Tectonophysics 600 (2013) 165–174

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Tectonophysics

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Interplate coupling along the Nankai Trough, southwest Japan, inferred frominversion analyses of GPS data: Effects of subducting plate geometry and spacing ofhypothetical ocean-bottom GPS stations

Shoichi Yoshioka a,⁎, Yoshiko Matsuoka b

a Research Center for Urban Safety and Security, Kobe University, Rokkodai-cho 1-1, Nada ward, Kobe 657-8501, Japanb NTT DATA Sekisui Systems Corporation, Umeda Center Building 29F, Nakazakinishi 2-4-12, Kita ward, Osaka 530-0015, Japan

⁎ Corresponding author. Tel./fax: +81 78 803 6598.E-mail address: yoshioka@port.kobe-u.ac.jp (S. Yosh

0040-1951/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.tecto.2013.01.023

a b s t r a c t

a r t i c l e i n f o

Article history:Received 6 April 2012Received in revised form 17 December 2012Accepted 27 January 2013Available online 4 February 2013

Keywords:Slip-deficit rateSouthwest JapanGPSInversionGeometric modelOcean-bottom GPS station

We estimated the slip-deficit rate distribution on the plate boundary between the subducting Philippine Seaplate and the continental Amurian plate along the Nankai Trough, southwest Japan. Horizontal and verticaldisplacement rates were calculated from land-based Global Positioning System (GPS) data during the5-year period from 1 January 2005 to 31 December 2009. We employed an inversion analysis of geodeticdata using Akaike's Bayesian information criterion (ABIC), including an indirect prior constraint that slip dis-tribution is smooth to some extent and a direct prior constraint that slip is mainly oriented in theplate-convergent direction. The results show that a large slip deficit exists at depths ranging from 15 to20 km on the plate boundary in a belt-like form. The maximum slip-deficit rate was identified off Shikokuand reached 6 cm/year. The slip-deficit rate differed by as much as 1 cm/year when using a different geomet-ric model of the subducting plate. On the basis of the spatial distribution of estimation errors and the resolu-tion of the obtained slip-deficit rate on the plate boundary, we also found that the offshore slip-deficit ratecannot be estimated with sufficient accuracy using only land-based GPS data. Therefore, we tested the im-provement in results when introducing hypothetical ocean-bottom GPS stations. The stations were arrangedin four along-arc and across-arc spacings of 80 km and 40 km. The ocean-bottom data improved the estima-tion errors and resolutions, and successful results were obtained for a checkerboard with each square75 km×76 km. Our results indicate that 40-km along-arc and across-arc two-dimensional spacing ofocean-bottom GPS stations is required to obtain reliable slip-deficit distributions near the trough axis, assum-ing the current estimation accuracy for ocean-bottom horizontal displacement rates.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

In southwest Japan, interseismic crustal deformation is caused byinteraction of the subducting oceanic Philippine Sea (PHS) platewith the overriding continental Amurian plate along the NankaiTrough (Fig. 1). According to the plate motion model by Sella et al.(2002), subduction directions are oriented N57.5°–59.0°W, and sub-duction velocities are 6.8–6.0 cm/year from off Shikoku to off theKii Peninsula. On the plate boundary, megathrust earthquakes haveoccurred repeatedly with a recurrence interval of about 90 to150 years (e.g., Ando, 1975). The most recent events were the 1944Tonankai (M 7.9) and 1946 Nankai (M 8.0) earthquakes. Coseismicslip distributions for these events were obtained by inversion analy-ses of geodetic data such as triangulation and leveling data (e.g., Itoand Hashimoto, 2004; Sagiya and Thatcher, 1999; Yabuki andMatsu'ura, 1992) and tsunami waveforms (e.g., Baba and Cummins,2005). Because largely slipped areas at the time of a megathrust

ioka).

rights reserved.

earthquake are considered strongly coupled regions, we can roughlyestimate expected coseismically slipped regions for a futuremegathrust event by estimating the spatial distribution of coupled re-gions during an interseismic period.

Fig. 1 is a tectonic map showing the epicenter distributions ofearthquakes with depths ranging from 20 to 180 km that occurredduring the 5-year period from 1 January 2005 to 31 December 2009.Most of these events were thrust-type earthquakes on a plate bound-ary or intraslab earthquakes. Earthquakes of M 6 to M 7 occurredfrequently on the plate boundaries in the Tohoku and Kyushu districtsduring the study period, whereas such earthquakes rarely occurredin association with subduction of the PHS plate beneath Shikokuand the Kii Peninsula.

