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 We monitored seafloor crustal deformation using the GPS/acoustic seafloor geodetic observation technique at three sites on the Kumano Basin, off southwestern Japan, which is located immediately above the source region of the anticipated Tonankai megathrust earthquake. We directly measured landward crustal movements of ∼40 mm/y in the ∼N80°W direction with respect to the Amurian Plate on the seafloor. The directions were found to be the same as those measured at the on-land GPS stations. The magnitudes of the velocity vectors indicated significant crustal shortenings of approximately 10–20 mm/y between the Kumano Basin and the southeastern coast of the Kii peninsula of the Japanese Islands. The present observational results show strong and direct evidence for interplate locking during the interseismic period. Coupling ratios were roughly estimated at ∼0.6–0.8 on the plate interface up to at least 10 km in depth.
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 The Nankai Trough, off southwestern Japan, is one of the most active plate boundaries in the world. The Philippine Sea Plate (PH) is subducting beneath the Amurian Plate (AM) along the trough, which has repeatedly caused M 8 class major interplate earthquakes at intervals of about 100–150 years [Ando, 1975]. Approximately 65 years have passed since the occurrence of the most recent earthquakes, namely the 1944 Tonankai and 1946 Nankai earthquakes. The probability of major earthquakes occurring along the Nankai Trough in the next 30 years is estimated to be 60%–70%, as reported by the Headquarters for Earthquake Research Promotion, Government of Japan (http://www.jishin.go.jp/main/choukihyoka/kaikou.htm). Therefore, it is necessary to monitor crustal deformation immediately above the source regions of major anticipated earthquakes. The GPS/acoustic seafloor geodetic observation system is an effective means of accomplishing this goal, because almost all the source regions are located in ocean areas.
 We began monitoring seafloor crustal deformation on the Kumano Basin, which is located immediately above the source region of the anticipated Tonankai Earthquake. In this study, we present observational results for seafloor crustal deformation during the interseismic period using the GPS/acoustic observation system developed by our group.
2. Monitoring of Seafloor Crustal Deformation
 We installed three seafloor benchmarks (KMN, KMS, and KME in Figure 1a) on the Kumano Basin. The benchmark positions were approximately 70–90 km landward from the trench axis of the Nankai Trough. The water depths at these sites were 1918–2033 m. Monitoring of seafloor crustal deformation started in 2004, 2005, and 2008 at the benchmarks KMS, KMN, and KME, respectively. We measured the positions of the KMN, KMS, and KME benchmarks 16, 20, and 5 times, respectively, until the end of 2011.
 Our seafloor benchmark for precise acoustic ranging was composed of three transponders. We measured the distances between the ship and sea-bottom transducers over the ocean area covering the seafloor benchmark employing an ultrasonic wave [Tadokoro et al., 2006]. The travel times of acoustic signals were automatically measured using the cross-spectrum technique. Large-amplitude waves, which were reflected from the sea surface and/or the body of the vessel, frequently arrived close to the onset of the direct wave, with slight time differences of 2.8 and 0.6 ms, resulting in misrecognition of the onset of the direct wave. We carefully checked all waveforms and manually corrected the misrecognized direct wave onsets when there was contamination due to reflected waves.
 The precise ship positions during the period of acoustic ranging were determined by means of the post-processing kinematic GPS positioning technique with an interval of 0.5 s, using the commercial software GrafNav from Waypoint Consulting Inc. We installed three onshore GPS reference stations, as shown inFigure 1a. The daily coordinates of the GPS reference stations were continuously resolved through static processing using Bernese GPS software ver. 5.0 [Hugentobler et al., 2004], fixing the coordinates of the IGS (International GNSS Service) stations surrounding Japan. We performed linear fits to the daily coordinates having a small offset and used the coordinates predicted by the linear fitting as the position of the reference station on each observational day to eliminate location errors due to the lack of data at the IGS station(s) and/or atmospheric delay. We fitted the reference station coordinates with a different line after the 2011 Tohoku Earthquake because the earthquake caused a co-seismic offset of 3.5 cm in the longitude component at the onshore GPS reference stations. The precise IGS ephemerides were used for the positioning of both onshore reference stations and the observation vessel. We also measured the ship's attitude using the data from three GPS antennas installed on the deck or using an optical-fiber gyrocompass. In the first case, we determined the GPS antenna positions using the software KINGS, developed at the Japan Aerospace Exploration Agency [Tsujii et al., 1998].
