Depth extent of the long-term slow slip event in the Tokai district, central Japan: A new insight

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1 JOURNAL OF GEOPHYSICAL RESEARCH: SOLID EARTH, VOL. 118, , doi: /jgrb.50355, 2013 Depth extent of the long-term slow slip event in the Tokai district, central Japan: A new insight Tadafumi Ochi 1 and Teruyuki Kato 2 Received 11 July 2012; revised 21 August 2013; accepted 22 August 2013; published 13 September [1] Temporal changes to interplate coupling and long-term aseismic slip in the Tokai Region of central Japan from July 1996 to June 2009 are statically inverted using continuous Global Positioning System (GPS) data and leveling observations, and examined using a new interpretation of aseismic slip. In this interpretation, the interplate coupling and the aseismic slip should be inferred and compared with reference to a state of no coupling on the plate interface rather than assuming steady state interplate coupling before the occurrence of the aseismic event as previous works have done. For this purpose, we used original time series data without subtracting any linear trends. The inferred distribution shows that the entire period can be divided into three subperiods based on the existence of the aseismic slip area from 2000 to The strength of the interplate coupling does not change throughout the observed period even though the distribution narrows along the dip direction after the aseismic slip terminates. The aseismic slip area inferred in this study, based on the no-coupling reference, was determined to be deeper than the area where the long-term slow slip event (SSE), defined as the slip corresponding to the residual displacement from the steady state, was hypothesized to have occurred in numerous previous studies. The total seismic moment released by the aseismic slip is equivalent to a M w 6.6 earthquake while the SSE in previous works was considered to be equivalent to a M w 7.0 to 7.1 earthquake. This difference can be attributed primarily to the effects on the interplate coupling, which previous studies did not take into account when defining the SSE. The aseismic slip area coincides well with the distribution of other types of plate interactions, such as short-term slow slip events and low-frequency earthquakes. Citation: Ochi, T., and T. Kato (2013), Depth extent of the long-term slow slip event in the Tokai district, central Japan: A new insight, J. Geophys. Res. Solid Earth, 118, , doi: /jgrb Introduction 1.1. Tectonic Settings of the Tokai Region [2] In the Tokai Region of central Japan, the Philippine Sea Plate converges toward the north-northwest to northwest direction beneath the continental plate (Figure 1). This area has been subjected to numerous large earthquakes, documented in historical records, due to interplate coupling resulting from plate convergence. The earthquake recurrence period is approximately 150 years [Ishibashi, 1981]. The most recent events were the 1854 Ansei Tokai Earthquake, the 1944 Tonankai Earthquake, and the 1946 Nankai Earthquake. Analyses of these events suggest that the rupture zone 1 Active Fault and Earthquake Research Center, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan. 2 Earthquake Research Institute, The University of Tokyo, Tokyo, Japan. Corresponding author: T. Ochi, Active Fault and Earthquake Research Center, National Institute of Advanced Industrial Science and Technology, Tsukuba Central 7, Higashi, Tsukuba, Ibaraki, Japan. (tadafumi.ochi@aist.go.jp) American Geophysical Union. All Rights Reserved /13/ /jgrb of the 1854 event covered the entire plate boundary from the Tokai Region to the Nankai Region [e.g., Ando, 1975] (see inset of Figure 1), while the rupture zones of the 1944 and 1946 events were limited to an area off the Sea of Enshu. Therefore, Suruga Bay, which is located further to the east, has been regarded as a seismic gap (where no large events have occurred in more than 150 years) and is the supposed site of the hypothetical Tokai Earthquake [Ishibashi, 1981]. Thus, it has become a focal point of earthquake prediction efforts in Japan. [3] In order to monitor crustal deformations caused by interplate coupling in the Tokai Region, various types of geodetic observations such as leveling, triangulation, trilateration, as well as strain and tilt measurements have been conducted. Proceeding in earnest from the late 1960s with the formation of the Coordinating Committee for Earthquake Prediction, crustal deformation data has been reported regularly by the Geospatial Information Authority of Japan (GSI), which was formerly known as the Geographical Survey Institute (GSI). [4] Earlier studies into plate coupling in the Tokai Region used forward modeling to explain the observed crustal deformations [e.g., Seno and Ishibashi, 1978; Fujii, 1979].

