Creep, dike intrusion, and magma chamber deflation model for the 2000 Miyake eruption and the Izu islands earthquakes

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2003jb002601, 2004 Creep, dike intrusion, and magma chamber deflation model for the 2000 Miyake eruption and the Izu islands earthquakes S. Ozawa Geographical Survey Institute of Japan, Tsukuba, Japan S. Miyazaki Earthquake Research Institute, University of Tokyo, Tokyo, Japan T. Nishimura, M. Murakami, M. Kaidzu, T. Imakiire, and X. Ji Geographical Survey Institute of Japan, Tsukuba, Japan Received 26 May 2003; revised 26 October 2003; accepted 1 December 2003; published 24 February [1] Analysis of Global Positioning System data shows shrinkage of Miyake Island and the widening between Nijima and Kozu Islands during the period of the Miyake island volcanic activity and the ensuing Izu islands earthquakes in The estimated time evolution of a model consisting of a dike, creeping faults, and a Mogi source suggests that a crack opening on Miyake Island occurred immediately after the start of the seismic activities on 26 June and ended within several days at the west coast of Miyake Island. After the seabed eruption on 27 June, magma migrated from Miyake Island to Kozu and Nijima Islands within several days. The estimated volume of intruded magma totals around m 3. Associated with the magma intrusion between Miyake and Kozu Islands, left-lateral and right-lateral creep motions occurred in regions off the west coast of Miyake Island and near Kozu Island. The accumulated moment energy is equivalent to an earthquake of M w 6.6 and 6.6 for right-lateral and left-lateral creeping faults, respectively. The estimated magma chamber continued deflation beneath the southwestern part of Miyake Island from 26 June, totaling around m 3 in volume change, in addition to the collapse volume of m 3 at the summit of Mount Oyama on Miyake Island. The volume change on Miyake Island can be compensated by the migrated magma toward Kozu Island from the deflation source beneath Miyake Island. The deflation speed of the magma chamber beneath Miyake Island decreased and increased before and after the eruption of July and 18 August, suggesting a change in balance of mass influx and draining out rate of the magma chamber. INDEX TERMS: 1208 Geodesy and Gravity: Crustal movements intraplate (8110); 8434 Volcanology: Magma migration; 8419 Volcanology: Eruption monitoring (7280); KEYWORDS: Miyake, Izu, 2000 Citation: Ozawa, S., S. Miyazaki, T. Nishimura, M. Murakami, M. Kaidzu, T. Imakiire, and X. Ji (2004), Creep, dike intrusion, and magma chamber deflation model for the 2000 Miyake eruption and the Izu islands earthquakes, J. Geophys. Res., 109,, doi: /2003jb Introduction [2] The Izu islands chain is located on the Philippine Sea plate paralleling with the Izu-Ogasawara trench. Figure 1a shows a tectonic setting of the Izu islands chain, where the Pacific plate is subducting underneath the Philippine Sea plate with an annual rate of 10 cm/yr in the westnorthwest direction from the Izu-Ogasawara trench. The Philippine Sea plate itself moves in a northwest direction at an annual rate of 4 cm/yr and subducts beneath the continental plate from the Suruga trough and the Sagami trough. Figure 1b shows the average annual velocity for the period between 1997 and As shown in Figure 1b, Copyright 2004 by the American Geophysical Union /04/2003JB002601$09.00 Ohshima and Miyake Islands show deviate ground motion from that of the Philippine Sea plate which is manifested by the motion of Hachijo Island, because of the effect of inflation of the magma source beneath these islands. Nijima and Kozu islands move away from each other, prompting a proposal of the existence of a magma inflation source between these two islands [Nagoya University et al., 1999]. [3] The formation of the volcanic islands of the Izu island chain is due to the subduction of the Pacific plate, which dehydrates water beneath the Philippine Sea plate. Among the Izu islands, Miyake Island has one of the most active volcanoes and experienced eruption at a time interval of around 20 to 40 years for the past 300 years [Miyazaki, 1984]. The last event on Miyake Island occurred in 1983 with a fissure eruption of basaltic magma occurring in the southeastern flank. From the interval of the historical events 1of12

2 Figure 1. (a) Tectonic setting in and around Japan. The solid lines indicate plate boundaries. (b) Magnified map of a rectangular area in Figure 1a. The black arrow represents observed ground displacement rate in cm/yr for the period between 1997 and 1999 with regard to Northwestward motion in the Kanto and Tokai regions is mainly due to the coupling effect between the Philippine Sea plate and the overriding continental plates. (c) Volcano seismological crustal deformation for the period between June and September Shrinkage of Miyake Island and the opening between the Nijima and Kozu islands are caused by the volcanic activity, which started on 26 June 2000 (Japan time). The last three digits of the station numbers of GPS sites are displayed. The circles show the location of selected GPS stations that we used in time-dependent inversion. White arrows show computed values from the optimal model in Table 1 and Figure 4a. of Miyake Island, a possibility of eruption within several years was