Spatiotemporal evolution of aseismic interplate slip between 1996 and 1998 and between 2002 and 2004, in Bungo channel, southwest Japan

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi:10.1029/2006jb004643, 2007 Spatiotemporal evolution of aseismic interplate slip between 1996 and 1998 and between 2002 and 2004, in Bungo channel, southwest Japan Shinzaburo Ozawa, 1 Hisashi Suito, 1 Tetsuo Imakiire, 1 and Makoto Murakmi 1 Received 21 July 2006; revised 19 December 2006; accepted 19 January 2007; published 11 May 2007. [1] Interplate aseismic slip in the Bungo channel area, southwest Japan, occurred during 1996 1998 and 2002 2004. We employed a square root information filter following the time-dependent inversion technique to time series of daily coordinates of global positioning system (GPS) sites. The results show that aseismic interplate slip occurred beneath the southwestern part of Shikoku Island from late 1996, then shifted southwestward to the Bungo channel area from May 1997 to February 1998, and subsided over time with a moment magnitude (M w ) of 7.1. In contrast, the 2002 2004 event shows slip in the area beneath the Bungo channel in an early stage from March 2003 to August 2003. From August 2003 to January 2004, the slip area expanded by around 30 km northeastward to the southwestern part of Shikoku Island and the northern part of the Bungo channel, and then decayed over time with M w reaching 7.1. In the 2002 2004 event, the start of the northeastward expansion and acceleration of the aseismic slip coincided with the occurrence of a short-term slow slip event and low-frequency earthquakes in a deep area. This is a different spatiotemporal evolution from that of the 1996 1998 event, despite having occurred in almost the same area with similar moment magnitudes. A balance of slip deficit and forward aseismic slip on the plate boundary suggests that part of the Bungo channel area releases strain energy mainly by episodic long-term slow slip events. Citation: Ozawa, S, H. Suito, T. Imakiire, and M. Murakmi (2007), Spatiotemporal evolution of aseismic interplate slip between 1996 and 1998 and between 2002 and 2004, in Bungo channel, southwest Japan, J. Geophys. Res., 112,, doi:10.1029/2006jb004643. 1. Introduction [2] Figure 1a shows the tectonic setting in and around Japan. The Philippine Sea plate is thrusting against the continental plate at an annual rate of 7 cm/year in the northwestward direction near the Bungo channel area [e.g., Miyazaki and Heki, 2001]. The Bungo channel area in southwest Japan is located between Shikoku and Kyushu Islands (Figure 1b). The trends of earthquake occurrences are very different between offshore of Shikoku and offshore of Kyushu. Large thrust earthquakes with M w > 8 have occurred offshore of Shikoku Island at time intervals of about 140 years [e.g., Kumagai, 1996], while M w 6.5 7.5 earthquakes occur offshore of Kyushu Island with time intervals of about 10 20 years [Shiono et al., 1980]. The latest events offshore of Kyushu Island occurred on 19 October 1996 and 3 December 1996 (Figure 1b). [3] Because of the differences between the earthquakes offshore of Kyushu and offshore of Shikoku, for the Bungo channel area, flanked by these two islands, the question of how the strain energy accumulated by the subduction of the Philippine Sea plate is released has been raised. 1 Crustal Dynamics Department, Geographical Survey Institute, Tsukuba, Japan. Copyright 2007 by the American Geophysical Union. 0148-0227/07/2006JB004643$09.00 [4] Figure 2 shows the velocity field of global positioning system (GPS) stations relative to the 0404 site in the Chugoku district for the period between 1999 and 2002, when there were no earthquakes or transient motions. Standard deviation (s) ranges from 1 to 2 mm in Figure 2. We can observe northwestward movements around the Bungo channel area, which is mainly caused by the subduction of the Philippine Sea plate, and a steady accumulation of strain in this area is shown. We call this velocity field in Figure 2 trend velocity and focus on the deviation from this trend velocity or detrended transient motion. [5] The continuous GPS network of the Geographical Survey Institute of Japan (GSI) detected detrended transient crustal deformation in the Bungo channel area for the 1996 1998 period and the 2002 2004 period. The spatial patterns of the detrended transient motion show southeastward motion in the above two periods, suggesting the occurrence of aseismic interplate slip in this area, considering the northwestward motion of the subducting Philippine Sea plate [e.g., Hirose et al., 1999; Ozawa et al., 2001, 2004a; Miyazaki et al., 2003; Hirose and Obara, 2005]. [6] New time series of the coordinates of the GPS sites are generated using Bernese software ver. 4.2 with a newly improved strategy [Hatanaka et al., 2003], so that highquality and sufficiently long time series of station coordinates are now available compared with the data we used previously [Ozawa et al., 2001]. In a study of the 2002 1of13