 The seafloor benchmark positioning was performed using the data of acoustic ranging (the travel time of the acoustic signal), kinematic GPS positioning, and ship attitude, as well as sound speed in the ocean obtained from conductivity, temperature, and depth measurements. First, we determined the triangular configuration of the three sea-bottom transponders using all the data acquired. We then estimated the motion of the triangle's centroid as crustal movement, fixing the triangular configuration through the least-squares technique, which minimizes the square sum of travel-time residuals. The above-mentioned procedure for fixing the triangular configuration is effective for deriving precise seafloor benchmark positions with errors of less than a few centimeters [Ikuta et al., 2009].
3. Results and Discussion
Figure 1bshows the monitoring results for the seafloor crustal deformation at the three sites. The 2011 Tohoku Earthquake caused co-seismic offsets at the locations of the seafloor benchmarks, which should be non-negligible compared with the crustal deformation due to the plate convergence at the Nankai Trough. We calculated the co-seismic offsets at each seafloor benchmark, assuming the simple rectangular fault model of the 2011 Tohoku Earthquake reported by the Geospatial Information Authority of Japan (http://www.gsi.go.jp/cais/topic110313-index-e.html). The calculated synthetic co-seismic offsets were 6, 6, and 7 mm to the north and 40, 36, and 42 mm to the east at the KMN, KMS, and KME benchmarks, respectively. We subtracted the synthetic co-seismic offsets from the resolved seafloor positions in 2011 to obtain stable interseismic deformations related to the subduction of the PH. We then obtained the long-term averaged horizontal site velocities (Table 1 and Figure 1b), fitting a straight line to the time series data for seafloor benchmark positions by means of a robust estimation method, employing Tukey's biweight function for the KMN and KMS sites to remove the effect of position bias. The unexpected biases in position were caused by spatiotemporal variations in sound speed during each observation period [Tadokoro et al., 2008]. We adopted the conventional linear least-squares fitting technique for the KME site, because it was difficult to distinguish the data with position bias from among only five observations. The estimation errors for the site velocities (linear trend) were 4–5 mm/y in each horizontal component at all three benchmarks (Table 1) for the observations of four years or more. The estimation error was small compared with the plate convergence rates of 60 mm/y predicted by the Euler vector of REVEL [Sella et al., 2002] and the 65 mm/y estimated by Miyazaki and Heki  in the present region.
Table 1. Seafloor Benchmark Positions and Monitoring Results (Site Velocities)
Velocity in ITRF2000
Velocity w.r.t. Amurian Plate
−7 ± 4
−13 ± 4
9 ± 4
−40 ± 4
−8 ± 4
−15 ± 5
8 ± 4
−43 ± 5
−8 ± 5
−15 ± 5
8 ± 5
−42 ± 5
 The site velocities derived from linear fitting were analyzed within ITRF2000 (International Terrestrial Reference Frame 2000). We calculated the synthetic rigid block motions of the AM at each seafloor benchmark position within the ITRF2000 coordinates using the Euler vector of REVEL; the calculated values were 16 mm/y to the south and 27 mm/y to the east at all three sites. By substituting these values from the velocities derived from the time series data, we obtained site velocities with respect to the AM (Table 1). Seafloor measurements through 2011 yielded steady horizontal displacement rates with respect to the AM of 41 ± 4 mm/y toward N77 ± 7°W, 43 ± 5 mm/y toward N80 ± 6°W, and 42 ± 5 mm/y toward N80 ± 7°W at the KMN, KMS, and KME sites, respectively (Figure 1a). The site velocity vectors were essentially the same at all three sites, indicating that there was no internal deformation in the Kumano Basin. A reverse-type active fault was recognized between the KMN and KMS sites [Research Group for Active Faults of Japan, 1992] (Figure 1a). The present seafloor crustal deformation measurements show no clear deformation or strain accumulation along the fault.
 Measurements recorded by a continuous dense GPS network, GEONET, operated by the Geospatial Information Authority of Japan (GSI) [Hatanaka et al., 2003], show on-land GPS horizontal velocities with respect to the AM of 23–33 mm/y toward N74–80°W along the southeastern coast of the Kii Peninsula (Figure 1a). The directions of the site velocities measured in the Kumano Basin are consistent with those measured along the coastline. These directions, however, are rotated counterclockwise by ∼20° compared with those of the AM–PH convergence of N59°W. The counterclockwise rotation is likely to be the result of the westward migration of a forearc sliver [e.g., Fitch, 1972]. The magnitudes of the velocity vectors along the coastline are significantly smaller than those at the Kumano Basin, by approximately 10–20 mm/y. This is a direct observation of significant crustal shortening between the Kumano Basin and the southeastern coast of the Kii Peninsula. The region of the Kumano Basin is considered to be moving landward as a result of interplate locking associated with the subduction of the PH along the Nankai Trough. The present observations of both landward motion and crustal shortening, are strong evidence for interplate locking between the AM and PH immediately beneath the Kumano Basin. Consequently, the plate boundary beneath the Kumano Basin could be a part of the rupture area during the next megathrust earthquake along the Nankai Trough.