thought to be quite high. [4] Under the above circumstance, an intense seismic swarm with a focal depth of around 5 km started beneath Miyake Island of the Izu islands chain, Japan on 26 June 2000 (Japan Time) [Sakai et al., 2001; Nishimura et al., 2001; Ito and Yoshioka, 2002]. Within one day, the seismic swarm had moved westward from the southwestern part of Miyake Island to the west coast and resulted in the seabed eruption on 27 June. After the sea bottom eruption, the seismic swarm migrated to the northwest from Miyake Island toward Kozu and Nijima Islands, starting the 2000 Izu islands earthquakes event [Sakai et al., 2001; Nishimura et al., 2001; Ito and Yoshioka, 2002; Toda et al., 2002]. The 2000 Izu islands seismic swarm continued in a NW-SE trending area stretching around 40 km between Miyake and Kozu islands for 3 months and gradually faded in September 2000, while Miyake Island erupted several times during the same period [e.g., Sakai et al., 2001; Nishimura et al., 2001; Kumagai et al., 2001]. [5] During this seismic swarm, more than six earthquakes with M w > 6 occurred with some of them causing coseismic deformation in the nearby area. In addition to coseismic deformation, large crustal deformation was also observed on the nearby islands from the 2000 Izu island earthquakes [Nishimura et al., 2001]. On Miyake Island, crustal deformation started immediately after the start of the seismic swarm on 26 June and amounted to m. Crustal deformation started on the Kozu, Nijima, and Shikine islands associated with the migration of the seismic swarm toward this area [Nishimura et al., 2001]. The effect of the 2000 Izu islands earthquakes covered a very wide area from the southern part of the Boso, Izu to the Tokai regions, where around 1 to 2 cm of crustal deformation was detected during the 2000 event. In this study, we estimate the source geometry of dike, creeping faults, and a Mogi pressure source from the crustal deformation data and apply a Kalman filtering method utilizing the time-dependent inversion scheme [Segall and Matthews, 1997; Segall et al., 2000] to estimate the time evolution process of the estimated dike intrusion, fault creep motion, and deflation of the Mogi source. 2. GPS Data [6] The GPS network (GEONET) of the Geographical Survey Institute of Japan (GSI) has been in operation since 1994 with dual P band receivers. GPS data are analyzed by Bernese GPS software version 4.2 with International GPS service for Geodynamics (IGS) precise ephemeredes and Earth orientation parameters. Troposphere delays are estimated at each station for every three hour period [Miyazaki and Hatanaka, 1998]. Figure 1c shows the GPS sites we used in this study. We used east-west, north-south, and up-down displacement data at 98 selected GPS sites on the Izu island chain and in the Kanto and Tokai regions. [7] Since the raw data includes annual and linear trend components, we remove them from the raw data by fitting a linear function and trigonometric functions to regress time series data for the period between 1997 and 1999, using the following function. y ¼ At þ B þ XN i¼1 C i sin 2pi T þ D i cos 2pi T ; ð1þ 2of12

3 where y, t, and T represent observation, time, and 1 year, respectively. Harmonic overtone with frequency >N/T is excluded in this expression. N is determined by AIC criteria [Akaike, 1974]. By extrapolating the above function for the entire period, we estimate the residual of the time series from the steady state deformation in Figure 1b. [8] As for the coseismic deformation from M w > 6 earthquakes in the 2000 Izu event, we estimate fault models employing linearized least squares method to the observed coseismic deformation and subtract the computed ground displacements from the observations instead of the observed ones, since it is difficult to estimate small displacements away from the earthquake sources. [9] More than 10,000 small earthquakes occurred during the 2000 event [Sakai et al., 2001]. Since it is known that the effects from small earthquakes are not negligible [Nishimura et al., 2001], we removed those effects by using point dislocation source models with hypocenters determined by the Earthquake Research Institute of Japan (ERI) [Sakai et al., 2001] for earthquakes whose focal solutions are estimated. Though we used precise hypocenters and magnitudes determined by the ERI, we used corresponding focal solutions determined by the National Research Institute for Earth Science and Disaster Prevention of Japan (NIED) to calculate crustal deformation. Figure 2 shows the final time series data at selected GPS sites in Figure 1c with annual components, trend components, and coseismic deformation removed for the period between June and September As shown in Figure 2, stations on Miyake Island such as 059, 060, 599, and 600, show step like large ground displacements on 26 June. As a notable feature, 059 changed the direction of their north-south motion from 27 June. In contrast, 058 on the Kozu Island and 057 on the Nijima Island started deviating in motion from the steady state displacements (Figure 1b) in this area several days after 26 June when stations on Miyake islands started ground displacements. Figure 3 shows the observed crustal deformation for 8 consecutive periods from June 2000 to March 2001, while Figure 1c shows total ground displacements from June to September At the start of the Miyake activity on 26 June, Miyake Island showed some opening and shrinkage, as shown in Figure 3a, followed by shrinkage (Figures 3b 3h). Several days later, the distance between Kozu and Nijima islands started elongating (see Figure 3b). The opening between Kozu and Nijima islands and the shrinkage of Miyake Island continued until September 2000 and gradually decreased its magnitude. For the same period, Miyake Island erupted on 8 July, July, 10 August, 18 August, and 29 August. 