Figure 1. (a) Tectonic setting in and around Japan. Solid lines indicate plate boundaries. (b) Enlarged map of the rectangular area in (a). Solid lines represent isodepth contours of the plate boundary between the Philippine Sea plate and the continental plate. The Philippine Sea plate is subducting beneath the continental plate at the Nankai trough at a rate of about 7 cm/year in the northwest direction. Central moment tensor (CMT) solutions of two earthquakes in 1996 are plotted at their epicenters. 2004 event, Ozawa et al. [2004a] assumed that transient motion started from around September 2003, since they considered the transient motion before September 2003 to be unreliable because of antenna changes in early 2003. Since then, offsets due to antenna changes were reexamined and estimated for each station with high precision. [7] In this research, we estimate the spatiotemporal evolution of slip distribution on the plate boundary in the Bungo channel area for the above two periods, applying a square root information filter to the latest detrended crustal deformation data or anomaly deviating from the trend velocity detected by the GPS network in Figure 2. In this analysis, we assume that the offsets caused by antenna changes in early 2003 are mostly removed from the data and that the transient motion before September 2003 indicates the actual crustal deformation of the 2002 2004 event. 2. Data and Analytical Procedure [8] GPS data of 24 hours are analyzed with Bernese GPS software version 4.2 on a daily basis. Hatanaka et al. [2003] recomputed the coordinates of GPS sites by an improved analytical procedure. The improved strategy includes new phase maps specific for antenna-monument types, new network configuration, coordinates of the fixed stations obtained from the local tie from the International Global Navigation Satellite System (GNSS) Service (IGS) sites based on the International Terrestrial Reference Frame of 1997 (ITRF97) coordinates and velocity, transformation of orbit information into ITRF97, and a new troposphere estimation model and strategy using the model of Saastamonian [1973] and the mapping function of Niell [1996]. The details are described in the work of Hatanaka et al. [2003]. [9] We use east-west (EW), north-south (NS), and up-down (UD) components at selected GPS sites in the Bungo channel area, for the period between 1996 and 2006, relative to the 0404 site in the Chugoku district (see Figure 2). In the first step, offsets due to antenna changes in early 2003 are Figure 2. Rates of movements at GPS sites relative to site 0404 for period between 1999 and 2002. Ellipse at the tip of each arrow represents threefold standard deviation (s). 2of13

Figure 3. Detrended time series of crustal deformation at selected GPS sites. EW, NS, and UD represent east-west, north-south, and up-down movements with eastward, northward and upward motions being positive. (a) 0086. (b) 0448, (c) 0437. (d) 0447. (e) 0473. (f) 0090. The locations of GPS sites are plotted in Figure 4a. estimated using a step function and are removed from the raw data. Since the raw data without offsets of antenna changes include annual and linear trend components, we estimate them for the period between 1999 and 2002 when there were no transient motions or earthquakes, and remove them from the raw data for the entire period [Ozawa et al., 2004b]. We call this procedure detrending of the time series in this paper. In this detrending process, we assumed that crustal deformation rates for the period between 1999 and 2002 are nearly constant and unaffected by either the 1996 1998 aseismic slow slip or the 2002 2004 aseismic slip. On this assumption, we believe that the derived crustal deformation rate or the trend velocity for the period between 1999 and 2002 represents interseismic linear trends. Although this is an assumption, the detrended time series after 2004 shows zero slant at most GPS sites (Figure 3) as is the case for the period between 1999 and 2002; this supports our hypothesis. As mentioned above, our focus in this research is on the detrended transient motion or deviation from the trend velocity. [10] Akaike s [1974] information criterion is used to select a degree of overtone for annual components in the fitting. M w 6.8 and M w 6.7 earthquakes occurred on 19 October 1996 and on 3 December 1996, respectively, in the sea of Hyuganada. Offsets due to these earthquakes are estimated using a step function and are removed from the time series without annual component and linear trend component. [11] On the assumption that standard deviation of observation does not change for the 1999 2002 period, the 1996 1998 period and the 2002 2004 period, uncertainties of each time series for these three periods are estimated by ordinary Kalman filtering and error ellipses are plotted in 3of13