In Japan, Global Positioning System (GPS) observation was initiatedby the Geospatial Information Authority of Japan (GSI) in 1994, and op-eration of the GPS continuous observation system (GEONET) started in1996.More than 1200 land-based GPS stationswere in operation acrossthe Japanese islands by 2004. GPS continuous observation can observenot only coseismic and postseismic crustal deformations associatedwith a large earthquake, but also steady crustal deformation associated

130˚E 131˚E 132˚E 133˚E 134˚E 135˚E 136˚E 137˚E 138˚E31˚N

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DEPTH (km)

M2

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Kyushu

Kii Peninsula

Chugoku Kinki

Hyogohidaka

Amurian plate

Philippine Sea plate

5cm/yr

130˚E 140˚E

30˚N

40˚NTohoku

Fig. 1. Tectonic map of southwest Japan. The black arrows are plate motion velocity vectors of the PHS plate with respect to the Amurian plate (Sella et al., 2002) along the NankaiTrough. The blue solid square is the reference point for the investigated GPS data. The solid color circles represent unified hypocenters determined by the JMA whose sizes aredepicted in proportion to their magnitudes, and colors denote their depths. Plotted are all the events with magnitude greater than 2.5 and depth range from 20 to 180 km thatoccurred during the period from 1 January 2005 to 31 July 2009. Depicted in the inset are all the events with magnitude greater than 5 for the same depth range during thesame period.

166 S. Yoshioka, Y. Matsuoka / Tectonophysics 600 (2013) 165–174

with subduction of an oceanic plate. Using such GPS data, as advocatedby Savage (1983), slip-deficit rate distributions on a plate boundaryduring an interseismic period have been estimated in southwest Japan(e.g., Ichitani et al., 2010; Ito et al., 1999; Liu et al., 2010; Loveless andMeade, 2010; Miyazaki and Heki, 2001; Nishimura and Hashimoto,2006).

In this study we obtained displacement rates from a time series ofGPS continuous data collected from 1 January 2005 to 31 December2009 and estimated the distribution of the slip-deficit rate on theplate boundary in southwest Japan. We chose this period becausethe following were not observed during it: crustal deformationscaused by long-term slow slip events, afterslips following large earth-quakes, and crustal deformations associated with stress relaxation ofthe uppermost mantle followed by earthquakes. We conducted an in-version analysis of geodetic data using Akaike's Bayesian informationcriterion (ABIC; Akaike, 1980), including an indirect prior constraintthat slip distribution is smooth to some extent and a direct prior con-straint that slip is mainly oriented in the plate-convergent direction(Matsu'ura et al., 2007). This method is useful because theslip-deficit rate on the plate boundary is considered to be parallel tothe plate-convergent direction.

When estimating the slip-deficit rate distribution, the geometry ofthe upper surface of the subducting plate is essential. Various geo-metric models of the plate have been proposed, including the CrustalActivity Modeling Program (CAMP) standard model determined fromInternational Seismological Center (ISC) hypocenter data (Hashimotoet al., 2004), a model obtained from seismic tomography (e.g., Hiroseet al., 2008), and a model obtained from receiver function analysis(e.g., Shiomi et al., 2008). The respective geometric models of theupper surface of the PHS plate have some slight differences. We in-vestigated the extent to which differences in geometric models ofthe slab affect estimations of the slip-deficit rate distribution.

Furthermore, although GEONET stations are densely spaced at ap-proximately 20 km intervals on land, there is no observation networkin the ocean. The Japan Coast Guard has progressively initiated oper-ation of an ocean-bottom crustal deformation observation network.

Using checkerboard tests, we also investigated whether estimationerrors and the resolution of the estimated slip-deficit rate could beimproved if certain distributions of ocean-bottom GPS stations areinstalled.

2. Data

2.1. Horizontal and vertical displacement rates

For this study, we used observation data from land-based GPS sta-tions provided by the GSI. Daily coordinate values (F3 solution;Nakagawa et al., 2009) were obtained for the 5 years from 1 January2005 to 31 December 2009. We employed times series of north–south, east–west, and up–down components obtained at 360land-based GPS stations located in the eastern Kyushu, Chugoku, Shi-koku, and Kinki districts. Following Yoshioka et al. (2004), weobtained crustal deformations caused by slip-deficit rate, using thefollowing equation:

y tð Þ ¼ aþ bt þ c sin2πtT

� �þ d cos

2πtT

� �þ e sin

4πtT

� �

þ f cos4πtT

� �þ gH tð Þ ð1Þ

where a, b, c, d, e, f, and g are unknown parameters to be determinedby least-square fitting to time series of respective components atland-based GPS stations, and T=1 year. The first and second termsin the right side of Eq. (1) represent the linear trend, and b is the dis-placement rate caused by the slip-deficit rate. The third and fourthterms are annual variations, and the fifth and sixth terms aresemi-annual variations. Annual variations are noises caused by atmo-spheric conditions such as temperature, humidity, and atmosphericpressure, whereas semi-annual variations can originate from varia-tions in the ionosphere, temperature, and tide. The seventh termH(t) represents the Heaviside step function, which we used whenthere was a step in a time series due to coseismic crustal deformation

167S. Yoshioka, Y. Matsuoka / Tectonophysics 600 (2013) 165–174

and antenna exchange. Because the calculated displacement rate ateach GPS-based control station is based on ITRF2005 (Nakagawaet al., 2009), we converted it to the displacement rate for a referencepoint, Hyogohidaka (Figs. 1 and 2), which is located far from the plateboundary.