3. Analytical Procedure to Estimate Time Evolution [10] Nishimura et al. [2001] and T. Nishimura (personal communication, 2001) proposed a model consisting of a dike, right-lateral fault off Kozu Island, left-lateral fault off the west coast of Miyake Island, and a Mogi source to explain the observed crustal deformation in the Izu islands chain. We also estimated optimal parameters of each component inverting the total ground displacements in Figure 1c employing linearized least squares method [Ozawa, 1996]. The estimated optimal parameters are shown in Table 1 and the geometry of the model in Figure 4a. As shown in Figure 4a, we set constraints that a right-lateral fault (1), a tensile fault (2), and a tensile fault (3) are connected with each other at the edges in linearized least squares fitting. A right-lateral creeping fault is required to explain southeastward motion of the southern part of the Izu peninsula (Figure 1c). Estimated right-lateral fault (1) and tensile faults (2) and (3) are located well within the seismic swarm area as shown in Figure 4a. Since it is highly likely that magma intruded into the seismic swarm area, causing fault creeping, the estimated fault geometry of faults 1 3 is a well resolved solution based on crustal deformation data. Since there also exists a N-S trending seismic swarm area which splays from the main NW-SE trending seismic swarm area (see Figures 3 and 4), we placed a left-lateral fault in the N-S trending seismic swarm area where M w 6 earthquake occurred on 31 August (Figure 3d). Furthermore this left-lateral creeping fault is necessary to explain northwestward motion of Mikura (Figure 2j) and Hachijo Islands (T. Nishimura, personal communication, 2001). With regard to source geometry, we think that our derived model is well in agreement with Nishimura et al [2001] and T. Nishimura (personal communication, 2001) in the point of the location match between the seismic swarm area and the estimated source geometry among the models. Though several estimated parameters such as width, opening, and creeping amount differ from those of Nishimura et al. [2001], we think this is within uncertainties considering the scarcity of stations around the source area and the many unknown parameters. Furthermore this discrepancy does not affect the following results as described below. As shown in Figure 1c, our optimal model reproduces the observed crustal deformation well. [11] In the following analysis, we adopt B spline function as a base function and express fault surface as a sum of B spline functions. First, we enlarge each rectangular fault area in Figure 4a, as shown in Figure 4b. The enlarged fault areas which contain estimated rectangular faults (Figure 4a) are represented by parametric spline surface [Ozawa et al., 2001] as follows: X ðx 1 ; x 2 Þ ¼ x ij N i ðx 1 ÞN j ðx 2 Þ; ð2þ Yðx 1 ; x 2 Þ ¼ y ij N i ðx 1 ÞN j ðx 2 Þ; ð3þ Zðx 1 ; x 2 Þ ¼ z ij N i ðx 1 ÞN j ðx 2 Þ; ð4þ where X(x 1, x 2 ), Y(x 1, x 2 ), and Z(x 1, x 2 ) represent east-west, north-south, and up-down coordinates of a fault surface. N i (x 1 ) and N j (x 2 ) represent the B spline function for the respective parameters of x 1 and x 2. Approximately x 1 and x 2 increase to the striking and dipping directions, respectively. Coefficients x ij, y ij, z ij are estimated so that spline surface includes adopted node points whose coordinates are known. That is the number of the coefficient of B spline functions equals the number of nodes. Figure 5 shows node points used to represent fault patches. We used 9 16 nodes in the striking and dipping directions to represent a tensile fault patch in Figure 4b, while right-lateral and left-lateral faults patches were represented by the B spline function with 7 7 nodes as shown in Figure 5. Since these derived fault 3of12

4 Figure 2. Time series data of east-west (EW, upper part), north-south (NS, middle part), and up-down (UD, lower part) displacements at selected GPS stations in Figure 1c: (a) 055, (b) 596, (c) 057, (d) 597, (e) 058, (f ) 059, (g) 060, (h) 599, (i) 600, and ( j) 601. Eastward, northward, and upward motions are positive. The unit of horizontal axis is year/month/day (Japan time). Steady state crustal deformation, shown in Figure 1b, and annual components are removed. When ground displacement levels off in these figures, it means that ground motion is reduced to the steady state deformation in Figure 1b. The selected stations show different initiation times and time evolution of transient crustal deformation. Blue lines represent computed values from the estimated model. Dates of the eruptions on Miyake Island are denoted by vertical dashed lines. 4of12

