LETTERSPUBLISHED ONLINE: 18 JANUARY 2009 DOI: 10.1038/NGEO421

Interplate seismogenic zones along theKuril–Japan trench inferred from GPSdata inversionChihiro Hashimoto1*†, Akemi Noda1, Takeshi Sagiya2 and Mitsuhiro Matsu’ura1

In the subduction zones around Japan, where four platesinteract with one another, large earthquakes have occurredrepeatedly1. These interplate earthquakes are part of theprocess of tectonic stress accumulation and release thatis driven by relative plate motion2–4. Stress accumulationbetween earthquakes results from slip deficit (slip that isinsufficient to fully accommodate plate movement). For theprediction of large earthquakes, it is therefore important tomonitor the distribution of slip deficit on plate interfaces.Here we apply an inversion method based on Bayesianmodelling (using direct and indirect prior information on themagnitude and distribution of fault slip5) to horizontal andvertical velocities from global positioning system data. For theseismically calm period between 1996 and 2000, we obtaina precise distribution of slip-deficit rates on the interfacebetween the North American and Pacific plates around Japan,which reveals a trench-parallel belt of slip deficit with sixpeaks in the depth range of 10–40 km. These peaks agreewith the source regions of past large interplate earthquakesalong the Kuril–Japan trench. We conclude that the slip-deficitzones identified with our method are potential source regionsof large earthquakes.

The definition of earthquake prediction is to specify thetime, location and size of a forthcoming earthquake. There aretwo extreme viewpoints on earthquake occurrence: an unstablephenomenon occurring in a nonlinear complex system and astress accumulation–release process driven by relative platemotion.From these extreme viewpoints, we obtain opposite (negative andpositive) answers for the predictability of earthquake occurrence.The truth is between them. For large interplate earthquakes, giventhe past fault-slip history in and around source regions, we cancompute the spatiotemporal change in the stress distribution, andso predict the next-step seismic/aseismic fault-slip motion therethrough physics-based computer simulations6. Then, the problemis how to precisely estimate the past fault-slip history from observedseismic and geodetic data.

The Japanese islands are in a very complex tectonic setting,where the Pacific plate is descending beneath the North Americanand Philippine Sea plates along the Kuril–Japan–Izu–Ogasawaratrench, and the Philippine Sea plate beneath the North Americanand Eurasian plates along the Sagami–Suruga–Nankai trough andthe Ryukyu trench (Fig. 1). To monitor the crustal movementsof the Japanese islands, a nation-wide dense global positioningsystem (GPS) network (GEONET) has been operated by the

1Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan, 2Graduate School of EnvironmentalStudies, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan. *Present address: Graduate School of Environmental Studies, NagoyaUniversity, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan. †e-mail: hashi@seis.nagoya-u.ac.jp.

Geographical Survey Institute of Japan since 1996. The GPSobservations revealed the continuous crustal deformation of theJapanese islands during interseismic periods7, mainly caused byinterplate coupling (slip deficit at plate interfaces). Hence, applyinginversion methods to GPS velocity data, many researchers triedto estimate the precise interseismic slip-deficit rate distributionon the North American/Pacific plate interface around Japan8–11.What makes this effort such a difficult problem is that the targetedslip-deficit regions are outside the GPS array on land.

In Bayesian statistical inference based on the entropymaximization principle12,13, incorporation of prior informationinto observed data permits well-conditioned flexible formulationof ill-conditioned inverse problems. For geodetic data inversion,two types of Bayesian formulae have been widely used: theJackson–Matsu’ura formula14 incorporating direct prior informa-tion about the magnitude of fault slip and the Yabuki–Matsu’uraformula15 incorporating an indirect prior constraint on theroughness of fault-slip distribution. The rational unification ofthese two formulae5 enabled us to incorporate the postulate of plate

50° N

40° N

30° N

20° N

Kuril trench

Japan trench

Nankai trough

Ryukyu trench

Izu¬Ogasawara trench

NA

EU

PAPH

130° E

140° E

150° E

Figure 1 | Plate interface geometry in and around Japan. The upperboundaries of the descending Pacific and Philippine Sea plates arerepresented by the iso-depth contours at intervals of 10 km. NA, PA, PHand EU indicate the North American, Pacific, Philippine Sea and Eurasianplates, respectively.