Fig. 2 shows the obtained horizontal and vertical displacementrates. Horizontal displacement rates are mostly oriented to the north-west, which is concordant with the subduction direction of the PHSplate (Fig. 2a). The horizontal displacement rate at the southern tipof Cape Muroto is approximately 4 cm/year. The southeast-orientedhorizontal displacement rates are dominant in the southeasternpart of Kyushu, which may be related to back-arc spreading of the

32˚N

34˚N

100 km

Cape Muroto

Cape Ashizuri

Cape Shiono

cal. −1 cm/yr

cal. +1 cm/yr

1σ = 0.5 cm/yr

obs. −1 cm/yr

obs. +1 cm/yr

b

132˚E 134˚E 136˚E

132˚E 134˚E 136˚E

32˚N

34˚N

100 km

Cape Muroto

KiiChannel

NKTZ

obs. 5 cm/yr1σ = 0.5 cm/yr

cal. 5 cm/yr

a

Fig. 2. (a) Horizontal displacement rates at the land-based GPS stations used in thisstudy. The red arrows denote observed horizontal displacement rates derived fromdaily coordinates of GEONET, namely, the F3 solution during the period from 1 January2005 to 31 July 2009. The ellipse at the tip of each arrow represents the standard devi-ation of horizontal components obtained from curve fitting of Eq. (1) to the GPS timeseries at its station. The yellow solid star is the reference point. The blue arrows repre-sent horizontal displacement rates calculated from the obtained slip-deficit rate distri-bution in Fig. 4a. The gray zone denotes the Niigata–Kobe Tectonic Zone (NKTZ). (b)Vertical displacement rates at the land-based GPS stations used in this study. The redand pink bars denote observed vertical uplift and subsidence rates, respectively, de-rived from the F3 solution. The circle at the tip of each bar represents the standard de-viation of the vertical component obtained from curve fitting of Eq. (1) to the GPS timeseries at its station. The yellow solid star is the reference point. The blue and light bluecolors represent uplift and subsidence rates, respectively, calculated from the obtainedslip-deficit rate distribution in Fig. 4a.

Okinawa Trough, which is located far west of Kyushu (e.g., Nishimuraet al., 2004). More westward horizontal displacement rates than thedirection of plate subduction can be identified in the eastern part ofthe Kinki district. This region is located on the east side of the Niigata–Kobe Tectonic Zone (NKTZ) that extends from Niigata southwest toKobe, resulting in strain concentration of crustal deformation (Sagiyaet al., 2000). From the spatial distribution of vertical displacementrates, subsidence rates of about 0.3 cm/year have been identified atcapes Ashizuri, Muroto, and Shiono, and uplift rates up to 0.8 cm/yearcan be found in most regions of Shikoku, the Kii Peninsula, and easternKyushu (Fig. 2b).

2.2. Geometric models of the subducting PHS plate

As geometric models of the upper surface of the subducting PHSplate, we used results from the following studies (Fig. 3a): Baba etal.'s (2002) 10-km isodepth contour line obtained from marine seis-mic refraction surveys; Hirose et al.'s (2008) 20- to 50-km isodepthcontour lines derived from seismic tomography; and Nakajima andHasegawa's (2007) isodepth contour lines deeper than 60 km

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m

a

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m

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m

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Fig. 3. (a) The assumed rectangular model region and geometry for Model 1. Theisodepth contour lines of 10 km, 20 to 50 km, and deeper than 60 km were referencedfrom the data of Baba et al. (2002), Hirose et al. (2008), and Nakajima and Hasegawa(2007), respectively. (b) The assumed rectangular model region and geometry forModel 2. The isodepth contour lines of 10 km and 20 km were derived from the dataof Baba et al. (2002) and Hirose et al. (2008), respectively. The isodepth contourlines deeper than a depth of 30 km were obtained by making the geometry of the oce-anic Moho reported by Shiomi et al. (2008) shallower by 7 km.

168 S. Yoshioka, Y. Matsuoka / Tectonophysics 600 (2013) 165–174

obtained from seismic tomography. The dip angle of the PHS platesubducting beneath Shikoku is gentle, whereas that of the subductingplate beneath the Kii Peninsula and Kyushu is steeper. Therefore, thegeometry of the subducting PHS plate along the Nankai Trough is verycomplicated.

3. Method and model

Referring to Matsu'ura et al. (2007), we obtained the spatial distri-bution of slip-deficit rate by solving the following Eq. (2). This methodincludes two prior constraints: an indirect prior constraint that theslip-deficit rate distribution is smooth to some extent, and a directprior constraint that slip-deficit rate directions are mainly oriented inthe direction of plate convergence:

d000

2664

3775 ¼

HP HS

αΔ 00 αΔ0 βI

2664

3775 aP

aS

� �ð2Þ

where d is displacement rate vector obtained from GPS time series byusing Eq. (1), H is the static response function matrix including a basisfunction representing the slip-deficit rate for half-space homogeneousperfect elastic body, and a is coefficient vector of the basis functionrepresenting the amount of slip to be estimated. A superscript letter Pindicates the plate-convergent direction, and S represents a directionperpendicular to plate convergence. Δ is a matrix showing spatialsmoothness, and I is the identity matrix. Spatial smoothness of theslip-deficit rate distribution can be represented by the second spatialderivative of displacement rates. Hyper-parameters α and β, whichare related to the indirect and direct prior constraints, respectively,were obtained so as to minimize ABIC (Akaike, 1980). According toMatsu'ura et al. (2007), model parameters for the slip-deficit rate canbe represented by

a ¼ a þ HTE−1Hþ α2Gþ β2F−1� �−1

HTE−1 d−Hað Þ ð3Þ

where a denotes values to be estimated,a represents most likely valuesof a, and E is the identitymatrix. Comparing Eq. (3) with Eq. (2), we ob-tain