2 km AM (2) PH 140 NA (1) PA Kii Peninsula AM Lake Hamana Sea of Enshu F Suruga Bay Omaezaki PH 50 km Izu Peninsula Figure 1. Tectonic settings around the Japanese Islands (inset) and study area of the Tokai Region. AM, NA, PA, and PH designate the Amurian, North American, Pacific, and Philippine Sea plates, respectively. The thick black lines show the plate boundary determined by Bird [2003]. (1) The Tokai and (2) the Nankai areas are shown. The subduction zone between the Tokai and the Nankai areas is called the Suruga-Nankai trough. The gray dashed lines are the depth of the upper boundary of the subducting plate contoured at 10 km intervals. Plus marks indicate the GPS stations used in the present study. The belt-like zone surrounded by solid lines is the surface projection of the model fault surface. However, a breakthrough occurred in the form of the model for estimating interplate coupling proposed by Savage [1983]. In this model, interplate coupling is modeled as a superposition of a uniform infinite reverse slip representing a steady state plate convergence without any coupling and a supplemental normal slip that is hypothesized as a manifestation of coupling along the plate interface. In this model, the crustal deformation in the continental wedge is compared with the deformation resulting from the dislocation calculated from the elasticity theory of dislocation [e.g., Steketee, 1958;Okada, 1985]. This type of model is called a slip deficit or back slip model. [5] Based on this model, numerous studies have inferred the existence of interplate coupling in the Tokai Region and other subduction zones. Yoshioka et al. [1993] compiled leveling data for the period from 1972 to 1984, along with trilateration data for the period from 1977 to 1988, to infer the presence of interplate coupling during those periods. Their results indicate that a strongly coupled area with a slip deficit rate of about 30 mm/yr runs from Kakegawa 4848 to Omaezaki (see Figure 6). Separately, El-Fiky and Kato [2000] compiled leveling data for the period from 1981 to 1995 and showed a spatial distribution similar to that of Yoshioka et al. [1993]. The inferred maximum slip deficit rate was about 27 mm/yr. [6] Since the 1990s, the Global Positioning System (GPS) has gained increasing importance as a technology that provides more frequent data than the conventional technologies mentioned above. Of special significance is the rich data collected by the GPS Earth Observation Network System (GEONET), which has been operated by the GSI since the 1990s. This information now plays an important role in the study of interplate couplings along subduction zones around Japan. The conclusions of Sagiya [1999], which analyzed Tokai Region GEONET data for the period from 1996 to 1998, indicate that the strong coupling region is located further offshore than had been estimated by Yoshioka et al. [1993] and El-Fiky and Kato [2000] Previous Works About the Tokai SSE [7] Because GEONET provides daily coordinates of its observation sites, crustal deformations can be monitored in detail and temporal changes in their time series can be identified. The black dots in Figure 5 provide some examples. Ozawa et al. [2002] examined the GPS data for the period from April 1996 to June 2002 and found that the trend of surface displacements changed after October They supposed that the observed displacements before mid-2000 reflect the usual linear trend caused by steady state interplate coupling, subtracted them from the original time series, and determined that the source of the residual displacements was the evolution of aseismic slips on the plate interface. Miyazaki et al. [2006] extended the period of the data and revealed that this aseismic event continued until mid Suito and Ozawa [2009] reexamined GEONET data for the period from 2000 to 2008 and concluded that the anomalous change ended in July The aseismic slips mentioned here are called a slow slip event (SSE) or a long-term SSE depending on the duration of the event. It is to be noted that these results are based on the assumption that the interplate coupling is time invariant. [8] Summarizing previous works, it has been suggested that the long-term SSE in the Tokai region occurred beneath the northwestern part of Lake Hamana (see Figure 6) and moved slightly to the northeast along the isodepth contour. The depth of the slow slip distribution center was estimated to be around 30 km. Because this slow slip distribution occurred next to the coupling area of the hypothetical Tokai Earthquake, previous studies have paid significant attention to the effect on the interplate coupling caused by the long-term SSE. [9] These kinds of SSEs have been found in other regions of the subduction zones along the Japanese Islands, such as in the Bungo Channel of southwest Japan in [Hirose et al., 1999] and 2003 [Ozawa et al., 2004a; Hirose and Obara, 2005], and off the east coast of the Boso Peninsula in central Japan in 1996, 2002, 2007, and 2011 [Ozawa et al., 2003]. [10] Slow slip events have been identified in parts of other subduction zones around the world. Examples include southern Alaska [e.g., Ohta et al., 2006] and Cascadia, in southern Mexico, and Costa Rica [e.g., Schwartz and Rokosky, 2007].