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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO421

44° N

42° N

40° N

38° N

36° N

138° E 140° E 142° E 144° E 146° E

5 cm yr¬1

1 cm yr¬1

¬1 cm yr¬1

Figure 2 | Interseismic GPS horizontal and vertical velocity data. The red arrows indicate the horizontal velocity vectors at 256 GPS stations in thenortheastern part of Japan relative to a reference point (the small square). The dark and light red bars indicate the uplift and subsidence rates relative tothe reference point, respectively. The plate interface geometry is represented by the iso-depth contours at intervals of 10 km. The inset shows the trianglenetwork composed of 256 GPS stations, determined by the Delaunay triangulation.

tectonics—that seismic/aseismic slip at plate interfaces is nearlyparallel to relative plate motion—into geodetic data inversion ina quantitative way.

The fundamental causes of interseismic crustal deformation aresteady slip along curved plate interfaces and its perturbation (slipexcess/deficit) in earthquake source regions; generally speaking,spatial changes in the direction and magnitude of fault-slipvectors16. Therefore, a realistic three-dimensional geometry ofthe plate interfaces is crucial in modelling the actual physicalprocess. Furthermore, unlike the case of coseismic deformation,we need to take into account the effects of stress relaxation in theviscoelastic asthenosphere16.

Taking everything mentioned above into consideration, weanalysed GPS horizontal and vertical velocity data in the northeast-ern part of Japan for the interseismic calm period of 1996–2000(Fig. 2; Supplementary Information, Table S1) with the unifiedinversion formula5. The vertical velocity data have the potential toprovide useful information, but they contain much larger observa-tion errors than the horizontal velocity data. The three-dimensionalplate interface geometry used for the analysis is shown in Fig. 1,which was precisely determined from International SeismologicalCentre and Japan Meteorological Agency hypocentre data17. Forthe rheological structure of the crust and mantle, we assumeda 60-km-thick perfectly elastic lithosphere overlying a Maxwellviscoelastic asthenosphere with a viscosity of 5 × 1018 Pa s. To

consider the effects of steady plate subduction, which cannot beneglected in the present problem, we take the whole of the four plateinterfaces as a formal model region, and divide it into a real modelregion and a virtual model region. In the virtual model region, wea priori assign the most probable steady slip rates calculated fromthe global plate motion model NUVEL-1A (ref. 18). In the realmodel region, we solve the inverse problem for slip-deficit ratesafter taking into account the effects of the assigned slip rates (seethe Methods section).

The slip-deficit rate vector in the real model region (Fig. 3) isdecomposed into the primary component parallel to the directionof plate convergence and the secondary component perpendicularto it. Each component is represented by the superpositionof bi-cubic B-splines, the amplitudes of which are the modelparameters to be determined from GPS data. From a physicalconsideration, we impose a prior constraint on the roughnessof slip-deficit rate distribution for both components. From platetectonics, we postulate that the most probable values of thesecondary components are zero.

In our modelling, the lithosphere is assumed to be perfectlyelastic. Actually, the Japanese islands are locally deformed byinternal brittle fracture and plastic flow7. Small block rotationdue to local inelastic deformation causes serious systematic errorsin inversion analysis. To remove the effect of block rotation,we take the changes in distance between adjacent GPS stations

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NATURE GEOSCIENCE DOI: 10.1038/NGEO421 LETTERS

140° E

36° N

38° N

40° N

42° N

44° N

142° E 144° E 146° E 148° E

NA

Hokkaido

Tohoku

Japa

n tr

ench

Kuril t

renc

h

PA

Figure 3 | Inverted slip-deficit rate distribution. The blue and redcontours show, respectively, the inverted slip-deficit and slip-excess ratesat intervals of 3 cm yr−1. The grey dots indicate the central points ofbi-cubic B-splines distributed on the North American/Pacific plateinterface. The arrows indicate the relative plate motion calculated fromNUVEL-1A (ref. 18).

as data, instead of the horizontal velocities. We also take thechanges in relative height between adjacent GPS stations as data,instead of the vertical velocities. The inset of Fig. 2 shows thetriangle network composed of 256 GPS stations, determined by theDelaunay triangulation. We used the 698 side-length changes and698 relative-height changes for the present inversion analysis. Itshould be noted that the side-length change data and relative-heightchange data contain not only GPS measurement errors but alsothe distance-dependent errors caused by imperfection in theoreticalmodelling, and so the non-singularity for the covariance matrix ofdata errors is always guaranteed. We also removed the transientcrustal movements due to stress relaxation in the asthenosphereassociated with the 1994 Sanriku-haruka-oki earthquake fromthe observed GPS data.