G ¼ ΔTΔ ΟΟ ΔTΔ

� �; F ¼ O O

O I

� �: ð4Þ

Assuming that observation errors have normal distribution N(0,σ2E) with zero mean and variance of σ2, a covariance matrix forestimation errors of the estimated model parameters can be calculatedfrom

C ¼ σ2 HTE−1Hþ α2Gþ β2F−1� �−1 ð5Þ

where α and β are estimated values of α and β, respectively. Werepresent the resolution matrix as follows:

R ¼ HTE−1Hþ α2Gþ β2F−1� �−1

HTE−1H: ð6Þ

In this study, using diagonal elements of the resolution matrix, werepresent a resolution value at a point on the plate boundary asfollows:

R ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRP2 þ RS2

2

sð7Þ

where RP and RS are the values of resolution for the plate-convergentdirection and those for the direction perpendicular to plate

convergence, respectively. Resolution indicates the degree to whichadjacent model parameters are obtained separately. On the otherhand, because prior constraint on the spatial smoothness of theslip-deficit rate is included in our inversion method, it is impossiblein principle to separate adjacent model parameters completely.Therefore, when the weight of the smoothing constraint is large, themaximum value of resolution tends to be small.

Daily variations in the up–down component of GPS time series arelarger than those in north–south and east–west components. Whenperforming inversion analysis, if we use vertical displacement rateswith the same weight as horizontal displacement rates, there is ahigh possibility that noise included in the former will affect the solu-tion. Therefore, we determined the weights of respective displace-ment rates by dividing the displacement rate vector d and the staticresponse function matrix H in Eq. (2) by the standard deviations ofrespective components that we obtained at the time of the curvefitting using Eq. (1). The standard deviations were 0.16–0.45 (averageis 0.20), 0.20–0.45 (average is 0.25), and 0.56–1.30 (average is 0.68)for displacement rates of north–south, east–west, and up–down com-ponents, respectively.

In this study, we set a model fault plane with 600 km in the strikedirection of 250° and 230 km in the dip direction on the curved plateinterface. We used a bi-cubic B-spline function as a basis function andestimated the slip-deficit rate distribution by distributing 27 and 12basis functions in the strike and dip directions, respectively. Follow-ing Sella et al. (2002), we assumed a plate convergence direction ofN58°W, which we used as direct prior information. Recently, Arguset al. (2010) and DeMets et al. (2010) published new plate-motionmodels. We have examined the differences in the convergence vec-tors along the Nankai Trough between their models and our presentmodel. The difference in direction was less than 2° among the models.Therefore, the results would be almost the same if we had used one ofthese other plate-motion models.

4. Results and discussion

4.1. Inverted slip-deficit rate distribution (Model 1)

Fig. 4a shows the slip-deficit rate distribution on the plate bound-ary obtained by inversion analysis. We refer to this model as Model 1.Hyper-parameter values for the indirect and direct prior constraintswere 1.7×10−1 and 1.4×10−1, respectively. Most large slip-deficitrates distribute in a belt-like form at depths ranging from 15 to20 km, and a maximum value of more than 6 cm/year can be foundoff Shikoku. We estimated the coupling coefficient by dividing the es-timated slip-deficit rate by the convergence rate of the PHS plate withrespect to the Amurian plate (Sella et al., 2002; Fig. 4b). Comparingthese results with coseismic slip distributions associated with the1946 Nankai earthquake (e.g., Baba and Cummins, 2005; Sagiya andThatcher, 1999; Yabuki and Matsu'ura, 1992), a large coseismicslipped region almost coincides with a large slip-deficit rate locatedoff Cape Muroto. Because the coupling coefficient there is more than80%, strain can accumulate effectively during an interseismic period,and a large amount of slip can be expected at the time of the nextmegathrust earthquake. However, a strongly coupled region appearsto extend to the west off Cape Ashizuri, where a large slip did notoccur at the time of the 1946 Nankai earthquake. Because the cou-pling coefficient there is also more than 80%, strain with the sameamount as that in the source region of the 1946 Nankai earthquakeis considered to have accumulated. Long-term slow slip events haveoccurred repeatedly on the plate boundary at the down-dip extensionof this region beneath the Bungo Channel with an interval of 5 to6 years (e.g., Kobayashi and Yamamoto, 2011). Because the accumu-lated strain may be partially or entirely released by such slow slipevents, a large slip might not have occurred at the time of the 1946Nankai earthquake.