3 (A) Displacement (B) Displacement Year Step 1: Supposing a steady state coupling Step 2: Detrending Year (b) (a) Step 3: The residual displacement corresponds to a slow slip. Figure 2. The schematic diagram of the procedure in previous works. (A) The original and (B) the detrended time series. The blue area on Figure 2a is the coupling area corresponding to the linear trend shown by the blue line in Figure 2A. The red area on Figure 2b is the slow slip area corresponding to the residual displacement shown by the red dots on Figure 2B. 2. A New Interpretation of SSE [11] In this section, we will summarize the previous works again concentrating on their definitions of slow slip events, with particular attention to the reference upon which the definition was based. We then propose a new reference and explain its advantages Proposal of No-Coupling Reference [12] Figure 2 is a schematic of the procedure employed in previous works. They defined the slow slip event as the variation from the interplate coupling that explained the displacement field before mid-2000 and discussed the effect of the slow slip event on interseismic stress accumulation. Thus, the discussion in the previous works was based on interplate coupling before mid-2000, which they regarded as steady state. However, if we want to account for the effect of the event on the whole seismic cycle, it is not necessary to take the interplate coupling before mid-2000 as the reference. We can choose the state between mid-2000 and mid-2005 or after mid-2005 instead. [13] We could also adopt a reference that does not depend on a change of interplate coupling. In this study, we propose a no-coupling state alternative as a reference and argue that it is the best way to evaluate the effects of interplate coupling and aseismic slip on the whole seismic cycle. [14] Previous works estimating the interplate coupling were based on a slip deficit model proposed by Savage [1983]. In this model, the estimated dislocation rate, which is considered to be the interplate coupling, can be regarded as the velocity V towards the down-dip direction along the bottom of the overriding plate. V =0indicates nocoupling and V = V pl,wherev pl is the plate convergence rate, indicates full coupling. In order to discuss interplate coupling based on a no-coupling reference, knowledge of the temporal evolution of V is necessary, which can be obtained directly through a geodetic inversion analysis using crustal deformation data without assuming a steady state or linear trend. [15] Figure 3 is a schematic that explains two types of temporal evolution of V. When0<V < V pl, the state can be interpreted two different ways. One is partial coupling, shown as A in Figure 3, and the other is partial slipping, shown as B in Figure 3. The former is based on the reference of no-coupling V = V 0, while the latter is based on full coupling V = V pl. Although both interpretations can express interplate interaction, the choice of reference should be fixed in a set of discussion topics. Figure 3. Conceptual diagram of the relationship between partial coupling, partial slip, and overslip. V is the velocity towards the down-dip direction at the bottom of the overriding plate and V pl is the convergence rate of the subducting plate. V = 0 and V = V pl are the states of no-coupling and full coupling, respectively. V 1 is the velocity for the period t < t 0, and A and B are the rates of partial coupling and partial slip for this period. V = V 2 is the velocity for t > t 0. In this case, 0<V 2 < V 1 and C is also the rate of partial coupling and D is the increment of partial slip (B). V = V 0 2 is another case for t > t 0. In this case, V 0 2 <0and E show overslip. 4849

4 Figure 4. Segmentation of the entire interval. [16] Now, let us assume that V decreases from V 1 to V 2 at time t = t 0. From the standpoint of previous works, in which a slow slip event was defined as a residual slip from interplate coupling in some time period, the state of V = V 1 is taken as a reference and the slow slip event is defined as the slip corresponding to the difference of V 1 V 2,which is shown as D in Figure 3. The interplate coupling before t = t 0 is shown as A. Because the same reference should be chosen to discuss interplate coupling or slip in the periods t < t 0 and t > t 0, as was described earlier, C should be compared with A rather than D. Therefore, the effect of the slow slip event between mid-2000 and mid-2005 on the interplate coupling should be discussed based on a no-coupling state. If the down-dip velocity V for t > t 0 is V 0 2 <0, as is also shown in Figure 3, we should use the same reference of V =0and evaluate the case with the amount of E Study Procedure and Definition of Terms [17] In order to evaluate the interplate coupling and slip using a no-coupling reference, we conducted a geodetic inversion analysis directly from the crustal deformation data without processing any detrending, allowing both normal and reverse slips. In the area of the normal slip, the velocity V defined above is V >0and represents the slip deficit, which is an alternative to interplate coupling. On the other hand, in the area of reverse slip, the velocity V is less than zero and represents a so-called slip excess, overslip, or forward slip. For simplicity, we use the phrase coupling area for the area of V >0and overslip area for the area of V <0in this study. Although the overslip area is an alternative to the area of long-term slow slip from the standpoint of the no-coupling reference, we do not use the phrase (longterm) slow slip area to distinguish between this study and previous studies. [18] The no-coupling reference has already been used to reveal the temporal changes to interplate coupling between the subducting Pacific and overriding North American plates (see Figure 1) in northeast Japan by Nishimura et al. [2004]. Their research focused primarily on the coupling zone and interprets the existence of the forward slip area as a reflection of afterslip and a slow earthquake. Ohta et al. [2006] also applied this approach to southern Alaska. Finally, they subtracted the estimated slip distribution due to steady state coupling from that of the SSE period and proposed the differential distribution as a reflection of the SSE. We applied the same methodology to the Tokai Region and compared our findings to the results obtained from previous studies. 