manuscript submitted to Geophysical Research Letters

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Extracting near-field seismograms from ocean-bottom pressure gauge inside the focal
area: application to the 2011 Mw 9.1 Tohoku-Oki earthquake

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T. Kubota1, T. Saito1, H. Tsushima2, R. Hino3, Y. Ohta3, S. Suzuki3, D. Inazu4561

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

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Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Japan

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Graduate School of Science, Tohoku University, Sendai, Japan

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Department of Marine Resources and Energy, Tokyo University of Marine Science andTechnology, Tokyo, Japan

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

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Key Points:•

We develop a method to extract low-frequency ground motion including permanent
deformation from ocean-bottom pressure gauge (OBP) data•

We obtain the seismograms inside the focal area of the 2011 Tohoku-Oki EQ, whichsuggest two dominant energy releases around the hypocenter•

High-frequency near-field OBP signals should be utilized more widely for geophysicalresearch as well as real-time tsunami forecasting

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manuscript submitted to Geophysical Research Letters

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Abstract

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Recent studies have shown that ocean-bottom pressure gauges (OBPs) can record
seismic waves in addition to tsunamis and seafloor permanent displacements, even if they are
installed inside the focal area where the signals are extremely large. We developed a method to
extract dynamic ground motion waveforms from near-field OBP data consisting of a complex
mixture of various signals, based on an inversion analysis along with a theory of tsunami
generation. We applied this method to the OBP data of the 2011 Tohoku-Oki earthquake. We
successfully extracted the low-frequency vertical seismograms inside the focal area (f < ~0.05
Hz), although those of the Mw ~9 megathrust earthquake had never previously been reported.
The seismograms suggested two dominant energy releases around the hypocenter. The seismic
wave signals recorded by the near-field OBP will be important not only to reveal earthquake
ruptures and tsunami generation processes but also to conduct real-time tsunami forecasts.

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Plain Language Summary
During tsunami generation, different types of waves such as ground motions, ocean
acoustic waves, and tsunamis coexist inside the focal area, forming complicated wavefields andpressure changes at the sea bottom. This study developed a method to appropriately decompose
the complicated ocean-bottom pressure gauge (OBP) waveforms into ground motion and tsunami
signals. Our method was applied to the near-field OBP data of the 2011 Tohoku-Oki earthquake
to extract the near-field seismic motion waveform which had never been reported previously.
The waveform suggested a complex earthquake rupture process along the plate boundary, inwhich the rupture happened twice near the hypocenter. The seismic wave signals recorded by thenear-field OBP will be important not only to reveal the processes of the earthquake rupture andtsunami generation but also to issue tsunami alarms.

manuscript submitted to Geophysical Research Letters

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1 Introduction48

Seismic observations are very important to estimate earthquake source parameters andphysical properties around the fault and to understand how an earthquake plays a role ingeodynamic frameworks. Far-field seismograms have been used for earthquake kinematic
rupture modeling (e.g., Lay et al., 2011). Near-field seismograms are also essential to resolve therupture kinematics, because far-field seismograms are affected by path effects such asattenuation and scattering and resolve very little about the short-wavelength information on thesource (e.g., Aki & Richards, 2002). Near-fault seismograms are also important for earthquake
rupture dynamics. Stress drop, defined as shear stress reduction on the fault due to an earthquake,and slip weakening distance Dc, the slip amount needed to reach residual friction, are often
inferred from near-field seismograms (e.g., Ide & Takeo, 1997; Mikumo et al., 2003; Fukuyama& Mikumo, 2007; Fukuyama & Suzuki, 2016; Kaneko et al., 2017).

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In the 2011 Tohoku-Oki earthquake (Mw 9.1, Global Centroid Moment Tensor[GCMT]; hereafter, the mainshock), various near-field observations were recorded, which were
not obtained for past megathrust earthquakes (e.g., Hino, 2015; Lay, 2018; Wang et al., 2018;
Kodaira et al., 2020). Seafloor geodetic observations (e.g., Fujiwara et al., 2011; 2017; Ito et al.,2011; Kido et al., 2011; Sato et al., 2011) have particularly played an important role in revealing
the mainshock rupture process and tsunami generation (e.g., Iinuma et al., 2012). However, nearfield seismograms associated with the mainshock with a reasonable quality have not beenreported. The high-sensitivity ocean-bottom seismometers (OBSs) installed off Miyagi (Suzuki
et al., 2012) went off-scale and whole seismograms were not recorded. The strong motion
accelerometers installed outside of the main rupture area (open triangles in Figure 1a) were
dynamically rotated by the strong shaking (Nakamura & Hayashimoto, 2019). Although somenear-source seismograms during past megathrust earthquakes have been recorded by onshore
seismometers and GNSS, such as in the 2010 and 2014 Chile earthquakes (Vigny et al., 2011;
Madariaga et al., 2019), the stations were located outside of the main rupture regions, where thepermanent displacement was small.

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Figure 1. (a) Location map of this study. Inverted triangles denote OBPs (green: Tohoku
University, orange: ERI). Open triangles denote OBS stations by ERI. Black triangles are the Fnet onshore seismometers. The white star is the mainshock epicenter (Suzuki et al., 2012) and the
red CMT solution is taken from GCMT. Yellow contours denote the distributions of the initialtsunami height (Saito et al., 2011, 2 m interval). Gray dots and rectangular areas indicate thelocations of the unit sources and the analytical area of the inversion analysis. The configurationof the unit sources in the space and time domains is schematically shown in the inset. (b)Pressure waveforms at GJT3. Gray, red, and blue traces are the de-tided, bandpass filtered (0.01–
0.05 Hz), and lowpass filtered (0.01 Hz) waveforms, respectively. (c) Spectral amplitude before
and after the mainshock (black and green, respectively), calculated based on Aki and Richards’(2002) definition. Passbands of the filters in Figure 1b are marked by colored rectangles.