Figure 4. (a) Detrended movements for the period between 1996 and 1998. Empty and solid circles show the locations of GPS sites used in our spatiotemporal evolution analysis for the 1996 1998 period. Solid circle shows the location of GPS sites whose time series are plotted in Figure 3. The ellipses at the tips of black arrows indicate 3s error of observations. Southeastward motion suggests the occurrence of interplate aseismic slip. Southeastward motion in the area of central Kyushu enclosed by the dotted line represents postseismic deformation after the two earthquakes in the sea of Hyuganada in 1996. (b) Detrended movements for the period between 2002 and 2004. Nomenclature is the same as that in (a). Transient motion similar to that in (a) is shown. Spatiotemporal evolution of a slow slip for the 2002 2004 period was estimated from using ground movements at the GPS site in this figure. Figures 2 and 4 6. The standard deviations of time series estimated by ordinary Kalman filtering are found to be similar among the GPS sites for the same period. [12] Using the detrended time series or deviation from the trend velocity in Figure 2 with the annual components and earthquake offsets removed (Figures 3 6), we applied square root information filtering [Ozawa et al., 2004b] following the time-dependent inversion technique [Segall and Matthews, 1997] for the 1996 1998 period and the 2002 2004 period to estimate the spatiotemporal evolution of the Bungo channel aseismic interplate slip. Since we use detrended data, the estimated spatiotemporal evolution of the aseismic interplate slip rate is deviation from that of a state for the period between 1999 and 2002. Although the time-dependent inversion uses Kalman filtering [Segall and Matthews, 1997] to estimate the spatiotemporal evolution, we adopted a square root information filtering that produces the same results as Kalman filtering [Bierman, 1977]. [13] In state-space modeling, we adopt a state of (u 1, v 1, u 2, v 2,..., u k, v k,..., u N, v N, r 1, r 2,..., r p ), where u k indicates the total slip at the kth knot, v k indicates the slip velocity at the kth knot, and r p represents a random walk of the pth GPS site. Filtering analysis consists of three processes. Firstly, we estimate the one-step-ahead prediction from the nth state X n n estimated based on all the observations up to time n, using transition equations. Transition equations consist of smoothing in time and space and have been described by Ozawa et al. [2004b] (see Appendix). [14] Next, we obtain an optimal state using the one-stepahead prediction state and observations at time n + 1 (see Appendix). This optimal state is based on all the observations up to time n + 1. This process is called filtering. By repeating these processes, we obtain the final state at the end of the time series. This final state is based on all the observations until the end of the time series. [15] After obtaining the final state, we conduct a smoothing process in which we calculate states based on all observations. The smoothing process has been described by Ozawa et al. [2004b]. [16] GPS sites used in the filtering analysis are plotted in Figures 4a and 4b. We used east-west (EW), north-south (NS), and up-down (UD) components at 56 GPS sites for the 1996 1998 event, while 46 GPS sites were used for the 2002 2004 event. [17] We weight EW, NS, and UD motions at a ratio of 1:1:1/3, considering the standard deviation of each time series estimated through ordinary Kalman filtering, as mentioned above. [18] The variance-covariance matrix of GPS analysis was not used since it is difficult to extract and modify the variance-covariance matrix from a database that stores analytical results for small subnetworks within a nationwide network in GPS analysis. [19] We assumed the standard deviation (s) of GPS observations to be constant for the analysis period and among GPS sites. Actually, s of each time series estimated by ordinary Kalman filtering on the assumption that s is constant over time changes nominally among GPS sites. Although s of each time series varies over time, we considered the variation of s over time to not be so large as to change the characteristics of the derived model. On these assumptions, we estimated s of observations and 4of13

Figure 5. Snapshots of detrended displacements at GPS sites relative to site 0404. Black arrows indicate observations while white arrows indicate computed values. Ellipses at the tips of red arrows indicate 3s error of observations. (a) 23 December 1996 to 29 May 1997. (b) 29 May 1997 to 12 October 1997. (c) 12 October 1997 to 25 February 1998. (d) 25 February 1998 to 11 July 1998. uncertainties of a model through a square root information filtering in time-dependent analysis. [20] In this filtering analysis, we used the same fault patches for the 1996 1998 event and the 2002 2004 event, as shown in Figures 7a and 8a. We adopt isodepth contour maps of the plate boundary estimated by the Kyushu University [1999] and by Satake [1993] in this region. A fault patch is represented by a parametric B-spline surface to fit the plate boundary estimated by the Kyushu University and by Satake, as described by Ozawa et al. [2001]. The knot spacing is around 20 km in the strike direction and 30 km in the dipping direction. Slip distribution on a fault patch is also represented by a parametric B-spline surface [Ozawa et al., 2001]. We used the roughness of slip distribution formulated by Ozawa et al. We incorporated inequality constraints by the method of Simon and Simon [2003]. [21] We examined whether changing the reference point significantly changes the estimated model. The result is that the characteristics of the estimated model do not change upon changing the reference point. 