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BungoChannel

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%

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1

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3

Baba & Cummins (2005)Baba & Cummins (2005)

Fig. 4. (a) Slip-deficit rate distribution estimated on the plate boundary, using the geo-metric models of the upper surface of the PHS plate by Baba et al. (2002), Hirose et al.(2008), and Nakajima and Hasegawa (2007) (Model 1). The arrows denote amountsand directions of the slip-deficit rates, and the circles at the tip of the arrows representthe estimation errors (cm/year). The contour lines show amounts of the slip-deficitrates (cm/year). Color and gray shading indicate areas with values of resolution largerand smaller than 0.15, respectively. The thick black arrows are plate motion velocity vec-tors of the PHS plate with respect to the Amurian plate (Sella et al., 2002). (b) Couplingcoefficient distribution on the plate boundary obtained by dividing the slip-deficit ratedistribution in a (Model 1) by plate convergent rates of the PHS plate with respect tothe Amurian plate by Sella et al. (2002). The green and blue contour lines (m) arecoseismic slip distributions associated with the 1946 Nankai and 1944 Tonankai earth-quakes, respectively, obtained by tsunami inversion analyses (Baba and Cummins,2005). The white dashed circle shows the rough location where the Bungo Channelslow slip events have occurred repeatedly.

169S. Yoshioka, Y. Matsuoka / Tectonophysics 600 (2013) 165–174

On the other hand, as for the source region of the Tonankai earth-quake located on the southeast side of the Kii Peninsula, the maxi-mum slip-deficit rate reaches 5 cm/year, and a coupling coefficientof up to 80% is estimated. Interplate coupling there is slightly weakerthan in the source region of the Nankai earthquake off Shikoku. Aregion with a slightly smaller coupling coefficient than the neighbor-ing belt-like strongly coupled zone exists on the east side of CapeShiono. This slightly weaker coupled region coincides well with theboundaries of the rupture areas of the 1944 Tonankai and 1946Nankai earthquakes, which were obtained from tsunami waveforminversion analysis (Baba and Cummins, 2005; Fig. 4b).

Because all the horizontal displacement rates in the eastern part ofthe Kinki district are oriented more westward than the direction of

plate subduction, the obtained slip-deficit rates at the eastern end ofthe model region are oriented more westward than the plate conver-gent direction, even though we introduced the direct prior constraint.Reliable results with estimation error of 0.6 cm/year were obtained inthe region off Shikoku, where a large slip-deficit rate was estimated.On the other hand, estimation error was 1.0–2.0 cm/year for aslip-deficit rate of less than 3.0 cm/year in the shallower plate bound-ary near the Nankai Trough. Resolution values there were about onesixth of that in the region with the best resolution. Thus, the solutionin the region near the Nankai Trough was not well resolved.

Fig. 2 shows displacement rates calculated from the estimatedslip-deficit rate in Fig. 4a and the observed displacement rates. Be-cause we weighted respective horizontal and vertical displacementrates by dividing them by their standard deviation for the curvefitting using Eq. (1), the slip-deficit rate distribution was estimatedmostly by fitting to the horizontal displacement rates.

Here we compare the estimated slip-deficit rate distributionobtained in this study with those obtained by recent studies. Our re-sults are consistent with those of Ichitani et al. (2010) and with Liu etal.'s (2010) model using the plate geometry of Nakajima andHasegawa (2007). On the other hand, although our results are gener-ally consistent with Liu et al.'s (2010) model using the plate geometryof Wang et al. (2004) and with Loveless and Meade's model (2010),the latter two models estimated slightly smaller slip-deficit rates offthe Kii Channel. Although GPS data period, reference point, and inver-sion method differ among the respective models, one of the main fac-tors differentiating the slip-deficit distributions is how the smoothingparameter was determined. We determined the optimum value of itssmoothness uniquely and objectively by using ABIC based on thequality and quantity of GPS data. Liu et al. (2010) determined thesmoothness parameter by constructing a trade-off curve betweenmodel roughness and model misfit. Loveless and Meade (2010) de-termined the value from the mean residual magnitude and percent-age of stations whose residual velocity magnitude was less than themean uncertainty magnitude of the GPS observations.

As the inversion method, we included both indirect and directprior constraints. Even with the direct prior constraint, ourslip-deficit rate distribution differed only slightly from the previousfindings in the region where the solution was well resolved. Inciden-tally, we also performed an inversion analysis using a method byYabuki and Matsu'ura (1992) in which the direct prior constraintwas not included. The obtained slip-deficit rate distribution andstrongly coupled region were almost the same as those presented inthis study. Although the observation stations were located only onland, we used numerous and spatially well-distributed data. Spatialvariations in the directions of the observed horizontal displacementrates were small, and their directions almost coincided with theplate convergent direction. We considered these to be the reasonswhy the direct prior constraint did not largely affect the results.

Observation errors for vertical displacement rates were signifi-cantly larger than the signals (Fig. 2b). We conducted an inversionanalysis in which we excluded the vertical displacement rates andused only the horizontal displacement rates. The results are com-pared with those using both horizontal and vertical rates in Fig. 4a.The slip-deficit rate obtained using only the horizontal displacementrates was larger by about 0.5 cm/year than that obtained using bothhorizontal and vertical displacement rates. The slip-deficit rate ofthe former extended slightly deeper than that of the latter. The esti-mation errors were larger and resolution was smaller for the formerthan for the latter, indicating that the latter was better resolvedthan the former.