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During the mainshock, some ocean-bottom pressure gauges (OBPs) were installedaround the main rupture area (inverted triangles in Figure 1). The deep-ocean OBPs often
observe tsunamis, which have dominant frequencies lower than ~0.01 Hz. Such tsunami data
have been widely utilized, because tsunamis constrain the spatial extent of the seafloor verticaldeformation (tsunami source) better than seismic waves (Kubota et al., 2018). This is attributed
to tsunamis' much slower propagation velocity and there being a less significant tradeoff between
the source dimension and rupture propagation velocity across the fault. Previous studies used themainshock OBP data to investigate the mainshock tsunami generation process (e.g., Saito et al.,2011 (yellow contour lines in Figure 1a); Maeda et al., 2011; Tsushima et al., 2011; Gusman etmanuscript submitted to Geophysical Research Letters

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al., 2012; Satake et al., 2013; Baba et al., 2015; Hossen et al., 2015; Dettmer et al., 2016;
Yamazaki et al., 2018). However, they did not utilize the OBPs installed inside the main tsunami
source region where the seafloor uplift was extremely large (e.g., GJT3, Figure 1). This is mainly
because there have been few near-field observation examples (e.g., Mikada et al., 2006) and themethod to utilize the permanent deformation for tsunami modeling was not established. In thisdecade, the well-established method to utilize the permanent deformation for tsunami modeling
was proposed (Tsushima et al., 2012) and many finite fault models using the OBPs inside thetsunami source have been obtained (e.g., Kubota, Hino et al., 2017; Nemoto et al., 2019).
Our understanding of the ocean-bottom pressure change inside the focal area during
tsunami generation has also progressed. The three-dimensional theory based on the tsunami
generation mechanics showed the initial sea-surface distribution is not identical to the seafloor
elevation (e.g., Kajiura, 1963; Saito & Furumura, 2009). Based on the three-dimensional theory,the pressure change inside the focal area includes a component related to vertically accelerating
seafloor (Filloux, 1982; Saito, 2013; 2017; 2019; An et al., 2017). This component was
confirmed by the actual observations and numerical simulations (e.g., Filloux, 1982; Webb,
1998; Nosov and Kolesov, 2007; Matsumoto et al., 2012; 2017; Saito & Tsushima, 2016; An etal., 2017; Kubota, Saito et al., 2017; Saito, 2019; Ito et al., 2020; Mizutani et al., 2020; Saito &Kubota, 2020; Kubota et al., 2020). Additionally, the pressure change field includes the highfrequency ocean-acoustic waves related to the seawater elasticity (Nozov & Kolesov, 2007, Saito& Tsushima, 2016; Lotto et al., 2018). Recently the attempts to numerically simulate thiscomplex pressure change field have started (e.g., Lotto et al., 2015; Saito et al., 2019; Abrahams
et al., 2020; Maeda et al., 2020). However, although the method to forwardly simulate more
realistic OBP signals inside the focal has been established, it has also been reported that a simple
bandpass filter cannot extract the seismic waves from the complex pressure change field (Saito &Tsushima, 2016). A method to appropriately decompose the OBP signal to the seismic andtsunami signals is not established yet.
The purpose of this study is to propose a method to appropriately extract the seafloor
dynamic motion time series from the near-field OBP data inside the focal area. To achieve this,
we attempt to decompose the OBP signals into seismic and tsunami wave signals based on atsunami generation theory. Section 2 describes a theory of tsunami generation inside the focalarea, the mainshock OBP data used in this study, and the procedure of our method. In section 3,
we show the results of the application of the method to the mainshock OBP data. Discussion andsummary of this study are given in sections 4 and 5, respectively.

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2 Data and Methods

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2.1 Ocean-bottom pressure inside the focal area133

We represent the ocean-bottom pressure change inside the focal area as the sum of thecontribution originating due to gravity (!!"#$%&' (#)) and that without gravity !()(*!"#$%&' (#)

134manuscript submitted to Geophysical Research Letters

135(Saito, 2019):

136!(#) = !!"#$%&' (#) + !()(*!"#$%&' (#).

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(1)

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Supposing that the wave period is long, we may consider the seawater as an incompressible
fluid. Also supposing that the sea-surface height change is small enough compared to the water
depth and that the wavelength is much longer than the sea depth, !!"#$%&' (#) is approximately
given by143!!"#$%&' (#) ≈ !+',")-&#&%. (#) = (/ )/ [+(#) − -0 (#)],

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(2)

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where (/ = 1030 kg/m1 and )/ = 9.8 m/s 2 are the seawater density and gravity acceleration,and +(#) and -0 (#) are the time series of the sea-surface height change (tsunami) and theseafloor vertically upward displacement, respectively. Hereinafter we refer to !+',")-&#&%. (#) as
the hydrostatic pressure change. The pressure change without gravity can be approximated as the
dynamic pressure change, related to the action-reaction forces of the vertically accelerating
seafloor, as (e.g., Saito, 2013; Saito & Kubota, 2019)152!()(*!"#$%&' (#) ≈ !,'(#3%. (#) = (/ ℎ/153

4 ! 5" (7)
47 !

,

(3)

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where ℎ/ is seawater depth. This relationship is basically valid at frequencies lower than the
acoustic resonant frequency: </ = =/ /4ℎ/ ~ 0.05 Hz (=/ : ocean-acoustic wave velocity). In thisstudy, we attempt to extract the vertical acceleration ? 2 -0 /?# 2 from the pressure change !(#).

