A dike intrusion model in and around Miyakejima, Niijima and Kozushima in 2000

Tectonophysics 359 (2002) 171 187 www.elsevier.com/locate/tecto A dike intrusion model in and around Miyakejima, Niijima and Kozushima in 2000 Takeo Ito a, *, Shoichi Yoshioka b a Research Center for Earthquake Prediction, Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan b Department of Earth and Planetary Sciences, Faculty of Sciences, Kyushu University, Hakozaki 6-10-1, Higashi ward, Fukuoka 812-8581, Japan Received 28 May 2001; accepted 18 August 2002 Abstract From June 26, 2000, an earthquake swarm started in Miyakejima, about 50 km south off Honshu, central Japan. Eruptions of Miyakejima and five large earthquakes with magnitudes 6.0 and above occurred for the following 2 months together with a large number of smaller earthquakes over 100,000. In this study, we focused on spatio-temporal crustal deformation observed at GPS stations in this area. In order to explain the seismicity and the crustal deformation, we considered a dike intrusion model placed between Miyakejima and Kozushima. Then, we attempted to obtain spatio-temporal distributions, the amount of the dike intrusion, deflation beneath Miyakejima, and fault slips of the seven large events by geodetic data inversion. For this purpose, we divided the time series of GPS data from June 12 to August 27 into 10 periods, which are related to significant events. In order to find location, depth, strike and dip of the dike plane and a depth of deflation beneath Miyakejima, we used the Monte Carlo method and tested 10,000 models for each period. As a result, we estimated that the total amount of the dike intrusion and the deflation beneath Miyakejima reached about 1.1 10 9 and 5.4 10 8 m 3, respectively. The maximum amount of the dike intrusion and the deflation beneath Miyakejima reached over 3.5 10 8 m 3 during the period from July 20 to July 28, 2000, and over 1.7 10 8 m 3 during the period from June 15 to June 28, 2000, respectively. Temporal change of the amount of the dike intrusion corresponds well to that of the deflation beneath Miyakejima until the middle of July. However, since large amount of the dike intrusion from July 20 to 28 did not correspond to that of the deflation beneath Miyakejima, we deduced that the magma source changed from Miyakejima to Kozushima and the magma might come from sub-crustal magma pockets from the middle of July. If we assume the open crack associated with the dike intrusion and the deflation beneath Miyakejima are filled with magma with a density of 2500 kg/m 3, the mass would be about 2.75 10 9 and 1.35 10 9 tons, respectively. We deduced that at least 1.4 10 9 tons of magma came from sub-crustal magma pockets. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Dike intrusion; Deflation beneath Miyakejima; Geodetic inversion; GPS; Magma pocket 1. Introduction * Corresponding author. Tel.: +81-774-38-4188; fax: +81-774- 38-4190. E-mail address: take@rcep.dpri.kyoto-u.ac.jp (T. Ito). Following an intrusive event near Miyakejima on June 26, 2000, the most active earthquake swarm ever 0040-1951/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S0040-1951(02)00510-3

172 T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 recorded in Japan occurred between Miyakejima and Kozushima, central Japan (Fig. 1). The earthquake swarm started at the western coast of the basaltic Miyakejima on June 26, and propagated northwestward toward the rhyolitic Kozushima volcanic Island. Earthquakes with magnitudes 6.4 and 6.1 occurred at the northwestern tip of the swarm (near the east coast of Kozushima) on July 1 and July 9, respectively (Japan Meteorological Agency (JMA), 2000) (Fig. 2). An earthquake with M6.3 occurred near the west coast of the Niijima on July 15, and earthquakes with M6.4 and M6.0 occurred at the southwest of Miyakejima on July 30 and near the east coast of Kozushima on August 18, respectively. The maximum seismic intensity from these events was over VI in the Japanese seismic intensity scale. More than 600 earthquakes with magnitudes greater than 4.0 occurred in these areas. Although the swarm propagation ceased between Kozushima and Miyakejima from June 26, 2000, regional crustal deformation became prominent. The crustal deformation and the northwestward migration of epicenters of earthquakes suggested that magma intruded underneath the southwestern part of Miyakejima and migrated to the northwest. This event was followed by a large deflation of Miyakejima and the intense earthquake swarm activity described above. The deformation rate observed by GPS stations of Geographical Survey Institute of Japan (GSI) was nearly constant until mid August, followed by a rapid decay of the deformation rate. It was reported that the crustal deformation associated with this swarm was observed even in the Boso Peninsula, which is located about 100 km away from Miyakejima. The swarm activity decayed gradually, though intermittent bursts with short duration time occurred. The purpose of this study is to obtain the spatio-temporal distribution of the migrated magma and the amount of dike intrusion into the northwest region of Miyakejima, through an Fig. 1. Index map of south off Honshu, central Japan. The inset shows the four plates in and around the Japanese Islands. AM: Amurian plate (or EU: Eurasian plate), PA: Pacific plate, PH: Philippine Sea plate, NA: North American plate. The barbed lines indicated trough axes. The dashed line denotes Izu-Bonin arc associated with subduction of the Pacific plate beneath the Philippine Sea plate. The arrow denotes the velocity and direction estimated from the plate motion models (Seno et al., 1993,1996).