3. Data [19] Tectonic movements in the Tokai Region were derived using both GPS and leveling data from July 1996 to June As schematically shown in Figure 4, we divided the entire period into 12 2 year long epochs and allowed neighboring epochs to overlap each other by 1 year. For the inversion analysis, the annual crustal deformation rates in each epoch were inferred from the GPS and leveling data separately GPS Data [20] Three components of the daily coordinates obtained from GEONET sites, which have been routinely solved and published as daily GPS coordinate F3 solutions by GSI [Nakagawa et al., 2009], were used in the present study. The number of sites varied from 102 to 147 depending on the epochs, and the distance between neighboring sites averaged approximately 20 km. Figure 5 shows an example of the GPS time series. [21] We fitted the following function to the daily time series data of the pth component of ith station in each epoch as x i,p (t) =c k i,p + vk i,p t + A i,p cos(2t) +B i,p sin(2t)+c i,p cos(4t)+d i,p sin(4t) + X E l i,p H(t t l)+f i,p H(t t EQ )e (t teq)/eq, l t 2 epoch #k. (1) The definitions of each term on the right-hand side of equation (1) are as follows. The first two terms and the next four terms correspond to a linear trend and an annual and a semiannual variation, respectively. The offset c k i,p and annual rate v k i,p are estimated for each epoch k. The next term corresponds to abrupt changes resulting from coseismic displacements and/or antenna exchanges. For coseismic displacements, we limited consideration to the earthquake that occurred southeast off the Kii Peninsula on 5 September 2004 (hereafter the 2004 event ), which was the strongest earthquake during the entire period. The antenna exchange dates were obtained from the information table released by GSI. The lth abrupt change that occurred at the time t l is 4850 described as a product of a magnitude E l i,p and a Heaviside step function H(t t l ). The last term of the right-hand side of equation (1) accounts for the transient postseismic effect of the 2004 event. Suito and Ozawa [2009] regarded it as a mixture of the effects of a postseismic slip and a viscoelastic relaxation. However, as discussed in Suito and Ozawa [2009], it is difficult to separate them completely. Thus, we assumed that their decay process could be expressed as an exponential function with a time constant EQ, and used the value of EQ = days, which was proposed by Suito and Ozawa [2009]. [22] In addition, the effect of a large seismo-volcanic event that occurred in the Izu Islands, emerged in the time series around July 2000 [e.g., Nishimura et al.,2001;ozawa et al., 2004b]. Summarizing their results, this event started on 25 June 2000 and faded out about the end of September

5 EW Displacement (cm) NS Displacement (cm) UD Displacement (cm) Year Figure 5. Time series of the Fukuroi site coordinates shown as F in Figure 1. The top, middle, and bottom figures are the time series of the east-west, north-south, and up-down components, respectively. Black dots indicate the original time series of F3 solutions of the site coordinates. Green and red curves on the black dots indicate the time series calculated using equation (1) connecting the odd- and even-numbered epochs. Green and red dots shown below the black dots indicate the corresponding residuals between the original and the calculated values. The vertical dashed line in each figure indicates the time of the 2004 earthquake that occurred southwest of the Kii Peninsula, and the shaded area shows the period when the data was suspected of being affected by the 2000 Izu seismo-volcanic events. plotted with green and red dots in Figure 5 as an example, the residuals of odd- and even-numbered series show similar features. Thus, the two series are consistent. The standard deviations of the estimated horizontal and vertical deformation are 0.53 and 1.06 mm/yr, respectively, on average Leveling Data [25] Leveling observations have been carried out for a period of about a hundred years to ascertain the vertical crustal movements in the Tokai Region. The leveling routes in this region are shown in Figure 6. Most notably, such leveling observations have been carried out four times a year since 1981 along the route from Omaezaki to Kakegawa, and along the other leveling routes surrounding this route once a year since [26] Using the same analogy as for the GPS data, the height of the ith benchmark is assumed to be described by the following equation: h i (t) =c k i + v k i t, t 2 epoch #k. (3) The other terms in equation (1) are ignored because the leveling data are too temporally sparse to explain them. The constraint equations are the same as that used for the GPS data proposed in equation (2). [27] As for the data between Omaezaki and Kakegawa, equation (3) is insufficient to account for seasonal changes. Therefore, we applied a low-pass filter with a 3 year cutoff period to remove undesired effects. The low-pass filter also has the advantage of removing unexpected abrupt changes that sometimes appear in leveling data because of their high sensitivity to environmental effects around the benchmarks. [28] Because leveling surveys observe the height difference of two neighboring benchmarks, the data l ij (t) at time t, which is the height difference of ith and jth benchmarks, is written as follows: l ij (t) =(h j (t) h i (t)) = (c k j c k i )+(vk j v k i )t, t 2 epoch #k. (4) [29] We applied equations (4) and (3) to all the data at the same time and estimated all the c k i and v k i using a least Therefore, we eliminated data from 16 June 2000 to 30 September [23] Because the coordinates must be continuous at the boundaries of neighboring epochs, the following equations were imposed as constraints to prevent steps at the boundaries: Lake Hamana Mori Kakegawa Shimizuminato Yaizu Suruga Bay c k i,p + vk i,p t = ck+2 i,p + vk+2 i,p t, (k =1,2,:::, 10). (2) We applied equations (1) and (2) to all three components of the daily coordinate separately and then estimated the crustal deformation rate components v k i,p for all stations in all epochs together using a least squares technique. We then converted the estimated values relative to that of the Omaezaki site. [24] As a consequence of the connecting conditions (2), there are no constraints between time series composed of odd-numbered and even-numbered epochs, and the two series do not need to have similar features. However, as Maisaka Sea of Enshu Omaezaki 20 km Figure 6. Leveling routes with benchmarks used in the present study. The solid squares indicate tidal station locations. The blue line extending from Omaezaki tidal station to Mori town indicates the survey route where observations are carried out four times a year. The red lines show the routes where the observations are carried out once a year.

