Bathymetry Change Investigation of the 2011 Tohoku Earthquake

Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography.
2015.
Jun,
33(3):
181-192

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

- Received : May 05, 2015
- Accepted : June 06, 2015
- Published : June 30, 2015

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Bathymetry change due to the 2011 Tohoku (M9.0) earthquake was investigated through satellite altimetry-derived free-air gravity anomalies (SAFAGA) and shipborne measurements. The earthquake occurred at the plate boundaries near the northeastern coast of Japan, where the oceanic plate subducts beneath the continental plate along deep-sea trench. Data analyzed in this study include SAFAGA from Scripps Institution of Oceanography (SIO), shipborne bathymetry (SB) from the U.S. National Geophysical Data Center (NGDC) and the Japan Agency for Marine-Earth-Science And Technology (JAMSTEC). To estimate the bathymetry change, a reference bathymetry before the earthquake was predicted by gravity-geologic method (GGM) and Smith & Sandwell’s (SAS) method. In comparison with the bathymetry models before the earthquake, GGM bathymetry model generated by a tuning density contrast of 17.04 g/cm
^{3}
by downward continuation method was selected because it shows better bathymetry in the short wavelength below about 6 km. From the results, remarkable bathymetry change of about ±50 m was found on the west side of the Japan Trench caused by the earthquake.
The tectonic plates map around Japan, The bathymetry as a background is from ETOPO1 (Amante and Eakins, 2009 ) bathymetry, The red lines indicate plate boundary
Since the 2000s, several megathrust earthquakes have occurred at convergent plate boundaries of major subduction zones. The Tohoku (M9.0) earthquake which occurred on the subduction zone near the northeastern coast of Japan on March 11, 2011 accompanied fault dislocation, produced a tsunami caused by displacement of the seabed, and generated intense and large scale mass redistribution. The mass redistribution caused by the megathrust earthquake resulted in gravity change in the Earth’s gravity field. The change in the Earth’s gravity field due to megathrust earthquake are caused by two processes: (i) density change of the surrounding material permanently due to volumetric strain, such as dilatation and compression and (ii) surface displacement in boundary with density contrasts (
Pollitz, 2006
;
Heki and Matsuo, 2010
).
Surface displacement caused by the 2011 Tohoku earthquake has been investigated through continuous Global Positioning System (GPS) measurement of both the coast and land areas around the epicenter before and after the earthquake (
Ozawa ., 2011
). Geodetic measurements obtained from submarine GPS/acoustic stations and shipborne measurements were used for investigating vertical displacement around the Japan Trench area after the earthquake (
Sato ., 2011
). In addition,
Fujiwara . (2011)
found remarkable difference of ±50 m in the west side of the Japan Trench axis by comparing multi-beam bathymetric measurements along several ship tracks before and after the earthquake. The results of vertical displacement of the seafloor around the epicenter of the earthquake by
Sato . (2011)
and
Fujiwara . (2011)
show significant variations at the Japan Trench area caused by the earthquake. However, investigation of the seafloor topography change caused by megathrust earthquake is required to understand vertical displacement generated from relatively short wavelengths and thus, accurate bathymetry modeling before the megathrust earthquake is necessary to monitor bathymetry change.
Bathymetry prediction combined by SAFAGA and SB has been developed using two methods: the gravity-geologic method (GGM) (
Roman, 1999
;
Kim ., 2011
) and
Smith and Sandwell’s (SAS) method (1994)
. SAFAGA which generate a reference bathymetry before earthquake can be utilized to fill gaps by computing topographic effects in off-track between shipborne bathymetric measurements in both GGM and SAS.
This study aims to investigate bathymetry change caused by the 2011 Tohoku earthquake that occurred at the convergent plate boundaries characterized by the major subduction zones. In order to investigate bathymetry change caused by the earthquake, a reference bathymetry model before the earthquake should be generated. In this study, two methods: the gravity-geologic method (GGM) and
Smith and Sandwell’s (SAS) method (1994)
were used to estimate the reference bathymetry before the earthquake. SAFAGA in GGM and SAS were incorporated to determine the tuning density contrast in GGM and the scaling factor which is inversely proportional to density contrast in SAS. The selected reference bathymetry was used to estimate bathymetry change in the Japan Trench by computing point-by-point differences with Japan Agency for Marine-Earth-Science And Technology (JAMSTEC,