3. Results [22] We can clearly see two transient motions in Figure 3, which shows detrended time series of displacements at six selected GPS sites. All the sites show transient eastward motion. Transient southward motion is revealed in most GPS sites, except for the 0448 and 0447 sites, in Figure 3. UD motion at the 0437 site shows upheaval for both the periods between 1996 and 1998 and between 2002 and 2004, although the upheaval seemed to have occurred in a shorter period of time for the 2002 2004 event (Figure 3c). The 0473 and 0086 sites show downward motion for the 5of13

Figure 6. Snapshots of detrended displacements at GPS sites relative to site 0404. Black arrows indicate observations while white arrows indicate computed values. Ellipses at the tips of red arrows indicate 3s error of observations. (a) 1 March 2003 to 4 August 2003. (b) 4 August 2003 to 7 January 2004. (c) 7 January 2004 to 11 June 2004. (d) 11 June 2004 to 14 November 2004. 2002 2004 event, while the 0447 site moves upward for the same period. [23] The spatial pattern of the detrended crustal deformation in the Bungo channel area shows southeastward motion of up to 3 cm for the 1996 1998 period and the 2002 2004 period relative to the 0404 site (Figures 4a and 4b). One standard deviation (s) of each displacement ranges from 1 to 2 mm. Figures 4a and 4b suggest the occurrence of aseismic interplate slip in this area, considering that the Philippine Sea plate is subducting in the northwest direction (Figure 2). [24] Figures 5 and 6 show snapshots of transient motion for the 1996 1998 event and the 2002 2004 event, respectively. Error ellipses of threefold standard deviation estimated by ordinary Kalman filtering are plotted in these figures. In the case of the 1996 1998 event, relatively large southeastward movements of GPS sites appear in the southwestern part of Shikoku compared with those in northern Kyushu for the period between December 1996 and May 1997 (Figure 5a). The transient motion at the GPS sites in the central part of Kyushu, enclosed by a dotted line in the figure, indicates postseismic deformation after the 1996 Hyuganada earthquakes. With time, transient motion in northern Kyushu increases in magnitude compared with that in the southwestern part of Shikoku (Figures 5b and 5c). This indicates aseismic slip propagation from the southwestern part of Shikoku to Kyushu. In the case of the 2002 2004 event, transient motions similar in magnitude appear for both Kyushu and Shikoku until August 2003 (Figure 6a). Relatively large slips appear in the southwestern part of Shikoku for the period between August 2003 and January 2004 (Figure 6b), indicating slip occurrences near the southwestern part of Shikoku in this period. From January 2004, transient motion gradually subsides (Figures 6c and 6d). 6of13

Figure 7. Spatiotemporal evolution of aseismic interplate slip for the 1996 1998 period. Solid line in (a) shows the fault patch used in estimating interplate slip. Solid circles show the location of knots that represent the spline surface. The fault patch is 16 knots in length and 10 knots in width. Broken line indicates the area we used in estimating the time evolution of the moment of aseismic interplate slip in the Bungo channel area. Red arrows show movements of the continental plate against the Philippine Sea plate. We adopted slightly irregular time intervals so that characteristic points of spatiotemporal evolution become evident. Ellipses at the tips of red arrows represent 3s error. (a) 1 April 1996 to 9 August 1996. (b) 9 August 1996 to 23 December 1996. (c) 23 December 1996 to 29 May 1997. (d) 29 May 1997 to 12 October 1997. (e) 12 October 1997 to 25 February 1998. (f) 25 February 1998 to 11 July 1998. (g) 11 July 1998 to 24 November 1998. (h) Total aseismic slip for the period between 1 April 1996 and 24 November 1998. [25] On the basis of the above detrended time series, our filtering analysis for the 1996 1998 period shows that the interplate aseismic slip appeared from around December 1996 to May 1997 beneath the southwestern part of Shikoku Island (Figure 7c). The threefold standard deviation of estimated slip is approximately 1 to 4 cm. From May 1997 to October 1997, the slip magnitude increased beneath the western part of the Bungo channel compared with the slip 7of13

