We investigated the migration mode of deep non-volcanic tremor activity beneath Kii Peninsula, southwest Japan. Major tremor episodes are characterized by long-term migration with a velocity of about 10 km/day, propagating along the strike of the subducting plate. Similar tremor migration in Cascadia is accompanied by reverse propagation at speeds on the order of 100 km/day and much faster slip-parallel migration at speeds on the order of 1000 km/day. We systematically searched for migrating tremor with clear linearity in space and time. As a result, we found tremor migrations at speeds ranging from 1 to 60 km/hr depending on the along-dip position in the tremor zone. The observed decrease in migration speed with increasing measurement time scale suggests that migration is controlled by a diffusion process. The along-strike migration at lower speeds, including both forward and backward directions relative to the long-term migration episode, is concentrated at the updip side of the tremor zone, whereas the faster slip-parallel migration is distributed over the entire zone. The long-term migration seems to consist of and be excited by the propagation of along-strike creep at the updip part. The concentration of along-strike migrating tremor sequences at the updip side may reflect the existence of abundant fluid that accumulates at the corner of the mantle wedge. The faster slip-parallel migrations represent projections of along-strike fluctuations in slip pulse propagation controlled by striations along the plate interface.
 The phenomenon of coupled non-volcanic tremor and slow slip events in southwest Japan [Obara, 2002; Obara et al., 2004] and in Cascadia [Dragert et al., 2001; Rogers and Dragert, 2003], known as episodic tremor and slip (ETS), provides evidence for weak coupling of the plate interface at the downdip side of the seismogenic zone. The generation mechanism of ETS remains unknown; however, it is important to understand the nature of earthquakes, subduction processes, and strong-motion seismic hazards.
 One of the most significant features of tremor is migration, of which three types have been described: along-strike long-term migration at a speed of about 10 km/day [e.g.,Obara, 2010; Houston et al., 2011]; rapid tremor reversal (RTR), which involves along-strike migration at speeds on the order of 100 km/day, propagating in the opposite direction to the long-term migration [Houston et al., 2011]; and much faster slip-parallel migration at speeds on the order of 1000 km/day, detected in southwest Japan [Shelly et al., 2007] and in Cascadia [Ghosh et al., 2010]. Long-term migration usually starts from the downdip portion of the tremor zone and propagates radially [Obara et al., 2011]. Because of the narrow dimensions of the tremor zone, tremor migrates updip during the initial stage of each episode, then laterally along the strike of the subducting plate. The initial upward migration is also observed in northern Cascadia [Wech and Creager, 2011]. It is possible that these three migration modes reflect the main and sub-rupture processes during a slow slip episode. The question of whether tremor migration occurs solely by the above three modes, or by additional modes, is important in constructing an appropriate physical model of slow slip phenomena. In this paper, we investigate tremor migration by the automatic detection of the linear distribution of tremor sequences beneath Kii Peninsula, southwest Japan.
2. Tremor Catalogs and Space–Time Distribution
 We analyzed a tremor catalog derived using the modified envelope correlation method [Maeda and Obara, 2009], considering tremor amplitude observed at High Sensitivity Seismograph Network (Hi-net) boreholes administrated by the National Research Institute for Earth Science and Disaster Prevention (NIED) of Japan [Obara et al., 2005] from 2001 to 2010. This original catalog, constructed at 1-minute intervals, is the basis of an hourly centroid tremor catalog obtained using a clustering process [Obara et al., 2010]. The clustering catalog is convenient for assessing the overall features of tremor activity.
