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Coseismic gravity and displacement changesof Japan Tohoku earthquake (Mw 9.0)
Xinlin Zhanga,b,c,*, Shuhei Okubob, Yoshiyuki Tanakab, Hui Lia,c
a Institute of Seismology, China Earthquake Administration, Wuhan 430071, Chinab Earthquake Research Institute, The University of Tokyo, Tokyo 1130032, Japanc State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy & Geophysics, Chinese Academy of
Sciences, Wuhan 430077, China
a r t i c l e i n f o
Article history:
Received 1 September 2015
Accepted 26 November 2015
Available online 25 March 2016
Keywords:
Tohoku earthquake (Mw 9.0)
Co-seismic gravity change
Co-seismic displacement change
Coseismic geoid change
Dislocation theory
Global Positioning System
Absolute gravity measurement
Relative gravity measurement
* Corresponding author. Institute of SeismolE-mail address: [email protected]
Peer review under responsibility of Instit
Production and Hosting by Elsev
http://dx.doi.org/10.1016/j.geog.2015.10.002
1674-9847/© 2016, Institute of Seismology, Ch
Communications Co., Ltd. This is an open acce
a b s t r a c t
The greatest earthquake in the modern history of Japan and probably the fourth greatest in
the last 100 years in the world occurred on March 11, 2011 off the Pacific coast of Tohoku.
Large tsunami and ground motions caused severe damage in wide areas, particularly many
towns along the Pacific coast. So far, gravity change caused by such a great earthquake has
been reported for the 1964 Alaska and the 2010 Maule events. However, the spatial-tem-
poral resolution of the gravity data for these cases is insufficient to depict a co-seismic
gravity field variation in a spatial scale of a plate subduction zone. Here, we report an
unequivocal co-seismic gravity change over the Japanese Island, obtained from a hybrid
gravity observation (combined absolute and relative gravity measurements). The time in-
terval of the observation before and after the earthquake is within 1 year at almost all the
observed sites, including 13 absolute and 16 relative measurement sites, which deduced
tectonic and environmental contributions to the gravity change. The observed gravity
agrees well with the result calculated by a dislocation theory based on a self-gravitating
and layered spherical earth model. In this computation, a co-seismic slip distribution is
determined by an inversion of Global Positioning System (GPS) data. Of particular interest
is that the observed gravity change in some area is negative where a remarkable subsi-
dence is observed by GPS, which can not be explained by simple vertical movement of the
crust. This indicated that the mass redistribution in the underground affects the gravity
change. This result supports the result that Gravity Recovery and Climate Experiment
(GRACE) satellites detected a crustal dilatation due to the 2004 Sumatra earthquake by the
terrestrial observation with a higher spatial and temporal resolution.
© 2016, Institute of Seismology, China Earthquake Administration, etc. Production and
hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access
article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
How to cite this article: Zhang X, et al., Coseismic gravity and displacement changes of Japan Tohoku earthquake (Mw 9.0),Geodesy and Geodynamics (2016), 7, 95e100, http://dx.doi.org/10.1016/j.geog.2015.10.002.
ogy, China Earthquake Administration, Wuhan 430071, China.(X. Zhang).
ute of Seismology, China Earthquake Administration.
ier on behalf of KeAi
ina Earthquake Administration, etc. Production and hosting by Elsevier B.V. on behalf of KeAi
ss article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
g e o d e s y and g e o d yn am i c s 2 0 1 6 , v o l 7 n o 2 , 9 5e1 0 096
1. Introduction
The Tohoku earthquake (Mw¼ 9.0) of March 11, 2011 is one
of the largest earthquakes that occurred in the Pacific coast of
Tohoku. For this earthquake, both deformations of the Earth'ssurface at the time of faulting and transient crustal move-
ments after the event have been disclosed by the Global
Positioning System (GPS) measurements. However, gravity
changes caused by earthquakes have been reported in many
earthquake investigation cases. First gravity change caused by
such a great earthquake has been detected for the 1964 Alaska
earthquake in March 1964 with a LaCoste and
Romberg geodetic meter (LCR) [1]. The gravity change caused
by earthquake was reported with a FG5 absolute gravimeter
[2]. First gravity change detection by an array of
superconducting gravimeters was made after the 2003
Tokachi-Oki earthquake (Mw ¼ 8.0), Japan [3]. The first map
of co-seismic change in gravity was drawn using the data
from the Gravity Recovery and Climate Experiment (GRACE)
satellites for the 2004 Sumatra-Andaman earthquake [4]. The
co-seismic gravity change was detected by satellite
gravimetry for 2010 Chile earthquake (Mw ¼ 8.8) [5,11]. In
this study, a hybrid gravity measurement campaign
(combined absolute and relative gravity measurement) was
conducted after the event for investigating coseismic gravity
changes.