5 Figure 3. Ground displacements at selected GPS sites for eight periods relative to site in Honshu, Japan (Figure 1): (a) June, (b) 27 June to 10 July, (c) July, (d) 10 July to 5 August, (e) 5 18 August, (f ) August, (g) 31 August to 13 September, and (h) 13 September 2000 to 1 March Dots represent epicenters for the same period with open squares showing the epicenters of earthquakes with M w > 5.9. White arrows show computed values from the estimated model for the same period. patches match the seismic swarm area closely, we think the adopted fault patches well represent a true source configuration which is probably manifested by the observed seismic swarm. In order to investigate the effect of the size of fault patches, we changed the size of adopted fault patches in several ways and found out that the main characteristics of the following results in section 4 do not change. [12] Slip components are also expressed as a superposition of the same B spline functions as those of fault representation as follows: u 1 ðx 1 ; x 2 Þ ¼ u 1ij N i ðx 1 ÞN j ðx 2 Þ; ð5þ u 2 ðx 1 ; x 2 Þ ¼ u 2ij N i ðx 1 ÞN j ðx 2 Þ; ð6þ Table 1. Optimal Model Parameters of Rectangular Faults and Mogi Pressure Source for the 2000 Izu Event a Model Latitude, deg (1s) Longitude, deg (1s) Depth, km (1s) (2.0) (5.0) (1.0) (0.4) (1.2) (1.4) (0.4) (1.2) (0.2) (9.3) (0.2) (0.2) (0.2) Strike, deg (1s) Dip, deg (1s) Width, km (1s) Length, km (1s) 95.0 (2.6) (8.0) (0.3) (4.9) (0.3) (1.2) (2.1) (8.0) Strike Slip, m(1s) 7.5 (9.5) 0.7 (0.6) Dip Slip, m(1s) 0.4 (1.2) 0.07 (0.3) Opening (1s) 28.8 m (0.6) 12.4 m (1.3) 0.12 km 3 (0.2) a Nomenclatures of rectangular faults are the same as those by Okada [1985]. Model number corresponds to that in Figure 4a. Values in parentheses represent 1 standard deviation. Bold face indicates fixed values in estimating an optimal model. 5of12

6 Figure 4. (a) Solid lines represent geometry of an estimated rectangular faults, together with the earthquakes distribution. Hypocneter data are from Sakai et al. [2001]. A model consists of (1) rightlateral fault, (2) a dike, (3) a dike, (4) left-lateral fault, and (5) Mogi source beneath the Miyake Island. (b) Adopted fault patches and Mogi source based on Figure 4a and earthquake distribution. where u 1 (x 1, x 2 ) and u 2 (x 1, x 2 ) represent the east-west, north-south, or up-down components of slip vectors on a creeping fault patch. Since we assume no opening on a creeping fault surface [Yabuki and Matsu ura, 1992], the other component is computed as u 3 ¼ n ð 1 u 1 þ n 2 u 2 Þ=n 3 ; ð7þ where n 1, n 2, and n 3 are the components of a normal vector on a fault surface. We chose two independent components based on the geometry of each fault patch. In the case of a tensile fault patch, we used the tensile component uðx 1 ; x 2 Þ ¼ u ij N i ðx 1 ÞN j ðx 2 Þ; ð8þ The time evolution of slip distribution and tensile motion on these fault patches and Mogi source was estimated as described below. [13] In order to estimate detailed time varying process, we apply a Kalman filter utilizing the time-dependent inversion scheme [Segall and Mattews, 1997; Segall et al., 2000] to the observed GPS time series for the period between 11 June and 4 September. East-west, north-south, and vertical components of ground motion are weighed with the ratio 1:1:3. [14] We set slip components to zero at the edge of the fault patch as a boundary condition. Furthermore we adopted the condition that the rake angle is within 180 ± 45 for the right-lateral and 0 ± 45 for the left-lateral faults with unidirectional motion over time for all the components including dike opening. These nonnegativity or inequality constraints are described in Appendix A. Under these constraints, we search for an optimal model of three faults and a Mogi source with eight smoothing parameters in time and space by maximizing the log likelihood of the system. Figure 5. Adopted fault patches. (a) A tensile fault patch viewed from east. (b) A left-lateral fault patch viewed from east. (c) A right-lateral fault patch viewed from north. Solid circles represent node points whose coordinates are given for estimating coefficients of superposition of B spline functions (see text). 6of12

7 Log likelihood computation is detailed in Appendix A [Ozawa et al., 2003a, 2003b]. 4. Results and Discussion [15] Figure 6 shows the result of Kalman filtering analysis. As shown in Figure 6, the opening area in the dike in Figure 4b appears beneath Miyake Island for the period between 14 and 27 June, the start of the 2000 Miyake Island event (Figure 6a, left). As time passes, the opening area moves toward the northwest from Miyake to Kozu Islands with its center depth reaching 10 km (Figure 6b, left). From 10 to 23 July, the dike opening area becomes shallower toward Nijima Island which reflects on the large crustal deformation that occurred from the middle of July to early August on Kozu, Shikine and Nijima Islands (Figure 6c, left). From late August, dike opening gradually subsided as shown in Figure 6f (left). Observed seismic activities are consistent with the estimated migration of the dike opening area in that the seismic swarm migrated from Miyake Island to Kozu and Nijima Islands [Sakai et al., 2001] and intensified from the middle of July to early August near Kozu Island (Figure 6). We think that discrepancy between the estimated dike opening area and seismic activity for the period of Figure 6b (left) is within the uncertainty level, considering there are no stations between Miyake and Kozu