysis 219
4.1 Seismic wave trains 220
We interpret the wave trains in the PG and the other instruments identified by the 221
spectrogram analysis based on the theory of seismic waves and tsunamis. The onset timing of the 222
first waves in the pressure records (~20 min) is identical to the onshore seismometer (Figure 2). 223
We calculate the theoretical travel time of the core phases such as the PKP phase, the P wave 224
penetrating into the outer core, at KSRF using the global earth structure model AK135 (Kennett 225
et al., 1995, Figure S4). We obtain a travel time of PKP phase of 1193.74 s (~19.8 min), which 226
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accurately reproduced the observed arrival time (Figure S4). Thus, we conclude that this wave 227
train is the seismic body P-waves including PKP, and PKIKP, PKiKP, PKPab, and PKPbc 228
phases (e.g., Blom et al., 2015). Furthermore, the theoretical travel time of the SS phases, free-229
surface reflected S waves leaving a source downward, at KSRF, is 2570.55 s (~42.7 min, Figure 230
S4). This also corresponds with the onset of the waves confirmed in the horizontal seismograms 231
at ~40–45 min (Figure 4e), and also indicates the body wave. The direct S waves do not arrive at 232
the stations off Hokkaido because they do not propagate into the fluid outer core (e.g., Shearer, 233
2009). 234
The dispersion is detected in the second seismic wave train at ~70 min. To identify the 235
origin of this wave, we examine the particle motion of the seismometers at KSRF and KOBS1 236
(Figure 5). The pressure waveform at KPG1 is depicted in Figure 5 (red trace). The particle 237
motions in both OBS and onshore seismometer records demonstrate retrograde motion during the 238
arrival of this wave at 4200–4800 s (black arrow in Figure 5). This indicates a seismic surface 239
wave (Rayleigh wave). For the time window during 100–110 min (6000–6600 s) from the origin 240
time, we confirm another retrograde particle motion with the rotation direction opposite to the 241
first Rayleigh wave (gray arrow in Figure 5). A corresponding spectral amplitude increase is also 242
confirmed (pink arrow in Figure 3). These comparisons suggest another Rayleigh wave train 243
from the opposite direction to the first Rayleigh wave arrival, and delayed by ~30 min. It is also 244
worth pointing out that the Rayleigh wave arrivals at 5-10 mHz is slightly delayed compared to 245
those at 20-50 mHz (Figures 3a and 3b). This observation has an opposite sense to typical 246
understanding of surface dispersion that the longer-period waves arrive earlier (e.g., Shearer, 247
2009). A similar dispersion pattern also appears in the KOBS1 record, in particular the vertical 248
component (Figure 4g). 249
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250
Figure 5. Particle motions and displacement waveforms of (a) onshore seismometer at KSRF 251
and (b) OBS at KOBS1. Particle motions during 3600–4200 s, 4200–4800 s, 4800–6000 s, 6000–252
6600 s, and 6600–7200 s from the origin time are shown at the top panels. White and black stars 253
indicate the start and end locations of the particle motion in each period, respectively. Black and 254
gray arrows denote the rotation direction of the particle motion. Displacement waveforms are 255
shown in the bottom. Vertical displacement expected at KPG1, obtained by the time-double-256
integration of pressure (based on p = ρH0az) is shown by pink trace. Pressure waveform at KPG1 257
(dark red trace) and pressure expected from the vertical acceleration and the dynamic pressure 258
relation (black) are also shown. 259
260
Examining the particle motion of the seismometers suggests that the wave train 261
arriving to the PG at ~70 min is the Rayleigh wave. We further examine the dispersive feature of 262
the Rayleigh wave train recorded by the PGs based on the elastic wave propagation theory. We 263
calculate the theoretical group velocity dispersion of the Rayleigh wave based on the AK135 264
global structure model (Kennett et al., 1995) incorporating a seawater layer with a thickness of 265
4.5 km. The velocity structure and the dispersion relationship is depicted in Figure S5. Figure 6 266
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shows the comparison between the theoretical arrival time of the Rayleigh wave and the 267
spectrograms. The theoretical Rayleigh wave arrivals at each period are consistent with the 268
spectral amplitude peak in the spectrograms (red lines in Figure 6). In addition, the onset of the 269
delayed Rayleigh wave train is also explained (pink lines) when considering a path along the 270
opposite direction of the great circle path on the earth (~23,000 km). This suggests that the 271
delayed wave train is also due to the Rayleigh wave, but radiated to the opposite direction of the 272
first Rayleigh wave train. 273
274
275
Figure 6. Comparison of theoretical arrival times of the seismic and tsunami waves and the 276
spectrograms for (a) KPG1, (b) Tide gauge at Hanasaki, (c–e) onshore seismometer at KSRF, 277
and (f–h) OBS at KOBS1. Theoretical arrival times of P and SS waves (black), the surface waves 278
(red and pink: Rayleigh, green: Love waves), and tsunamis (blue). The pink line is the arrival of 279
the Rayleigh wave along the opposite direction of the great circle path on the earth. 280
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281
We also calculate the theoretical dispersion relationship using different structure 282
models to compare with the observed seismograms. We reveal that a model excluding the 283
seawater layer from the AK135 structure model (Figure S6) cannot explain the short-period 284
Rayleigh waves (>~50 mHz, Figure S7). We also compare the theoretical arrival time based on 285
the PREM global structure model (Dziewonski & Anderson, 1981), which includes a seawater 286
layer (Figure S8). The observed dispersive features in the Rayleigh waves are reasonably 287
reproduced by the PREM model, although the theoretical arrival time is slightly delayed by ~10–288
20 min in periods at ~10–50 s (~10–100 mHz, Figures S9 and S10). This result demonstrates that 289
the earth structure model is important for reproducing the dispersive feature, which suggests 290
Rayleigh wave dispersion recorded by the PG record can be useful to constrain the subseafloor 291
structure, as well as the ocean bottom seismometers. 292
In the particle motion of the onshore seismometer, a particle motion along the 293
transverse direction is also confirmed during 3600–4200 s (Figure 5). This indicates the Love 294
wave is also observed in the horizontal components of the seismometers. In order to examine the 295
Love wave train in the PGs, we calculate the group velocity and theoretical arrival times of the 296