In this study, we assumed that all the crustal deformations shownin Fig. 2 originated from interaction of the PHS plate with the overrid-ing plate on the plate boundary. Therefore, there is a possibility thatcrustal deformation other than the effect of plate subduction isreflected in the obtained slip-deficit rate. Although a strongly coupled

170 S. Yoshioka, Y. Matsuoka / Tectonophysics 600 (2013) 165–174

region was obtained at the eastern end of the model source region,we consider this to be attributed to deformation of the Niigata–Kobe Tectonic Zone. Here, we discuss its effect on the estimationfor the Tonankai region, which is located southwest of the above-described eastern end of the model source region. To avoid attribut-ing non-subduction-related deformation to interplate loading, Liu etal. (2010) performed inversion analysis, choosing GPS sites thatwere considered to be mainly subject to plate-loading processes.Dividing the Japanese islands into 20 tectonic blocks bounded bymajor tectonic zones, Loveless and Meade (2010) also conductedinversion analysis, accounting for rotation vectors of crustal blocks,kinematically consistent slip rates on block bounding faults, and spa-tially variable fault slip rates on subduction zone interfaces. The re-sults show that most of the inland faults have average slip rates of afew millimeters per year, which is much smaller than the plate con-vergence rate. In fact, the slip-deficit rates and coupling ratio in theTonankai region obtained in the present study are almost the sameas those obtained by Liu et al. (2010) and Loveless and Meade(2010). On the basis of these results, we consider the effect of inlandfaults on the estimation of slip-deficit rates in the Tonankai region tobe negligible.

coupling coefficient

0 50 100%

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567

a

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3

5 4

1

2 3

4

5

4

5

Fig. 5. (a) The same as Fig. 4a except that the slip-deficit rate distribution is estimatedon the plate boundary, using the geometric models of the upper surface of the PHSplate by Baba et al. (2002), Hirose et al. (2008), and Shiomi et al. (2008) (Model 2).(b) The same as Fig. 4b except that Model 2 in a is used for the slip-deficit ratedistribution.

4.2. Effect of geometry of the subducting plate

When estimating the slip-deficit rate distribution on the plate in-terface, the geometry of the upper surface of the subducting PHS platealong the Nankai Trough may be significant. Various geometricmodels have been proposed based on different data and differentmethods. In this section, we investigate the effects of geometry ofthe subducting PHS plate on the estimated solution.

To perform the inversion analysis, we employed a geometricmodel of the PHS plate estimated using the receiver function analysisby Shiomi et al. (2008; Fig. 3b). Because a sharp seismic velocity dis-continuity obtained in the analysis corresponded to the oceanicMoho, we made the discontinuity shallower by 7 km when settingthe upper surface geometry of the PHS plate (e.g., Kodaira et al.,2002). Furthermore, Shiomi et al.'s (2008) data for the receiver func-tion analysis were only beneath land areas; thus we used the geomet-ric models of Baba et al. (2002) and Hirose et al. (2008) for theoceanic side. As in the case of Model 1, we assumed that the modelsource region was 600 km in the strike direction of 250° and230 km in the dip direction.

32˚N

34˚N

100 km

cal. −1 cm/yr

cal. +1 cm/yr

1σ = 0.5 cm/yr

obs. −1 cm/yr

obs. +1 cm/yr

b

132˚E 134˚E 136˚E

132˚E 134˚E 136˚E

32˚N

34˚N

100 km

obs. 5 cm/yr1σ = 0.5 cm/yr

cal. 5 cm/yr

a

Fig. 6. (a) The same as Fig. 2a except that the blue arrows are calculated from theslip-deficit rate distribution of Model 2 in Fig. 5a. (b) The same as Fig. 2b except thatthe blue and light blue bars are calculated from the slip-deficit rate distribution ofModel 2 in Fig. 5a.

171S. Yoshioka, Y. Matsuoka / Tectonophysics 600 (2013) 165–174

The estimated slip-deficit rate distribution and coupling coeffi-cient are presented in Fig. 5a and b, respectively. We refer to thismodel as Model 2. Hyper-parameter values for the indirect and directprior constraints are 1.4×10−1 and 1.4×10−1, respectively. Themaximum slip-deficit rate for Model 2 was estimated to be about1 cm/year larger than that for Model 1. This difference can beexplained by the slab geometric model of Model 2 being slightlydeeper than that of Model 1. The region with large slip-deficit ratein Model 2 (Fig. 5a) is almost the same as that in Model 1 (Fig. 4a). Be-cause the major geometric difference in the two models originatesfrom the deeper portion of the plate boundary where the slip-deficitrate hardly exists, and the same geometric model was used for theshallower portion where a large slip-deficit rate was estimated, nosignificant difference was found between the slip-deficit rate distri-butions for the two models. Calculated displacement rates for Model

