We extract sequences of small repeating earthquakes to clarify inter-plate coupling of subducting plates over a large area of the Japanese Islands. As a result, many sequences are detected at the Philippine Sea plate subducting from the Ryukyu trench and Pacific plate subducting from the Kuril-Japan trench. The average slip-rates and standard deviations estimated from the sequences show substantial spatial changes of inter-plate coupling. The large deviations of slip-rates correspond to the occurrence of episodic slips such as after-slips following large earthquakes. Constant slip-rates approaching the relative plate motion indicate weak coupling areas. Slip deficits and sparse distributions of repeating groups suggest locked areas. In the Nankai trough, deep low-frequency earthquakes in the transition zone and burst-type repeating sequences within plates have not been located in the downdip direction of groups with slow slip-rates. This suggests that the space-time characteristics of inter-plate coupling affected these seismic events.
 The Japanese Islands form one of the major seismic zones of the world. Large earthquakes frequently occur at the plate boundary of the Pacific plate subducting to the west-northwest from the Kuril-Japan trench and the Philippine Sea plate subducting to the northwest from the Sagami-Nankai trough and the Ryukyu trench (Figure 1). It is important to investigate the space-time characteristics of inter-plate coupling to understand the subducting process. GPS data enable continuous observations with high-sampling rates and have been widely used to estimate slip velocities at subducting plates [e.g., Hashimoto et al., 2009]. However, the GPS network is limited to observations on land. Heterogeneous slip distributions in offshore areas are smoothed due to the lack of spatial resolution [Miyazaki et al., 2006]. Slip amounts and slip velocities may be smaller than the actual value or show an apparent slip in a locked area.
 Recently, small repeating earthquakes, which occur at almost the same locations repeatedly, have been detected on transform faults such as the San Andreas fault [e.g., Nadeau and Johnson, 1998; Schaff et al., 1998], subducting plate boundary in NE Japan [e.g., Igarashi et al., 2003], arc-continent collision boundary in Taiwan [e.g., Chen et al., 2007], and active faults in China [e.g., Li et al., 2007]. Their recurrence intervals are proportional to the scalar moment and are consistent with geodetic slip rates among these regions [Chen et al., 2007]. Small repeating earthquakes have not been detected at the asperities of large inter-plate earthquakes [e.g., Igarashi et al., 2003]. It has been suggested that seismically slipped areas of large earthquakes and quasi-statically slipped areas are partitioned in a complementary style [e.g., Yagi et al., 2003]. Thus, sequences of small repeating earthquakes are caused by repeating slips of small asperities surrounded by stable sliding areas, and are regarded as a kind of slip sensor for detecting aseismic slip in their areas. Although the temporal resolution of slip-rates from small repeating earthquakes depends on the recurrence intervals of sequences, we estimated slip rates with higher spatial resolutions in a region far from seismic stations in previous studies [e.g., Uchida et al., 2003]. However, these studies mainly interpreted the slip-rate distribution at regions where repeating sequences were concentrated in a relatively small area.
 In this study, we extracted sequences of small repeating earthquakes over a large area of the Japanese Islands, and identified the characteristics of spatial distributions. Furthermore, we investigated spatial changes of inter-plate coupling at the subducting Philippine Sea plate and the subducting Pacific plate by estimating slip-rates of these sequences.
2. Detection of Small Repeating Earthquakes
 To extract small repeating earthquakes, we calculated cross-correlation coefficients between observed seismograms at each station following Igarashi et al. . Seismograms for this analysis were selected from records of stations operated by the National Research Institute for Earth Science and Disaster Prevention (NIED), the Japan Meteorological Agency (JMA), and Earthquake Research Institute (ERI), University of Tokyo. They are located throughout the Japanese Islands (Figure 1). We used the unified JMA hypocenter catalogue and selected waveform data of earthquakes of M2.0 or larger for the period from January 2002 to December 2009. The total number of earthquakes was about 163000 (Figure 1). We picked up earthquake pairs whose epicenter separations are up to 20 km, and calculated cross-correlation coefficients. The time window is from P-wave onset to three seconds after direct S-wave arrival. The maximum length of the time window was 50 seconds because the largest epicentral distance used was about 400 km. We selected as a repeating earthquake pair, those whose cross-correlation coefficients were greater than 0.95 at two or more stations. For this calculation, we used three band-pass filters with passbands of 1–4, 2–8, and 4–16 Hz as a quarter wavelength of S-wave, which corresponds to the source size of analyzed earthquakes. Similarities at all passbands were identified for M2 earthquakes. These procedures were applied to all selected pairs. If several pairs shared the same event, they were grouped as the same sequences of repeating earthquakes.