The inverted slip-deficit rate distribution on the NorthAmerican/Pacific plate interface (Fig. 3) shows a trench-parallelslip-deficit belt with six peaks distributed in the depth range of10–40 km. Here, we omitted the secondary components, becausethey are not significant. The peak slip-deficit rates are comparableto the plate convergence rate expected fromNUVEL-1A, indicatingcomplete interplate coupling there. The slip-deficit rate distributionis mainly determined by the horizontal components of GPS databecause of the low signal-to-noise ratio of the vertical component(see Supplementary Information, Figs S1,S2). The estimationerrors are 3–4 cm yr−1 over the real model region except for itsnortheasternmargin (see Supplementary Information, Fig. S3).

Along the Kuril–Japan trench, ten large interplate earthquakes(moment magnitude Mw > 7.5) have occurred in the past century(see Supplementary Information, Table S2)1. All of these are shallowthrust-type submarine earthquakes accompanied by tsunamis.Thus, we can use the tsunami source region as a good indicatorof the earthquake source region. In Fig. 4, we show the epicentresof the ten interplate earthquakes and their tsunami source regionsestimated from tsunami travel times19–22. A notable fact is that thesix peaks of slip deficit agree with the source regions of the past largeevents along the Kuril–Japan trench. This gives definite evidence

44° N

42° N

40° N

38° N

36° N

140° E 142° E 144° E 146° E 148° E

73 MW7.5

73 MW7.8

52 MW8.1

03 MW8.1

31 M7.668 MW8.2

94 MW7.8

78 MW7.6

36 M7.5

38 MW7.7

38 MW7.8

Fukushima-oki

Miyagi-oki

Sanriku-oki

Tokachi-oki

Nemuro-oki

Figure 4 | Comparison of slip-deficit zones and tsunami source regions.The blue and red contours indicate, respectively, the slip-deficit andslip-excess rates at intervals of 3 cm yr−1. The green stars and the greenellipses indicate the epicentres and the tsunami source regions,respectively, for the large interplate earthquakes (Mw > 7.5) that occurredin the past century. The green dotted ellipse indicates the tsunami sourceregion of the 2003 Tokachi-oki earthquake.

that the slip-deficit zones are the potential source regions of largeinterplate earthquakes.

The ten past large events can be sorted into five groups bytheir source regions: the Nemuro-oki, Tokachi-oki, Sanriku-oki,Miyagi-oki and Fukushima-oki slip-deficit zones. The Nemuro-okislip-deficit zone has a single peak including the 1973 Nemuro-okiearthquake and its largest aftershock. TheGPS data inversion clearlydistinguishes the Nemuro-oki and Tokachi-oki slip-deficit zones,but not the split of the slip-deficit peak in the Nemuro-oki zone.So, we may consider this zone as one seismogenic unit with twostrength asperities. The Sanriku-oki slip-deficit zone has a singlepeak, but it includes three large events: the 1931 Sanriku-oki,1968 Tokachi-oki and 1994 Sanriku-haruka-oki earthquakes. Thetsunami source regions of these events suggest that the 1931 and1994 events occurred in the broad source region of the 1968 event.The seismic waveform inversion23 indicates that the 1968 event hasthree peaks of seismic slip: the northern main peak, the centralpeak corresponding to the 1931 and the 1994 events and thesouthern peak corresponding to a rather small event (Mw = 7.0)in 1989. So, wemay consider this zone as one seismogenic unit withthree strength asperities. The GPS data inversion distinguishes theMiyagi-oki slip-deficit zone with two peaks and the Fukushima-okislip-deficit zone with a single peak. In the Miyagi-oki slip-deficitzone, two large seismic events have occurred in 1936 and 1978.The sizes and epicentre locations of these events are similar, buttheir tsunami source regions are significantly different from eachother. So, we may consider this seismogenic unit to be composedof two strength asperities at least. In the Fukushima-oki slip-deficitzone, two large thrust-faulting events and two large normal-faultingevents have occurred during the earthquake swarm activity in 1938.So,we consider that this zone has a very complex strength structure.