http://www.jamstec.go.jp
) SB measurements after the earthquake. Bathymetry change in the Japan Trench caused by the earthquake is presented as the final result in this study.
g_{REG}
) from depth and gravity anomalies measured at
j
-control points. In general, the observed Bouguer gravity anomalies (BGA), known at control points (
j
), include residual gravity effect resulted from variations of local bedrock and regional gravity effect generated from deeper mass variations. The observed gravity (
g_{OBS}
), unknown at all other sites (
i
) is composed of the residual gravity (
g_{RES}
) and the regional gravity (
g_{REG}
) expressed by the following equation:
Schematic geometry of the gravity-geologic method and downward continuation method in marine applications
In Eq. (2), we assume that the residual gravity field (
g_{RES}
) generating the shorter wavelength effect is estimated by using a simple Bouguer slab formula at control points,
j
, with measured depths in
Fig. 2
:
where
G
is the gravitational constant, 6.672×10
^{−8}
cm
^{3}
/g·sec
^{2}
;
Δρ
is the density contrast in g/cm
^{3}
;
E
(
j
) is the bedrock elevation measured in meter at
j
-control points; and
D
is the deepest depth of the control points as a reference measured in meter.
The regional gravity field (
g_{REG}
) that represents the longer wavelength effect at control points (
j
) is computed by subtracting the residual gravity representing the effect of the bedrock surface from the observed Bouguer gravity:
The regional gravity,
g
_{REG}
(
i
), at sites of unmeasured depth,
i
, can be predicted as gridding the generated regional gravity,
g_{REG}
(
j
), at sites of measured depth,
j
. The residual gravity,
g
_{RES}
(
i
), for predicting depth-to-bedrock at sites of unmeasured depth,
i
, is estimated by eliminating the regional gravity,
g
_{REG}
(
i
), at site from the observed gravity,
g
_{OBS}
(
i
) as given Eq. (4).
By rearranging Eq. (2), the elevation of the bedrock above the reference where bedrock depths are unmeasured at site
i
can be estimated with the following formula:
In marine applications of the GGM,
Roman (1999)
,
Kim . (2010)
,
Kim . (2011)
, and
Hsiao . (2011)
used shipborne depth and SAFAGA instead of bedrock elevation and BGA at the control points. The determination of density contrast between seawater and the ocean bottom topographic mass is an important factor for GGM bathymetric estimations. It is known that the density contrast (
Δρ
) in Eq. (5) controls the amplitude of bathymetric estimates.
For more effective bathymetric predictions, a tuning value of density contrast, which was determined from the control points of measured shipborne depths, was used (
Kim ., 2011
). Although an acceptable range of a tuning density contrast by the check-points method in the GGM can be selected, there is a limitation to choose a single tuning density contrast in the range. In this study, the downward continuation method is employed to mitigate the limitations by use of a single-density Bouguer slab for analyzing multi-density terrain with rugged relief components (
Nagarajan, 1994
;
Kim ., 2011
).
z
=
h
_{1}
plane to
z
=
h
_{2}
plane in Fourier domain:
where
G
(
u
,
v
)｜
_{h1}
and
G
(
u
,
v
)｜
_{h2}
are the two-dimensional Fourier transforms of the gravity field at
h
_{1}
and
h
_{2}
, respectively;
u
and
v
are the frequencies for
x
and
y
directions, respectively;
; and
d
=
h
_{2}
−
h
_{1}
.
As inversion of upward As inversion of upward. (6), downward continuation of the gravity field in the Fourier transform from
z
=
h
_{2}
plane to plane
z
=
h
_{1}
can be expressed as:
The downward continued gravity field was determined in each downward continued level from the sea surface to the ocean bottom of the deepest point by applying the Gaussian filter in Eq. (7), as shown in
Fig. 2
:
where
represents the downward continued gravity field;
G
(
u
,
v
) represents the original gravity field;
d
denotes the distance of the downward continuatio; and
F
(
u
,
v
) is a Gaussian filter.
Fig. 2
involves computing density contrast (
Δρ
)and gravity (
Δg_{DWC}
) in each level using downward continuation method. The density contrasts dependent on mass variations beneath the ocean bottom are determined in several downward continued levels(1, 2, 3,...,
n
−2,
n
−1,
n
), as shown in
Fig. 2
, using the downward continuation method until the deepest seafloor topography is reached. The gravity
Δg_{DWC}
(
i
) at point
i
in each downward continued level, as shown in
Fig. 2
, can be derived from the mean value of the downward contimued gravities. The gravity ratio in each downward continued level is computed as the ratio of gravity of each downward continued level,