Love wave (green line in Figure 6). The spectral amplitude increase due to the Love wave cannot 297
be confirmed in the KPG1 spectrograms, while the corresponding signal is recognized in the 298
transverse component of the seismometer at KSRF (green arrow in Figure 4f). This result is 299
expected given the transverse motion of Love waves (e.g., Shearer, 2009) while the pressure 300
changes due to the seafloor motion are primarily caused by the seafloor vertical accelerations 301
(e.g., Saito, 2019). 302
303
4.2 Tsunami wave trains 304
The wave train arriving at ~24 h which was attributed to a tsunami, also demonstrated 305
the dispersion. Based on the gravity wave theory (e.g., Pedlosky, 2013; Saito, 2019), the tsunami 306
phase velocity c and group velocity U are given as: 307
308
𝑐 = &)*$= "
*, (3) 309
310
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𝑈 = +&21 + &*,"
-./0(&*,")4, (4) 311
312
where k is wavenumber (=2π/λ; λ is wavelength), T is period, and ω is angular frequency. The 313
angular frequency ω follows the dispersion relation: 314
315
𝜔& = 𝑔3𝑘 tanh(𝑘𝐻3), (5) 316
317
where g0 is the gravitational acceleration and H0 is the water depth. We calculate the theoretical 318
arrival time of the tsunami energy using the group velocity at each period (blue line in Figure 319
S5b and S5c). The theoretical arrival time explains the spectral peak in the PG (Figure 6a). The 320
tide gauge spectrogram, meanwhile, did not show clear tsunami dispersion (Figure 6b). The main 321
cause for this is its low sampling rate (1/60 Hz). However, the complex coastal site effect 322
associated with local bathymetry might be another possible cause (e.g., Geist, 2018; Tanioka et 323
al., 2019). The dispersive feature was also not clearly recognized in the tiltmeter spectrogram 324
(Figures 4b and 4c). 325
We investigated the spectral feature of the PGs of the DART stations (Titov et al., 326
2005; Mungov et al. 2013, black inverted triangles in Figure 1). The information of the DART 327
stations is listed in Table S2, the waveforms are depicted in Figure S1 and the spectrogram of the 328
DART data is in Figure 7. The dispersive feature can also be confirmed, even in the spectrogram 329
of the DART station 32412, closest to the epicenter (~2,400 km from the source, Figure 7a), 330
although the temporal delay of the shorter period components is too large for other distant DART 331
stations (Figures 7b to 7e) and KPG stations (Figure 4). We can also recognize the dispersive 332
Rayleigh wave signals in these DART records. However, because the sampling rate of these 333
DART systems is low (≤ 1/15 Hz), it is difficult to recognize the dispersive feature from the 334
spectrograms. 335
336
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337
Figure 7. Spectrograms for the DART records in the Pacific Ocean. The horizontal axes are 338
displayed on a logarithmic scale. The time window length of each bin (TL) of 1024 s and the 339
time shift (ΔT) of 60 s were used in this calculation. Red and blue lines are the theoretical 340
arrival times of the Rayleigh waves and tsunamis. See the caption in Figures 3 for the other 341
description. 342
343
In the KPG1 and KPG2 spectrograms (Figures 3c and 3d), after the tsunami arrival 344
at 24 h, the amplitudes at periods of 50–500 s (20–200 mHz) increase between 24–36 h. 345
This feature is also confirmed in the DART spectrograms (Figure 7). We also verify 346
amplitude variations above 20 mHz following tsunami arrival in the onshore seismometer at 347
KSRF (Figures S3f and S3g) and nearshore tiltmeter at SAMH (Figure S3k and S3l). No 348
local earthquakes or aftershocks occurred during the tsunami arrivals, so this may suggest 349
that these shorter-period tsunamis are generated by long-period ones with the effects of 350
reflections and scattering by local bathymetry. 351
In addition, the delayed shorter-period tsunamis (T < ~100 s) at > ~30–40 h are not 352
recognized in the DART spectrograms. The static pressure change at seafloor 𝑝 due to sea-353
surface height change (i.e., tsunami) can be expressed as follows (e.g., Saito, 2019): 354
355
𝑝 = 4","5"67-0(*,")
, (6) 356
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357
where𝑘 is the wavenumber, 𝜌3 is the seawater density, 𝐻3 is the water depth, and 𝜂3 is the 358
sea-surface height change. Tsunami amplitude decay in the seafloor pressure gauge is 359
expressed by the factor 1/cosh(kH0). Figure S11a shows this decay factor as a function of 360
kH0 (also shown in Saito, 2019) and Figure S11b is the decay factor as a function of 361
frequency assuming a constant seawater depth, which is obtained from the tsunami 362
dispersion relation (equation (5)). At a depth of > 3,000 m, the ocean bottom pressure 363
change due to shorter-period tsunami has an amplitude less than ~0.5 times of the sea-364
surface tsunami, suggesting that the shorter period tsunamis do not reach the seafloor, and 365
thus are not recorded by the DART stations. 366
367
5 Quantitative relation between pressure and vertical seismogram 368
In section 4.1, we verify that the PG clearly observed the Rayleigh wave signal. The 369
current section compares the quantitative relationship between the pressure change and the 370
seafloor seismic vertical motion in detail. When the period is longer than the resonant period of 371
the acoustic fundamental mode, T0 = 4H0/c0 ~6 s (c0 ~ 1.5 km/s: the velocity of the ocean 372
acoustic waves, H0 ~2200 m: seawater depth in this region), the relation between the pressure 373
change p(t) and vertical acceleration az(t) can be expressed as (e.g., Filloux, 1982; Nosov & 374
Kolesov, 2007; An et al., 2017; Saito, 2019): 375
376
𝑝(𝑡) = 𝜌8𝐻3𝑎9(𝑡), (7) 377
378
where ρw is the seawater density. Hereafter, we refer to this relationship as dynamic relation. 379
Using the dynamic relation, we examine the quantitative relationship between the pressure 380
change at KPG1 and vertical acceleration at KOBS1. We focus on the period bands of 10–200 s 381
(5–100 mHz), in which Rayleigh waves are the most dominant signal in the records. The 382
amplitudes and phases of the pressure change (p) and pressure-converted acceleration (ρwH0az) 383
are very similar (Figure 8a). The vertical displacement expected at KPG1 obtained from equation 384
(7) is similar to the vertical displacement at KOBS1 as well (pink trace in Figure 5). We assess 385
the similarity of the pressure change and vertical acceleration based on the correlation 386
coefficients (CC), which is defined as: 387
manuscript submitted to Earth and Space Science
388
𝐶𝐶(𝑡) =∫ ;(#<()=#(#<()>($!/&'$!/&
?∫ ;(#<()&>($!/&'$!/&
∫ =#(#<()&>($!/&'$!/&
, (8) 389
390