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 173 Fig. 2. Observed horizontal displacements at the GPS stations and epicentral distribution of earthquake swarm in the studied area during the period from June 12 to August 27 (arrows). The observed horizontal displacements are relative to the TSKB station (latitude 36.103j, longitude 140.088j in the inset of Fig. 1). Letters a to j represent sites of GPS stations. The epicenters of earthquakes with magnitudes 6.0 and above, which are determined by Japan Meteorological Agency, are shown with open star symbols. inversion analysis using the observed GPS data in the region. 2. Tectonics and volcanism in and around the Izu islands The Philippine Sea plate, on which these Islands are located, moves northwestward with a velocity of about 4 cm/year and collides with the mainland (Honshu) of Japan (Seno et al., 1993). The collision produces the large differential stress with compression in the NW SE direction and tension in the NE SW direction (Imoto et al., 1981; Ishida, 1987; Shimazaki, 1988; Hashimoto and Tada, 1990). Earthquakes which have occurred in this region show strike-slip motion with P- axes in the NW SE direction axes (Imoto et al., 1981; Ishida, 1987). Why is the NE SW oriented tensile stress predominant in this region? Nakamura (1980) explained the cause of the tensile stress as follows: The Philippine Sea plate must bend to the northeast in order to subduct along the Sagami trough, and this bending results in the NE SW tensile stress. In this case, tensile and compressive state of stress are dominant in the shallower and deeper parts of the Philippine Sea plate. As a result, the magma reservoir which was generated by the subduction of the Pacific plate beneath the Philippine Sea plate is squeezed, pushing magma into the tensile cracks of the upper portion of the Philippine Sea plate. The main volcanic front is basaltic along the easternmost Islands (i.e. Izu Peninsula, Izu-Oshima and Miyakejima) and trends in the NNW SSE direction of the Izu-Bonin arc (Fig. 1). The volcanism behind the main volcanic front is rhyolitic (i.e. Kozushima and Niijima), and has produced large amounts of pyroclastics at every 1000 years (Tsukuda et al., 2000).

174 T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 3. Data We used data from the GPS Earth Observation Network (GEONET), which is operated by the GSI (Kaizu et al., 2000). The crustal deformation of Miyakejima was observed by GPS from the beginning of the earthquake swarm and indicated a deflation of Miyakejima which continued until the beginning of September. Fig. 2 shows total displacements at the GPS stations in the area during the period from June 12 to August 27. The observed horizontal displacements relative to the TSKB station (latitude 36.103j, longitude 140.088j) are shown (Fig. 1). We used the GPS data, which is denoted by an alphabet at each station in this analysis. On the other hand, the earthquake swarm activity migrated northwestward from Miyakejima for the same period. Typical evidence for crustal deformations due to the swarm activity is the increase in baseline length between the Niijima and Kozushima. Fig. 3 represents temporal baseline length changes in the NS, EW, and UD components between sites b (Niijima) and e (Kozushima2) and sites f (Miyakejima1) and g (Miyakejima4). The arrows denote occurrence of earthquakes with magnitudes 6.0 and above and the eruptions at Miyakejima. The list of these events is given in Table 1. Baseline length changes between the sites b (Niijima) and e (Kozushima2) became very large at the beginning of July, which was slightly delayed from the beginning of the series of the swarm activity (June 26). The amount of crustal deformation decreased considerably at the end of August. The total amount of extension of baseline length changes between b (Niijima) and e (Kozushima2) is over 0.8 m since the beginning of the Fig. 3. Temporal changes in the baseline b e (Niijima Kozushima2) and baseline f g (Miyakejima1 Miyakejima4). (a) Crustal deformation of the site e (Kozushima2) relative to the site b (Niijima). The NS, EW and UD components increase when the site e (Kozushima2) moves northward, eastward and upward, respectively. The arrows denote occurrences of earthquakes with magnitude 6.0 and above. (b) Crustal deformation of the site g (Miyakejima1) relative to the site f (Miyakejima4). The arrows denote eruptions of Miyakejima and occurrence of an earthquake with magnitude 6.4 which occurred near Miyakejima. The vertical dashed lines indicate divided time span.