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2.2 OBP data160

We use seven OBPs installed off Miyagi (green inverted triangles in Figure 1a, Hino etal., 2014) and two OBPs installed off Iwate (orange inverted triangles, Kanazawa & Hasegawa,
1997; Maeda et al., 2011). See Text S1 for the detail of these instruments. Station locations arelisted in Table S1. We subtract the tidal components using the model of Matsumoto et al. (2000).
We then apply a 4th-order Butterworth lowpass filter with a cutoff of 0.05 Hz in both forward
and backward directions to reduce higher-frequency ocean-acoustic wave components. The
cutoff of 0.05 Hz is determined considering the acoustic resonant frequency f0 for the OBP at
GJT3 (~ 0.11 Hz). All records are resampled to 1 Hz after the filtering.

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The de-tided waveform at GJT3 is shown in Figure 1b (gray trace). In Figure 1c, spectral
amplitudes of the de-tided records before and after the mainshock are shown, which arecalculated based on Aki and Richards’ (2002) definition (time windows of 3276.8 s are used).
High-frequency ocean-acoustic wave signals can be recognized even 1800 s after the origin time,and are dominant in frequencies higher than the acoustic resonant frequency f0 ~0.11 Hz.

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Dynamic pressure changes (Eq. (3)) are evident during the first few minutes, particularly for thefrequency range 0.01–0.05 Hz (red traces in Figure 1b). Subsequently, low-frequency hydrostaticpressure changes (Eq. (2)) are also confirmed (< 0.01 Hz, blue).

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2.3 Extracting ground motions from OBP data

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This study attempts to extract the vertical acceleration ? 2 -0 /?# 2 in Eq. (3) from the
OBP data. In other words, our goal is to appropriately decompose the observed pressure change
into its hydrostatic and dynamic components. To achieve this, we develop a method based on the
inversion for the temporal evolution of the seafloor vertical deformation combined with thetheory for ocean-bottom pressure inside the focal area described in section 2.1. We represent thevertical displacement at the seafloor (-0 (@, B, #)) by the superposition of functions C0,:; and D< ,

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=

=

=

$
%
#
∑;>?
∑<>?
-0 (@, B, #) = ∑:>?
F:;< C0,:; (@, B)D< (#).

(5)

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The basis function for the spatial distribution of the seafloor vertical displacement C0,:; (@, B) is
given by

189%&'()*)! )%190!!,#$ (#, %) = (& + & cos -

,"

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for

,

,

%

%

&'-.*.#/./ 0& + & cos 1
,

,$

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,

## − &" ≤ # ≤ ## + &" , %$ − &$ ≤ % ≤ %$ + &$ ,

(6)

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which takes the maximum value at G@: , B; H. The displacement time function D< (#) is given by

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%

1%

60 (7) = 81 (7 − &' sin %1&'(2*2& )1%for 7 ≤ 70./ for 70 ≤ 7 ≤ 70 + ?3 ,(7)

for 70 + ?3 ≤ 7

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where the function begins to increase at # = 74 and reaches 1 after the duration ?3 . The
coefficient F:;< in Eq. (5) represents the displacement amplitude of the (I, J, K)-th function
C0,:; (@, B)D< (#).
The hydrostatic pressure change at the L-th OBP located at (@@ , B@ ) is given by

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!+',")-&#&%. (@@ , B@ , #) = (/ )/ [+(@@ , B@ , #) − -0 (@@ , B@ , #)].

(8)

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The first and second terms represent the pressure changes due to the tsunami and the vertical205

displacement at the seafloor at (@@ , B@ ), respectively. The tsunami height +(@, B, #) ismanuscript submitted to Geophysical Research Letters

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numerically calculated by solving the linear tsunami equation from the seafloor vertical

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displacement -0 (@, B, #) (Eq. (5)). Since the !+',")-&#&%. (@@ , B@ , #) is linear with respect to the208seafloor displacement, we represent Eq. (9) as the superposition using F:;< :

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=

=

=

+',")-&#&%.

$
%
#
∑;>?
∑<>?
!+',")-&#&%. (@@ , B@ , #) = ∑:>?
F:;< M:;<,@

210(@@ , B@ , #).

(10)

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+',")-&#&%.

(@, B, #) as the hydrostatic pressure Green's function in this study, which212

We refer to M:;<,@

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is the hydrostatic pressure change at (@, B) excited by the unit vertical displacement of

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C0,:; (@, B)D< (#).

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The dynamic pressure change at the L-th OBP located at (@@ , B@ ) (Eq. (3)) is given by
the displacement of Eq. (5):

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!,'(#3%. (@@ , B@ , #) = (/ ℎ/

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=

=

A ! 5" (B& ,C& ,7)A7 !
=A ! D' (7)

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$
%
#
∑;>?
∑<>?
= (/ ℎ/ ∑:>?
F:;< C0,:; (@@ , B@ )

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=$
=%
,'(#3%.
#∑;>?
∑=(@@ , B@ , #),= ∑:>?
<>? F:;< M:;<,@

A7 !

(11)

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where

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A ! D' (7)

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A7 !

= N27
82d

0
sin O

for 7 ≤ 74 , 74 + ?d ≤ 727(9−9) )8d

Pfor 74 ≤ 7 ≤ 74 + ?d

.

(12)

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,'(#3%.

(@, B, #) as the dynamic pressure Green's function, which represents the226

We refer to M:;<,@

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dynamic pressure change at (@, B) excited by the unit vertical displacement of C0,:; (@, B)D< (#).

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By using Eqs. (10) and (11), we represent the pressure change at the L-th OBP excited by
the vertical seafloor motions as

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=

=

=

+',")-&#&%.