where TL is the length of the time window. We use the two time window lengths for the CC 391
calculation; TL = 60 s (gray line in the middle panel in Figure 8a) and TL = 300 s (black line). We 392
obtain CC ~1 during the dominant Rayleigh wave arrival (~70 min) and also other seismic waves 393
(~1–3 h). Recent studies have reported the validity of equation (6) in the time domain in the 394
coseismic dataset of a few minutes from the origin time (An et al., 2017; Kubota et al., 2017). 395
Since the signal-to-noise (SN) ratios in the KPGs are so high, they had good agreement with 396
seismograms for a much longer duration than the results from previous studies. We further 397
compare the pressure change at KPG1 and the vertical acceleration at KOBS1 for other local to 398
regional moderate earthquakes and regional or global major earthquakes; the 2006 Kuril 399
earthquake (Mw 8.3, epicentral distance ~890 km, Figure 8b), the 2007 Kuril earthquake 400
(Mw8.1, 950 km, Figure 8c), the largest foreshock of the 2011 Tohoku earthquake (Mw 7.3, 401
~390 km, Figure 8d), the 2011 Tohoku earthquake (Mw 9.0, 420 km, Figure 8e), the 2012 402
Sumatra earthquake (Mw 8.6, ~6700 km, Figure 8f), and the 2018 Hokkaido Iburi Eastern 403
earthquake (Mw 6.6, 230 km, Figure 8g). We obtain similar results regardless of their very 404
different source-station distances and magnitude, which suggests the robustness of the observed 405
relation. 406
407
manuscript submitted to Earth and Space Science
408
Figure 8. Comparison of the pressure and vertical acceleration for (a) the 2010 Chile earthquake, 409
(b) the Kuril earthquake, (c) the 2007 Kuril earthquake, (d) the 2011 Off-Miyagi earthquake (e) 410
the 2011 Tohoku earthquake, (f) the 2012 Sumatra earthquake, and (g) the 2018 Hokkaido 411
earthquake. Magnitudes and epicentral distances are shown in each panel. Blue and red traces are 412
pressure change at KPG1 and vertical acceleration at KOBS1 converted to apparent pressure 413
change using the relation p=ρwH0az, respectively. Bandpass filter with passband of 10–200 s is 414
applied. Correlation coefficient between pressure and acceleration is also shown (gray: TL = 60 s, 415
black: TL = 300 s). Coherency and phase difference between two waveforms are shown in the 416
bottom two figures. In the phase difference, the region where the coherency is less than 0.9 is 417
masked. 418
419
We calculate the temporal variation of the coherency and phase difference between 420
two waveforms in the frequency domain. The procedure to calculate the coherency and phase 421
difference is summarized in Text S2. Our results confirm the high coherency (> ~0.9) and zero-422
phase-difference at periods of ~10–50 s (~20–100 mHz, Figures 8d and 8e) during the Rayleigh 423
wave arrival. We further assess the correlation between the pressure and vertical acceleration 424
manuscript submitted to Earth and Space Science
with different dominant periods (Figure 9). The correlation between the pressure and 425
acceleration is low in the shortest period bands (T < 10 s). This is due to the dynamic relation 426
being derived under the assumption that the wave period is longer than the resonant period of the 427
acoustic fundamental mode T0 = 4H0/c0 ~6 s. We also find that the correlation between the 428
pressure and acceleration is very high in periods of T ~10–50 s (Figures 9c and 9d), which infers 429
that the dynamic relation holds well at the period bands of ~10–50 s. Conversely, at longer 430
periods (T > 50 s) the correlation is not as high and unstable (Figures 9e to 9h). The low 431
correlation at the longer period is caused by the noises attributed to the seafloor vertical 432
displacement due to the long-period ambient oceanographic water waves. This is referred to as 433
the compliance noise (e.g., Crawford et al., 1991; 1998; Webb, 1998; Webb & Crawford, 1999; 434
An et al., 2020). However, we detected relatively high correlation during the Rayleigh wave 435
arrival (~70–100 min) even at the longer periods up to T ~400 s (~2.5 mHz, bottom panels in 436
Figures 9e to 9g). This indicates that the PGs can observe the Rayleigh wave signals up to the 437
periods of ~ 400s where the Rayleigh wave signals are larger than these compliance noises. 438
439
manuscript submitted to Earth and Space Science
440
Figure 9. Comparison of the pressure and vertical acceleration at period bands of (a) 4–6 s, (b) 441
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. 442
See Figure 8 for the other description. 443
444
In contrast to the dynamic pressure relation (equation (7)), a relationship between the 445
pressure change and vertical velocity vz(t) is proposed in several previous studies (e.g., Nosov et 446
al., 2007; Bolshakova et al., 2011; Matsumoto et al., 2012): 447
448
𝑝(𝑡) = 𝜌@𝑐3𝑣9(𝑡). (9) 449
450
manuscript submitted to Earth and Space Science
We also compare the pressure change at KPG1 and the vertical velocity at KOBS1, with periods 451
shorter than the acoustic resonant period T0 ~ 6 s. As a result, we can recognize high correlation 452
(~1) during the theoretical P wave arrival in this period band (Figure 10a). The comparisons 453
between pressure change at KPG1 and the vertical velocity at KOBS1 for other moderate to 454
major earthquakes confirm that this tendency is robust (Table S3, Figures 10b–10g). 455
If we carefully review the P-wave arrivals, we find that the amplitude of the pressure 456
change p(t) does not agree with ρwc0vz(t), although the phases agree with each other. The 457
amplitude ratio between p and ρwc0vz in the first arrival of the seismic waves differs for each 458
event (see Figure 10). This tendency is most evident in the 2011 Tohoku-Oki earthquake (Figure 459
10e). The local site effect due to the station location difference might be the possible cause. 460
However this seems implausible because the station difference between KPG1 and KOBS is only 461
~ 4 km, and any systematic relation in the amplitude ratio among these events cannot be 462
identified. 463
We also point out that the high correlation is confirmed only in the P-wave arrivals, but 464
neither in the entire wave trace nor in the later arrivals such as S waves (Figures 10b–10g).The 465
pressure p tends to be larger than ρwc0vz around the P arrivals. We should note that a relation 466
p=ρwc0vz can be derived assuming a P-wave propagation through fluid medium (e.g., Saito, 467
2019). However, the wavefields are more complicated than a P-wave propagation through fluid 468
medium, in particular, in the later wave arrivals where the waves are trapped by the reflections 469
between the sea surface and the seafloor. The previous results of numerical simulations suggest 470
this feature; the pressure changes at the seafloor due to trapped P-waves, or ocean-acoustic 471