Figure 8. Spatiotemporal evolution of aseismic interplate slip for the 2002 2004 period. Solid circles in (a) show the locations of the knots to represent the fault surface. The fault patch is 10 knots in length and 16 knots in width. Slip histories at 45, 55, and 65 points are shown in Figures 9c, 9d, and 9e. Red arrows show movements of the continental plate against the Philippine Sea plate. Black dots represent the epicenters of low-frequency earthquakes. Epicenter data are from the Japan Meteorological Agency. Ellipses at the tips of red arrows represent 3s error. We adopted slightly irregular time intervals so that characteristic points of spatiotemporal evolution become evident. (a) 4 January 2002 to 22 April 2002. (b) 22 April 2002 to 25 September 2002. (c) 25 September 2002 to 1 March 2003. (d) 1 March 2003 to 4 August 2003. (e) 4 August 2003 to 7 January 2004. The green boxes show the area of the short-term slow slip event from late August to early September 2003 [from Hirose and Obara, 2005]. 1. The early stage of the short-term slow slip. 2. The late stage of the short-term slow slip. The slip area moved from region 1 to region 2 over a 9-day period [Hirose and Obara, 2005]. (f) 7 January 2004 to 11 June 2004. (g) 11 June 2004 to 14 November 2004. (h) Total aseismic slip for period between 4 January 2002 and 14 November 2004. 8of13

area beneath the southwestern part of Shikoku. From October 1997 to February 1998, the slip area beneath the southwestern part of Shikoku died out, while the slip area beneath the Bungo channel remained. From this result, we think that the slip area shifted southwestward to the Bungo channel for the above period, and then subsided over time (Figures 7d, 7e, and 7f ). Slip offshore of the central part of Kyushu Island, enclosed by a dotted line in the figure, indicates the postseismic slip area after the 1996 Hyuganada earthquakes (see Figure 7h). Since, in this study, our focus is on the Bungo aseismic slip, we will not detail the postseismic slip that followed the 1996 Hyuganada earthquakes (Figure 1b). At its maximum, slip magnitude reached approximately 30 cm in the Bungo channel area (Figure 7h) with a M w of 7.1 (Figure 10a). Since the 1996 1998 event contains postseismic deformation after the 1996 Hyuganada earthquakes, we computed the moment of the Bungo slow event within the rectangular area enclosed by the broken line in Figure 7a. Rigidity is assumed to be 30 GPa throughout this paper. As shown in Figure 10a, estimated moment gradually increases from late 1996 to the middle of 1997, slightly accelerates from the middle of 1997 to late 1997, and subsides after late 1997. These results are consistent with those of previous works [Ozawa et al., 2001; Miyazaki et al., 2003; Yagi and Kikuchi, 2003]. [26] For the 2002 2004 period, our analysis shows that the slip area was beneath the Bungo channel until August 2003 (Figure 8d). From August 2003 to June 2004, the estimated slip magnitude increased relatively in the southwestern part of Shikoku Island and the northern part of the Bungo channel compared with the slip beneath the central part and the southern part of the Bungo channel (Figure 8e), and subsequently subsided with time. From this result, we think that the slip area slightly expanded northeastward by around 30 km for the period between August 2003 and June 2004. In this analysis, the threefold standard deviation of estimated slip is around 1 to 2 cm. The dots in Figure 8 indicate epicenters of low-frequency earthquakes or Obara s tremor, the existence of which was first discovered by Obara [2002]. Epicenter data are from the Meteorological Agency of Japan. As shown in Figure 8e, the magnitude of estimated aseismic interplate slip increased sharply in the period between August 2003 and January 2004 when displacements at GPS sites increased in speed, coinciding with the rapid increase in the number of low-frequency earthquakes from late August in 2003 (Figure 9a). The estimated slip histories at points 45, 55, and 65 on the fault patch in Figure 8a indicate acceleration from early September 2003, as shown in Figures 9c, 9d, and 9e. Figure 10b shows the time evolution of the estimated moment magnitude for 9of13 Figure 9. (a) Cumulative number of low-frequency earthquakes in and around the Bungo channel area. Data are from the Japan Meteorological Agency. (b) Detrended east-west displacement at GPS site 0437 with eastward motion being positive. An increase in low-frequency earthquakes from late August to early September 2003 coincides with an increase in the velocity of detrended eastward motion at GPS site 0437. (c) Slip history at point 45 in Figure 8a. Green line (EW) and red line (NS) indicate east-west and north-south components with east and north being positive. Dotted lines show 3s range. (d) Slip history at point 55 in Figure 8a. Nomenclatures are the same as those in (c). (e) Slip history at point 65 in Figure 8a. Nomenclatures are the same as those in (c).