$
%
#
∑;>?
∑<>?
!(@@ , B@ , #) = ∑:>?
F:;< QM:;<,@==,'(#3%.
(@@ , B@ , #) + M:;<,@(@@ , B@ , #)R

=

$
%
#
∑;>?
∑<>?
= ∑:>?
F:;< M:;< (@@ , B@ , #),

(13)

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where the Green's function M:;< (@, B, #) is given by

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+',")-&#&%.

M:;< (@, B, #) = M:;<,'(#3%.
(@, B, #) + M:;<(@, B, #),(14)

manuscript submitted to Geophysical Research Letters

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which represents the pressure change at (@, B) excited by the unit vertical displacement of
C0,:; (@, B)D< (#).
We estimate the displacement amplitude F:;< as model parameters in a linear inversion
problem given by Eq. (13), where the pressure change at the L-th OBP is used as the data. Using
the estimated F:;< with Eqs. (10) and (11), the observed pressure change at the L-th OBP can be
decomposed into the hydrostatic and dynamic components. The time history of the verticalacceleration can also be extracted using Eq. (11), as245
A ! 5" (B& ,C& ,7)

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A7 !

?

=

=

=

,'(#3%.

$
%
#
∑;>?
∑<>?
= E F ∑:>?
F:;< M:;<,@
( (

=

=

=

(@@ , B@ , #)

$
%
#
∑;>?
∑<>?
= ∑:>?
F:;< C0,:; (@@ , B@ )247

A ! D' (7)
A7 !

.

(15)

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In the same manner, vertical velocity and displacement can also be obtained. For example,
vertical velocity is expressed as

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A5" (B& ,C& ,7)

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A7

=

=

=

$
%
#
∑;>?
∑<>?
= ∑:>?
F:;< C0,:; (@@ , B@ )AD' (7)

(16)

A7

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where

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AD' (7)
A7

= S1
8d

0

Q1 − cos O

for 7 ≤ 74 , 74 + ?d ≤ 727(9−9) )8d

PRfor 74 ≤ 7 ≤ 74 + ?d

.

(17)

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2.4 Calculation of Green's function and inversion

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We summarize the procedures of the Green's function calculation and the inversion
analysis (see Text S2 for more detail). We suppose the @- and B-directions are along the trenchnormal and trench-parallel directions, respectively. We distribute the spatial basis function C0,:;in an area of 220 km × 270 km (gray dots in Figure 1a). We suppose the elliptical-shaped unit
sources to be TB = 20 km and TC = 60 km and each of them overlaps with their adjacent ones
(inset of Figure 1a). We also distribute the temporal basis functions D< with the temporal intervalof Δ# = 5 s, during the 120 s from the origin time (inset of Figure 1a). Duration of D< is assumed
as Y, = 10 s. To calculate the hydrostatic Green's function, tsunami height is numericallysimulated from the initial tsunami height distribution using the linear dispersive tsunami equation(e.g., Saito, 2019). We use the bathymetry data of GEBCO Bathymetric Compilation Group(2020), decimating to a spatial grid interval of 2 km. The input sea-surface height for the tsunami
calculation is calculated from the unit seafloor displacement with the water wave theory
assuming a constant depth of 6 km (Kajiura, 1963). The dynamic Green's functions are

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calculated, using the seawater depth h0 for each station (Table S1). After the calculation of theGreen's functions, the same filter as applied to the observation is also applied to the Green's
functions.
In the inversion, we impose the constraints of the spatial smoothing (Baba et al., 2006)
and spatial damping. The weights of each constraint are determined based on trial and error. The
deformations are allowed to begin at # = 0 s. We use 3600-s time windows for the OBPs off
Miyagi and 1800-s for the OBPs off Iwate.

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3 Results

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In Figure 2a, we compare the observed pressure changes at GJT3 with the synthesized
ones (see Figure S1 for the other OBPs, Figures S2 and S3 for the spatial distribution of the total
displacement and its temporal evolution). Figure 2b shows the extracted vertical accelerograms
at the OBPs using the estimated model parameter F:;< in Eq. (12). Compared to the observedpressure changes divided by ρ0h0 (black traces), the extracted accelerograms (red traces) do notcontain the low-frequency pressure signals due to the tsunami, which are evident after ~120 sfrom the origin time. High-frequency pressure changes for the first 120 s are explained by the
dynamic pressure components (green trace in Figure 2a) and the subsequent low-frequencypressure changes are modeled by the hydrostatic components (blue trace), and the overallpressure changes were explained very well by both pressure changes (red trace). From theamplitude spectra of the pressure change at GJT3 (Figure S4), we confirm that the calculatedhydrostatic and dynamic pressure changes are dominant only in the low- and high-frequency
ranges, respectively. In Figure 2b, we also plot the accelerograms of the onshore broadband
strong-motion seismometer from the F-net (Okada et al., 2004, black triangles in Figure 1a) bygray traces. Although the arrivals of the main wave packet are delayed, the onshore seismograms
are similar to the extracted ocean-bottom seismograms at the OBPs near each station (compare
N.TYSF with TM1 and TM2, N.KSNF with P02 and P06, and N.KSKF with P03 and P07). We
also show the vertical velocity and displacement waveforms in Figures 3a and 3b, respectively.
The amounts of the calculated vertical displacements are surprisingly consistent with theobserved pressure offset changes due to the permanent deformation (Figure 3c, Figure S5 shows
comparisons for longer time window). These comparisons indicate the validity of the extracted
seismograms.

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Figure 2. (a) Comparison of the observed OBP waveform (black) at GJT3 and the synthesized
ones (blue: hydrostatic, green: dynamic, and red: both pressure changes). (b) Extracted verticalaccelerograms at the OBPs (red traces). Observed pressure changes divided by ρ0h0, which
includes both tsunamis and dynamic pressure change components, are also shown by black
traces. Gray traces are the observed accelerograms at the onshore seismometers.