 This procedure detected many sequences in and around the Japanese Islands, including the subducting Pacific plate, the subducting Philippine Sea plate, and shallow earthquakes beneath land areas (Figure 1). It is difficult to accurately identify locations between paired earthquakes due to large hypocentral errors in offshore earthquakes. We can only classify their sequences based on their duration, the period from the first event to the latest event. Repeating sequences with long-term durations (we call them continual-type sequences) occurred in the inter-plate in NE Japan [e.g., Igarashi et. al., 2003]. In this analysis, we assumed that a sequence of earthquakes occurred at the same location when they had durations of over three years. This threshold roughly corresponds to the expected recurrence intervals of M2.0 events where the average slip-rate is 26 mm/yr (close to minimum of relative plate motion around Japan).
 Most continual-type sequences are located in inter-plate coupling areas at the Philippine Sea plate subducting from the Ryukyu trench and the Pacific plate subducting from the Kuril-Japan trench (Figure 1). Most of their focal mechanisms are of the low-angle thrust-fault type along the dip angles of plate boundaries. The deepest limits of continual type sequences are about 30–50 km for the Philippine Sea plate of the Ryukyu arc and about 50–70 km for the Pacific plate of the Kuril-Japan arc, respectively. In the Kanto district, both plates subduct, reaching depths of about 55 km at the upper boundary of the Philippine Sea plate and about 80 km at the boundary between the Pacific plate and Philippine Sea plate as shown by recent studies [Kimura et al., 2006; Uchida et al., 2009; Igarashi, 2009]. On the other hand, sequences with highly correlated waveforms during a short period only (we called burst-type sequences) are also found within overriding plate, subducting plates, or outer-rise. In particular, many inland shallow sequences only last for a very short period of within a day (Figure S1 of the auxiliary material), and are found in swarm activities and aftershock activities of large earthquakes.
3. Slip-Rate Estimated From Sequences of Small Repeating Earthquakes
 We investigated slip characteristics in inter-plate coupling areas of the subducting Pacific plate and the subducting Philippine Sea plate. Slip amount at each event was calculated from seismic moment–slip relation proposed by Nadeau and Johnson . The scalar moment was calculated from magnitude using the relationship between magnitude and scalar moment [Hanks and Kanamori, 1979]. We assumed that the slip-rate within each inter-seismic period of repeating sequence is constant and equal to the slip-rate of their surrounding areas (Figure S2). The slip-rate was obtained by dividing the slip amount of the next small repeating earthquake by the recurrence interval. If an expected previous or next earthquake was outside the analysis period, we extrapolated the average slip-rate. Some sequences were almost co-located. We considered that sequences occurring at almost the same location indicate a quasi-static slip of the same areas, and used the average slip-rate and centroid as a representative value of a group (Figure S2). There are 597 slip series groups − 165 groups at the Philippine Sea plate and 432 groups at the Pacific plate. A harmonic surface which does not have local maxima or minima except at data points was obtained to show the spatial distributions of slip-rates on a map. We masked areas that were more than 30 km away from the nearest data points considering asperity sizes of large earthquakes. An observation time span of eight years allows slip rates greater than about 20 mm/yr to be resolved (Figure 2).
 The resultant average slip-rates show substantial spatial changes of inter-plate coupling divided into several segments in Japan (Figure 2). The average slip-rates correspond to relative plate motion [DeMets et al., 1994; Nishimura et al., 2004] in the Ryukyu arc and a deeper part of the Kuril-Japan arc. On the other hand, source regions of older large earthquakes and the shallow part of the Kuril-Japan arc indicate slip deficits of inter-seismic-periods or lack of slip areas.
 We identified spatial changes from relative standard deviation (RSD; the ratio of the standard deviation to the average) of slip-rates calculated at each repeating group. The RSDs showed remarkable spatial changes in the Kuril-Japan arc (Figure 3). In particular, they were larger than 0.4 near the source regions of large earthquakes that occurred in the period under analysis. These suggest slip acceleration areas with post-seismic slips of large earthquakes (Figure S3) as shown by previous studies in NE Japan [e.g., Uchida et al., 2003].