Ontheotherhand,thetheoryofchangesintheEarth'sgravityfield associated with earthquakes has been nearly completed
recently [6e9]. In this study, the theoretical co-seismic gravity
changes caused by Tohoku earthquake were calculated by a
dislocation theory based on a self-gravitating and layered
sphericalearthmodel [10]. Inthiscomputation,aco-seismicslip
distribution is determined by an inversion of GPS data and
constrained by coseismic observation gravity changes.
Finally, comparing the observed co-seismic gravity
changes with theoretical results, we found that they agreed
well with each other. However, for some particular area, we
cannot interpret gravity changes simply with the vertical
movement of the crust and also need to consider the effect
caused bymass redistribution of the interior of the Earth. This
result supports that GRACE satellites detected a crustal dila-
tion due to the 2004 Sumatra earthquake by the terrestrial
observation with a higher spatial and temporal resolution [4].
Fig. 1 e Calculated coseismic gravity changes by a
dislocation theory based on a self-gravitating and layered
spherical earth model. The red and blue points denote the
absolute and relative gravity measurement sites. The
gravity change computed with a dislocation theory [10].
The unit of the contour line is microgal (1
microgal ¼ 10¡8 m/s2). Spherical geometry is considered
and the elastic structure and the density profile is
Preliminary Reference Earth Model (PREM). A co-seismic
slip distribution is inferred by a geodetic inversion for GPS
data of GEONET. The node of the gravity change passes
near the coast of the Pacific Ocean on the Tohoku region,
where the sign of the gravity change varies from positive to
negative with the increasing epicentral distance.
2. Observations
2.1. Co-seismic gravity change
The hybrid gravity measurement campaign covering the
whole east coastline of Japan was conducted after the Tohoku
earthquake. Wemeasured the absolute gravity with same FG5
(#241) at the sites in red points and relative gravity with same
LCRs (#581, #705) at the sites in blue points in Fig. 1. The time
interval before and after the earthquake is within 1 year at
almost all the observation sites which are including 13
absolute and 16 relative measurement sites. The absolute
gravity sites are Miyazaki, Muroto, Toyohashi, Omaezaki, Ito,
Tokyo, Tsukuba, Tsukubane, Sendai, Hachinohe, Usu, Erimo,
Akkeshi from the south to the north. And the relative gravity
sites are Yamato, Ogihama, Ayukawa, Onagawa, Oshu,
Aikawa, Shizugawa, Natari, Miyato, Kahoku, Rifu, Yamagata,
Shinjo, Soma, Mizusawa, Ofunato in the Tohoku region.
In the Fig. 2, black points show the coseismic observation
gravity changes of main shock area sites in the near and far
field with the observation error about 2e5 microgal. From
point 1 to point 10 and from point 27 to point 29 represent
the absolute observation sites and the others are the relative
observation sites. Coseismic observation gravity changes of
Tokyo, Tsukuba, Tsukubane, Sendai and Hachinohe are
greater than the other sites in the far field (Miyazaki,
Muroto, Toyohashi, Omaezaki, Ito, Usu, Erimo and Akkeshi).
The gravity changes of Tokyo, Tsukuba and Tsukubane are
increased about 10.0 microgal. However, the gravity changes
of Sendai and Hachinohe are about �10.0 microgal. The
greatest and least gravity changes of other sites are about
5.0 microgal and 0.0 microgal. And the observation error is
about 2e5 microgal. Furthermore, the gravity changes of
south sites (Miyazaki, Muroto, Omaezaki and Ito) are
Fig. 2 e Comparison between calculated (red) and observed (black) gravity changes. The horizontal axis denotes the site ID
(1e10, 27e29: absolute measurement, 11e26: relative measurement).
g e o d e s y a nd g e o d yn am i c s 2 0 1 6 , v o l 7 n o 2 , 9 5e1 0 0 97
negative except Toyohashi and the gravity changes of north
sites (Usu, Erimo and Akkeshi) are nonnegative.
Besides, to show more details of the gravity change in the
Tohokuarea,we alsomeasured 16 relative gravity sites around
the terrestrial main shock region. Gravity changes are
increased large along the coast butwith lowaccuracy (with the
observation error about 10 microgal). Most sites show that the
gravity changes are positive with the amount about 10e100
microgal except gravity change of some sites are negative,
such as Sendai, Hachinohe, Mizusawa, Shinjo and Yamagata.