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Figure 3. Time series of the extracted vertical seismograms from the OBPs (red traces), for (a)velocity and (b) displacement. Gray traces are the observed seismograms at the onshore
seismometers. (c) Comparison of the observed pressure time series (black) and those expectedfrom the extracted displacement (red). The final pressure offsets, calculated by averaging the last
600 s time window, are also shown.

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It is worth pointing out that the near-field seismograms inside the tsunami source wherethe vertical displacement was extremely large during the Tohoku-Oki earthquake had never beenmanuscript submitted to Geophysical Research Letters

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reported previously. In the accelerograms at the OBPs inside the main rupture area (GJT3, P08,
and P09), two dominant positive pulses are confirmed (Figure 2b). The duration of the second
pulse at GJT3 is relatively short compared to the first one, whereas the durations in both pulses at
P08 and P09 are similar. From the velocity seismogram at GJT3, located ~50 km landward fromthe trench axis, only one peak with a relatively long duration is confirmed (Figure 3a). On theother hand, at P08 and P09, located near the epicenter and ~100 km from the trench axis, there
are two velocity peaks at t ~40 and ~70 s (Figure 3a). These characteristics may reflect therupture kinematics of the mainshock. One possible interpretation is that the rupture, or energy
release, at the fault beneath P08 and P09, which are located near the epicenter, occurred twice.
This feature is also suggested by the kinematic modeling of the mainshock from the regional or
global seismograms (Lay, 2018).

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4. Discussions

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This study used a lowpass filter with a cutoff of 0.05 Hz to satisfy the condition that theseawater is considered as incompressible fluid. However, if the contribution of the seawater
elasticity cannot be neglected in this frequency range, the extracted seafloor seismogram may beincorrect. To confirm validity of the extracted seismograms at f ≤ 0.05 Hz, we conduct a
numerical simulation of the two-dimensional seismic wave propagation (Maeda et al., 2017, see
Text S3 for the detailed settings). We assume the vertical cross-section passing through GJT3
along the trench-normal direction from the extended Japan Integrated Velocity Structure Model(Koketsu et al., 2012, top panel in Figure 4) and distribute point sources along the plateboundary. We apply lowpass filters with different cutoffs to compare the simulated pressure(! = −Z00 , red traces) and the pressure-converted vertical acceleration ((/ ℎ/ ? 2 -0 /?# 2 , blue
traces) at the station GJT3. When the waveforms include high-frequency components of f > ~0.1
Hz, the two waveforms are different from each other. When only focusing on the lower
frequency ranges (f ≤ 0.05 Hz), the two waveforms agree with each other. Based on thissimulation, we conclude that Eq. (3) holds in the frequency range of f ≤ 0.05 Hz, and our
extracted seismograms are valid.

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Figure 4. Result of the two-dimensional simulation of the seismic wave propagation. Structure
model, point source location, and station location are shown in the top panel, and bottom panels
show comparisons of the pressure-converted vertical accelerogram (blue) and the pressure
waveform (red) in which lowpass filters with different cutoffs are applied.

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We adopted the inversion-based method to extract the ground motion signals from the
OBP data. However, one might think that the bandpass filters are also capable of extracting theseismograms by removing the low-frequency hydrostatic components. In order to evaluate this,
we investigate the accelerograms calculated based on a bandpass filter with passbands of 0.01–
0.05 Hz, shown in Figure S6a (black dashed line traces). The bandpass filtered accelerograms
seem to agree with those extracted by our approach. However, the waveforms do not agree at allwhen integrating to the displacement (Figure S6b). This is because the permanent offsets are
removed by the bandpass filter. Considering a slow rupture near a trench as in a tsunami
earthquake (e.g., Lay et al., 2012), the megathrust earthquake rupture process possibly spans
broadband frequency ranges. Because the spectral components of the mainshock ground motions
possibly range into the low-frequency tsunami-dominant spectral bands, we must not use ahighpass filter, which reduces the low-frequency components. It is essential to use a lowpass
filter and to employ an inversion-based method with the tsunami generation theory tomanuscript submitted to Geophysical Research Letters

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appropriately extract the broadband vertical ground motion including the low-frequency
permanent offset component.
We could extract near-field seismograms from OBPs, which could never be achieved in
the past when no OBP was installed inside the focal area and the tsunami generation theory was
not established. By combining near-field OBP observation and the tsunami generation theory, it
is expected that the parameters for the rupture kinematics and dynamics can be constrained more
precisely, particularly for the subduction zone (e.g., Ide & Takeo, 1997; Kozdon & Dunham,
2014; Ma & Nie, 2019). In addition, developments in deep-ocean OBP observation enable us tocapture the higher-frequency ocean-acoustic wave signals (Webb & Nooner, 2016; Heidarzadeh& Gusman, 2018; Kubota et al., 2020, Figure 1), which can be modeled by numerical simulationconsidering the seawater as the elastic body (Figure 4, Maeda et al., 2017; Saito et al., 2019).
Recent studies have started to simulate pressure changes inside the focal area based on the
numerical simulations, accounting for both the hydrostatic and non-hydrostatic seismic
components (e.g., Saito et al., 2019; Abrahams et al., 2020; Maeda et al., 2020). Besides, indeep-ocean measurements, it is still hard to control the installation environment and some studies
have reported that the near-field OBS rotated due to strong shaking on the seafloor (Nakamura &Hayashimoto, 2018; Takagi et al., 2019). In such a situation, the near-field OBPs must produce
powerful datasets to constrain the earthquake source information. Taking these facts into
account, the high-frequency near-field OBP data should be more utilized to deepen ourgeophysical understanding of the subduction zone, as widely as the data from onshore andoffshore seismic instruments.
Our approach utilizing dynamic pressure may also be applicable to practical real-timetsunami early warnings (e.g., Melger & Hayes, 2019; Tsushima et al., 2011; 2012). Inside thefocal area, the OBPs observe no hydrostatic pressure changes just after the origin time, because
the sea-surface height change and seafloor vertical displacement are almost equivalent soon after
the earthquake occurrence (Tsushima et al., 2012). If we utilize the dynamic pressure changes asvertical motion signals, which are dominant in the first few minutes, the accuracy of the tsunami
forecast immediately after the earthquake rupture starts will be improved. In Figure S7, we apply
the bandpass filter to the extracted seismograms (0.01–0.05 Hz, red traces) and compare to theseismograms expected from the observed pressure within that passband (black dashed traces).
These two traces agree well with each other. This indicates the information of the band-limited
velocity or displacement could be obtained from the bandpass-filtered pressure records, only in a
few minutes from the focal time.