waves exceed ρwc0vz (Bolshakova et al., 2011; Saito, 2017). Although Matsumoto et al. (2012) 472
compared the Fourier amplitudes of the seismograms and pressure records and found the 473
consistency with the relation p=ρwc0vz in the frequency domain, they discussed only the Fourier 474
amplitudes and not the phases. Our results show that the validity of the theoretical relationship 475
between the pressure and velocity is very limited, and holds only at the first arrival of the seismic 476
waves, not at the latter arrivals. 477
Notably, the time window at ~6300 s demonstrates relatively high correlation (Figure 478
10a, Figure S12a for more detail), which might be due to the P wave associated with the Mw 7.4 479
aftershock (GCMT) which occurred ~1.4 h after the Chile earthquake. We also examined the 480
manuscript submitted to Earth and Space Science
correlation between the pressure and vertical velocity with several different period bands (Figure 481
S12), although it seems the correlation is low in longer period ranges (T > T0 ~ 6 s). 482
483
484
Figure 10. Comparisons of the pressure and vertical velocity for the multiple events. Blue and 485
red traces are pressure change at KPG1 and vertical velocity at KOBS1 converted to apparent 486
pressure change using the relation p=ρwc0vz, respectively. Correlation coefficient between 487
pressure and vertical velocity is also shown (gray: TL = 60 s, black: TL = 20 s). Bandpass filter 488
with passband of 4–6 s is applied. Comparisons of the pressure change and vertical velocity at 489
the time window around the P wave arrival are also shown at the bottom. Theoretical arrival 490
times of the direct P and S phase are also shown. 491
492
6 Quantitative comparison in amplitudes of tsunami and seismic waves 493
We finally investigate the quantitative relationship between the spectral amplitude and 494
the background noise, using the 10-Hz sampled original data. The time window of 58.25 h (=0.1 495
× 222 s) is used for the Fourier transform. Figure 11 shows the spectral amplitudes of the onshore 496
manuscript submitted to Earth and Space Science
and offshore records for background (gray) and coseismic (black) signals. In order to 497
quantitatively compare the amplitudes between each record, the units are converted to apparent 498
pressure change ([Pa·s] = [(m-1· kg1·s-2)·s]). We assume that a sea height change of 1 cm equals 499
a pressure change of 1 hPa (102 Pa) to convert to apparent pressure change for the tide gauge at 500
Hanasaki. The vertical accelerations in the OBS at KOBS1 and onshore seismometer at KSRF 501
are converted to the apparent pressure change by using equation (6), with ρw = 1.03 g/cm3 and H0 502
= 2218 m (water depth at KOBS1). 503
PG spectra (Figure 11a) demonstrates an amplitude increase for the period range of 504
~60–5000 s, which are associated with tsunamis. Conversely, in the tide gauge spectra, the 505
significant increase in the tsunami amplitude is limited within the period range of ~2000–4000 s 506
(~0.25–0.5 mHz, Figure 11b), which is due to the coastal site effect (e.g., Geist, 2018; Tanioka et 507
al., 2019). The broadband amplitude increase in the PG spectra demonstrates that PGs are 508
capable of detecting the wider period range of tsunamis and are much less affected by the coastal 509
site effect than coastal tide gauges. 510
Our results further confirm that amplitude increases are related to the seismic waves in 511
the spectra of the PG and seismometers (Figures 11a, 11c, and 11d). Small spectral amplitude 512
increases at periods of ~5 s correspond to the body waves (marked by green arrow). In the 513
periods of ~10–50 s (~20–100 mHz), where the Rayleigh wave is dominant, we verify the signals 514
amplitude increases in the PG (orange text). This Rayleigh wave-related amplitude increase can 515
also be observed in the spectra of the OBS and onshore seismometer. The background noise level 516
in the frequency band of Rayleigh waves in the KPG1 is small compared to the KOBS1. This 517
suggests that the KPG1 can detect seismic Rayleigh wave signals with qualities similar to or 518
better than the KOBS1 during this event. One challenge in the seafloor seismic observation is 519
that the installation environment (i.e., we cannot fix the sensor to the ground) cannot be 520
controlled. This can easily be achieved in the onshore seismic observation. The lower noise level 521
in the PG in this frequency band may suggest that the PG will provide good supplementary 522
information for seafloor seismic observation. 523
524
manuscript submitted to Earth and Space Science
525
Figure 11. Fourier amplitude for (a) KPG1, (b) HANA, and vertical components for (c) 526
KOBS1 and (d) KSRF. The gray and black lines depict the power spectra with a time 527
window of ~2.5 days before and after the 2010 Chile earthquake, respectively. 528
Characteristic spectral bands of tsunami and seismic waves are shown by blue and red 529
arrows, respectively. Note that the instrumental responses are not removed. 530
531
7 Future applicability of the high-sampling PG 532
We summarize the key results of the spectral analyses in Figure 12. Five key findings 533
can be drawn from our analyses: 534
(1) High-sampling-rate (≥ 1 Hz) is necessary for PGs to detect the dispersive Rayleigh waves in 535
broadband periods (~10–400 s, ~2.5–100 mHz) and dispersive tsunamis (~50–1000 s, ~1–20 536
mHz) very clearly. 537
(2) Sampling rate of the typical DART system (~1/15 Hz) is not sufficient to fully analyze the 538
wave propagation processes of the seismic waves and tsunamis. 539
(3) Seismometers (≥ 100 Hz sampling) can record seismic wave signals clearly but do not record 540
manuscript submitted to Earth and Space Science
tsunamis, even when installed at the ocean floor. 541
(4) Coastal tiltmeters observe both seismic wave and tsunami signals but do not clearly record 542
the dispersion. 543
(5) Tide gauges cannot clearly detect tsunami dispersion or seismic waves. 544
545
546
Figure 12. Schematic illustration of geophysical phenomena in the ocean. The geophysical 547
phenomena which can be observed by the high-sampling-rate ocean bottom pressure gauges 548
and other instruments are shown by colored arrows. Note that the application of PG to 549
geodetic phenomena is shown by the dashed arrow, because this time-scale range is not 550
covered in this study. 551
552
In particular, finding (1) cannot be explicitly indicated if the sampling rate of the PG is 553
low (e.g., the third-generation DART system, 1/15 Hz, e.g., see Rabinobich & Eble, 2015). Our 554
result suggests that the high-sampling PG observation would be a good candidate for the 555
alternative and backup tools of seismic wave observations. This corresponds with An et al. 556