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 175 Table 1 Time chart of earthquakes with magnitude 6.0 and above and eruptions at Miyakejima Date Events June 27 Eruption at sea bottom July 1 M6.4 earthquake in the vicinity of Kozushima July 8 Mountain collapse (9.7 10 4 m 3 ) at Miyakejima July 9 M6.1 earthquake in the vicinity of Kozushima July 14 15 Eruption (2.1 10 6 m 3 ) at Miyakejima July 15 M6.3 earthquake at Niijima July 30 M6.4 earthquake in the vicinity of Miyakejima August 10 Eruption (2.3 10 5 m 3 ) at Miyakejima August 18 Eruption (5.2 10 6 m 3 ) at Miyakejima M6.0 earthquake near Kozushima activity. Since the baseline length is 22 km, the average linear strain is 3.7 10 5. The crustal deformation occurred not only in and around the Izu Islands but also in regions for away from region: Displacements in the NE direction were observed in the Boso Peninsula, which is located over 100 km away from the epicentral region of the earthquake swarm (Fig. 2). Displacements in the SE direction were observed in the Izu Peninsula. The observed GPS data at Miyakejima indicated rapid crustal deformation from June 26 when the seismic activity began (Fig. 3(b)). The length changes of GPS sites at Miyakejima (Miyakejima1 Miyakejiam4) increased when the earthquake swarm activity started, but they turned the trend to the opposite direction, indicating deflation of the volcano on June 28. The vertical components of GPS data show subsidence of the western part of Miyakejima. The total amounts of the horizontal and vertical components at site i in Miyakejima are about 80 cm in the NW SE direction and subsidence of about 70 cm, respectively, from June 26 to August 27. These indicate evidence for dike intrusion from Miyakejima to Kozushima. In this study, we used three-component data at the 10 (sites a to j) GPS observation stations in and around Miyakejima during the period from June 12 to August 27, 2000. 4. Model and method of analysis 4.1. Inversion method In this section, we briefly describe the model used in this analysis. In order to understand the spatio-temporal distribution of dike intrusions and deflation of magma beneath Miyakejima, we divided the time series of the observed GPS data into 10 periods, which are related to seismic and volcanic events. We used the geodetic data inversion to deduce dike intrusions in relation to the seismic swarm activity and deflation of magma beneath Miyakejima from GPS data of each period. In this method, the moment tensor, which corresponds to source on plane dike and sill-like deflated planes, is expressed by superposing basis functions. Therefore, we can deduce the amounts of dike intrusions and deflation of magma by determining the coefficients of each basis function. We used dislocation theory in a semi-infinite homogeneous perfect elastic body to calculate displacement at each GPS station from tensile crack on the dike, explosion beneath Miyakejima and slip on fault planes of earthquakes with magnitude 5.4 and above (Maruyama, 1964). Here, we can express observation equations with N observation data as d ¼ Ha þ e efnð0; r 2 EÞ ð1þ where d, H, a and r 2 are data, an N M dimensional coefficient matrix, model parameters and unknown scale factor for the covariance matrix of E, respectively. M is the number of model parameter. We assume the errors e to be Gaussian, with zero mean and covariance r 2 E. The solution a* of Eq. (1) is given by a* ¼ðH T E 1 HÞ 1 H T E 1 d ð2þ where T is transpose of a matrix. In this study, we constructed the model source region on the dike, the deflation and fault planes. The size of the model source regions on the dike, the deflation were taken to be 18 15 and 12 12 km, respectively. The size of the fault planes are different, depending on magnitude of earthquakes. We divided the respective model source regions into 3 3, 2 2 and 2 2 subsections, respectively. We deduced 13(9 + 4) to 21(9 + 4 + 4 2) model parameters from 20(10 2) horizontal and 10 vertical displacements of GPS data and determined the spatial distribution of the amounts of intrusion along the dike, deflation beneath Miyakejima and slip on fault plane of each earthquake if the earthquake occurs during the investigated period. Moreover, the observation errors for