Δg_{DWC}
(
i
), to gravity of the sea surface level,
Δg_{SEA}
(
i
), where at point
i
of each downward continued level and the sea surface level.
The density contrast(
Δρ_{DWC}
) at point
i
of every downward continued level can be estimated by multiplying the gravity ratio,
Δρ_{DWC}
(
i
)/
Δρ_{SEA}
(
i
), at point
i
of each downward continued level and the sea surface level by
Δρ_{SEA}
, which is the density contrast of 1.03 g/cm
^{3}
at the sea surface level (
Strykowski ., 2005
). The estimated density contrast in final level, which is the deepest depth(
D
), can be applied for altimetry-derived GGM bathymetry predictions.
h
) into gravity anomalies (
Δg
) is explained as a non-linear equation in Fourier transform by
parker (1972)
:
where
G
is the gravitational constant;
Δρ
is the density contrast between seawater and the seafloor topography;
d
is the mean depth beneath the ocean surface;
k
is the radial frequency
; 𝒌 is (
k_{x}
,
k_{y}
) = (1/λ
_{x}
, 1/λ
_{y}
), where (
k_{x}
,
k_{y}
) and (λ
_{x}
, λ
_{y}
) are frequencies and wavelengths in the
x
and
y
directions, respectively; and, 𝔍[ ] is the Fourier transform operator.
The first term in Parker formula in Eq. (9) is only dependent on
d
, and is a linear relationship between gravity anomalies and bathymetry in the Fourier domain as in the following equation:
where
G
(𝒌) and
H
(𝒌) are the Fourier transforms of gravity anomalies and bathymetry, respectively;
Z
(𝑘) is the admittance function as a transfer function that is isotropic and spatially invariant; 𝒌 is the frequency in two-dimensions; the 2
πG
(
Δρ
) term is a Bouguer constant as an infinite slab of material; and, the
e
^{−2π𝑘d}
term represents upward continuation (from seafloor to sea surface) through the mean ocean depth as exponential decay with increasing frequency.
By inverting the forward model for the first term in linear relationship between gravity anomalies and bathymetry in Eq. (10), we can estimate bathymetry from gravity anomalies in Fourier domain as shown in Eq. (11):
For a stable condition of downward continuation, which is represented as the term
e
^{2π𝑘d}
in Eq. (11), the transfer function
Z
^{−1}
(𝑘) is suppressed by windowing the limited range of wavelengths of topography to estimate bathymetry from gravity anomalies. A band-pass filter,
W
(𝑘), is used to stabilize the downward continuation in predictions of the seafloor topography (
Smith and Sandwell, 1994
). The Wiener filter is constructed as high-pass filter,
W
_{1}
(𝑘), and low-pass filter,
W
_{2}
(𝑘).
where
W
_{1}
(𝑘) = 1 −
e
^{−2(π𝑘s)2}
;
W
_{2}
(𝑘) = [1 +
A
𝑘
^{4}
e
^{(4π𝑘d)}
]
^{−1}
;
d
is the mean depth beneath the ocean surface; 𝑘 is the radial frequency
; and
s
is the Wiener filter parameter. The
A
-value in low-pass filter, which is 6,233 km
^{4}
, influences the cut-off wavelength scale at the resolution of the predicted bathymetru in Eq. (12).
The gravity-to-topography scaling factor (
S
) is determined by linear regression between the band-pass filtered, and downward continued gravity anomalies to a mean depth in Eq. (13) and the band-pass filtered gridded SB in Eq. (14) in band-limited wavelength (15~160 km):
where
G
(𝒌) is the band-pass filtered and downward continued gravity field;
H
(𝒌) is the band-pass filtered gridded SB; and
W
(𝑘) is the Wiener filter. The SAFAGA in the frequency domain,
G
_{0}
(𝒌), are first band-pass filtered and downward continued to a mean depth (
d
). The gridded SB in the frequency domain,
B
_{0}
(𝒌), are also band-pass filtered by the Wiener filter
The SAS bathymetry by Smith and Sandwell’s (SAS) method (1994) is finally estimated by combining two bathymetry results: (1) regionallow-pass filtered bathymetry in wavelengths more than 160 km and (2) bathymetry computed in band-limited wavelengths between about 15 and 160 km:
where
D_{SAS}
is the SAS bathymetry.
d_{LP}
(
x
) and
S
•
g
(
x
) are the low-pass filtered bathymetry in longer wavelengths and band-limited bathymetry in 15~160 km wavelengths, respectively, in spatial domain.
http://www.ngdc.noaa.gov
) GEODAS database of the National Oceanic and Atmospheric Administration (NOAA,
http://www.noaa.gov
). Red dots indicate points with depth and gravity anomalies from NGDC in
Fig. 3(a)
. In addition, we used local SB (denoted as the green dots in
Fig. 3(a)
) measured by five different RVs (Natsushima, Kaiyo, Yokosuka, Mirai, and Kairei) of JAMSTEC between 1999 and 2010 in the Japan Trench area before the earthquake. Blue and green dots have only depth data from NGDC and JAMSTEC, respectively, in
Fig. 3(a)
. Control points and check points used for determination of density contrast in the study area are shown as black triangles and as white dots, respectively, in
Fig. 3(b)
.