Figure 10. Time evolution of moment magnitude. (a) 1996 1998 event. The moment of Bungo aseismic slip is calculated for the patch designated by the broken line in Figure 7a. Dotted lines indicate 3s range. (b) 2002 2004 event. The moment is computed for the patch designated by the broken line in Figure 7a. Nomenclatures are the same as those in (a). the 2002 2004 event. We computed the moment magnitude within the area enclosed by the broken line in Figure 7a to compare the two events on a par. As shown in Figure 10b, the moment magnitude of the 2002 2004 event gradually increased from the middle of 2002, slightly accelerated from the middle of 2003 and then gradually subsided over time. A small bulge in the middle of 2002 in Figure 10b reflects a bump in the detrended crustal deformation, similar to that shown in Figure 9b. The slip magnitude reached approximately 30 cm at its maximum (Figure 8h) with an estimated M w of 7.1 for the 2002 2004 event (Figure 10b). Compared with that in Figure 7h, the total aseismic slip of the 2002 2004 event covers almost the same area as that of the 1996 1998 event (see Figures 7h and 8h). Our estimated models well reproduce the observed crustal deformation, as shown in Figures 5, 6, and 11. 4. Discussion 4.1. Low-Frequency Tremor, Short-Term Slow Slip, and Long-Term Slow Slip Between 2002 and 2004 [27] From here, we use long-term slow slip event for aseismic slip which lasts for 1 year or more and short-term slow slip event for aseismic slip which lasts for several days. [28] In this Bungo channel area, low-frequency earthquakes are active and it is reported that short-term slow slip events occur over several days, coinciding with the activation of low-frequency earthquakes [Obara et al., 2004]. The slip area of short-term slow slip events in the Bungo channel area moves from southwest to northeast or from northeast to southwest, in turn, with a quasiperiodicity of 2 6 months [Obara et al., 2004]. The above mentioned different slip initiations and propagations of long-term aseismic slip events are similar to those of short-term slow slip events in this Bungo channel area, in that slip propagation occurs differently case by case, although the timescale is very different. [29] With regard to the high activity of low-frequency earthquakes from late August to early September 2003, Hirose and Obara [2005] reported the occurrence of a short-term slow slip event in the Bungo channel area based on tiltmeter data in the same period, which moved from west to east over approximately 9 days (see Figure 8e). Even after this short-term slow slip event, the activity of low-frequency earthquakes remained high (Figure 9a), and Hirose and Obara suggested the long-term slow slip event to be the cause of the high activity of low-frequency earthquakes. However, a close-up view of Figures 9a and 9b shows that the number of low-frequency earthquakes increased for several days from late August to early September; this increase subsequently slowed down, although eastward transient motion at site 0437 increased almost linearly, which indicates different effects of short-term and long-term slow slip events on the activity of low-frequency earthquakes. Furthermore, our study suggests aseismic slip occurred before September 10 of 13

Figure 11. Observed and computed values of detrended movements at selected GPS sites. EW, NS, and UD represent east-west, north-south, and up-down movements with eastward, northward and upward motions being positive. Blue lines indicate computed values while solid circles show the observed movements (see Figure 4 for site locations): (a) 0086, (b) 0448, (c) 0437, (d) 0447, (e) 0473, and (f ) 0090. 2003, when there was no remarkable activity of lowfrequency earthquakes. In summary, low-frequency earthquakes correlate well with short-term slow slip events [Hirose and Obara, 2005], while the relationship between long-term slow slip events and low-frequency earthquakes is not clear. One possible reason why there was no remarkable activity of low-frequency earthquakes before September 2003, when the long-term slow slip occurred in a shallower area in the Bungo channel, may be that a shallower aseismic slip area does not overlap the low-frequency earthquake area in the Bungo channel. In addition, the stress change caused by the long-term slow slip before September 2003 may be too small to cause low-frequency tremor. [30] While a short-term slow slip event occurred in a deep area from late August to early September 2003, overlapping the low-frequency earthquake area [Hirose and Obara, 2005] (see Figure 8e), the long-term slow slip occurred mainly in a shallower area with its lower region partly overlapping the low-frequency earthquake area after September 2003 in this study. In this case, the extent to which the long-term slow slip area overlaps the lowfrequency earthquake area may also partially explain the difference in the influences of long-term and short-term slow slip events on low-frequency earthquakes. [31] On the basis of these results, we hypothesize, for the 2002 2004 event, that a long-term slow slip event became evident in early August 2003 when low-frequency earthquakes were not so active. Then, it increased in speed and propagated by around 30 km to southwestern Shikoku and the northern part of the Bungo channel from September 11 of 13