6 to those at Omaezaki, the GPS vertical and leveling data must show similar features. In order to test for such similarity, Figure 7 shows two kinds of deduced rates for the same epoch #2 (from July 1997 to June 1999). Although the spatial distributions of the GPS and leveling data are significantly different, and the features of the crustal deformation field cannot be compared precisely, Figure 7 shows acceptable consistency between the two data types. Figure 7. Consistency of the GPS vertical components, shown by open red arrows, and vertical crustal deformations deduced from the leveling data, shown by solid blue arrows. Both data sets show 2 year averaged crustal deformation rates of epoch #2 (July 1997 to June 1999). squares technique. However, because leveling data does not provide any actual information about absolute vertical velocity, the problem to be solved here inevitably becomes a rank deficit system. [30] In order to obtain absolute vertical rates, numerous previous studies such as Yoshioka et al. [1993], El-Fiky and Kato [2000], and Ochi and Kato [2011] supplementarily used absolute vertical sea level movements inferred from tidal records based on the method proposed by Kato and Tsumura [1979]. As shown in Figure 6, there are four tidal stations in the Tokai Region that provide information about absolute vertical movements. However, tidal records are influenced not only by vertical crustal deformations but also by sea level changes due to marine tides, ocean flow, climate change, and other factors. Thus, even though the effect of ocean flow is removed by the analysis of Kato and Tsumura [1979] to some extent, eustatic sea level changes cannot be separated from vertical land movements. Therefore, in the present study, instead of using the tidal records, we impose a zero constraint on the vertical deformation rates of the benchmark at the Omaezaki tidal station (see Figure 6). The physical meaning of this constraint is that all vertical deformation rates estimated here are relative to that at Omaezaki. [31] The observation error of leveling surveys is assumed to be proportional to 2.5 p L mm, where L is the distance between neighboring benchmarks in Kilometers. This assumption is based on the maximum permission limit of leveling observation closure differences in Japan. In most cases, the distance between two benchmarks is within 2 km. However, in the area around Kakegawa, some are as much as 10 km apart due to benchmark relocations. For simplicity, each observation was carried out independently so that observation covariances could be eliminated. The standard deviation of the deduced vertical deformation rates is 0.6 mm/yr, and all the deduced deformation rates were well determined Consistency Check Between GPS Vertical and Leveling Data [32] As both the deformation rates deduced from the GPS data and the leveling data were converted to be relative Inversion Analysis [33] Using annual crustal deformation rates v i from the GPS (equation (1)) and the leveling (equation (3)) data, we conducted a static inversion analysis and inferred coupling and slip distributions for the 12 epochs (see Figure 4). The inversion analysis used here was based almost entirely on the method proposed by Yabuki and Matsu ura [1992]. As the inversion analyses were executed for each epoch separately, no smoothing constraint for time was imposed Observation Equations [34] According to the representation theorem of elastodynamics, the static displacements d i (x)(i = 1,2,3) at point x on a free surface caused by a buried dislocation source on a fault surface are expressed as d i (x) = 2X Z j=1 d G ij (x; ) u j (), (5) where d is an infinitesimal area on the fault surface, u j ()(j =1,2)are displacement discontinuities, or dislocation sources, at point on the surface, andg ij (x; ) is the ith displacement component at x due to the jth unit point source at, respectively. u 1 and u 2 correspond to the strike and dip components of the amount of dislocation. The integral is calculated throughout the fault surface.we assumed the medium to be a homogeneous isotropic elastic half space, and no geographical effects on the land surface were taken into consideration. For evaluating G ij (x; ), theoretical displacements on the free surface due to a buried point source were calculated by Okada [1985]. The model source region, whose surface projection is shown in Figure 1, is defined not as a rectangle, but as a belt-like shape. The isodepth contours of the upper boundary of the Philippine Sea plate used in this study were determined by Miyake et al. [2008]. The shallowest and deepest boundaries are along the 4.0 and 61.5 km isodepth contours, respectively. The eastern boundary is restricted by the eastern end of the Philippine Sea plate and the western boundary is determined to cover the spatial distribution of the GPS sites to avoid side effects in the inversion analysis. Dislocations on the four sides of the model region are fixed at zero in order to stabilize the inversion problem solution. For displacement d i (x), we used the 1 year averaged crustal deformation rate v i from equations (1) and (3). Therefore, u j is the 1 year accumulated dislocation. [35] In order to discretize the continuous distribution of u j (), we express u j () as a linear combination of the spatially distributed basis functions N kl (): XK 1 XL 1 u j () = N kl ()w jkl, (j =1,2), (6) k=0 l=0

7 where K and L are the number of basis functions in the length and width directions of the model fault surface, and w jkl is the weighting factor of the basis function N kl. In the present study, we used fourth-order bicubic B-spline functions as the basis functions and assumed K =20and L =15. This corresponds to the fact that we take nodal points of the basis function approximately every 20 km. [36] Substituting (6) into (5), d i (x) is expressed as d i = 2X XK 1 XL 1 H ijkl w jkl, (7) j=1 k=0 where Z H ijkl = d G ij (x; )N kl (). (8) [37] Therefore, the observation equation is l=0 d = Hw + e, (9) where d is a data vector, H isadatakernel,w is a model parameter vector, and e is an observation error vector. For simplicity, we assume the error vector e to be Gaussian with a zero mean and covariances 2 d : e N(0, 2 d ), (10) where 2 is an unknown scale factor of d. The diagonal components of the matrix d are evaluated by the variance of the corresponding value of the vector d.as d is composed of the annual crustal deformation rate v i in equations (1) and (3), d is determined by the standard deviations of the data, mentioned in the previous section. The non-diagonal components of d are assumed to be zero for simplicity. From equations (9) and (10), we create a stochastic model expressed as p(d w; 2 )=(2 2 ) N/2 k d k 1/2 exp 1 2 (d 2 Hw)T 1 d (d Hw), (11) where k d k is the determinant of the matrix d and N is the number of data vector components d Prior Constraints [38] In order to stabilize the solution, we imposed two sorts of prior constraints. The first constraint concerns the roughness of the fault slip distribution, r 1,definedbythe following equation: Z r 1 = k4 uk 2 d, (12) where 4 is the Laplacian operator along the curved fault surface. [39] The second constraint concerns the direction of the slip vector as introduced by Matsu ura et al. [2007]. Because the slip on the fault represents interplate coupling under the slip deficit model of Savage [1983], the component of the slip vector u? whose direction is perpendicular to the plate convergence direction (ˇ) must be small. As is the case of the first constraint, the smallness of this component over the fault surface is evaluated by an integral over the curved fault surface: Z r 2 = k u? k 2 d. (13) The explicit form of u? is u? = u 1 sin( ˇ)+ u 2 cos( ˇ), (14) where is the local strike direction and is evaluated at each point on the curved surface in the integral (13). In the present study, the plate convergence direction ˇ is assumed to be N55 ı WafterMiyazaki and Heki [2001]. Since r 1 and r 2 can be written in matrix forms as r i = w T S i w (i =1,2) (15) and these are positive definite forms of the model parameter vector w, the prior constraints can be expressed in the form of pdf with unknown scale factors 2 1 and 2 2 as p(w; 1 2, )=(2) M/2 1 2 S /2 2 2 S 2 1 exp w T 21 2 S S 2 w, (16) where M is the rank of (S 1 /1 2+S 2/2 2 ) [Fukahata et al., 2004] Bayesian Modeling and Akaike s Bayesian Information Criterion (ABIC) [40] We now incorporate the prior distribution p(w; 1 2, 2 2 ) into equation (16) with the data distribution p(d w; 2 ) in equation (11) into a highly flexible Bayesian model with hyperparameters. As a result, we obtain p(w; 21, 22 d) =c (22 ) (N+M)/2 k d k 1/2 k 21 S S 2k 1/2 exp 1 2 s(w), (17) 2 with s(w) =(d Hw) T 1 d (d Hw)+wT ( 21 S S 2)w. (18) Here, c is a normalization constant. In the present study, we determine the hyperparameters 21 and 22 using Akaike s Bayesian information criterion (ABIC) proposed by Akaike [1980] based on the entropy maximization principle. According to the definition given in Ito and Hashimoto [2004], ABIC is ABIC( 21, 22 )=Nlog s(w, 21, 22 ) log 2 1 S S 2 +log H T E 1/2 d H + 21 S S 2 + c 0, (19) where c 0 is a constant independent of 1 and 2. We estimate the hyperparameters 1 and 2 using a grid search method. Once 1 and 2 are fixed, the best estimate of the model parameters w and their covariances C d can be obtained by w = H T E 1 d H + 21 S S 1 2 H T E 1 d d, (20) 4853 C d = 2 H T E 1 d H + 21 S S 2 5. Inversion Results 1, 2 = s(w ) N. (21) 5.1. Temporal Change of the Coupling Area [41] Figure 8 shows the inversion results for all 12 epochs. Blue and red areas represent the interplate coupling and overslip areas, respectively. Focusing on the existence of overslip areas, the entire period from July 1996 to June

8 Figure 8. Inferred temporal evolution of the interplate coupling and overslip. The start and end times of the analysis period are shown in the top left of each figure. The contours represent the annual coupling/overslip rate and have a spacing of 5 mm/yr. Areas where the rate is more than 15 mm/yr are colored in cyan or magenta. Areas where the posterior standard deviation is larger than the absolute values of the estimated value are shaded. The green solid circles are low-frequency event hypocenters and the dark red rectangles are the fault geometries of the short-term SSE determined by Sekine et al. [2010] can be divided into three subperiods: [A] before 2001 (Figures 8a 8d), [B] (Figures 8e 8h), and [C] after 2004 (Figures 8i 8l). Three results shown in Figure 9 are representative examples from each subperiod. Purple lines on Figure 9 show the deeper extent of the coupling area in subperiod [A] and are used in the discussion below. [42] Because each figure shown in Figure 8 shows the average state for the 2 year long epochs, the exact time of the transition from one subperiod to the next cannot be resolved Subperiod A: Before 2001 [43] From Figure 9A, the maximum value for the coupling area is between 30 and 35 mm/yr and the coupling rate is between 75 and 100 % depending on the plate convergence rate in previous studies. Although the contour of the plate interface used in the present study differs from those in previous studies, and thus the estimated distribution cannot be compared in detail, the results are consistent with the results of previous studies concerning plate coupling before 2000, such as El-Fiky and Kato [2000] and Ochi and Kato [2011]. The distribution is shifted slightly offshore compared with the coupling distribution inferred from microearthquakes by Matsumura [1997] Subperiod B: From 2000 to 2005 [44] Figure 9B shows that the maximum value in the coupling area is still around 30 mm/yr, but the area does not extend to the deeper portion of the plate boundary. 4854

9 A B C [#1] 1996/07/ /06/30 [#7] 2002/07/ /06/30 [#12] 2007/07/ /06/ mm/yr mm/yr mm/yr km km km Figure 9. Inferred interplate coupling and overslip in subperiods [A], [B], and [C] (see text). These are the same figures as Figures 8a, 8g, and 8l, except for the hypocenters of low-frequency events and the fault geometries of the short-term SSE. Purple dashed lines are drawn at the same position in each figure to compare the center and the width at the depth of the coupling region, respectively. In addition, the overslip area emerges in a much deeper portion of the plate boundary. The center of the overslip area is located at a depth of around km beneath the northwest Lake Hamana area, and the maximum overslip amount is about 20 mm/yr. The change in the spatial distribution of the coupling area suggests that the interplate coupling may change temporally, especially in connection with the existence of overslip areas Subperiod C: After 2004 [45] Figure 9C shows that the overslip area in the deeper portion of the plate boundary that appeared in subperiod [B] disappears. Considering that the purple lines in Figure 9 show the deeper extent of the coupling area in subperiod [A], the coupling area in subperiod [C] does not recover to the subperiod [A] condition. In this sense, the distribution of the coupling area is dissimilar to that in subperiod [A] but similar to that in subperiod [B]. This may be interpreted as the interplate coupling caused by the subducting plate being influenced by overslip, and the interplate coupling that existed after the so-called long-term Tokai SSE having not recovered Validity of Inversion Results Amount of the Coupling [46] Because the amount of coupling is expressed as the normal slip on the plate interface or the down-dip velocity V that was defined in section 2, V should be required to be smaller than the plate convergence rate V pl. A number of convergence rates V pl for the Philippine Sea plate toward the continental plate have been proposed. For example, Seno et al. [1993] estimated the convergence rate as 35 mm/yr using earthquake slip data, while a model of plate movement by Sella et al. [2002], which was inferred from worldwide GPS data, requires the convergence rate to be about 55 mm/yr. In any case, the maximum value of the normal slip inferred here is less than 35 mm/yr and is less than the plate convergence rate. Therefore, the