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We developed a method to extract near-field seismograms from the OBP data inside thefocal area. We applied the method to the near-field OBP data of the 2011 Tohoku-Oki
earthquake to extract the ground motions inside the focal area, whereas the near-fieldseismograms during the Tohoku-Oki earthquake have never been reported yet. Our analysis

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successfully decomposed the OBP data into the dynamic pressure changes dominant in the first~120 s and the subsequent hydrostatic pressure changes due to tsunamis and permanent seafloor
deformation. The extracted seismograms suggested that two dominant energy releases occurred
beneath the OBPs near the epicenter. We confirmed the validity of the extracted seismograms
based on the numerical seismic wave propagation simulation. Because the bandpass filter toreduce the low-frequency hydrostatic components also reduces the low-frequency ground motion
components, our inversion-based method is essential to appropriately extract the ground motion
waveform including the low-frequency permanent offset components. The high-frequencypressure change signals in the near-field OBP should be utilized more widely, for geophysicalresearch as well as real-time tsunami forecasting.

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Data Availability Statement

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The Supplementary Data Set is available at https://doi.org/10.5281/zenodo.4420394. The
Supplementary Dataset S1 includes the results obtained by the inversion analysis, such as theamplitudes of the source functions (mijk), the NetCDF grid file of the sea-surface displacement,
and the spatial and temporal configuration of the basis functions. The OBP data off Miyagi
installed by Tohoku University are available in Data Set S2. The OBP data off Kamaishi were
provided upon request to Earthquake Research Insititute, the University of Tokyo. The
bathymetry data of GEBCO 2020 Grid (GEBCO Bathymetric Compilation Group 2020, 2020)are available at https://www.gebco.net/data_and_products/gridded_bathymetry_data/. The F-net
onshore seismometer data are available at http://doi.org/10.17598/nied.0005. The numericalsimulation of the P-SV seismic wave propagation was conducted by using OpenSWPC (Maeda
et al., 2017) Version 5.0.2, available at https://doi.org/10.5281/zenodo.3712650. We used
Seismic Analysis Code (SAC) software for data processing (Goldstein et al., 2003). Figures wereprepared using Generic Mapping Tools Version 6 (GMT6) software (Wessel et al., 2019).

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Acknowledgments

437This study was financially supported by the research project “Research concerning
Interaction between the Tokai, Tonankai, and Nankai Earthquakes” of Ministry of Education,
Culture, Sports, Science and Technology (MEXT), Japan, and by Japan Society for the
Promotion of Science (JSPS) KAKENHI Grant Numbers JP20244070, JP26000002,
JP15K17752, JP19H00708, JP19H02409, 19H05596, JP19K04021, and JP19K14818. TK thanks
Yoshihiro Ito of Kyoto University for fruitful comments. TK also thanks Naotaka Y. Chikasada,
Hisahiko Kubo, and Osamu Sandanbata of National Research Institute for Earth Science andDisaster Resilience for insightful discussions. The installation and retrieval of the OBPs of
Tohoku University were conducted via Research Vessel (R/V) Keifu-maru and R/V Ryofu-maru(Japan Meteorological Agency), Supply Vessels (S/Vs) Kaiko and Kaiyu (Offshore Operation
Co., Ltd.) and S/V Shinsei-maru (Fukada Salvage Co., Ltd). The OBPs at P03, P07, P08, and P09

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were recovered in September 2011 by using Remotely Operated Vehicle (ROV) Hakuyo-3000(Fukada Salvage Co., Ltd.) (Hino et al., 2012; Arai et al., 2013). TK also thanks the captains andcrews of these vessels and the staff and technicians at ERI for their efforts for their operation.
We thank the Editor Germán Prieto, the Associate Editor, and Prof. Thorne Lay and anotheranonymous reviewer for their constructive comments.

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Geophysical Research Letters
Supporting Information for
Extracting near-field seismogram from ocean-bottom pressure gauge inside thefocal area: application to the 2011 Mw 9.1 Tohoku-Oki earthquake
T. Kubota1, T. Saito1, H. Tsushima2, R. Hino3, Y. Ohta3, S. Suzuki3, D. Inazu41

National Research Institute for Earth Science and Disaster Resilience, Tsukuba, Japan
2
Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Japan
3
Graduate School of Science, Tohoku University, Sendai, Japan
4
Department of Marine Resources and Energy, Tokyo University of Marine Science and Technology, Tokyo,
Japan

Contents of this file
Text S1 to S3
Figures S1 to S7Table S1

Additional Supporting Information (Files uploaded separately)

Datasets S1 contains the results obtained by the analysis in this study, such as thespatial and temporal configuration of the basis functions. Dataset S2 contains the
OBP data used in this study.