176 T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 the vertical movement are generally several times as large as those of the horizontal movement. We assume that the weight of the horizontal component is three times as large as that of the vertical component. 4.2. Evaluation of the observation error In this study, the observed crustal deformation is large and the observation period is short. Thus, we can not determine the observation error of GPS data in Eq. (1) from observation alone. In order to evaluate the observation error, we used ABIC proposed by Akaike (1980) on the basis of the entropy maximization principle. Using a hyper-parameter a in this model, the model can extract maximum information from the data, by suppressing the influence of the error included in the data to the minimum. According to Yabuki and Matsu ura (1992), the errors e of Eq. (1) almost coincide with measurement errors when the value of ABIC is minimum. We briefly describe the method used in this analysis. The solution of Eq. (1) with prior constraints that the roughness of solution is smooth to some degree is given by a* ¼ðH T E 1 H þ a 2 GÞ 1 H T E 1 d ð3þ where a 2 and G are hyper parameter and an M M dimensional symmetric matrix, whose concrete expression is given in Yabuki and Matsu ura (1992). We can determine the value of a 2 to minimize the ABIC. Once the value of a 2 minimizing the ABIC has been found, denoting it by â 2, we can obtain the best estimate of rˆ 2 as ˆr 2 ¼ sðâ*þ=ðn þ P MÞ ð4þ with sðâ*þ ¼ðd Hâ*Þ T E 1 ðd Hâ*Þþâ 2 â* T Gâ* ð5þ where P and â* are the rank of matrix G and the best estimate of a determined by ABIC. 4.3. Setting of Monte Carlo method In this analysis, we need 14 fault parameters, including location (latitude and longitude), dip, strike, depth, width, and length of plane for both the dike intrusion and the deflation of magma beneath Miyakejima. We attempted to determine these fault parameters by Monte Carlo method. However, the 14 fault parameters are too many for Monte Carlo method. If all the fault parameters are determined by the method, there is a lot of calculation time. In order to reduce the number of unknown fault parameters, we assumed the width and length of the dike intrusion between Miyakejima and Kozushima, and the location, width, length, dip and strike of the deflation beneath Miyakejima (Fig. 4). We assumed fault parameters of Fig. 4. The geometry of dike and deflation planes beneath Miyakejima. The bold letters show six unknown parameters (latitude, longitude, depth, strike, and dip of the dike plane and depth of the deflation plane), which were estimated by the Monte Carlo method.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 177 earthquake for each period from distribution of epicenters and focal mechanism determined by Freesia broadband seismograph network. We assumed width and length of the dike intrusion to be 15 and 18 km, respectively, so that the dike plane can cover the hypocentral distribution. We assigned the following values for location (latitude, longitude) at southwest corner, dip, strike, width and length of deflation beneath Miyakejima: 34.04j, 139.45j, 0j, N90jE, 12 and 12 km, respectively. Thus, the deflation source beneath Miyakejima is located on the horizontal plane. In order to find the rest of the six unknown parameters (latitude, longitude, dip, strike, depth of the dike plane and depth of deflation source beneath Miyakejima), we used the Monte Carlo method, as shown in Fig. 5. In order to determine the optimal six unknown parameters for each period independently, we carried out the inversion analyses using a set of parameters. In order to find the optimal parameters to minimize R.M.S. of residual between observed data and calculation, which are obtained from amounts of tensile crack along the dike, deflation beneath Miyakejima, and slips on fault planes of earthquakes, we repeated the Monte Carlo analyses of 10,000 times for each period. Hence, we determined 6 10 parameters for all the periods by Monte Carlo method. In this analysis, we use ABIC only for the purpose of evaluation of minimization of the observation error. The reason is that the determination method of the best solution is different between ABIC and the Monte Carlo method. If we employ the inversion analysis using ABIC to obtain the solution, contradiction cause in the method of analysis. We determine the solutions only by minimizing R.M.S. using Monte Carlo method. Reliability of the solutions is evaluated by checkerboard test and R.M.S. as described in the next section. 5. Results and discussion 5.1. Evaluation of Monte Carlo method and resolution Through the analyses in the preceding section, the spatio-temporal distributions of the dike intrusion and the deflation beneath Miyakejima are obtained by the geodetic data inversion and the Monte Carlo method. Before describing the features of the obtained results, we first show the reliability of the Monte Carlo method and resolution of the dike intrusion and the deflation beneath Miyakejima. Fig. 6 shows R.M.S. of residuals between observation and calculation as functions of the six parameters, which were obtained Fig. 5. Scheme of the inversion analyses.