 On the other hand, the RSDs were relatively small in the Ryukyu-arc. Slip-rates corresponded to relative plate motion and their moderate deviations do not change greatly at different depths in most parts of the Ryukyu arc. This suggests that it is difficult for large inter-plate earthquakes to be generated with weak coupling in these regions. The RSD in southwestern area of the Ryukyu arc is also slightly higher than those of other parts. This implies that slip changes are related to some inter-plate earthquakes and repeating slow slip events shown by GPS data inversion [Heki and Kataoka, 2008].
 Two exceptional intra-plate sequences, which occurred at intermediate depths of the subducting Pacific plate and outer-rise of both plates, also showed large deviations (labeled “a–b” in Figure 2a). These suggest that post-seismic deformation by creep or viscoelastic deformation caused sequences in the fault plane of a large intra-plate earthquake as shown in the Loma Prieta aftershock zone [Schaff et al., 1998].
 On the other hand, areas without repeating sequences suggest either a locked region with slip-rates less than about 20 mm/yr or a stable sliding area. In the former case, strain accumulation is proportional to relative plate velocity, and in the latter case, it is expected that large earthquakes do not occur in the region. In previous analyses, we estimated fast slip-rates at and around the epicenter of the 1994 Sanriku-haruka-oki earthquake (labeled “A” in Figure 2a) [Igarashi et al., 2003; Uchida et al., 2003]. Large earthquakes occurring periodically are also reported in other areas (labeled “B” in Figure 2a [Katsumata and Yamanaka, 2006] and western Kanto to Nankai areas in Figure 2b [Sato et al., 2005; Baba and Cummins, 2005]). Therefore, we interpret that these areas have stopped slipping.
 There are several small slip-rate and small deviation areas, which are labeled “C–D” and “F.” These correspond to asperities of past large earthquakes (Figures 2 and 3). Furthermore, areas labeled “B–D” also correspond to slip deficit areas inferred from the GPS data analysis [Hashimoto et al., 2009]. There is no record of an earthquake with a single asperity in the slip-deficit area labeled “E.” This information is important for identifying an area that may generate large earthquakes in the future. We should pay attention to spatio-temporal changes of plate coupling in these areas. In region “G,” slip-rates are somewhat slow, but they show moderate deviations. The slip deficits may suggest slip areas related to a M6.8 inter-plate earthquake that occurred on October 30, 2009.
 Although we cannot show slip-rate distributions in most areas of the Nankai trough with a few exceptions, burst-type sequences were extracted at the overriding plate and intra-plate near the subducting plate boundary (Figure 1). The locations correspond to the deeper limit of source regions of giant inter-plate earthquakes. The occurrences of these sequences within a plate may be caused by rapid stress changes between strong couplings at a shallower plate boundary and stable sliding at a deeper part. Deep low-frequency tremors and earthquakes occur in the transition zones of Nankai trough [Obara, 2002] (Figure 2). They coincide with the activities of slow earthquakes and episodic slow slip events, and they are thought to reflect a stress accumulation and relaxation process in the transition zone [Ito et al., 2007]. In contrast, very few were located in the downdip direction of repeating groups with slow slip-rates. These results suggest that space-time characteristics of inter-plate coupling around strongly locked areas affected the occurrence of all these seismic events. The period we analyzed is short compared to the recurrence intervals of giant earthquakes. Spatio-temporal changes of these seismic activities should be investigated in further analyses.
 Slip-rate information estimated from the sequences of small repeating earthquakes contributes to estimating inter-plate coupling as well as moment releases of large earthquakes and/or the slip information on the subducting plate boundary obtained by a GPS data analysis. We can get new slip sensors located at the plate boundary beneath the ocean in Japan. This kind of analysis is less subject to station separations if seismic waveforms are recorded well at each station. We could monitor slip deformations such as the inter-plate coupling of the subducting plates and post-seismic deformation after large earthquakes throughout the Japanese Islands with quasi-real-time procedures.
 We thank S. Miyazaki, N. Kato, and T. Iidaka for useful discussions. Constructive comments by K. Wang and an anonymous reviewer have significantly improved the paper. We thank the NIED and JMA for allowing us to use waveform data collected at each telemetric station. We used unified hypocenter catalogue of JMA and moment tensor solutions of F-net, NIED.