(a) The local shipborne measurements from NGDC (red and blue dots) and JAMSTEC (green dots) in the study area before the earthquake, (b) The 1×1 arc-minute bathymetry by ETOPO1 with superimposed control and check points for determination of density contrast in the study area, (c) SAFAGA from Sandwell and Smith (2009) in the study area before the earthquake, (d) The local shipborne bathymetric locations measured by JAMSTEC after the earthquake, Attributes listed for this and subsequent maps include the amplitude range (AR = minimum and maximum values), amplitude mean (AM), amplitude standard deviation (ASD), and amplitude unit (AU)
1×1 arc-minute SAFAGA used to predict reference bathymetry before the earthquake were obtained by regridding the original gravity data of Scripps Institution of Oceanography (SIO,
http://www.sio.ucsd.edu
), University of California at San Diego (
Sandwell and Smith, 2009
) generated from Geosat and ERS-1 satellite altimeters in this study, as shown in
Fig. 3(c)
. In
Fig. 3(c)
, the SAFAGA in the study area show large variations because the gravity anomalies in the Japan Trench area increases to an extent about −163.0 mGal (1 mGal = 1×10
^{−5}
m/sec
^{2}
) caused by the steep bathymetric gradient.
After the earthquake, a bathymetric survey around the earthquake epicenter (denoted as red star in
Fig. 3(d)
) in the Pacific Ocean was conducted by operating a Sea Beam 2112.004 multi-beam echo sounder with a 12 kHz frequency and a 2° by 2° beam width by three different R/Vs (Yokosuka, Mirai, and Kairei), JAMSTEC. 23,829,295 shipborne depth measurements (denoted as the gray dots in
Fig. 3(d)
) obtained from JAMSTEC in the study area was used to estimate bathymetry change of point-by-point differences in the study.
^{3}
and greater in
Fig. 4(a)
. The estimated density contrast between seawater and the ocean bottom bedrock for marine GGM applications is relatively larger than the geologically reasonable density contrast of 1.67 g/cm
^{3}
between seawater density of 1.03 g/cm
^{3}
and the ocean bottom bedrock density of 2.70 g/cm
^{3}
(
Jin, 1995
;
Kim ., 2011
), because SAFAGA obtained on the sea surface represent the mass variations under ocean bottom (
Roman, 1999
;
Kim ., 2011
).
(a) A trade-off diagram for determining the tuning density contrast by check points with the gravity-geologic method, (b) The density contrast and gravity ratio estimated in each downward continued level by the downward continuation method
Downward continuation method in the study area was used to select the tuning value of density contrast in the acceptable range of density contrast in the trade-off diagram of
Fig. 4(a)
. The density contrast in each downward continued level at 760 m intervals in the study area was computed by multiplying gravity ratio below sea level and seawater density of 1.03 g/cm
^{3}
. The gravity ratio is the ratio of mean value of downward continued gravity in each downward continued level to mean gravity value on the sea surface. The fi nal density contrast was computed as 7,660 m in the study area, which is the deepest level in the study area. The curves of the gravity ratio and density contrast calculated in each downward level show the convex shape with increase of density contrast in
Fig. 4(b)
. From the curves, a tuning density contrast of 17.04 g/cm
^{3}
in the deepest level of the study area, as shown in
Fig. 4(b)
by downward continuation method was selected for GGM estimates. This is because the tuning density contrast is within the acceptable range of the check point method with GGM. We adopted the single tuning density contrast,
Δρ
=17.04 g/cm
^{3}
in the study area for GGM bathymetry predictions before the earthquake occurred.
Bathymetry modeling based on
Smith and Sandwell’s (SAS) method (1994)
was implemented with inversion of high resolution gravity anomalies for bathymetry predictions in a linear approximation to a nonlinear problem. Low-pass fi ltering of shipborne gridded bathymetry predicted by 10,838 NGDC and 34,144,423 JAMSTEC shipborne depths in the study area and Wiener filtering of downward continued gravity anomalies by
Sandwell and Smith (2009)
in band-limited wavelengths in the study area were performed. Band-pass filtered and downward continued gravity anomalies in Fourier domain in Eq. (13) were performed to compute the gravity-to-topography scaling factor by linear regression with band-pass fi ltered shipborne gridded bathymetry at short- and intermediate-wavelengths between 15 and 160 km in Eq. (14). The scaling factor of 4.29 m/mGal in the study area was adapted to compute SAS bathymetry in band-limited wavelengths (15~160 km). Finally, SAS bathymetry model in the study area was estimated by combining two bathymetric outputs: (1) regional bathymetry in longer wavelengths (> 160 km) by low-pass fi ltering of the shipborne gridded bathymetry and (2) bathymetry calculated by multiplying the scaling factor and the band-pass fi ltered, and downward continued gravity anomalies in band-limited wavelengths.