results of the inversion are reasonable in this case [47] In all results, small overslips appeared in the very deep portion the northwestern part of the model region. Although we cannot rule out the possibility that this small overslip occurs constantly at the deeper portion, no previous works discovered such a small overslip before mid In addition, this overslip is too small and deep to produce any detectable displacement on the earth surface. Thus, we consider that these overslips were caused by some artificial effects such as smoothing conditions in the inversion analysis at this point Comparison Between Observed Data and Calculated Values [48] Figure 10 compares the observed data and the calculated displacements at GPS sites and leveling benchmarks obtained from the estimated coupling and overslip distributions. There are two features: [49] 1. The calculated values agree better with the leveling data and GPS vertical data than with the horizontal data. [50] 2. There are discrepancies between the calculated values and the observed data near the border of the model region. [51] Because the leveling data variances are smaller than those of the GPS vertical data, the inferred coupling and overslip distributions provide a better explanation for the leveling data. In the present study, even though the GPS vertical data have larger variances than the horizontal data, the calculated values agree better with the vertical components. The reason seems to be that the vertical components of the GPS data are consistent with the leveling data, and the inferred distributions that explain the leveling data also explain the GPS vertical data. [52] The discrepancies between the observed data and calculated values might be caused by a combination of reasons such as data noise, simplicity of the elastic half-space model, and artificial effects of the inversion analysis. One likely major reason is the boundary condition of zero-fixed constraints imposed on the four sides of the model region. This condition was necessary to stabilize the inversion

10 (a) Epoch #2: OBS CAL 100 km OBSCAL (b) Epoch #7: km OBSCAL OBS CAL 100 km OBSCAL (c) Epoch #11: km OBSCAL OBS CAL 100 km OBSCAL km OBSCAL Figure 10. Comparisons between observed and calculated site velocities. The solid blue and open red arrows are the observed and calculated values from the inferred slip distribution. The two left panels of each row show the results for the GPS horizontal and vertical components, while the rightmost panels show the leveling data. All values are converted to relate to the values at Omaezaki, shown as open squares. solutions, as was mentioned in section 4.2, but prevented us from discussing coupling and overslip near the boundaries. In addition, near the western boundary around the Kii Peninsula, the crustal deformation must be caused not only by interaction in the Tokai Region targeted in the present study but also by plate couplings in the Tonankai Region. In order to discuss these areas properly, all the geodetic data in southwest Japan must be processed as a whole, as was done in studies by Sagiya and Thatcher [1999], Miyazaki and Heki [2001], and Ito and Hashimoto [2004]. 6. Discussion 6.1. Reconstruction of SSE From the Results of This Study [53] According to previous studies, such as Ozawa et al. [2005], Miyazaki et al. [2006], and Suito and Ozawa [2009], the long-term Tokai SSE started in the middle of 2000 beneath the northwest area of Lake Hamana and moved to the northeast portion of the lake in the middle of In order to discuss the differences between the long-term SSE 4856

11 (a) (b) C B A C B A Dislocation [mm] (c) C B A Distance from the trench [km] Figure 11. (a) Coupling and forward slip distribution for epoch #7 from the standpoint of previous studies. Blue dashed contours are the coupling distribution for epoch #2, which is the same as Figure 8b and is the reference state in the previous studies. Solid black contours are the residual distribution for epoch #7 with respect to epoch #2. (b) Coupling and overslip distribution for epoch #7 from the standpoint of this study (see Figure 8g). (c) Cross-sectional view of the distribution along the green lines in Figures 11a and 11b. The origin of the distance is marked by green stars in Figures 11a and 11b. A, B, and C in all figures indicate the same locations. Red and blue dashed lines in Figure 11c are the cross section of the solid and dashed contours in Figure 11a, while the solid line in Figure 11c is the cross section of the solid contours in Figure 11b. defined in previous studies and the overslip area determined in the present study, the former was reconstructed from the latter. [54] As mentioned in section 2, the long-term SSE in the Tokai Region from mid-2000 to mid-2005 was defined as slip relative to the interplate coupling before mid Therefore, similar images can be obtained from the results of this study by taking the differences between the inferred coupling and overslip distributions during the first half of the 2000s and the last half of the 1990s. As an example, the difference in the results between epochs #7 (from July 2002 to June 2004) and #2 (from July 1997 to June 1999) are shown in Figure 11a. In this figure, an area of large forward slip, with a maximum value of 35 mm/yr, appears at a depth about 25 km beneath the northwest portion of Lake Hamana. The phrase forward slip in this context and in Figure 11 means a slip relative to the coupling in epoch # 2. [55] Because this forward slip area, shown in Figure 11a, corresponds to the Tokai SSE from previous studies, the result of this study is consistent with those of previous studies in this sense. In addition, the maximum forward slip rate estimated by these previous studies varied between 35 and 50 mm/yr, while we calculate it as about 35 mm/yr in the present study. No obvious eastward migration of the overslip area was detected by this study, as had been detected by previous studies. The main reason is this study s lack of temporal resolution. The 2 year averaged crustal deformation rates were insufficient to detect temporal changes in the overslip area Comparison of Overslip and Slow Slip [56] While Figure 11a shows the forward slip area corresponding to the SSE area in previous studies, Figure 11b shows the coupling and overslip areas in the same epoch (#7) as inferred by the present study. In order to clarify the differences, three points A, B, and C are plotted on a profile that is parallel to the plate convergence direction, N55 ı W,used in the inversion analysis. As shown in Figure 11a, all three points are located in the SSE area and point B is located at the center of it. However, Figure 11b suggests a different interpretation. This figure indicates that point A is not in the overslip area but is still in the coupling area, point B is neither in the coupling area nor in the overslip area, and only point C is in the overslip area. Point C is located at the center of the overslip area in the present study, while it was considered to be near the lower border of the SSE area in previous studies.