(2017) and Kubota et al. (2017) who also demonstrated that the seismic waves retrieved from the 557
PG records greatly contribute to accurately determining the centroid moment tensor solution of 558
moderate-sized offshore earthquakes. New, wide, and dense offshore observation networks 559
incorporating OBSs and PGs were recently installed in the deep-sea region (e.g., Kaneda et al., 560
2015; Kawaguchi et al., 2015; Rabinovich & Eblé 2015; Kanazawa et al., 2016; Mochizuki et al., 561
2016; Uehira et al., 2016; Howe et al., 2019). These new PG networks feature a higher sampling 562
manuscript submitted to Earth and Space Science
rate (≥ 1 Hz). Furthermore, the sampling rate of the next generation DART system (DART4G) 563
will possibly be higher than the third-generation system (e.g., Rabinobich & Eblé, 2015; An et 564
al., 2017; Angove et al., 2019). Utilizing the array of high-sampling PGs will enable us to 565
analyze the ultra-broadband geophysical wave propagation, including tsunamis and seismic 566
waves. Developments of the offshore PG networks will facilitate the analysis of ultra-broadband 567
pressure signals covering periods of 100–103s. PGs can further be employed for observing much 568
longer time-scale phenomena (e.g., Baba et al., 2006; Inazu et al., 2012; Wallace et al., 2016; 569
Tonegawa et al., 2018; Fukao et al., 2019, Figure 12). Using these new PG networks will create 570
new possibilities for understanding the geophysical wave propagation processes in the solid-fluid 571
coupled system and the generation processes of earthquakes and tsunamis. Several studies have 572
already begun to use an array of the high-sampling PGs for the broadband geophysical wave 573
propagation analyses (Fukao et al., 2018; 2019; Sandanbata et al., 2018; Mizutani & Yomogida, 574
2019). 575
Real-time earthquake early warnings are especially important for developing nations 576
exposed to a high tsunami risk (e.g., Mulia et al., 2019). For more reliable and early earthquake 577
warnings, it is desirable to install OBSs in these networks, despite the higher economic costs 578
associated with construction. Nevertheless, this present study demonstrates that seismic wave 579
signals can still be observed by high-sampling-rate PGs, even if they do not incorporate OBSs. 580
Recently, Nakamura et al. (2019) estimated earthquake body-wave magnitudes based on high-581
frequency seismic wave signals in PGs for real-time data analyses. The present study 582
demonstrates the significant potential of longer and wider period seismic signals in near-field 583
high-sampling PG records for real-time estimation of the moment magnitude and centroid 584
moment tensor (e.g., Kubota et al., 2017). The broadband observations of high-sampling PG are 585
significantly valuable for real-time earthquake warnings and disaster mitigation. 586
587
8 Conclusions 588
We examined the performance of PGs in a wide frequency range by investigating the 589
spectral features in the PG records in northern Japan associated with the 2010 Chile earthquake, 590
and comparing these with nearby onshore and offshore instruments. We calculated the 591
spectrograms and revealed that the PGs clearly detected the wave trains due to body waves, 592
Rayleigh waves, and tsunamis. The dispersive features were visibly recognized in the Rayleigh 593
manuscript submitted to Earth and Space Science
wave (periods covering ~10–400 s) and tsunami (~60–5000 s) wave trains, which were explained 594
by the propagation theories of seismic waves and tsunamis, respectively. The quantitative 595
comparison between the pressure change and the vertical acceleration demonstrated that the 596
dynamic relation holds for ~ 3h from the origin time, whereas, the relationship between the 597
pressure change and the vertical velocity at higher period range (< ~6 s) holds only at the first P 598
wave arrival. This validity was confirmed in time domain from the real observation. Similar 599
results seen for multiple earthquakes, regardless of their very different source-station distance 600
and earthquake magnitude, suggest the robustness of the observed relation. This study 601
demonstrated that high-sampling PGs can observe the broadband seismic wave and tsunami 602
signals. In particular, seismic wave signals can be detected with similar quality as the OBS. The 603
broadband geophysical wave observations of the high-sampling PG are important for furthering 604
our understanding of the geophysical analyses and developing practical disaster mitigations. 605
606
Acknowledgments, Samples, and Data 607
We thank the Editor Benoît Pirenne and two anonymous reviewers for their comments. We thank 608
Katsuhiko Shiomi for the information of the coastal tilt observation of NIED. This work was 609
financially supported by Sasakawa Scientific Research Grant (Grant Number 2019-2037) from 610
the Japan Science Society and JSPS KAKENHI Grant Number JP19K14818 from the Japan 611
Society for the Promotion of Science. Coastal tide gauge data is available at the 612
Intergovernmental Oceanographic Commission (IOC)’s website (http://www.ioc-613
sealevelmonitoring.org). PG and OBS data are acquired by JAMSTEC 614
(http://www.jamstec.go.jp/scdc/top_e.html). DART tsunami data is available at the NOAA’s 615
website (https://www.ngdc.noaa.gov/hazard/dart/2010chile_dart.html). Onshore broadband 616
seismometer is available at the NIED F-net (NIED, 2019, https://doi.org/10.17598/NIED.0005). 617
Tiltmeter record used in this study, which is operated by NIED, is available in 618
https://doi.org/10.17598/NIED.0018. We used TauP Toolkit (Crotwell et al., 1999) version 2.4.5 619
(https://www.seis.sc.edu/taup/) to calculate the theoretical arrival times. Figures in this paper was 620
prepared using Generic Mapping Tools (GMT) software version 6.0.0 (Wessel et al., 2019). We 621
used Editage (www.editage.com) for English language editing. 622
manuscript submitted to Earth and Space Science
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1
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 the procedure employed to calculate the coherency and phase spectra. Figure S1 shows the time series 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 the seismic 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 the comparison between the spectrograms and theoretical arrival times. Figure S10 compares theoretical arrival times of the Rayleigh waves between different structure models. Figure S11 shows tsunami amplitude decay in the seafloor pressure gauge. Comparison between the pressure change and vertical velocity at varying period bands are shown in Figure S12. Tables S1 and 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.