Watanabe et al. performed a feasibility study that addresses the question of whether the seafloor geodetic measurements are effective in depicting the spatial distribution of the coupling ratio (the ratio of the back-slip rate to the convergence rate) on the plate interface beneath the Kumano Basin. The discussions were based on theoretical surface crustal deformation patterns perpendicular to the trench axis, which are predicted by the back-slip model. The interplate locking in the present region has been inferred from the on-land GPS data provided by GEONET [Ito et al., 1999; Ozawa et al., 1999; Mazzotti et al., 2000; Heki and Miyazaki, 2001; Miyazaki and Heki, 2001]. Nevertheless, Watanabe et al. concluded that (1) neither the up-dip limit of locking depth nor the coupling ratio under the ocean area are well resolved when based only on on-land GPS data and that (2) seafloor geodesy data are essential for this purpose.
 We calculated theoretical surface crustal deformation patterns predicted by the commonly used back-slip model, applying the method byOkada , for rough estimation of the interplate locking condition. A slip deficit rate of 51 mm/y, whose direction (N28°W) was perpendicular to the strike of the trench axis (N118°W), was applied to the plate interface modeled with rectangular sub-faults (Figure 2a). The value of the slip deficit rate was calculated from the AM–PH convergence of 60 mm/y toward N59°W. We assumed that the up-dip segments without interplate locking have steady slip by following the conventional back-slip model, although the steady slip of the up-dip end is controversial because there is no restoring force for the hanging wall to remain motionless [e.g.,Wang, 2007]. Upon comparing the present observational results with the calculated theoretical surface crustal deformation pattern, the deformation rates for the Kumano Basin observed on the seafloor, and those observed on land, are found to be well explained by the interplate locking on the plate interface deeper than 10 km, with coupling ratios of 0.6–0.8 (Figure 2b).
 On the basis of seafloor geodetic data, Gagnon et al. estimated that the uppermost plate interface along the Peru-Chili Trench did not slip during the interseismic period. In contrast, the present seafloor geodetic data are insufficient for resolving the coupling ratio on the uppermost segment along the Nankai Trough. This is because of the lack of geodetic data for the region immediately above the plate boundary close to (between 0 and ∼50 km from) the trench axis. Even then, the present observational results have great value because they were obtained immediately above the area of interplate locking along the Nankai Trough.
 The uppermost plate interface slipped greatly, by up to ∼60 m, during the 2011 Tohoku Earthquake [Ito et al., 2011; Lay et al., 2011; Shao et al., 2011], generating a tsunami with an impulsive large amplitude [Fujii et al., 2011; Maeda et al., 2011]. The 1605 M 7.9 event along the Nankai Trough is thought to have been a tsunami earthquake with slip on the shallowest segment of the plate boundary. Hence, it is essential to measure crustal deformations on the seafloor close to the Nankai Trough immediately above the uppermost plate interface.
 We directly measured landward (in the direction of ∼N80°W) crustal rates of ∼40 mm/y with respect to the Amurian Plate using the GPS/acoustic geodetic technique on the seafloor in the Kumano Basin, off southwestern Japan. The observational results show strong and direct evidence for interplate locking during the interseismic period between the Amurian and Philippine Sea Plates in the assumed source region of the anticipated Tonankai megathrust earthquake. The interplate locking portion, with coupling ratios of approximately 0.6–0.8, extends up to at least 10 km in depth. These observational results provide important data that can be used in composing hazard maps of seismic intensity and tsunami height for anticipated megathrust earthquakes. It is essential to observe seafloor crustal deformation in ocean areas substantially closer to the Nankai Trough, in order to obtain information about interplate locking on the uppermost plate interface.
 We would like to thank C. David Chadwell and an anonymous reviewer for their constructive comments. This study was partly promoted by the Ministry of Education, Culture, Sports, Science and Technology, Japan. We are grateful to the captain and crew of R/V Asama, belonging to the Mie Prefecture Fisheries Research Institute, Japan.
 The Editor thanks C. Chadwell and an anonymous reviewer for their assistance evaluating this manuscript.