 Beneath the Kii Peninsula, tremor is distributed within a narrow belt-like zone with a width of 30 km, concentrated at the updip and downdip sides of the zone (Figure 1a). Beneath the northeastern part of the peninsula, tremor episodes have a recurrence interval of approximately 6 months (Figure 1b). In this region, many of the tremor episodes are characterized by long-term migration from northeast to southwest [Obara, 2010]; however, tremor sometimes migrates from southwest to northeast, as observed in January 2006 [Ito et al., 2007] (Figure 1c). In this example, the long-term migration had a velocity of 15 km/day and we observed near-vertical features (arrows inFigure 1c). These features indicate a speed of about 10 km/hr in the opposite direction to the long-term migration, as observed in an expanded view of the space–time plot (Figure 1d). The migration mode with a reverse direction is similar to RTR detected in Cascadia [Houston et al., 2011]. In order to estimate the migration velocity and direction, the time progression of tremor epicenters rather than just projected locations are analyzed. To this end, we extracted the linear distribution of tremor from 43 episodes (large circles in Figure 1a) listed in the original catalog.
 In order to extract various migrating tremor sequences, we use time scales of 0.5, 1.0, 2.0, and 4.0 hours because migration velocity sometimes changes smoothly [Ide, 2010]. The detection procedure is divided into two steps. The first step is to extract a linear trend from the space–time plot projected on the southwest–northeast profile, as shown in Figure 1. Outliers located at distances from the regression line that are greater than twice the standard deviation are removed from the analysis. The second step is data selection based on three principal component analyses (PCAs). The first PCA is applied to three-dimensional space with horizontal epicentral location and time. The second PCA is applied to two-dimensional epicentral data, and the third is applied to two-dimensional space with the data projected to the first principal component axis in the second PCA and time (Figure 2). We used three parameters to extract quality data: linearity, which is represented by the ratio of the first eigenvalue to the second eigenvalue derived from the third PCA; the angular difference between the horizontal projection of the first principal component axis from the first PCA and the first principal component axis from the second PCA; and the total number of tremor data points in a given time window. For each parameter, we set thresholds to ensure the same selection rate of 30% of the cumulative distribution function as that in the result of the first step obtained for each time scale. For the linearity, we set a minimum threshold of 6.0, 4.0, 2.5, and 2.5 for time scales of 0.5, 1.0, 2.0, and 4.0 hours, respectively. For the angular difference, we set a maximum threshold of 5, 5, 8, and 10 degrees, and for the total number of data points we set a minimum threshold of 7, 12, 22, and 40, for time scales of 0.5, 1.0, 2.0, and 4.0 hours, respectively. Moreover, in order to remove cases of clustering that arise with a shorter time duration, the minimum duration of the data are set to be equal to 60% of the given time-window length. These thresholds are applied together to ensure the extraction of quality data. For each time scale, we performed the above process for the entire time period of each major episode with a time shift of half the length of the given time scale.
4.1. Depth Dependence of Migration Mode
 The total numbers of migrating tremor sequences extracted for time scales of 0.5, 1.0, 2.0, and 4.0 hours are 223, 170, 127, and 74, respectively. The direction of migration clearly differs with the time scale. The rose diagrams in Figure 3 show the migration direction for each time scale. For a time scale of 0.5 hours, the migration direction is mainly parallel to the slip direction to the southeast and northwest, indicating that tremor propagates updip and downdip, respectively. The migration velocity is 20–60 km/hr (Figure 4a). In contrast, for time scales longer than 1 hour, the migration direction is mainly along-strike and the velocity decreases at longer time scales (Figure 4). The migration direction is roughly separated into slip-parallel and along-strike modes.Figure 3also shows the spatial distribution of the extracted migrating tremor sequences and their directions. At shorter time scales, tremor sequences with slip-parallel migration are distributed over the entire zone. The along-strike migration at longer time scales is concentrated on the updip side of the tremor zone (Figures 3b and 3c). These tremor sequences migrate in directions that are the same, opposite, or perpendicular to that of the long-term migration. The pie chart at bottom right inFigure 3shows the percentage of each migration direction of detected events during the background long-term migration, showing clear propagations to the northeast or southwest. At longer time scales, the number of detected events with backward propagation relatively to the long-term migration is similar to the number of events propagating in the same direction as the long-term migration.