The GGM, SAS, and shipborne gridded bathymetry models around Japan Trench area, as shown in
Fig. 5
were compared to determine a reference of bathymetry model before the earthquake. The shipborne gridded bathymetry model was estimated by the 10,838 NGDC and 34,144,423 JAMSTEC shipborne bathymetric measurements in study area using the “surface” routine with a tension factor of 0.25 in the GMT software (
Wessel and Smith, 1998
). Statistical comparisons of GGM, SAS, and shipborne gridded models in the study area are summarized in
Table 1
. The GGM model in the study area showed correlation coeffi cients of 0.99 and 0.99 with SAS and shipborne gridded models, respectively in
Table 1
. SAS model in the study area also shows high correlation in comparison with shipborne gridded model. GGM, SAS, and shipborne gridded models are identical because their standard deviation values in the study area are similar as seen in
Table 1
.
Bathymetry models by (a) the gravity-geologic method (GGM), (b) the Smith and Sandwell (SAS) method (1994), and (c) shipborne gridded model before the earthquake
Statistics of bathymetry models by the gravity-geologic method (GGM), Smith and Sandwell’s (SAS) method (1994), and shipborne gridded model in the study area before the earthquake, CC is correlation coefficient
In addition, the power spectral density (PSD) of the GGM and SAS models was analyzed to investigate energy variations in different wavelengths. Shipborne gridded model generated by GMT software was not effectively predicted because many gaps between shipborne tracks were simply gridded, in comparison with GGM and SAS models. Thus, we evaluated PSD for GGM and SAS models. In comparison of the GGM model with SAS model in the power spectral density in
Fig. 6
, GGM was found to have high energy power in short wavelengths less than about 6 km. The results of the power spectral density analysis in the study area show that the GGM model has better bathymetry for short wavelengths than SAS. The GGM bathymetry model (GGM in
Fig. 5
) in the study area can be selected as the best reference model for bathymetry before the earthquake according to the results of the power spectral density.
The comparison of power spectral density (PSD) between GGM and SAS bathymetry models before the earthquake
(a) Bathymetry measured by the JAMSTEC shipborne after the earthquake, (b) Bathymetry interpolated into the JAMSTEC shipborne locations from the reference bathymetry model before the earthquake, (c) Bathymetry change computed from differences (a – b) between them
In
Fig. 8(a)
, bathymetry before and after the earthquake was compared with fi ve Profi les in the Japan Trench (denoted as blue boxes). For more details, the bathymetry variations in the Japan Trench by the earthquake were magnifi ed in
Fig. 8(b)
. Bathymetry after the earthquake is greater than that before the earthquake at the Japan Trench axis (denoted as dotted lines) in all Profi les, as shown in
Fig. 8(b)
. As fi nal results of this study,
Fig. 8(c)
shows bathymetry change in the Japan Trench from differences of bathymetry before and after the earthquake. The west side of the trench axis shows large variations of the seafl oor topography. In particular, bathymetry change of about ±50 m was found at the west side of the Japan Trench in Profi les #4 and #5 of
Fig. 8(c)
. The results of the remarkable bathymetry change at the Japan Trench axis are likely to be submarine landslide due to the megathrust earthquake and are consistent with the results of
Fujiwara . (2011)
.
(a) Comparison of bathymetry before and after the earthquake around the Japan Trench for five Profiles, (b) Comparison of bathymetry before and after the earthquake at the Japan Trench axis for five Profiles, (c) Comparison of bathymetry change by the earthquake in the Japan Trench for five Profiles
^{3}
determined by the check points of the gravity-geologic method and downward continuation method could be effectively applied to predict bathymetry around the Japan Trench before the earthquake. Accurate bathymetry estimations are dependent on the stabilization of bathymetry estimates from gravity effects of variable density and rugged bathymetric relief at distances up to several kilometers (
Kim ., 2010
). Bathymetry change of about ±50 m was found at the west side of the Japan Trench from point-by-point differences of bathymetry before and after the earthquake in two Profiles. These large bathymetry changes at the Japan Trench are consistent with the results of
Fujiwara . (2011)
probably caused by the landslide of the seafloor.