Figure 12. Schematic illustrations of slip propagation. Red circle indicates slip area in an early stage. Green area indicates the slip region which expanded from that in an early stage. (a) For the 1996 1998 event. (b) For the 2002 2004 event. 2003, when low-frequency earthquakes became active and a short-term slow slip event occurred and migrated from west to east over several days in a deeper region [Hirose and Obara, 2005] (see Figure 8e). Subsequently, the long-term slow slip event subsided. The Coulomb Failure Function (CFF) change caused by the short-term slow slip from late August to early September 2003 is very small, ranging from 1000 to 1000 Pa, and in the wrong sense for the long-term aseismic slip to accelerate [Hirose and Obara, 2005] and expand to the northern part of the Bungo channel and southwestern Shikoku. 4.2. Comparison Between the 1996 1998 Event and the 2002 2004 Event [32] The total transient motions for the 1996 1998 period and the 2002 2004 period are very similar to each other, although the magnitude of transient movement is slightly larger for the 2002 2004 period and the snapshots of transient motions are slightly different from each other (Figures 5 and 6). In both events, time series at some GPS sites show a rise period in which transient motion slowly starts, preceding a sharp increase in velocity (Figures 3 and 9b). This feature of a rise period and subsequent acceleration is also observed in the event of a slow slip beneath the Manawatu region, New Zealand [Wallace and Beavan, 2006]. [33] The estimated moment of the 2002 2004 event is slightly larger than that of the 1996 1998 event, while the duration of the 2002 2004 event seems slightly longer than that of the 1996 1998 event (Figure 10). By comparison of the two long-term slow slip events, the initiations and expansions of the slip area are found to have occurred in different ways, despite having occurred in almost the same area with similar magnitudes as characteristic slow slip events. Figure 12 shows a schematic illustration of the slip propagation for the 1996 1998 and the 2002 2004 events. Southwestward shift of the slip area of the 1996 1998 event is consistent with previous studies, as mentioned above. In the case of the 2002 2004 event, the slip area expanded northeastward or to a deeper area where a shortterm slow slip occurred from late August to early September 2003. This kind of small amount of spatial evolution is also found in the slow slip event of the Manawatu region, New Zealand [Wallace and Beavan, 2006]. [34] Because of there being no data for low-frequency earthquakes nor tiltmeter data of the National Research Institute for Earth Science and Disaster Prevention (NIED) for the 1996 1998 period, we do not know whether or not low-frequency earthquakes and short-term slow slip events occurred in the Bungo channel area together with the longterm slow slip. [35] From our results, we assume that there is an area where aseismic slips occur with similar magnitudes but different rupture processes. It is unclear which factor affects slip initiation, propagation, and acceleration of long-term slow slip events in this Bungo channel region. As described above, short-term slow slip events and low-frequency earthquakes which last several days may be important leads for solving this problem. [36] With regard to the slip balance on the plate boundary, the 2002 2004 event occurred six years after the previous long-term slow slip event. The estimated slip magnitude of the 2002 2004 event is approximately 30 cm and roughly compensates the 7 cm/year slip deficit [Miyazaki and Heki, 2001] in this region for a 6-year interval, suggesting that part of the Bungo channel area releases strain energy mostly by episodic long-term slow slip events, on the assumption that the recurrence interval is 6 years. Appendix A [37] The transition equation of a square-root information filter becomes 2 3 2 3 W 1 0 0 4 R 1 F 1 R 1 F 1 5 w ¼4 R X 1 X njn 5 ða1þ nþ1jn 0 amj 0 where w, X n +1 n, and X n n, represent the system noise of an ordinary transition equation in time, the one-step-ahead predicted state, and the state at time n, respectively. M, J, and F represent the smoothing matrix in space, the matrix used to select the slip velocity component from a state, and the transition matrix in an ordinary transition equation, respectively. The variable a represents the smoothing parameter in space. W 1 is the upper triangular matrix with WW T equaling the covariance of system noise w in time, where the superscript T means a transpose matrix. 12 of 13