2
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 are converted 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 Institute for 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 the Fourier 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 ±256 s, in every 30 s step. Using the cross spectra SXY(ω) and the power spectra SXX(ω) and SXY(ω), the coherency 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: /!"(#) = /!(#) − /"(#) = tan*+ 5,-./0[⟨!(')⟩]50.6[⟨!(')⟩] 6 − tan
*+ 5,-./0[⟨"(')⟩]50.6[⟨"(')⟩] 6. (S3)
1
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).
0 12 24 36 48 60 72 84 96 108 120 132 144
Elapsed time from the origin time [h]
(a) No filter
21413 100hPa
51407 100hPa
51406 100hPa
32411 100hPa
32412 100hPa
0 3600 7200 10800 14400 18000 21600
Elapsed time from the origin time [s]
(b) Highpass 10800s
21413 5hPa
51407 5hPa
51406 5hPa
32411 5hPa1min15s
32412 5hPa
0 12 24 36 48 60 72 84 96 108 120
Elapsed time from the origin time [h]
(c) Bandpass 30s-10800s
21413 10hPa
51407 10hPa
51406 10hPa
32411 10hPa15min
32412 10hPa
1
Figure S2. Spectrograms for seismic waves. (a) Theoretical arrival time of seismic waves. (b–l) Spectrograms for onshore and offshore instruments. See the caption in Figure 3 for a description of each panel.
2
51020
50100200
500F
requency
[m
Hz]
0 1 2 3
Elapsed time [h]
(a)
P SS R
ayl
eig
hL
ove
0 1 2 3
Elapsed time [h]
(b) PG KPG1
101 102
[hPa!s]
0 1 2 3
Elapsed time [h]
(c) PG KPG2
101 102
[hPa!s]
0 1 2 3
Elapsed time [h]
(d) Tidegauge Hanasaki
102 103
[cm!s]
2
51020
50100200
500
Period [s]
2
51020
50100200
500
Fre
quency
[m
Hz]
0 1 2 3
Elapsed time [h]
(e) Onshore seismometer KSRF.U
102
[µm/s2!s]
0 1 2 3
Elapsed time [h]
(f) Onshore seismometer KSRF.R
102 103
[µm/s2!s]
0 1 2 3
Elapsed time [h]
(g) Onshore seismometer KSRF.T
102 103
[µm/s2!s]
0 1 2 3
Elapsed time [h]
(k) Tiltmeter SAMH.T
101 102
[µrad!s]
2
51020
50100200
500
Period [s]
2
51020
50100200
500
Fre
quency
[m
Hz]
0 1 2 3
Elapsed time [h]
(h) OBS KOBS1.U
103
[µm/s2!s]
0 1 2 3
Elapsed time [h]
(i) OBS KOBS1.R
103
[µm/s2!s]
0 1 2 3
Elapsed time [h]
(j) OBS KOBS1.T
103
[µm/s2!s]
0 1 2 3
Elapsed time [h]
(l) Tiltmeter SAMH.T
101 102
[µrad!s]
2
51020
50100200
500
Period [s]
2
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.
0.20.5
125
102050
100200500
Fre
quency
[m
Hz]
0 24 48 72 96 120 144
Elapsed time [h]
(a)
Tsu
na
mi
0 24 48 72 96 120 144
Elapsed time [h]
(b) PG KPG1
101 102
[hPa!s]
0 24 48 72 96 120 144
Elapsed time [h]
(c) PG KPG2
101 102
[hPa!s]
0 24 48 72 96 120 144
Elapsed time [h]
(d) Tidegauge Hanasaki
102 103
[cm!s]
25102050100200500100020005000
Period [s]
0.20.5
125
102050
100200500
Fre
quency
[m
Hz]
0 24 48 72 96 120 144
Elapsed time [h]
(e) Onshore seismometer KSRF.U
101 102
[µm/s2!s]
0 24 48 72 96 120 144
Elapsed time [h]
(f) Onshore seismometer KSRF.R
100 101 102
[µm/s2!s]
0 24 48 72 96 120 144
Elapsed time [h]
(g) Onshore seismometer KSRF.T
100 101 102
[µm/s2!s]
0 24 48 72 96 120 144
Elapsed time [h]
(k) Tiltmeter SAMH.R
100 101 102
[µrad!s]
25102050100200500100020005000
Period [s]
0.20.5
125
102050
100200500
Fre
quency
[m
Hz]
0 24 48 72 96 120 144
Elapsed time [h]
(h) OBS KOBS1.U
102 103 104
[µm/s2!s]
0 24 48 72 96 120 144
Elapsed time [h]
(i) OBS KOBS1.R
102 103 104
[µm/s2!s]
0 24 48 72 96 120 144
Elapsed time [h]
(j) OBS KOBS1.T
102 103 104
[µm/s2!s]
0 24 48 72 96 120 144
Elapsed time [h]
(l) Tiltmeter SAMH.T
100 101 102
[µrad!s]
25102050100200500100020005000
Period [s]
3
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.