Introduction
Text S1 describes the detail for the OBP instruments used in this study. Procedure forcalculating the Green’s function and for the inversion analysis is explained in Text S2. In
Text S3, the procedure of the P-SV seismic wave simulation is shown. Calculation of thehydrostatic and dynamic pressure changes from the inversion result is shown in Figure
S1. Figures S2 and S3 show the spatial distribution of the total displacement andtemporal evolution of the displacement, respectively. Comparison of the amplitude
spectra at GJT3 is shown in Figure S4. Figure S5 is the comparison of the observedpressure pressure and the simulated displacement. Figure S6 compares the seismograms
obtained by this study and those expected from the bandpass filter and Figure S7
compares the bandpass-filtered seismograms. The station list is shown in Table S1.

1

Text S1.

This text describes the detail of the OBP instruments. We use seven
OBPs installed off Miyagi by Tohoku University (green inverted triangles in Figure1a), which utilize Paroscientific Digiquartz precise quartz pressure sensors,
8B7000 series (Hino et al., 2014). We also use two cabled OBPs installed off Iwate
by the Earthquake Research Institute (ERI), the University of Tokyo (orange
inverted triangles), which use the quartz pressure sensor manufactured by
Hewlett-Packard Inc. (Kanazawa & Hasegawa, 1997; Maeda et al., 2011). Although
the frequency response of a quartz pressure sensor generally depends on the
counting method of the quartz oscillation, the response of the quartz pressure
sensor is typically flat at lower frequency band of < ~1 Hz regardless of its
counting method (Webb & Nooner, 2016). Station locations are listed in Table S1.
Text S2.
This text shows the further detail of the calculation of the Green's
function and the inversion analysis. We suppose the x- and y-directions are along
the trench-normal and trench-parallel directions, respectively (i.e., azimuth of xdirection is 105°). We distribute the spatial basis function Uz,ij (Eq. (6)) in an areaof 220 km × 270 km (gray dots in Figure 1a). This is determined based on thespatial extent of the initial sea-surface height (i.e., tsunami source) derived by theprevious study (Saito et al., 2011). We suppose the elliptical-shaped unit sources
to be Lx = 20 km and Ly = 60 km, and that each of them overlaps with theiradjacent ones at horizontal intervals of Δx = Lx/2 and Δy = Ly/2 (inset of Figure1a). These horizontal sizes and spatial intervals are also determined based on thespatial extent of the initial tsunami height obtained by the analysis of Saito et al.
(2011), in order to resolve the tsunami height with the spatial scale of a few tensof km. Total number of the unit sources in the space domain is Nx = 21 and Ny =17 along the x- and y-direction, respectively (total number of the unit sources inthe space domain is Nx × Ny = 357). We also distribute the temporal basis
functions, τk, in time domain, during the first 120 s from the origin time, with thetemporal interval of Δt = Td/2 = 5 s (inset of Figure 1a). In other words, theparameter tk, the beginning of the time function τk, is assumed as tk = (k-1)Δt, 1 ≤k ≤ Nt. Nt = 23 is the total number of the basis functions in time domain. This
temporal basis function has a sine-type shape (Eq. (7), e.g., Maeda et al., 2017)
and the duration of the displacement is assumed as Td = 10 s. The duration andthe temporal interval are determined in order to appropriately reproduce thesignals with the frequency lower than the cutoff period of the lowpass filter, 0.05
Hz (period of 20 s).
To calculate the hydrostatic Green's function, tsunami height isnumerically simulated from the initial tsunami height distribution using the linear2

dispersive tsunami equation (e.g., Saito et al., 2019) with a time step interval of 1s. We use the bathymetry data of GEBCO Bathymetric Compilation Group (2020),
decimating to a spatial grid interval of 2 km. The input sea-surface height for thetsunami calculation is calculated from the unit seafloor displacement Uz,ij(x, y)with the water wave theory assuming a constant depth of 6 km (Kajiura, 1963).
The dynamic Green's functions are also calculated based on Eq. (3), using theseawater depth h0 for each station (Table S1). After the calculation of the Green's
functions, the same filter as applied to the observation is also applied to theGreen's functions.
In the inversion, we impose the constraints of the spatial smoothing(Baba et al., 2006) and spatial damping. The weights of each constraint are
determined based on trial and error. The deformations are allowed to begin at t
= 0 s. We use 3600-s time windows for the OBPs of Tohoku University and 1800-s
for the OBPs of ERI for the inversion.
Text S3.
This text shows the detail of the numerical simulation of the twodimensional P-SV seismic wave propagation (Figure 4). We solve the equations
for the elastic body using the finite difference method (Maeda et al., 2017). We
assume the vertical cross-section passing through GJT3 along the trench-normal
direction (azimuth = 105°) from the extended Japan Integrated Velocity Structure
Model (Koketsu et al., 2012) with a grid interval of 0.2 km (top panel in Figure 4).
We distribute point sources along the plate boundary. We assume their rupture
begins at the same time and the source durations are 4 s. After the calculation,
we apply lowpass filters with different cutoffs to compare the pressure (p = −σzz,
red traces) and the pressure-converted vertical acceleration (ρ0h0d2uz/dt2, blue
traces) at the station GJT3. The amplitudes in each subfigure are normalized sothat the maximum amplitude of the traces without the lowpass filter (left top
subfigure in Figure 4) takes 1.