To determine changes in gravity associated with the event
accurately, we removed known signals from the data. A lot of
geophysical phenomena cause temporal changes in surface
gravity. The largest effect is lunar and solar tidal deformation
of the solid Earth. Oceanic tides have a minor contribution to
the observed gravity through loading. The combined signals of
body and oceanic tides are accurately known for each station
from years of gravity observations and are readily removed
from the data. The atmosphere affects gravity through New-
tonian attraction by the atmosphericmass and deformation of
land due to loading. Although this effect could be fully un-
derstood only by taking into account the global distribution of
atmosphere pressure, it is roughly proportional to the change
in local atmospheric pressure, especially for short periods
with admittance around �3*10�9 ms�2 hPa�1. The effects of
polar motion can be calculated from Earth rotation parame-
ters provided by the International Earth Rotation and Refer-
ence Systems Service. Seasonal variations also have a
contribution to the observed gravity through atmosphere,
oceans and continental water variations with season alter-
nation. Its regular period is about one year. And our repeated
gravity measurement interval is just one year so that the
seasonal variation effects are removed automatically from the
gravity changes (Fig. 2). Besides, comparing with the observed
gravity change, the annual gravity change and the effect of
foreshock, aftershock and after slip on the gravity are very
small which can be ignored. Therefore, we regarded the
observed gravity data as coseismic gravity change.
Fig. 3 e Comparison between calculated (red) and observed
(black) vertical displacement changes. The yellow star
denotes the hypocenter.
2.2. Co-seismic displacement change
In this section, we show the co-seismic displacement
changes associated with the Tohoku event. In the Fig. 3 black
arrows show the observed vertical displacement changes. The
yellow star denotes the hypocenter. Along the Japan coastline,
all GPS sites down thrust with a magnitude of 50 cm and
attenuate rapidly deviating from the hypocenter. Some GPS
sites show different changes near the hypocenter because of
complex surface deformation caused by the earthquake. We
also plot the observed horizontal displacement changes in
the Fig. 4. All GPS sites move forward to the southeast with
an amount around 5 m in the Japan mainland and 25 m for
some islands locating in the sea and near the hypocenter.
3. Co-seismic gravity, displacement andgeoid changes by modeling
Coseismic slip distribution on the fault plane of plate
boundary has been estimated by Geospatial Information
Fig. 4 e Comparison between calculated (red) and observed
(black) horizontal displacement changes. The yellow star
denotes the hypocenter.
Fig. 5 e Coseismic fault slip distribution. The yellow star
denotes the hypocenter. The broken lines denote fault
depth and the contours of slip distribution are drawn per
5 m.
Fig. 6 e Coseismic geoid change. The yellow star denotes
the hypocenter.
g e o d e s y and g e o d yn am i c s 2 0 1 6 , v o l 7 n o 2 , 9 5e1 0 098
Authority of Japan (GSI) (coseismic slip distribution model on
the plane of plate boundary based on GPS land and sea-floor
positioning, 2011, http://www.gsi.go.jp/common/000060854.
pdf) by combining GPS data from terrestrial stations and
ocean bottom stations. Finally, we improved the fault model
with observedgravity changes. Fig. 5 shows the slipdistribution
projected onto the Earth surface. The maximum slip of
approximately 40 m is located about 50 km northeast of the
epicenter. The broken lines denote the fault depth which
shows that the fault extends from the Earth surface into the
inner about 100 km. The contours of slip distribution are
drawn every 5 m. Using this fault model, we calculated co-
seismic gravity (Figs. 1 and 2), displacement (Figs. 3 and 4) and
geoid (Fig. 6) changes following themethod of Tanaka et al. [10].
The red points of Fig. 2 show the computed values for all
absolute sites and relative sites in Tohoku region. Black
points and red points coincide well means that computed
values agree well with the observed gravity changes except
surrounding noise is large for few observation sites such as
point 16 (Shizugawa) and point 18 (Miyato).
Figs. 3 and 4 show the modeled and observed vertical and
horizontal displacements changes. They coincide well with
each other both in direction and magnitude for sites in the
Japan land.And theyarequite similar for fewsites in theocean.
Because, the fault that we used for calculating the coseismic
displacement changes with the dislocation theory, is inversed
by the GPS and seismic observatory locating in the land.
Therefore, the constraint is weak for calculating the coseismic
displacement changes for the sites in the ocean. And the
modeledandobserveddisplacement changesof thesites in the
ocean do not coincide so well as the sites in the land.