178 T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 Fig. 6. R.M.S. of residuals between observed data and calculation obtained by the Monte Carlo method for the period from June 12 to June 28, 2000. The repeated time of the inversion for the period is 10,000 times. by the Monte Carlo method for the period from June 12 to June 28. In order to evaluate the results, we introduce a coefficient which indicates reliability. As a function of the parameter in the horizontal axis, we draw a quadratic curve to delineate the minimum residual values. We define the reliability as the coefficient of the quadratic curve. The larger these values are, the better the reliabilities are. Tables 2 and 3 represent the estimated geometry parameters by the Monte Carlo method. The bracketed value is the reliability of each parameter. The searched span of strike, dip, location (latitude and longitude), depth of the dike plane and depth to the top of the deflation beneath the Miyakejima are 138.5j F 10j, 88.6j F 10j, 34.073j F 0.05j, 139.482j F 0.05j (latitude and longitude), 0 5 and 0 10 km, respectively. The reliability for depth parameters of the deflation beneath Miyakejima are generally better than other parameters. Especially, poor reliability can be found for the dip and depth parameters of the dike plane. In order to investigate how the dike intrusion and deflation beneath Miyakejima are well-solved in our calculation, we carried out a checkerboard test. The checkerboard test which investigate resolution of solutions has been used in the tomographic inversion of seismic velocity structure (e.g. Zhao et al., 1992). The first basic idea of the checkerboard resolution test was proposed by Humphreys and Clayton (1988). In order to carry out the checkerboard test, deflation (150 cm) and inflation ( 150 cm) are assigned alternatively to

Table 2 The estimated depth of deflation source and the coefficient of quadratic (bracketed) Periods Depth (km) June 15 June 28 3.9 (13.2) June 29 July 5 3.8 (15.1) July 6 13 1.4 (2.4) July 14 19 7.3 (3.3) July 20 28 2.2 (3.3) July 28 August 2 0.1 (1.0) August 3 8 2.5 (5.2) August 9 11 8.3 (2.0) August 12 19 3.8 (4.7) August 20 27 2.8 (3.7) the 4 subfaults of horizontal plane beneath Miyakejima, whereas zero and extension (150 cm) are assigned alternatively to the 16 subfaults of the dike plane. We also investigated the checkerboard test for reverse pattern of the perturbations on the dike plane and the horizontal plane beneath Miyakejima. This is because the distribution of the patterns influences on the results of resolution. In order to evaluate the resolution, we introduce the following quantity for each subfault: R:M:S: ¼ T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 179 the image of the synthetic inversion of the checkerboard, one can understand whether the resolution is good or poor. The resolution is generally high on the horizontal plane beneath Miyakejima. The R.M.S. on the deflation beneath Miyakejima is smaller than 10 cm for all the periods. Fig. 7 shows the result of the checkerboard test for the dike plane. The resolution is generally good for the periods from June 12 to 28, from August 9 to 11, and from August 20 to 27 (Fig. 7(a), (h) and (j)). This is because there are not model parameters for fault planes of earthquakes for these three periods, resulting in less unknown model parameters than the models for other periods. The resolution is generally poor at the deeper subfaults, especially, for the periods from July 6 to 13 and from July 20 to 28 (Fig. 7(c) and (e)). This is because the fault planes of earthquakes are close to the dike plane for these periods. The solutions have large trade off between the amounts of dike intrusion and slips on the fault planes. However, the results are generally reliable on subfaults at both sides and shallower parts of the dike plane for all the periods. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðcalculate normal Assume normal Þ 2 þðcalculate reverse Assume reverse Þ 2 Þ 2 ð6þ where Calculate and Assume are the amounts of slips obtained by the synthetic inversion and given slip, respectively. The subscripts represent the distribution which is normal and reverse checkboard patterns. The smaller the value of R.M.S. in Eq. (6) is, the better the resolution is. Therefore just seeing 5.2. The spatio-temporal distribution of dike intrusion and deflation beneath Miyakejima Fig. 8 represents the estimated spatial distributions of the open crack due to the dike intrusion projected on the dike plane and deflation on the horizontal plane Table 3 The estimated parameters of a plane for the dike intrusion and the coefficient of quadratic (bracketed) Periods Location (latitude, longitude) Depth (km) Strike Dip June 15 28 34.07j(41.8), 139.47j(11.3) 0.8(12.4) N50.5jW(7.2) 83.6j( 0.6) June 29 July 5 34.10j(2.9), 139.41j(1.4) 1.6(0.7) N55.9jW(7.6) 98.3j(0.2) July 6 13 34.13j(1.0), 139.36j(1.1) 0.9(0.0) N50.5jW(0.2) 95.3j(0.0) July 14 19 34.11j(2.4), 139.33j(1.0) 0.2(0.0) N35.8jW(0.7) 93.6j( 0.1) July 20 27 34.11j(2.7), 139.37j(1.6) 0.1(0.3) N40.4jW(4.0) 96.7j(0.2) July 28 August 2 34.11j(1.3), 139.38j(1.0) 2.2(0.0) N43.4jW(1.1) 93.6j(0.4) August 3 8 34.15j(0.2), 139.34j(0.2) 0.2( 0.4) N48.5jW(0.4) 95.2j(0.1) August 9 11 34.13j(1.3), 139.32j(1.9) 1.9(0.0) N45.2jW(0.1) 96.3j( 0.6) August 12 19 34.13j(1.3), 139.34j(2.3) 0.1( 0.6) N46.5jW(1.2) 99.7j(0.2) August 20 27 34.10j(2.7), 139.36j(2.3) 0.4(0.3) N40.7jW(1.1) 95.0j( 0.4)

180 T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 Fig. 7. The spatial distribution of resolution on the dike plane for the 10 periods. The time period is shown at the top of each figure. The horizontal and vertical axes represent length of the dike plane and depth, respectively.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 181 beneath Miyakejima for the 10 periods. The observed crustal deformation and calculated one from the inverted distributions are also shown. Locations of the focal mechanisms correspond to the epicenters of the earthquakes. Horizontal projections of the location of the estimated dike plane, fault planes of earth-