R 1 is the upper triangular matrix with RR T equaling V n n which is the covariance of X n n. [38] The filter equation becomes 2 3 2 3 U 1 U 1 X n þ1jn 4 5 X n þ1jn þ1 ¼ 4 5 ða2þ S 1 H S 1 y n þ1 U 1 is the upper triangular matrix with UU T equaling V n +1 n which is the covariance of X n + 1 n. H is an observation equation matrix. y n +1 is the observation at time n +1.S 1 is the upper triangular matrix with SS T equaling the covariance of y n +1. [39] Acknowledgments. We are grateful to our colleagues for the helpful discussion. We are also grateful to the Japan Meteorological Agency for providing us with hypocenter data of low-frequency earthquakes. We really appreciate many comments and instructions by reviewers. References Akaike, H. (1974), A new look at the statistical model identification, IEEE Trans. Autom. Control, AC-19, 716 723. Bierman, G. J. (1977), Factorization Methods for Discrete Sequential Estimation, Elsevier, New York. Hatanaka, Y., et al. (2003), Improvement of the analysis strategy of GEONET, Bull. Geogr. Surv. Inst., 49, 11 37. Hirose, H., and K. Obara (2005), Repeating short- and long-term slow slip events with deep tremor activity around the Bungo channel region, southwest Japan, Earth Planets Space, 57, 961 972. Hirose, H., et al. (1999), A slow thrust slip event following the 1996 Hyuganada earthquakes beneath the Bungo Channel, southwest Japan, Geophys. Res. Lett., 26, 32,337 32,340. Kumagai, H. (1996), Time sequence and the recurrence model for large earthquakes along the Nankai trough revisited, Geophys. Res. Lett., 23, 1139 1142. Kyushu University (1999), Contour map of the Wadati-Beniof zone in Kyushu, southwestern Japan, Rep. Coord. Commit. Equake. Predict., 63, 424. Miyazaki, S., and K. Heki (2001), Crustal velocity field of southwest Japan: Subduction and arc-arc collision, J. Geophys. Res., 106, 4305 4326. Miyazaki, S., et al. (2003), A transient subduction zone slip episode in southwest Japan observed by the nationwide GPS array, J. Geophys. Res., 108(B2), 2087, doi:10.1029/2001jb000456. Niell, A. (1996), Global mapping functions for the atmosphere delay at radio wavelengths, J. Geophys. Res., 100, 3227 3246. Obara, K. (2002), Nonvolcanic deep tremor associated with subduction in southwest Japan, Science, 296, 1679 1681. Obara, K., et al. (2004), Episodic slow slip events accompanied with nonvolcanic tremors in southwest Japan subduction zone, Geophys. Res. Lett., 31(23), L23602, doi:10.1029/2004gl020848. Ozawa, S., et al. (2001), Time-dependent inversion study of the slow thrust event in the Nankai trough subduction zone, southwestern Japan, J. Geophys. Res., 106, 787 802. Ozawa, S., et al. (2004a), Aseismic slip and low-frequency earthquakes in the Bungo channel, southwestern Japan, Geophys. Res. Lett., 31, L07609, doi:10.1029/2003gl019381. Ozawa, S., et al. (2004b), Creep, dike intrusion, and magma chamber deflation model for the 2000 Miyake eruption and the Izu Islands earthquakes, J. Geophys. Res., 109, B02410, doi:10.1029/2003jb002601. Saastamonian, I. I. (1973), Contribution to the theory of atmospheric refraction, Bull. Géod., 107, 13 14. Satake, K. (1993), Depth distribution of coseismic slip along the Nankai trough, Japan, from joint inversion of geodetic and tsunami data, J. Geophys. Res., 98, 4553 4565. Segall, P., and M. Matthews (1997), Time-dependent inversion of geodetic data, J. Geophys. Res., 102, 22,391 22,409. Shiono, K., T. Mikumo, and Y. Ishikawa (1980), Tectonics of the Kyushu- Ryukyu arc as evidenced from seismicity and focal mechanisms of shallow to intermediate-depth earthquakes, J. Phys. Earth, 28, 17 43. Simon, D., and D. L. Simon (2003), Aircraft turbofan engine health estimation using constrained Kalman filtering, paper GT2003-38584 presented at ASME Turbo Expo 2003, Atlanta, Ga, June. Wallace, L.M., and J. Beavan (2006), A large slow slip event of the central Hikurangi subduction interface beneath the Manawatu region, North Iceland, New Zealand, Geophys. Res. Lett., 33, L11301, doi:10.1029/ 2006GL026009. Yagi, Y., and M. Kikuchi (2003), Partitioning between seismogenic and aseismic slip as highlighted from slow slip events in Hyuga-nada, Japan, Geophys. Res. Lett., 30(2), 1087, doi:10.1029/2002gl015664. T. Imakiire, M. Murakmi, S. Ozawa, and H. Suito, Crustal Dynamics Department, Geographical Survey Institute, Kitasato-1 Tsukuba, Ibaraki 305-0811, Japan. (ozawa@gsi.go.jp) 13 of 13