!100
0
100
200
300
[cm
/s]
PK
IKP
PK
PP
KiK
P
PK
P
U
R
T
KSRF (Raw)
!100
0
100
200
300
[cm
/s]
1150 1200 1250 1300
Elapsed time [s]
PK
IKP
PK
PP
KiK
P
PK
P
U
R
T
KSRF (BPF 4-6s)
!200
0
200
400
600
SS
U
R
T
KSRF (Raw)
!200
0
200
400
600
2400 2500 2600 2700 2800 2900 3000 3100 3200
Elapsed time [s]
SS
U
R
T
KSRF (BPF 20-200s)
4
Figure S5. (a) Velocity structure model based on AK135. (b) The phase velocity (dashed lines) and group velocity (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 is the arrival of the Rayleigh wave along the opposite direction of the great circle path on the earth.
0
20
40
60
80
100
120
140
160
180
200
Depth
[km
]
0 2 4 6 8 10
Vel [km/s], ! [g/cm3]
PS!
(a) AK135
10!3
10!2
10!1
100
101V
elo
city
[km
/s]
0.2 0.5 1 2 5 10 20 50 100200 500
Frequency [mHz]
25102050100200500100020005000
Love
Rayleigh
TsunamiPhase velocityGroup velocity
(b)
1
2
5
10
20
50
100
200
500
Fre
quency
[m
Hz]
0.1 1 10 100
Elapsed time [h]
2
5
10
20
50
100
200
500
1000
Period [s]
(c)
P SS
Ra
yle
igh
Lo
ve
Tsu
na
mi
5
Figure S6. (a) Velocity structure model based on AK135 without seawater layer. (b) The phase velocity (dashed lines) and group velocity (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 is the arrival of the Rayleigh wave along the opposite direction of the great circle path on the earth.
0
20
40
60
80
100
120
140
160
180
200
Depth
[km
]
0 2 4 6 8 10
Vel [km/s], ! [g/cm3]
PS!
(a) AK135 without seawater
10!3
10!2
10!1
100
101V
elo
city
[km
/s]
0.2 0.5 1 2 5 10 20 50 100200 500
Frequency [mHz]
25102050100200500100020005000
Love
Rayleigh
Phase velocityGroup velocity
(b)
1
2
5
10
20
50
100
200
500
Fre
quency
[m
Hz]
0.1 1 10 100
Elapsed time [h]
2
5
10
20
50
100
200
500
1000
Period [s]
(c)
P SS
Ra
yle
igh
Lo
ve
6
Figure S7. Comparison of theoretical arrival times of the seismic and tsunami waves based on the AK135 without seawater layer and the spectrograms.
12
51020
50100200
500
Fre
quency
[m
Hz]
0.1 1 10 100
Elapsed time [h]
P
Rayl
eig
h
Tsu
nam
i
(a) PG KPG1
101 102
[hPa!s]
0.1 1 10 100
Elapsed time [h]
Tsu
nam
i
(b) Tidegauge Hanasaki
102 103
[cm!s]
2
51020
50100200
5001000
Period [s]
12
51020
50100200
500
Fre
quency
[m
Hz]
0.1 1 10 100
Elapsed time [h]
P
Rayl
eig
h(c) Onshore seismometer KSRF.U
101 102 103
[µm/s2!s]
0.1 1 10 100
Elapsed time [h]
SS
Rayl
eig
h(d) Onshore seismometer KSRF.R
102 103
[µm/s2!s]
0.1 1 10 100
Elapsed time [h]
SS
Love
(e) Onshore seismometer KSRF.T
102 103
[µm/s2!s]
2
51020
50100200
5001000
Period [s]
12
51020
50100200
500
Fre
quency
[m
Hz]
0.1 1 10 100
Elapsed time [h]
P
Rayl
eig
h(f) OBS KOBS1.U
103
[µm/s2!s]
0.1 1 10 100
Elapsed time [h]
SS
Rayl
eig
h(g) OBS KOBS1.R
103
[µm/s2!s]
0.1 1 10 100
Elapsed time [h]
SS
Love
(h) OBS KOBS1.T
103
[µm/s2!s]
2
51020
50100200
5001000
Period [s]
7
Figure S8. (a) Velocity structure model based on the PREM model. (b) The phase velocity (dashed lines) and group velocity (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 depicts the arrival of the Rayleigh wave along the opposite direction of the great circle path on the earth.
0
20
40
60
80
100
120
140
160
180
200
Depth
[km
]
0 2 4 6 8 10
Vel [km/s], ! [g/cm3]
PS!
(a) PREM
10!3
10!2
10!1
100
101V
elo
city
[km
/s]
0.2 0.5 1 2 5 10 20 50 100200 500
Frequency [mHz]
25102050100200500100020005000
Love
Rayleigh
Phase velocityGroup velocity
(b)
1
2
5
10
20
50
100
200
500
Fre
quency
[m
Hz]
0.1 1 10 100
Elapsed time [h]
2
5
10
20
50
100
200
500
1000
Period [s]
(c)
P SS
Ra
yle
igh
Lo
ve
1
Figure S9. Comparison of theoretical arrival times of the seismic and tsunami waves based on PREM and the spectrograms.