182 T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 quakes, and the deflation plane beneath Miyakejima are shown in the 10 left figures together with the epicentral distributions. We find that most of the observed displacements are well explained by our model. However, the calculated vertical displacements poorly fit the observations at Kozushima, Shikinejima

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 183 and Niijima for the period from August 9 to 27 (Fig. 8(h), (i) and (j)). The reason is that the vertical movements are much larger than the horizontal movements in the region of Kozushima and Shikinejima for the period, and observation errors for the vertical displacements are assumed three times as large as those for the horizontal displacements. In Fig. 8, by and large, the peaks of the maximum amount of the deflation are located at the southwestern part beneath Miyakejima for all the periods except for the period from August 9 to 11. As opposed to these features, inflation can be found in the northeastern part beneath Miyakejima for the periods from June 12 to July 5, from July 14 to 19, from August 9 to 11, and from August 20 to 27 (Fig. 8(a), (b), (d), (h) and (j)). Fig. 9 shows temporal change of the amounts of the deflation beneath Miyakejima and the dike intrusion. These amounts are calculated by multiplying the area of the dike plane or the deflation plane beneath Miyakejima and the amount of open crack or deflation, respectively. The amounts of the deflation beneath Miyakejima decreased gradually for the period from June 28 to July 13. The amount of the deflation beneath Miyakejima increased again for the period from July 14 to 19. The maximum amount of deflation beneath Miyakejima is about 2.7 m on the southwestern subfault for the period from June 12 to 28. The total amount of the deflation for all the periods is about 5.4 10 8 m 3. Kumagai et al. (2001) estimated the volume change of the magma chamber beneath Miyakejima, using very-long-period seismic signals. The estimated cumulative volume change beneath Miyakejima is about 1.2 10 8 m 3 for the period from July 20 to August 17. The estimated amount of the deflation beneath Miyakejima in this study is about 1.3 10 8 m 3 for the period from July 20 to August 19. Our result is in good agreement with the volume change of the magma chamber estimated by Kumagai et al. (2001). On the other hand, the distributions of the dike intrusion indicate generally large amount of dike intrusion at the edge of the dike plane for all the periods (Fig. 8). The reason is that the resolutions at the central parts of the dike plane are poorer than the edge parts for the all periods. The amounts of the intrusion at the central parts are almost zero for all the periods. Therefore, the amounts at the poor resolution part of dike planes are almost zero. Especially, the tendency is remarkable for the periods from July 6 to 13, from July 20 to 28, and from August 3 to 8 (Fig. 7(c), (e) and (g)). However, the amounts of the sides and shallower parts of the dike planes are reliable. Total amount of the dike intrusion estimated from this calculation is about 1.1 10 9 m 3 (Fig. 9). The temporal change of the amount of the intrusion on the dike plane has two peaks for the periods from June 29 to July 5 and from July 20 to 28. The maximum amount of the open crack is about 6.4 m on a subfault for the period from June 29 to July 5. The amount of the dike intrusion decreased until the middle of July, and increased rapidly just after the period. The maximum amount of the open crack is about 9.4 m on a subfault for the period from July 20 to 28. The observed crustal deformations are in good agreement with the calculated ones for the two periods. However, the seismic moment of the M6.4 and M5.9 earthquakes which occurred for these periods obtained in this study are 7.06 10 17 and 1.06 10 18 Nm, respectively. The seismic moment of these earthquakes does not agree with that from seismological observations by the Freesia broadband seismograph network (Table 4). The observation error for the period from June 29 to July 5 is especially larger than those for other periods (Table 5). Details of the calculation method of observation errors were written Fig. 8. The spatial distribution of dike intrusion and deflation beneath Miyakejima inverted from the observed crustal deformation for the successive 10 periods from June 12 to August 27, 2000. Vertical and horizontal axes represent width and length for the central figures and depth and length for the right figures, respectively. The positive and negative values in the central figures denote deflation and inflation, respectively. The positive values in the right figures denote intrusion. In the left figures, crustal deformation at each GPS station calculated from the inverted distribution on the dike plane, fault slips and the deflation beneath Miyakejima (gray) and the observed displacement (black) are shown. The arrows and vertical bars denote the horizontal and vertical displacements, respectively. Horizontal projections of the estimated dike plane for the intrusion, each fault plane for the earthquakes and the deflation beneath Miyakejima are also shown together with epicentral distribution. Solid lines of the projected planes show the upper margin of the plane for the dike intrusion and the fault plane. The focal mechanism and fault plane correspond to each earthquake with magnitude 5.0 and above. The magnitude and date of each earthquake are shown at the top of each figure. The period of analysis is shown at the bottom of the each figure. It should be noted that different scales are used for (a) and (b).