4.2. Rapid Tremor Reversal-Like Sequence
 Here we examine the detailed time evolution of an RTR-like tremor sequence (arrow inFigure 1d) that occurred from 0300 to 0800 on 11 January, 2006 as part of an episode of long-term migration from southwest to northeast. As a result, four migration sequences were extracted. Between 0300 and 0500, tremor migrated to the south (updip) at a velocity of 16 km/hr (Figure 2a), then migrated northward (downdip) at a speed of 50 km/hr (Figure 2b). Finally, it migrated south (updip) again along a different path from the first updip migration at a velocity of 35 and 18 km/hr for the time scales of 1 and 2 hours, respectively (Figures 2c and 2d, respectively). The faster initial speed for the shorter time window indicates that the migration speed decreases with time. This sequence consists of two sub-events migrating along an oblique path from the downdip to the updip sides of the tremor zone. The return migration occurred just after the arrival in the region of the front of the long-term migration.
5. Discussion and Conclusions
 Based on the present results, tremor migration is roughly classified into two modes; along-strike migration at a lower speed in the updip part of the tremor zone, and slip-parallel migration at a higher speed across the entire zone. The former mode is similar to long-term migration [Obara, 2010] and the latter type is similar to tremor streaks with high-speed migration [Shelly et al., 2007; Ghosh et al., 2010; Ide, 2012]. The estimated migration velocity depends on the length of the time scale, suggesting that tremor migration is generally controlled by a diffusive process [Ando et al., 2010; Ide, 2010; Houston et al., 2011]. Nakata et al. proposed that constant-velocity migration, which is often observed during long-term migration episodes, is explained by the successive occurrence of diffusion-limited rupture process. If we consider that the updip-most along-strike migration detected from the present results is an element of slower long-term migration, it may boost each diffusive sub-event and drive the long-term migration. This raises the possibility of a guide for the direction of creep propagation at the updip corner of the mantle wedge, if tremor occurs below the intersection between the slab surface and continental Moho [Kato et al., 2010]. At the corner of the mantle wedge, fluid released from the slab by dehydration processes is expected to accumulate because of the sealing effect of the low-permeable Moho [Katayama and Hirauchi, 2010]. Such an abundance of fluid may drive the observed along-strike propagation of tremor.
 Comparing the space–time evolution of the slip distribution with tremor location, Bartlow et al. suggested that active tremor at the rupture front reflects a high slip rate in this region, and tremor represents slip on small asperities due to slow slipping in the surrounding area. Therefore, variation in tremor migration is a direct reflection of slip fluctuations or small-scale slip pulses. The observed return migration of sub-events in the RTR-like feature may suggest the existence of various slip pulses during a period with a high slip rate. The migration velocity of these sub-events, propagating obliquely from the downdip to the updip sides of the zone, is slightly faster than that of RTR observed in Cascadia [Houston et al., 2011]. Therefore, this sub-event might be a combined phenomenon comprising slip-parallel and along-strike migration modes.
 The high-speed slip-parallel migration is interpreted to be associated with interaction between the creep front and a slip-parallel linear structure [Ando et al., 2010; Ghosh et al., 2010], such as striations along the lower surface of the overriding plate that formed during the past subduction of seamounts [Ide, 2010]. If the creep event migrates along the northeast–southwest profile, the distribution of the migration velocity shows a peak at around 20 km/hr for a time scale of 0.5 hours (Figure 4a, right), which is similar to the distribution of projected velocity for time scales of 1.0 and 2.0 hours (Figures 4b and 4c, right). This finding suggests that faster slip-parallel migration may represent projections of along-strike fluctuations in slip pulse controlled by striations along the plate interface.
 We would like to thank Heidi Houston and an anonymous reviewer for their valuable comments and kind suggestions. We thank the staff of NIED's Hi-net for providing quality data. Maps were drawn using the Generic Mapping Tools [Wessel and Smith, 1998].
 The Editor thanks Heidi Houston and an anonymous reviewer.