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

32˚N

34˚N

100 km

1

1

11

11

1

2

2

2

2 2

2

2

2

2

3

4

4 4

4

4

44

4

4

4

5

5

555

55

5

5 cm/yrslip (cm/yr)

a

0 2 4 6 8

32˚N

34˚N

100 km

2

2

3

3

3

3

4

4

4

5 cm/yrslip (cm/yr)

c

0 2 4 6 8

32˚N

34˚N

100 km

2

22

4

4

4

4

5

5 cm/yrslip (cm/yr)

e

0 2 4 6 8

b

32˚

34˚

d

32˚

34˚

f

Fig. 7. (a) The slip-deficit rate distribution on the plate boundary given for the checkerboardtour lines show the slip-deficit rates (cm/year). (b) The results of the checkerboard testland-based GPS stations. (c) The results of the checkerboard test obtained using raocean-bottom stations (the solid light-blue circles) with spacing of approximately 80 kmland-based GPS stations. (d) The same as c, except that 2D ocean-bottom GPS stations wiThe same as c, except that spacing is approximately 40 km. (f) The same as d, except that s

2 are shown in Fig. 6 together with observed displacement rates.The calculated displacement rates for Model 2 (Fig. 6) are almostidentical to those for Model 1 (Fig. 2), indicating that calculated dis-placement rates fit well with the observed displacement rates.

4.3. Effects of the distribution of ocean-bottom GPS stations

As mentioned previously, solutions estimated on the plate bound-ary near the trough axis, where observation stations are absent, havelarge estimation errors and poor resolution. Ocean-bottom GPS ob-servations of crustal deformation are expected to improve slip-deficit rate estimations in the offshore region. We investigated theeffect of hypothetical ocean-bottom GPS stations on solutions, byconducting checkerboard tests and evaluations of estimation errorsand resolutions.

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

32˚N

34˚N

100 km

1

1

223 3

4

4

4

4 5

5 cm/yrslip (cm/yr)

0 2 4 6 8

N

N

100 km

2

2

23

34

4 444

5 cm/yrslip (cm/yr)

0 2 4 6 8

N

N

100 km

2

2

23

3

4

4

44

5 cm/yrslip (cm/yr)

0 2 4 6 8

tests. The arrows denote amounts and directions of the slip-deficit rates, and the con-obtained using random-noise added to horizontal and vertical displacement rates atndom-noise-added horizontal displacement rates at hypothetical along-arc linear

in addition to random-noise-added horizontal and vertical displacement rates atth a spacing of approximately 80 km both in along-arc and across-arc directions. (e)pacing is approximately 40 km.

172 S. Yoshioka, Y. Matsuoka / Tectonophysics 600 (2013) 165–174

As shown in Fig. 7a, we set slip-deficit rates of 0.0 cm/year and6.0 cm/year alternatively in the N58°W direction on the plate bound-ary and calculated horizontal and vertical displacement rates at theGPS stations (Fig. 2). Each area of the checkerboard was 75 km inthe strike direction and 76 km in the dip direction. We added randomnoises homogeneously distributedwithin±0.3 cm/year to the north–south and east–west displacement rates and ±0.7 cm/year to thevertical displacement rates, and carried out inversion analysis. Theestimation accuracy for ocean-bottom horizontal displacement rateswas previously reported to be ±1–2 cm/year for 3-year observations(Eto et al., 2010). Thus, we added random noises of ±2.0 cm/year todisplacement rates of north–south and east–west componentsobtained at hypothetical ocean-bottom GPS stations. Because the ver-tical movements determined using acoustic distance measurementswere reported to have insufficient accuracy (Fujita, 2006), we didnot use vertical displacement rates at the hypothetical ocean-bottomGPS stations. We aligned hypothetical ocean-bottom GPS stations inthe along-arc and across-arc directions with spacing of approximately80 and 40 km, and estimated slip-deficit rate distributions for therespective cases. The value of 80 km was determined based on thepresent along-arc spacing of ocean-bottom observation stations forcrustal deformation (Japan Coast Guard, 2011). Here, we used theModel 1 geometric model of the PHS plate.

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

32˚N

34˚N

11.5

22.53

a

32˚N

34˚N 0.5

11.5

2

c

32˚N

34˚N 0.5

1

e

Fig. 8. Distributions of estimation errors (cm/year) for slip-deficit rate distributions on the pFig. 7f.

Fig. 7b shows inverted results obtained using only the land-basedobservation stations shown in Fig. 2. The hyper-parameter values forthe indirect and direct prior constraints were 0.088 and 0.74, respec-tively. We show the results for the four cases with different spatialdistributions of the hypothetical ocean-bottom GPS stations: 80 kmalong-arc line spacing (Fig. 7c), 80 km along-arc and across-arctwo-dimensional (2D) spacing (Fig. 7d), 40 km along-arc line spacing(Fig. 7e), and 40 km along-arc and across-arc 2D spacing (Fig. 7f). Ascompared with Fig. 7b, the results improve as the number of hypo-thetical ocean-bottom GPS stations increases. The checkerboardtests appear to be relatively well-resolved offshore for all the cases(Fig. 7b, c, d, e, and f). To clarify the reason for the improvement,we performed two kinds of tests regarding the direct prior informa-tion. In Fig. 7a, a slip-deficit rate direction of N58°W is assumed tobe the most preferable direction for the direct prior information.When we gave directions of 30°, 60°, and 90° deviating from N58°Was the direct prior information, the results of the checkerboard testsbecame worse as the angle of deviation increased, especially nearthe trough axis. When we fixed the hyper-parameter value for the di-rect information to 0.5, 0.25, and 0.088 in Fig. 7b, the checkerboardtests became worse as the value decreased, especially near the troughaxis. Therefore, we conclude that the relatively well-resolved check-erboard tests for the offshore region in Fig. 7 originated from the