Bathymetry Change
;
2011 Tohoku Earthquake
;
Satellite Altimetry-derived FAGA
;
Gravity-Geologic Method (GGM)
;
Japan Trench

1. Introduction

In Japan, four different tectonic plates, which are the Eurasian plate, the North American plate, the Pacific plate, and the Philippine Sea plate, meet around the Honshu Island as shown in
Fig. 1
. The boundary between the Eurasian and the North American plates in the eastern margin of the East Sea (Sea of Japan) has been delineated as a nascent convergent zone (
Nakamura, 1983
). The Pacific plate subducts under the North American plate along the Japan Trench and the Kuril Trench at a rate of 7.3∼7.8 cm/year (denoted as red arrows) as shown in
Fig. 1
(
Sella ., 2002
;
Apel ., 2006
).
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2. Bathymetry Prediction by Altimetry-derived Gravity Anomalies

- 2.1 Gravity-Geologic Method

Gravity-Geologic Method (GGM) was originally developed to predict the depth-to-basement through observed gravity anomalies and borehole measurements in comparison of density contrast between glacial sediment and bedrock (
Ibrahim and Hinze, 1972
;
Nagarajan, 1994
). As shown in
Fig. 2
, geometry of the GGM in marine applications is related to calculating a regional gravity field (
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- 2.2 Determination of density contrast by downward continuation

The downward continuation method can be implemented for selecting an improved single density contrast within an acceptable range determined by the check-points method of the GGM.
Parker (1977)
described upward continuation in the frequency domain from the gravity field at
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- 2.3 Smith and Sandwell’s (SAS) method

The forward model to convert bathymetry (
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3. Data and Study Area

In this study, SB and SAFAGA in the study area (37.5° ~ 39.3°N and 142.5° ~ 144.5°E) located around the Japan Trench are utilized to estimate a 1×1 arc-minute bathymetry model before the earthquake, where sparse shipborne depth measurements were available. 10,838 shipborne measurements, denoted as red and blue dots in the study area as shown in
Fig. 3(a)
, were obtained from the National Geophysical Data Center (NGDC,
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4. Results