Islands and the extent of crustal deformation on Kozu and Nijima Islands was not so large during the corresponding period or in the early stage of the Izu Islands earthquakes. Left-lateral creep off the west coast of Miyake Island showed a large slip at the start of the 2000 Miyake volcanic activity on 26 June and continued over time and gradually subsided from late August 2000 (Figure 6, middle). The right-lateral fault off the east coast of Kozu Island occurred several days after the start of the dike opening and the left-lateral creeping off Miyake Island, which gradually subsided beginning in late August (Figure 6, right). Figure 7 shows time evolution at several points on the adopted fault patches in Figure 6. As shown in Figure 7, point 1 on a tensile fault, which is located beneath southwestern Miyake Island shows a sudden opening from 26 June when seismic activity started beneath Miyake Island and then ended within several days. Points 2 and 3 on the tensile fault open with a time delay of several days from point 1 and proceeded with time varying speed and subsided from late August. Point 4 on left-lateral fault shows a steep rise in up-down and north-south slip components from 26 June and then slowed down its pace and gradually subsided. Point 5 on right-lateral fault shows right-lateral slip motion several days after the start of the opening at point 1 and slip motion at point 4. [16] Figure 8a shows time evolution of the Mogi source beneath Miyake Island. As shown in Figure 8a, deflation of Figure 6. (left) Estimated time evolution of (1) a dike, (2) a left-lateral fault, and (3) a right-lateral fault in Figures 4b and 5: (a) June (b) 27 June to 10 July, (c) July, (d) 10 July to 5 August, (e) 5 18 August, and (f ) August Colors show the magnitude of slip or opening on the fault patches. Arrows represent the slip vector of creeping faults. (middle) Slip showing motion of the western wall against the eastern part viewed from the east on the left-lateral fault patch. (right) Slip showing motion of the northern wall against the southern wall viewed from the north on the right-lateral fault patch. Dots represent hypocenter of earthquakes for the same period determined by Sakai et al. [2001]. Displacement history of the points 1 5 denoted by white circles on these fault patches is plotted in Figure 7. 7 of 12

8 the Mogi source continued at a varying speed for the period between June and September From 26 June, the magma chamber quickly started to deflate and slowed down over time. [17] The eruption time of Mount Oyama on Miyake Island is denoted in Figure 8a by vertical dashed lines. As notable features, the estimated deflation speed changed its rate before and after the major eruptions at the summit of Miyake Island on July and 18 August. Though magma was quickly draining from the magma chamber until around 8 July, magma chamber changed to inflation from 8 to 14 July, as shown in Figure 8a, suggesting more mass influx into the magma chamber than mass draining out. [18] Gravity measurements conducted 2 days before the 8 July eruption detected gravity change exceeding 1000 mgal, suggesting the existence of vacant space just beneath the summit of Mount Oyama [Furuya et al., 2001], followed by caldera collapse at Mount Oyama from the 8 July eruption [Nakata et al., 2001; Hasegawa et al., 2001; Kumagai et al., 2001]. From these observations, mass withdrawal from the caldera summit is estimated to have started shortly before 8 July eruption [Furuya et al., 2001]. [19] It is most likely that influx material into the magma chamber is derived from a caldera collapse, considering a large quantity of material extinction which totals m 3 at the summit of Mount Oyama on Miyake Island [Hasegawa et al., 2001]. From this viewpoint, inflation from 8 July to before the July eruption was caused by a large amount of mass influx from a caldera which started collapsing from or shortly before the 8 July eruption. As for the 18 August eruption which was the largest eruption, the magma chamber slowed down its deflation speed before the eruption and increased the speed after the eruption. This estimate also suggests some change in the balance between mass influx which is mostly from a caldera collapse and draining from the magma chamber. [20] In total, the volume change of the magma chamber beneath Miyake Island amounted to m 3. The total extinct mass of Miyake Island is estimated at around m 3 taking into account the collapse volume of the summit of Mount Oyama on Miyake Island [Hasegawa et al., 2001]. Since the migrated magma volume toward Kozu Island is estimated at m 3 (Figure 8b), the total mass removed from Miyake Island can be roughly compensated by the magma migration toward Kozu Island from Miyake Island as is pointed out by Nishimura et al. [2001] and Ito and Yoshioka [2002]. As shown in Figure 8b, the volume of magma that migrated between Miyake and Kozu Islands shows a steep rise on 26 June, 8of12 Figure 7. Estimated time evolution at points 1 5 on the dike, right-lateral fault, and left-lateral fault in Figure 6. Figures 7a 7e correspond to points 1 5 in Figure 6. Dates of 26 June and the eruptions on Miyake Island are denoted by vertical dashed lines. EW, NS, and UD represent eastwest. north-south, and up-down components with eastward, northward, and upward motion positive, respectively.