12
51020
50100200
500
Fre
quency
[m
Hz]
0.1 1 10 100
Elapsed time [h]
P
Rayl
eig
h
Tsu
nam
i
(a) PG KPG1
101 102
[hPa!s]
0.1 1 10 100
Elapsed time [h]
Tsu
nam
i
(b) Tidegauge Hanasaki
102 103
[cm!s]
2
51020
50100200
5001000
Period [s]
12
51020
50100200
500
Fre
quency
[m
Hz]
0.1 1 10 100
Elapsed time [h]
P
Rayl
eig
h(c) Onshore seismometer KSRF.U
101 102 103
[µm/s2!s]
0.1 1 10 100
Elapsed time [h]
SS
Rayl
eig
h(d) Onshore seismometer KSRF.R
102 103
[µm/s2!s]
0.1 1 10 100
Elapsed time [h]
SS
Love
(e) Onshore seismometer KSRF.T
102 103
[µm/s2!s]
2
51020
50100200
5001000
Period [s]
12
51020
50100200
500
Fre
quency
[m
Hz]
0.1 1 10 100
Elapsed time [h]
P
Rayl
eig
h(f) OBS KOBS1.U
103
[µm/s2!s]
0.1 1 10 100
Elapsed time [h]
SS
Rayl
eig
h(g) OBS KOBS1.R
103
[µm/s2!s]
0.1 1 10 100
Elapsed time [h]
SS
Love
(h) OBS KOBS1.T
103
[µm/s2!s]
2
51020
50100200
5001000
Period [s]
2
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
5
10
20
50
100
200
500
Fre
quency
[m
Hz]
0 1 2 3 4
Elapsed time [h]
2
5
10
20
50
100
200
500
Period [s]
AK
135
w/o
wate
r
PR
EM
(b) PG KPG1
101 102
[hPa!s]
3
Figure 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.
10!3
10!2
10!1
100
1/c
osh
(kH
0)
0.01 0.1 1 10 100Normalized Wavenumber, kH0
(a)10!3
10!2
10!1
100
1/c
osh
(kH
0)
1 2 5 10 20 50 100Frequency [mHz]
1020501002005001000Period [s]
H0 =
1000m
2000m
6000m
(b)
1
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 other description.
(a)
!240
!120
0
120
240
[Pa
]
BPF 4-6sKPG1 p
!240
!120
0
120
240
[Pa
]
BPF 4-6sKOBS1 !wc0vz
!1
0
1
Co
rre
latio
n
0 3600 7200 10800 14400 18000 21600
Elapsed time [s]
CC(TL=60s)Correlation
(b)
!240
!120
0
120
240
[Pa
]
BPF 6-10sKPG1 p
!240
!120
0
120
240
[Pa
]
BPF 6-10sKOBS1 !wc0vz
!1
0
1
Co
rre
latio
n
0 3600 7200 10800 14400 18000 21600
Elapsed time [s]
CC(TL=60s)Correlation
(c)
!240
!120
0
120
240
[Pa
]
BPF 10-20sKPG1 p
!240
!120
0
120
240
[Pa
]
BPF 10-20sKOBS1 !wc0vz
!1
0
1
Co
rre
latio
n
0 3600 7200 10800 14400 18000 21600
Elapsed time [s]
CC(TL=60s)Correlation
(d)
!240
!120
0
120
240
[Pa
]
BPF 20-50sKPG1 p
!240
!120
0
120
240
[Pa
]
BPF 20-50sKOBS1 !wc0vz
!1
0
1
Co
rre
latio
n
0 3600 7200 10800 14400 18000 21600
Elapsed time [s]
CC(TL=60s)Correlation
(e)
!120
!60
0
60
120
[Pa
]
BPF 50-100sKPG1 p
!120
!60
0
60
120
[Pa
]
BPF 50-100sKOBS1 !wc0vz
!1
0
1
Co
rre
latio
n
0 3600 7200 10800 14400 18000 21600
Elapsed time [s]
CC(TL=60s)Correlation
(f)
!60
!30
0
30
60
[Pa
]
BPF 100-200sKPG1 p
!60
!30
0
30
60
[Pa
]
BPF 100-200sKOBS1 !wc0vz
!1
0
1
Co
rre
latio
n0 3600 7200 10800 14400 18000 21600
Elapsed time [s]
CC(TL=60s)Correlation
(g)
!30
!15
0
15
30
[Pa
]
BPF 200-400sKPG1 p
!30
!15
0
15
30
[Pa
]
BPF 200-400sKOBS1 !wc0vz
!1
0
1
Co
rre
latio
n
0 3600 7200 10800 14400 18000 21600
Elapsed time [s]
CC(TL=60s)Correlation
(h)
!30
!15
0
15
30
[Pa
]
BPF 400-800sKPG1 p
!30
!15
0
15
30
[Pa
]
BPF 400-800sKOBS1 !wc0vz
!1
0
1
Co
rre
latio
n
0 3600 7200 10800 14400 18000 21600
Elapsed time [s]
CC(TL=60s)Correlation
1
Table S1. Summary of the records used in this study.
Station Latitude [°N]
Longitude [°E]
Altitude [m] Instrument Sampling
ratea observation # of component
KPG1 41.7040 144.4375 -2218 Pressure gauge 10 Hz Pressure 1
KPG2 42.2365 144.8454 -2210 Pressure gauge 10 Hz Pressure 1
Hanasaki 43.2833 145.5667 N/A Tide gauge 1/30 Hz (30 s)
Sea-surface height 1
KSRF 42.9820 144.4851 18 Onshore seismometer 100 Hz Velocityb 3
KOBS1 41.6870 144.3945 -2329 Ocean-bottom seismometer 100 Hz Acceleration 3
SAMH 42.1330 142.9164 -63 Tiltmeter 10 Hz Tilt 2
aAll records are re-sampled to 1 Hz. bVelocity records are converted to accelerograms. Table S2. Summary of the DART records used in this study.
Station Latitude [°N]
Longitude [°E]
Altitude [m]
Approx. distance from 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 Hz
aSampling rate depends on the time (see Figure S1 for details).
2
Table S3. Summary of the earthquakes analyzed in this study.a
Event name Date (yyyy/mm/dd)
Time (hh:mm:ss UTC) Mw
Approx. Epicentral distance
[km]
Latitude [°N]
Longitude [°E]
Depth [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 46.243 154.524 10.0
2011 Off Miyagi 2011/03/09 02:45:20.330 7.3 390 38.435 142.842 32.0
2011 Tohoku 2011/03/11 05:46:24.120 9.0 420 38.297 142.373 29.0
2012 Sumatra 2012/04/11 08:38:36.720 8.6 6720 2.327 93.063 20.0
2018 Hokkaido
Japan
2018/09/05 18:07:59.150 6.6 230 42.686 141.929 35.0
aSource information derived from the U.S. Geological Survey (USGS).