In the Tokachi-oki slip-deficit zone, only one large event, the1952 Tokachi-oki earthquake (Mw= 8.1), has occurred in the past

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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO421

century. The tsunami source region of this earthquake almostcompletely agrees with the slip-deficit zone. So, we suppose thatthis seismogenic unit entirely ruptured at the time of the 1952 event,and then the gradual moment accumulation driven by relative platemotion restarted for the next large event there. From the inversionresult, taking the rigidity of the lithosphere to be 40GPa, we cancalculate the moment accumulation rate as 4.0× 1019 Nmyr−1. Ifthe next event has a seismic moment comparable to the 1952 event(M0 = 1.7×1021 Nm), we can simply estimate its occurrence timeas 44 years after the previous event. Actually it occurred in 2003withalmost the same size24 in the slip-deficit zone25.

In the above estimation, we assumed that the Tokachi-okiseismogenic unit is perfectly isolated from the other seismogenicunits. Recently, from the analysis of tsunami deposits, it has beenrevealed that extraordinary large earthquakes rupturing multipleseismogenic units occurred along the Kuril trench about every500 years on average over the past 2000–7000 years26. This suggestsweak but significant interaction between the adjacent seismogenicunits along the Kuril trench. Even in such a case the precise inver-sion analysis of continuous GPS data gives us crucial information toimprove the predictability of forthcoming interplate earthquakes.The most essential point is that earthquake occurrence is the stressaccumulation–release process driven by relative platemotion.

MethodsAccording to the unified inversion formula5, the optimum solution a and thecovariancematrixC(a) of its estimation errors are generally given by

a= a+ (HTE−1H+ α2G+ β2F−1)−1HTE−1(d−Ha) (1)

C(a)= σ 2(HTE−1H+ α2G+ β2F−1)−1 (2)

Here, H is a coefficient matrix that relates a model parameter vector a to a datavector d with Gaussian errors characterized by a mean 0 and a covariance matrixσ 2E, α2G is an indirect prior constraint matrix that regulates the model structureand β2F−1 is a direct prior constraint matrix that bounds the values of a about themost probable values a. α2, β2 and σ 2 denote the optimum values of the scalingfactors α2, β2 and σ 2, which are determined with ABIC (ref. 13).

Now we divide the model parameter vector a into two sub-vectors a1 and a2,corresponding to a real model region and a virtual model region, and impose thestrict constraint on the values of a2 by setting F−112 =O, F−121 =O and F−122 =∞I, whereO and I denote a nullmatrix and a unitmatrix, respectively. Then, denoting

a=( a1a2

), a=

( a1a2

), H= (H1,H2),

G=(G11 G12

G21 G22

), F−1=

( F−111 OO ∞I

) (3)

and substituting them into equation (1), we can obtain the optimum solutionsa1 and a2 separately:

a1= a1+(HT

1E−1H1+ α

2G11+ β2F−111

)−1HT

1E−1 [d−(H1a1+H2a2)]

a2= a2(4)

Here, it should be noted that the optimum solution a1 in the real model regiondepends on not only a1 but also a2 unless a2= 0.

Received 14 July 2008; accepted 30 December 2008;published online 18 January 2009

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AcknowledgementsWe thank Roland Bürgmann for his useful suggestion to improve the manuscript.Computation of viscoelastic slip-response functions was carried out on the EarthSimulator at the Earth Simulator Center, Japan Agency for Marine-Earth Science andTechnology (JAMSTEC).

Additional informationSupplementary Information accompanies this paper on www.nature.com/naturegeoscience.Reprints and permissions information is available online at http://npg.nature.com/reprintsandpermissions. Correspondence and requests for materials should beaddressed to C.H.

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