9 Figure 8. Estimated time evolution of the cumulative volume change of the Mogi source, dike, total moment of the left-lateral fault, right-lateral fault, and small earthquakes with M w < 6. (a) Mogi source, (b) dike, (c) left-lateral fault, (d) right-lateral fault, and (e) cumulative moments of earthquakes (M w < 6). Dates of 26 June and the eruptions on Miyake Island are denoted by vertical dashed lines. which reflects magma intrusion into the west coast of Miyake Island. The total volume of the dike opening increased and gradually subsided from late August until early September. Figures 8c and 8d show the estimated time history of moment release from the creeping leftlateral and right-lateral faults, respectively. As shown in Figures 8c and 8d, the left-lateral fault started releasing energy from 26 June when the seismic swarm started beneath Miyake Island and continued over time. The right-lateral fault motion started several days later from 26 June and gradually subsided by late August. Comparison of Figures 8c, 8d, and 8e shows that moment release from creeping faults correlated well with seismic activity in that the intensified seismic activity increases moment release from the assumed creeping faults. In total, moment release from right-lateral and left-lateral faults amounted to the energy of an earthquake of M w 6.6 and 6.6, respectively. [21] Our estimated model described above reproduces the observations well as shown in Figures 2 and 3. From these results, we estimate the following scenario of the 2000 Miyake eruption and the ensuing Izu Islands earthquakes (Figure 9). Magma intrusion occurred immediately after 26 June when seismic activity started beneath Miyake Island with a focal depth shallower than 5 km and led to the seabed eruption on 27 June. Within several days thereafter, the magma intrusion area moved northwestward from Miyake Island to Nijima Island and deepened in the center area to around 10 km. From the middle of July to early August 2000, the intrusion near Kozu Island shallowed accompanied by intensified seismicity. After that, the magma intrusion in the area between Miyake and Kozu islands subsided gradually. We cannot rule out the possibility of magma supply from the deep part of the estimated dike area, because of the poor resolution with increasing depth. However, we think that most of the intruded magma between Nijima and Miyake Islands are from the magma source of Miyake Island, considering the roughly satisfied mass balance between these two areas, as is pointed out by Nishimura et al. [2001]. [22] For the same period, the deflation of the magma chamber continued at a varying speed. Estimated inflation several days before the July eruption probably reflected the influx of a large amount of collapsed material from the summit of Mount Oyama in Miyake Island into the assumed magma chamber. The 18 August eruption was the largest eruption; the last major eruption was on 29 August. Accelerated deflation of the magma chamber after the 18 August eruption shows a change in the balance between mass draining out and mass influx into the magma chamber. If material influx is mostly from a caldera collapse, the 18 August eruption may have changed the condition of the conduit which links the caldera and the magma chamber changing a mass influx rate into the magma chamber, since the northeastward draining of magma seems not to have intensified based on seismic activity and crustal deformation extent associated with the 18 August eruption. In fact, caldera collapse rate is gradually slowing down from around the 18 August eruption, though it remains to be solved what change was really caused by the 18 August eruption, since a visible change on the surface such as the start of the 9of12

10 Figure 9. Schematic illustration of the 2000 Miyake eruption and the Izu Islands earthquakes from 26 June See explanation in text. caldera collapse at the time of 8 July eruption was not observed. Appendix A: Method of Kalamn Filtering [23] In our analysis, we adopt the following state vector: x njn ¼ ðu; v; p 1 ; p 2 ;...; p L Þ; ða1þ where u and v represent fault slip and slip velocity, respectively; p i is a random walk of station site i. Inthis representation, the initial state is x 0j0 ¼ ðv 0 t; v 0 ; p 1 ; p 2 ;...; p L Þðt 0Þ: ða2þ We adopt v 0 = 0 with covariance (a 2 G) 1 and p i0 = 0 as the initial state in the first Kalman filtering. Assuming prior distribution, pvja ð Þ ¼ Z exp a v 22 T Gv for slip velocity, where Z is a normalization factor, we incorporate the following equation into a transition equation of information square root filter [Bierman, 1977]. amjx nþ1=n ¼ e 2 M T M ¼ G ða3þ where a, J, G, and x n+1jn represent spatial