Fig. 6 shows the coseismic geoid change. The maximum is
50 mm locating east of the epicenter and the geoid is changed
g e o d e s y a nd g e o d yn am i c s 2 0 1 6 , v o l 7 n o 2 , 9 5e1 0 0 99
in several thousand kilometers area from focal region and
decreased with the distance.
Fig. 7 e Coseismic vertical displacement change of gravity
observation sites in Tohoku region. The yellow star
denotes the hypocenter.
4. Deformation in Tohoku region
Generally, the gravity field change is caused by two
mechanisms, i.e. deformation of layer boundaries with den-
sity contrasts (e.g., surface uplift and subsidence), and density
changes of rocks due to volumetric strain (co-seismic dilation
and compression). Surface uplift and co-seismic dilationmake
gravity decrease. And contrariously, surface subsidence and
co-seismic compression cause gravity increase. Therefore, the
quantitative relationship between gravity change and vertical
displacement change may have more important geophysical
significance than surveying significance.
The force of gravity at a station on the Earth's surface is a
function of both the distance of the station from the center of
the Earth and of the rock mass redistribution. If the Earth'ssurface is locally deformed so that the mass redistribution
influencing the gravity change can be ignored, the gravity
change would be related to the vertical displacement change
by approximately 0.309 mGal/m, the normal free-air gradient
of gravity above the Earth's surface. If the Earth's surface is
deformed, the effect of mass redistribution are added or
subtracted. Therefore, the gravity changes should be related
to the vertical displacement changes by a factor closer to
0.197 mGal/m which is named Bouguer modification.
Unfortunately, we do not have coseismic vertical
displacement observation data for gravity observation sites.
Therefore, base on coseismic vertical displacement data
(Fig. 3), we fit the coseismic vertical displacement changes for
these sites in Tohoku region by surface fitting method and
figure them in Fig. 7. Fig. 7 shows gravity observation sites
locate in an obvious subsidence region. The vertical
displacement of each site is downward approximately 0.8 m
Fig. 8 e Relations between coseismic vertical displacement an
which cause gravity increase in the surface of the Earth.
Then, we calculated the ratios of vertical displacement
changes with gravity changes for 18 gravity observation
sites, and compared them with free-air and
Bouguer gradient (Fig. 8). We found that the effects of mass
d gravity changes for observation sites in Tohoku region.
g e o d e s y and g e o d yn am i c s 2 0 1 6 , v o l 7 n o 2 , 9 5e1 0 0100
redistribution on gravity change are negative neither
considering free-air nor Bouguer corrections. Such results, to
a large extent, are regarded as dilatation of rocks occurred
above the down-slip end of fault.
5. Conclusions
Co-seismic gravity changealong the Japaneseeast coastwas
detectedbyhybridgravityobservationafterTohokuearthquake
March 11, 2011. The observed data shows the basic gravity
change contour in Fig. 1. In addition, a theoretical co-seismic
gravity changes were calculated based on a dislocation theory
with a self-gravitating and layered spherical earth model in
Fig. 1 and for 29 reference sites in Fig. 2. The observed gravity
and displacement changes agree well with the calculated
results which also confirm that the theory correctly estimates
co-seismic gravity and displacement changes.
And the modeled coseismic geoid change with the
maximum value is 50 mm locating east of the epicenter and
the geoid is changed in several thousand kilometers area from
focal region and decreased with the distance.
Furthermore, the observed gravity changes are not coin-
cided the theoretical results completelywhich imply thatmore
realistic earth model and reliable fault model are necessary.
Finally, the observed gravity changes in some region are
negative where an obvious subsidence is detected by GPS,
which can not be explained simply by vertical displacement of
the crust. This indicates that the mass redistribution in the
underground affects the gravity changewhich can be regarded
as dilatation of rocks occurred above the down-dip end of the
fault. This result supports the conclusion ofHan et al. [4]which
showed that GRACE satellites detected a crustal dilatation due
to the 2004 Sumatra earthquake by the terrestrial observation
with a higher spatial and temporal resolution.
Acknowledgments
We greatly appreciate the helpful suggestions from editors
and anonymous reviewers. This study is supported by the
Research Fund Program of Institute of Seismology, Chinese
Earthquake Administration (IS201226045), the Open Research
Fund Program of the State Key Laboratory of Geodesy and
Earth's Dynamics (SKLGED2013-3-7-E), and the National Nat-
ural Science Foundation of China (41404065).
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Xinlin Zhang, assistant researcher, Insti-tute of Seismology, Chinese EarthquakeAdministration. His interests includedislocation theory and gravity observationdata interpretation and application.