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

32˚N

34˚N 0.5

11.5

2

2.5

b

32˚N

34˚N

1

1.5

2

2.5

estimation error (cm/yr)

d

0 1 2 3 4

late boundary. (a) For Fig. 7b; (b) for Fig. 7c; (c) for Fig. 7d; (d) for Fig. 7e; and (e) for

173S. Yoshioka, Y. Matsuoka / Tectonophysics 600 (2013) 165–174

large weighting of the obtained hyper-parameter value for the directprior information. In other words, in the present study, checkerboardtests are inappropriate for evaluating the effects of hypotheticalocean-bottom GPS stations on improvement of the inverted results.Therefore, we evaluate our results using estimation errors andresolutions.

Figs. 8a, b, c, d, and e and 9a, b, c, d, and e represent estimationerrors and resolutions, corresponding to Fig. 7b, c, d, e, and f, respec-tively. The estimation error near the trough axis obtained using onlyland-based GPS stations is 3.5 cm/year (Fig. 8a), whereas it improvesto 1.5 cm/year for the case with hypothetical 40-km along-arc andacross-arc 2D ocean-bottom GPS stations (Fig. 8e). The resolutionnear the trough axis obtained using only land-based GPS stations isless than 0.05 (Fig. 9a). Offshore resolutions are much improvedwith increasing numbers of ocean-bottom GPS stations and increaseup to 0.15 for the 40-km along-arc and across-arc 2D spacing(Fig. 9e).

Therefore, in the case of approximately 80-km spacing, the resultswere improved slightly in the offshore region but were still not satis-factory (Figs. 8b,c and 9b,c). For approximately 40-km spacing, espe-cially along-arc and across-arc 2D spacing, the offshore region waswell resolved, which enabled us to distinguish the given 75 km×76 km slip-deficit rate distribution (Figs. 8e and 9e).

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

32˚N

34˚N

0.2 0.

25

0.25

0.3

a

32˚N

34˚N

0.1

0.2 0.

25

0.25

0.3

c

32˚N

34˚N

0.15

0.2 0.25

0.25

0.3

e

Fig. 9. Distributions of resolution for slip-deficit rate distributions on the plate bounda

5. Conclusions

We estimated the slip-deficit rate distribution on the plate bound-ary between the subducting PHS plate and the overriding Amurianplate along the Nankai Trough, southwest Japan, by inversion analysisof GEONET data during the period from 1 January 2005 to 31 Decem-ber 2009. Our results showed that the slip-deficit rate off Shikoku isapproximately 6 cm/year at depths of 15 to 20 km on the plateboundary, indicating that the coupling coefficient is more than 80%there. On the other hand, the maximum coupling coefficient of theexpected source region of the Tonankai earthquake located southeastof the Kii Peninsula is estimated to be at most 80%, suggesting slightlyweaker interplate coupling than the expected source region of theNankai earthquake. The estimated slip-deficit rate changed slightlywith different geometries of the upper surface of the subductingPHS plate along the Nankai Trough. Furthermore, the estimatedslip-deficit rate at the offshore plate boundary was not sufficiently re-liable, according to the estimation errors and resolutions, when onlyland-based GPS stations were used. However, the results were wellresolved when an array of along-arc and across-arc hypotheticalocean-bottom GPS stations was introduced, and both estimation er-rors and resolutions improved. Our results indicate that 40-kmalong-arc and across-arc 2D spacing of ocean-bottom GPS stations is

0.2

32˚N

34˚N

0.1

0.25

0.25

0.3

b

32˚N

34˚N

0.05

0.2

0.25

0.25

0.3

0.3

resolution

d

0.0 0.1 0.2 0.3 0.4

132˚E 134˚E 136˚E 138˚E

132˚E 134˚E 136˚E 138˚E

ry. (a) For Fig. 7b; (b) for Fig. 7c; (c) for Fig. 7d; (d) for Fig. 7e; and (e) for Fig. 7f.

174 S. Yoshioka, Y. Matsuoka / Tectonophysics 600 (2013) 165–174

required to obtain a reliable slip-deficit rate distribution near thetrough axis, assuming the current estimation accuracy for ocean-bottom horizontal displacement rates.

Acknowledgments

We thank Tetsuichiro Yabuki for sharing his original source codeof the inversion analysis. We also thank Junichi Nakajima andKatsuhiko Shiomi for providing us with the geometric models ofthe upper surface of the PHS plate. We also thank two anonymousreviewers and the Editor for improving the manuscript. We used uni-fied hypocenter data provided by the Japan Meteorological Agency(JMA) and daily coordinates of GEONET, namely, the F3 solution,operated by the Geospatial Information Authority of Japan (GSI). Allthe figures were created using the Generic Mapping Tools (GMT) de-veloped by Wessel and Smith (1998). This paper was partly sup-ported by a grant-in-aid for scientific research no. 21107007 fromthe Ministry of Education, Culture, Sports, Science and Technology,Japan.

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