smoothing parameter, matrix to select slip velocity components from a state vector, smoothing matrix, and one step ahead predicted state [Ozawa et al., 2001, 2002]; e 2 represents Gaussian with covariance of identity matrix I. The concrete transition equation is expressed as follows: 2 A4 w 1 x nþ1jn e 1 W ¼ 6 R 1 x njn ; A ¼ 6 R 1 F 1 R 1 F ; ða4þ e 2 0 amj where w 1, x njn, e 1, e 2, V njn = RR T, and F represent system noise of an ordinary transition equation with covariance of WW T, a state at time n, Gaussians with covariance of I, a covariance matrix of a state of x njn, and transition matrix in an ordinary transition equation, respectively. This transition equation is equivalent to using 2 3 e x nþ1jn ¼ CA T 6 R 1 x njn ; B 1¼ AT A 4 5: ða5þ C e 2 In backward smoothing, we used this transition expression in a smoothing equation of ordinary Kalman filtering instead of using that of information square root filter. Though we can use equation (A5) directly both in filtering and smoothing of Information Square Root Filter, we adopted equation (A4) in filtering process, since this requires less memory in backward smoothing. [24] The above treatment is also equivalent to using the following transition equations (T. Higuchi, personal communication, 2003): V p V 1 p þ a 2 G x nþ1jn av p M T w 2 ¼ Fx njn þ w 1 ; W 1 w 1 ¼ e 1 ; w 2 ¼ e 2 ; V p ¼ FV njn F T þ WW T ; ða6þ where V p and w 2 represent covariance matrix of a state of x n+1jn = Fx njn + w in an ordinary transition equation without spatial smoothing and system noise of spatial smoothing equation of amjx n+1jn = w 2 with covariance of I, respectively. [25] We also used amj(x n+1/n x njn )/t = e 2 instead of equation (A3), where J selects a slip component from a state and t is lapse time, modifying equations (A4) and (A5) with spatial system noise parameters w 2 = e 2 included in equation (A4) like w of 12

11 [26] In Kalman filtering, log likelihood of the system is expressed as follows [e.g., Kitagawa and Gersch, 1984]: Lðt; a; s; v 0 Þ ( ¼ 1 X N l n log 2p 2 Res ¼ XN þ XN ) log HV njn 1 H T þ R n þ Res ða7þ T y n Hx njn 1 HVnjn 1 H T 1 þ R n yn Hx njn 1 ; where N is number of step, l n is number of observations at n step, R n is a covariance matrix of observation y n, H is observation matrix, V njn 1 is covariance of one step ahead predicted state in Kalman filtering, and t and a represent smoothing parameters in time and space, respectively. [27] Since initial slip velocity v 0 and its covariance V 0 are determined by smoothing priors t and a in the first Kalman filtering, we adopt the once estimated initial velocity v 0 and its covariance V 0 and go through Kalman filtering again and compute the log likelihood. This computed log likelihood is a conditional probability with initial state (v 0 t, v 0, p 1,..., p L ) in the limit of t =0. [28] The true log likelihood is approximately computed by adding Z log Z exp 1 ð 2 v 0 v 0 Þ T V0 1 ðv 0 v 0 Þ dv 0 where v 0 and V 0 are estimated v 0 and its covariance in the first filtering, to logarithm of the above conditional probability of equation (A4) with in the second filtering, since Z exp a2 2 vt 0 Gv 0 / exp 1 ð 2 v 0 v a2 v 0 Gv 0 ; ðconditional probabilityþ Þ T V0 1 ðv 0 v 0 Þ : [29] As a result, the total log likelihood is ( Lðt; a; sþ ¼ 1 X N l n log 2p þ XN log HV njn 1 H T þ R n 2 ) log½jv 0 jš log a 2 G þ Res þ a 2 v T 0 Gv 0 Res ¼ XN T y n Hx njn 1 HVnjn 1 H T 1 þ R n yn Hx njn 1 ða8þ By introducing the following t = ^t, sa = ^a /s, V njn 1 = s ˆvariables, 2 ^V nj n 1, V nj n = sv nj n 1, R n = s 2^R n, we can reduce one paramete r, or observation variable s, using as follows: Lð^t; ^a Þ ¼ 1 2 ^s 2 ¼ 1 X N ( s 2 ð Þ j s¼^s ¼ 0; l n log 2p^s 2 þ XN ) log ^V 0 log ^a 2 X G N þ l n l n X N log H ^V njn 1 H T þ ^R n T y n Hx njn 1 H ^V njn 1 H T þ ^R n y n Hx njn 1 þ a 2 v T 0 Gv 0! 1 ða9þ : ða10þ Though in this study, we assumed prior distribution for slip velocity, we can also assume prior for total slip. These two approaches resulted in quite similar results in this case. [30] In this research, we adopted the method of hard constraints of Simon and Simon [2003] to incorporate inequality constraints. Though we used inequality constraints to compute state vector and observation variance ^s, we used values for other terms in equation (A9) without inequality constraints in computing the log likelihood of the system. The terms other than ^s in equation (A9) are related to covariance of the estimated state divided by the square of the observation variance ^s, ^t, and ^a. This approximated approach is similar to a treatment in a usual geodetic inversion with inequality constraints in which all the observation equations are inverted