184 T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 Fig. 9. Temporal change of the amounts of the dike intrusion and the deflation beneath Miyakejima. in Section 4.2. Therefore, the results of these periods may be caused by the trade off between the amounts of the dike intrusion and slips on the fault of the earthquakes. However, the crustal deformations for these periods are large. The amounts of the dike intrusion are not an artificial result. Temporal change of the location of the maximum amount of the dike intrusion for the 10 periods with the Table 4 The amount of the deflation beneath Miyakejima, and the dike intrusion, estimated seismic moment of the earthquakes Periods Amount of the deflation beneath Miyakejima (10 8 m 3 ) Amount of the dike intrusion (10 8 m 3 ) Seismic moment (10 18 Nm) June 15 28 1.719 0.556 June 29 July 5 1.227 2.181 0.7056(2.28) July 6 13 0.105 1.611 0.6400(0.78) July 14 19 1.060 0.388 0.9920(1.24) July 20 27 0.211 3.523 1.0640(0.33) July 28 August 2 0.110 0.901 2.3680(5.02) August 3 8 0.288 0.287 0.2040(0.13) August 9 11 0.017 0.811 August 12 19 0.489 0.101 0.6128(0.47) August 20 27 0.225 0.526 The bracketed values of seismic moment of the earthquake are determined by Freesia broadband seismograph network. For the calculation of the seismic moment, the rigidity is assumed to be 40 GPa. epicentral distribution of the earthquake swarm is shown in Fig. 10. These locations of the peak of the dike intrusion correspond well to the migration of the epicenters of the earthquakes (Fig. 8) (JMA, 2000). The location of the dike intrusion appears to move from Miyakejima to Kozushima from the first to the second period. We estimated the location and the amount of the dike intrusion, taking account of the northwestward movement of the epicenters of the earthquake swarm. The location of the estimated plane Table 5 The rate of the deflation beneath Miyakejima, the dike intrusion, and observation error Periods Rate of the deflation beneath Miyakejima (10 7 m 3 /day) Rate of the dike intrusion (10 7 m 3 /day) Observation error (cm) June 15 28 1.32 0.43 2.085 June 29 July 5 1.75 3.12 5.031 July 6 13 0.15 2.30 1.856 July 14 19 2.12 0.78 3.525 July 20 28 0.26 4.40 1.882 July 28 August 2 0.22 1.80 0.893 August 3 8 0.58 0.57 1.906 August 9 11 0.09 4.01 1.619 August 12 19 0.70 0.14 2.665 August 20 27 0.32 0.75 2.014 The detail of observation error is described in Section 4.2.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 185 Fig. 10. Temporal change of the location of the maximum amount of the dike intrusion for the 10 periods with epicentral distribution of the earthquake swam. The number of each dot shows the order of the analyzed period. of the dike intrusion by the Monte Carlo method corresponds well to the epicentral distribution of the earthquake swarm for each period. It is still controversial from where the vast amount of magma came. The existence of a magma chamber directly beneath Miyakejima seems to conflict with the continuous deflation of Miyakejima until September. Hence, these conflict the deformation due to dike intrusion decrease after the middle of August. A more plausible model may be that the magma came from a sub-crustal magma pocket, where magma is thought to be stagnant due to the density contrast between the crust and the uppermost mantle. In this case, it would be possible to supply the long-lasting magma by sustaining density difference between the magma and the surrounding material (Yamaoka et al., 2000). According to Q structure, which was investigated by three-dimensional inversion method, using seismic P- and S-wave spectral ratios (Sekiguchi, 1991), low Q p zone exists at shallow depth (0 32 km) around Kozushima region. Moreover, P n velocity near Kozushima is low (Hashida, 1989). Therefore, a magma chamber would exist beneath Kozushima. In this study, the amount of the dike intrusion corresponds to that of the deflation beneath Miyakejima until the middle of July (Fig. 9). However, the amount of the dike intrusion is much larger than that of the deflation beneath Miyakejima for the following period. Therefore, we deduce that the magma source changed from Miyakejima to Kozushima in the middle of July. After the middle of July, the magma might come from the sub-crustal magma pockets. If we assume that the open crack along the dike plane and the deflation beneath Miyakejima were filled with the magma with a density of 2500 kg/m 3, the mass would be about 2.75 10 9 and 1.35 10 9 tons, respectively, for all the periods. Hence, we find that the magma of 1.4 10 9 tons came from a sub-crustal magma pocket. Moreover, we estimated rate (m 3 /day) of the dike intrusion and the deflation beneath Miyakejima (Table 5). The rate of the dike intrusion has three peaks. From the location of the estimated dike, we deduce that the first peak (the period from June 29 to July 5) corresponds to the magma inflow to the dike from the magma chamber beneath Miyakejima. The other peaks (the periods from July 20 to 28 and from

