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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: xinlinzhang2012@163.com

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.