simultaneously, since we often use covariance divided by the square of observation variance without inequality constraints to calculate log likelihood in such a case [e.g., Yabuki and Matsu ura, 1992]. [31] Acknowledgments. We are grateful to S. Sakai for providing us with hypocentral data. We also used focal mechanism solutions published by NIED on its Web site. References Akaike, H. (1974), A new look at the statistical model identification, IEEE Trans. Auto. Control, AC-19, Bierman, G. J. (1977), Factorization Methods for Discrete Sequential Estimation, Academic, San Diego, Calif. Furuya, M., S. Ohkubo, Y. Tanaka, W. Sun, H. Watanabe, J. Oikawa, and T. Maekawa (2001), Caldera formation process during the Miyakejima 2000 volcanic activity detected by spatio-tmpral gravity changes (in Japanese), J. Geogr., 110, Hasegawa, H., M. Murakami, and K. Matsuo (2001), Caldera subsidence measurement at Miyakejima summit (in Japanese), J. Geog. Surv. Inst., 95, Ito, T., and S. Yoshioka (2002), A dike intrusion model in and around Miyakejima, Nijima and Kozushima in 2000, Tectonophysics, Kitagawa, G., and W. Gersch (1984), A smoothness priors-state space modeling of time series with trend and seasonality, J. Am. Stat. Assoc., 79, Kumagai, H., T. Ohminato, M. Nakano, M. Ooi, A. Kubo, H. Inoue, and J. Oikawa (2001), Very-long-period seismic signals and caldera formation at Miyake Island, Japan, Science, 293, of 12

12 Miyazaki, T. (1984), Characteristics of eruption at Miyakejima volcano recorded in history, Volcanology, 29, S1 S15. Miyazaki, S., and Y. Hatanaka (1998), The continuous GPS observation system of the Geographical Survey Institute of Japan (in Japanese), edited by H. Nakamura, Meteorol. Res. Note 192, pp , Jpn. Meteorol. Soc., Tokyo. Nagoya University, Maritime Safety Agency, Kochi University, Tokai University, and Geographical Survey Institute (1999), Crustal movements in Kozu Island, Izu Islands in southern central Japan, detected by GPS measurements (in Japanese), Rep. Coord. Comm. Earthquake. Predict., 62, Nakata, S., et al. (2001), Chronology of the Miyakejima 2000 eruption: Characteristics of summit collapsed crater and eruption products (in Japanese), J. Geogr., 110, Nishimura,T.,S.Ozawa,M.Murakami,T.Sagiya,M.Kaidzu,and T. Ukawa (2001), Crustal deformation caused by magma intrusion in northern Izu Islands, Geophys. Res. Lett., 28, Okada, Y. (1985), Surface deformation due to shear and tensile faults in half-space, Bull. Seismol. Soc. Am., 75, Ozawa, S. (1996), Geodetic inversion for the fault model of the 1994 Shikotan earthquake, Geophys. Res. Lett., 23, Ozawa, S., M. Murakmai, and T. Tada (2001), Time-dependent inversion analysis of the slow thrus event in the Nankai trough subduction zone, southwestern Japan, J. Geophys. Res., 106, Ozawa, S., M. Murakami, M. Kaidzu, T. Sagiya, Y. Hatanaka, H. Yarai, and T. Nishimura (2002), Detection and monitoring of ongoing aseismic slip in the Tokai region, central Japan, Science, 298, Ozawa, S., S. Miyazaki, Y. Hatanaka, T. Imakiire, M. Kaidzu, and M. Murakami (2003a), Characteristic silent earthquakes in the eastern part of the Boso peninsula, central Japan, Geophys. Res. Lett., 30(6), 1283, doi: /2002gl Ozawa, S., et al. (2003b), Tokai silent earthquake and a possible coupling change between the Pacific plate and the Philippine Sea plate off Boso peninsula, central Japan (in Japanese), Mon. Chikyu, 41, Sakai, S., et al. (2001), Magma migration from the point of view of seismic activity in the volcanism of Miyake-jima Island in 2000 (in Japanese), J. Geogr., 110, Segall, P., and M. Matthews (1997), Time-dependent inversion of geodetic data, J. Geophys. Res., 102, 22,391 22,409. Segall, P., R. Burgmann, and M. Matthews (2000), Time-dependent triggered afterslip following the 1989 Loma Prieta earthquake, J. Geophys. Res., 105, Simon, D., and D. L. Simon (2003), Aircraft turbofan engine health estimation using constrained Kalman filtering, paper GT presented at ASME Turbo Expo 2003, Atlanta, Ga., June. Toda, S., R. Stein, and T. Sagiya (2002), Evidence from the AD 2000 Izu islands earthquake swarm that stressing rate governs seismicity, Science, 419, Yabuki, T., and M. Matsu ura (1992), Geodetic data inversion using a Bayesian information criteria for spatial distribution of fault slip, Geophys. J. Int., 109, T. Imakiire, X. Ji, M. Kaidzu, M. Murakami, T. Nishimura, and S. Ozawa, Geographical Survey Institute of Japan, Geography and Crustal Dynamics Recearch Center, Kitasato-1, Tsukuba, Ibaraki , Japan. (imq@gsi. go.jp; ji@gsi.go.jp; kaizu@gsi.go.jp; mccopy@gsi.go.jp; t_nisimura@gsi. go.jp; ozawa@gsi.go.jp) S. Miyazaki, Earthquake Research Institute, University of Tokyo, Yayoi, Bunkyo-ku, Tokyo, , Japan. 12 of 12