3

(a) Only dynamic(c) Only hydrostatic(e) Both dynamic and hydrostatic

TM2

TM2

TM2

TM1

TM1

TM1

P06

P06

P06

P02

P02

P02

P03

P03

P03

P07

P07

P07

P08

P08

P08

P09

P09

P09

GJT3

GJT3

GJT3

1200 hPa
−60

0

60

120

180

1200 hPa
240−60

0

60

120

180

1200 hPa
240−60

(b)

(d)

(f)

TM2

TM2

TM2

TM1

TM1

TM1

P06

P06

P06

P02

P02

P02

P03

P03

P03

P07

P07

P07

P08

P08

P08

P09

P09

P09

GJT3

0

GJT3

400 hPa
1800

Time [s]

3600

5400

0

Time [s]

3600

60

120

GJT3

400 hPa
1800

0

5400

0

180

240

400 hPa
1800

3600

5400

Time [s]Figure S1. Comparison between the observed pressure waveforms (black) with the simulated waveforms, for (a,b) dynamic (green), (c,d) hydrostatic (blue), and (e,f) both pressure changes. The lowpass filter with a cutoff of 0.05 Hz is applied.

1(a) Seafloor displacement(b) Sea surface displacement

41°

40°

39°

38°

37°

36°
−800 0
0
35°

140°

142°

km

800

−800 0

[cm]

100

144°

0
146°

140°

142°

km

800

[cm]

100

144°

146°

Figure S2. The spatial distribution of (a) the seafloor and (b) the sea-surface height obtained by the inversion analysis. The contour
interval is 2 m.

1

10s

20s

30s

40s

50s

70s

80s

90s

100s

110s

60s

40°

38°

36°

40°

38°

36°

0

[cm/s]

15−15

Figure S3. The temporal evolution of the seafloor displacement rate obtained by the inversion analysis.

2Period [s]2000 1000
106

500

200

100

50

20

Observed
Hydrostatic+Dynamic
Only hydrostatic
Only dynamic

Amplitude [hPa⋅s]

105

104

103

102
0.0005 0.001 0.002

0.005 0.01

0.02

0.05

Frequency [Hz]Figure S4. Comparison of spectral amplitudes at GJT3 between the observed one (black)and calculated ones; red: both hydrostatic and dynamic, blue: only hydrostatic, green:
only dynamic pressure changes. The time window of 2048 s from the origin time is used
for the spectral calculation.

1

Pressure change
pobs

Extracted seismogram
55 hPa61 hPaTM2

85 hPa98 hPaTM1

132 hPa
100 hPa
P06

105 hPa
78 hPa

P02
P03

39 hPa42 hPaP07-39 hPa-21 hPa

P08-162 hPa-153 hPa

P09-291 hPa-272 hPa

GJT3

400 hPa
0

1800

3600
Time [s]-388 hPa-362 hPa

5400

7200

Figure S5. Comparison of the observed pressure time series (black) and those expected from the extracted displacement (red) for
two hours from the origin time. The final pressure offsets, calculated by averaging the last 600 s time window, are also shown.

1(a) Vertical acceleration(b) Vertical displacement

Obs (LP 0.05 Hz) Cal (LP 0.05 Hz) Obs (BP 0.01-0.05 Hz)

Cal (LP 0.05 Hz) Obs (BP 0.01-0.05 Hz)
TM2

TM2

TM1
TM1
P06
P06
P02
P02

P03

P03
P07
P07
P08
P08
P09

4 cm/s2

GJT3

−60

P09

300 cm

GJT3

0

60
120
Time [s]180240 −60060120Time [s]180240Figure S6. Comparison between the extracted seismograms (red), and the lowpass-filtered (0.05 Hz, gray) and the bandpass-filtered(0.01–0.05 Hz, black dashed) waveforms, for (a) vertical acceleration and (b) vertical displacement.

2(a) Vertical acceleration(b) Vertical velocity(c) Vertical displacement

Cal (LP 0.05 Hz) Cal (BP 0.01-0.05 Hz)Obs (BP 0.01-0.05 Hz)

Cal (LP 0.05 Hz) Cal (BP 0.01-0.05 Hz)Obs (BP 0.01-0.05 Hz)

Cal (LP 0.05 Hz) Cal (BP 0.01-0.05 Hz)Obs (BP 0.01-0.05 Hz)

TM2

TM2

TM1

TM1

P06

P06

P02

P02

P03

P03

P07

P07

P08

P08

TM2
TM1
P06
P02
P03

P07

P08

P09

4 cm/s2

GJT3

−60

P09

20 cm/s

GJT3

0

60
120
Time [s]180240 −60P09

300 cm

GJT3

0

60
120
Time [s]180240 −60060120Time [s]180240Figure S7. Time series of the extracted vertical seismograms based on the inversion with the bandpass-filter (0.05–0.01 Hz, red
traces), for (a) acceleration, (b) velocity and (c) displacement. Gray traces are the extracted vertical seismograms with the lowpass filter(0.05 Hz). Black dashed traces are the bandpass-filtered observed data (0.01–0.05 Hz).

3

Table S1. List of the stations used in this study.a
LatitudeLongitude
Depth
Station
[°N]
[°E]
[m]

Inversion time window[s]

AgencyTohokuUniversity
TohokuUniversity
TohokuUniversity
TohokuUniversity
TohokuUniversity
TohokuUniversity
TohokuUniversity

GJT3

38.2945

143.48143293

0 – 3600

P0238.5002142.5016

1104

0 – 3600

P03

38.1834

142.3998

1052

0 – 3600

P06

38.6340

142.5838

1254

0 – 3600

P07

38.0003142.4488

1059

0 – 3600

P08

38.2855

142.8330

1418

0 – 3600

P09

38.2659

143.0006

1556

0 – 3600

TM1

39.2312142.7684

1618

0 – 1800

ERI

TM2

39.2489142.4412

1013

0 – 1800

ERIa

All data were resampled to 1 Hz after the filtering process.

1