- 4.1 Reference bathymetry modeling

The bathymetry modeling, proposed by two methods: GGM and SAS, was performed by combining shipborne measurements (bathymetry and gravity anomalies) with SAFAGA obtained before the earthquake occurred. The GGM bathymetry was generated from the NGDC shipborne measurements and SAFAGA from
Sandwell and Smith (2009)
. For the GGM estimates, we selected 4,704 NGDC shipborne measurements in the study area that contain both depth and gravity anomalies denoted as red dots in
Fig. 3(a)
. The shipborne measurements selected in the study area are divided into control points for two thirds of the points and check points for remaining one third of the points. Every third point of shipborne measurements along ship tracks was picked as a check point to evenly distribute and evaluate the bathymetric accuracy in the study area. In the study area, 3,142 and 1,562 of total 4,704 NGDC shipborne measurements were selected as control points and check points, respectively. The control points in the study area were used to check the stability of the GGM estimations over a range of density contrasts by the check-points method with GGM.
In GGM predictions, a root-mean-square (RMS) difference and its rate of change between the control points and the check points using a single density Bouguer slab for different density contrasts in a trade-off diagram, as shown in
Fig. 4(a)
, are used to select an acceptable range in tuning value of density contrast. In this study, the acceptable range of the density contrasts, which minimize the RMS estimation errors from 7.00 m to −4.71 m on the blue one of three curves in the trade-off diagram, was selected in 14.0 g/cm
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Statistics of bathymetry models by the gravity-geologic method (GGM), Smith and Sandwell’s (SAS) method (1994), and shipborne gridded model in the study area before the earthquake, CC is correlation coefficient

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- 4.2 Bathymetry change

Bathymetry change caused by the earthquake was investigated through estimating a reference bathymetry generated in the study area around the Japan Trench. Bathymetry modeling before the earthquake was proposed by GGM and SAS using SB and gravity anomalies, SB; and SAFAGA obtained from NGDC, JAMSTEC, and SIO, respectively, in the study area, as shown in
Fig. 3
. In this study, GGM bathymetry model can be effectively predicted in short wavelengths with a tuning density contrast estimated from downward continuation method to overcome the limitation of dependency on density contrast. Bathymetry model estimated by the gravity-geologic method (GGM) was selected as a reference bathymetry in the study area before the earthquake from the results of the power spectral density, as shown in
Fig. 6
. GGM bathymetry model was used to estimate bathymetry change on the JAMSTEC shipborne locations measured after the earthquake. Bathymetry before the earthquake, as shown in
Fig. 7(b)
, was computed by interpolating 2-dimensional GGM bathymetry model into the JAMSTEC shipborne locations measured after the earthquake in the study area. Bathymetry change by the earthquake was computed by subtracting bathymetry (
Fig. 7(b)
) interpolated on the JAMSTEC shipborne locations from the reference (GGM) model from bathymetry (
Fig. 7(a)
) after earthquake on the JAMSTEC shipborne tracks.
PPT Slide

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PPT Slide

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5. Conclusion

Investigation of bathymetry change through utilizing estimated reference bathymetry in the tectonic plate boundaries of the 2011 Tohoku earthquake reveals importance to advance comprehension of variations related to vertical displacement before and after the megathrust earthquake. Bathymetry change using the GGM with SAFAGA and SB is useful to estimate potential variations of the seafloor topography in trench area on the subduction zone by the megathrust earthquake.
This study investigates bathymetry change caused by the 2011 Tohoku earthquake through SAFAGA and shipborne measurement data which include (1) shipborne depth and gravity anomalies from NGDC and JAMSTEC before and after the earthquake, and (2) SAFAGA before the earthquake. To estimate bathymetry change caused by the earthquake, a reference bathymetry before the earthquake was predicted by gravity-geologic method (GGM) and Smith and Sandwell’s (SAS) method, which are effectively estimated by combining the shipborne depth measurements with SAFAGA. Because the variations of the gravity anomalies are theoretically correlated with the undulations of crustal density variations of the local bedrock under the ocean floor, SAFAGA, where the shipborne bathymetric measurements lack, provide important geophysical information for accurate bathymetry modeling before earthquake.
We conclude that GGM before the earthquake estimates better bathymetry in short wavelength (below about 6 km) than SAS. A tuning density contrast of 17.04 g/cm
Acknowledgements

We thank Professor Jeong Woo Kim at University of Calgary for his constructive comments, which have been instrumental in the improvement of this study.

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Citing 'Bathymetry Change Investigation of the 2011 Tohoku Earthquake
'

@article{ GCRHBD_2015_v33n3_181}
,title={Bathymetry Change Investigation of the 2011 Tohoku Earthquake}
,volume={3}
, url={http://dx.doi.org/10.7848/ksgpc.2015.33.3.181}, DOI={10.7848/ksgpc.2015.33.3.181}
, number= {3}
, journal={Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography}
, publisher={Korean Society of Surveying, Geodesy, Photogrammetry and Cartography}
, author={Kim, Kwang Bae
and
Lee, Chang Kyung}
, year={2015}
, month={Jun}