186 T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171 187 August 9 to 11) are the dike intrusion which came from the sub-crustal magma pockets. On the other hand, the peak of deflation rate beneath Miyakejima (the period from July 14 to 19) corresponds to an eruption at Miyakejima on July 14 and 15. In this study, we obtained spatial change of the dike intrusion and the deflation beneath Miyakejima for the 10 periods. The estimated amount of the dike intrusion is fairly large compared to another dike intrusion event in northeastern Izu Peninsula. The amount of the dike intrusion for the event was estimated to be about 2.3 10 8 m 3, using the leveling data during the period from 1978 to 1988 (Tada and Hashimoto, 1991). The amount of the dike intrusion in our study is about four times larger than that of the event in northeastern Izu Peninsula, though the observed period for the latter is much longer. Yamaoka et al. (2000) suggested the existence of an aseismic point source in the Kozushima region. The long-lasting crustal deformation in Miyakejima Kozushima region can be modeled by a dike and the aseismic point source, corresponding to an M7 class earthquake. The dike intrusion plane of their study is constrained by detailed hypocentral distribution and takes the same amount on the dike plane. Their observation period is from the beginning of June to the beginning of September. Since the crustal deformation in the SE direction of Shikinejima (Fig. 2) could not be explained by the dike intrusion alone, they introduced the aseismic point source between Shikinejima and Kozushima. However, it is not necessarily correct that the hypocentral distribution corresponds to the plane of the dike intrusion. In our result, the southeastward crustal deformation at Shikinejima can be explained by the combination of the dike intrusion and the fault slips associated with the earthquakes. Although the hypocentral distribution concentrates at depths shallower than 10 km, we think that the dike intrusion plane must reach depths deeper than 10 km. This is because the crustal deformation caused by the dike intrusion appears to be observed far away in the Izu and Boso Peninsulas. 6. Conclusion In this study, we calculated the spatial distribution of the dike intrusion and the deflation beneath Miyakejima, based on the crustal deformation obtained from the continuous GPS observations by GSI. We estimated that the total amount of the dike intrusion and the deflation beneath Miyakejima reached about 1.1 10 9 and 5.4 10 8 m 3, respectively. The spatial distribution of the dike intrusion is concentrated in the area between Kozushima and Miyakejima. The maximum amount of the dike intrusion and the deflation beneath Miyakejima reached over 3.5 10 8 m 3 during the period from July 20 to July 28, 2000 and over 1.7 10 8 m 3 during the period from June 15 to June 28, 2000, respectively. From Fig. 9, we can deduce that the amount of the dike intrusion corresponded to that of the deflation beneath Miyakejima until the middle of July. However, we may conclude that the magma source changed from Miyakejima to Kozushima in the middle of July, and the magma might come from sub-crustal magma pockets. Acknowledgements The authors are grateful to T. Yabuki for allowing us to use his source code of geodetic data inversion. We are indebted to K. Furlong and three anonymous reviewers for their critical reviews. All the figures were created using GMT(Generic Mapping Tools) Software (Wessel and Smith, 1995). We also thank M. Hashimoto and J. Mori for their valuable comments and kind help. References Akaike, H., 1980. Likelihood and the bayes procedure. In: Bernardo, J.M., DeGroot, M.H., Lindley, D.V., Smith, A.F.M. (Eds.), Bayesian Statistics. University Press, Valencia, pp. 143 166. Hashida, T., 1989. Lateral variation of P n velocity and crustal delay time in the Kanto-Tokai district, Japan, Physics. Earth Planet. Inter. 54, 106 115. Hashimoto, M., Tada, T., 1990. Crustal deformations associated with the 1986 fissure eruption of Izu-Oshima Volcano, Japan and their tectonic significance. Phys. Earth Planet. Inter. 60, 324 338. Humphreys, E., Clayton, R.W., 1988. Adaptation of back projection tomography to seismic travel time problem. J. Geophys. Res. 93, 1073 1085. Imoto, M., Karakama, K., Matsu ura, R., Yamazaki, H., Yoshida, A., Ishibashi, K., 1981. Focal mechanisms of the 1980 earthquake

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