12 Figure 12. Schematic diagram showing temporal changes of the accumulated seismic moment. The duration of an aseismic slip extends from t 1 to t 2. (B) is the released seismic moment from the no-coupling reference, while (A) is the seismic moment as evaluated by previous studies, which is equivalent to the moment (A) released by one seismic event. [57] Figure 11c is a cross-sectional view of the slip distributions along the green line in Figures 11a and 11b. When compared with the distribution of the Tokai SSE obtained by previous studies, it is clear that the distribution of the overslip area moved deeper into the plate boundary and has its peak at around 130 km in the cross-sectional view, as shown by the solid red line in Figure 11c. On the other hand, its peak is not very sharp because the lower boundary of the overslip area is not well constrained in the inversion analysis of such an ill-posed problem with its lack of data and small deformation relative to the noise level, as was noted in section Balance of Coupling and Released Seismic Moment [58] The total released seismic moment in the overslip area of the present study is equivalent to a M w 6.6 earthquake, assuming that the rigidity is 30 GPa. In this evaluation, we took into account the effect of the overslip area where the estimated value is larger than the posterior standard deviation. Because the Tokai SSE continued from mid to mid-2005, we assumed that the results for epochs #4 ( ) and #9 ( ) and epochs #5 #8 continued for a half year and 1 year, respectively. Although this value was obtained from a rough evaluation, it is significantly less than previous estimates; for example, M w 7.0 to 7.1 [e.g., Suito and Ozawa, 2009]. Although the difference between the two values just stems from the reference of the analysis, the value M w 6.6, which was obtained based on the no-coupling reference is feasible for considering the effect of the aseismic event on seismic cycles, as explained in section 2. [59] This difference also can be understood by taking into consideration the background effects of interplate coupling. Figure 12 is a schematic diagram of the stress accumulation process based on interplate coupling and overslip in a subduction zone. Suppose that the black solid line is the process of stress accumulation and release based on the nocoupling reference. The released seismic moment appears as (B) in the picture. Because previous studies did not take into account the background field of the plate convergence shown by the gray line [a] [b] in Figure 12, they regarded the real process as shown by the dashed line [a] [d] instead of [a] [c]. Therefore, in previous models, (A) was considered to be the amount of moment released. Furthermore, because (A) is always larger than (B), the previous models clearly overestimated the amount of released seismic moment. [60] In the case of the Tokai Region, a seismic moment of M w 6.6 ((B) in Figure 12) was definitely released by the aseismic slip referred to as the overslip area in this paper. If the same final state ([c] in Figure 12) had been achieved by an earthquake that released all the accumulated stress (A) at one time, the seismic moment of the earthquake would have been M w 7.0 to 7.1. Thus, the statement that the Tokai SSE released a seismic moment equivalent to a M w 7.1 earthquake is correct in this sense Relationship With Short-Term SSE and Low-Frequency Events [61] In addition to long-term SSEs, there are other events along the strike of the subducting Philippine Sea plate. These include short-term SSEs [Hirose and Obara, 2006; Sekine et al., 2010] and low-frequency events (LFEs) [Katsumata and Kamaya, 2003], which comprise a portion of the nonvolcanic low-frequency tremors [Shelly et al., 2006]. Based on an analysis of the source region of the longand short-term SSEs, the recurrence times of the events, and their released magnitudes, Obara [2002] suggested that the coincidence of the SSEs and tremors could be a characteristic behavior at a deeper part of the subduction zone, and Hirose and Obara [2006] concluded that the source areas of the short- and long-term SSE overlapped each other. [62] Since the overslip area must be distributed at a deeper portion of the plate boundary than had been considered from previous pictures of the long-term SSE, the relationship among the various types of seismic and aseismic events along the subduction zone in the interseismic period needs to be reexamined. Figure 8 shows that the distribution of LFE hypocenters agrees well with the distribution center of the overslip area inferred in the present study. LFEs occur regularly whether overslip occurs (Figures 8e 8h) or not