Geomagnetic changes associated with the dike intrusion during the 2000 Miyakejima eruptive activity, Japan

Earth and Planetary Science Letters 245 (2006) 416 – 426 www.elsevier.com/locate/epsl

Geomagnetic changes associated with the dike intrusion during the 2000 Miyakejima eruptive activity, Japan Hideki Ueda a,⁎, Takumi Matsumoto a , Eisuke Fujita a , Motoo Ukawa a , Eiji Yamamoto a , Yoichi Sasai b , Meilano Irwan c , Fumiaki Kimata c a

National Research Institute for Earth Science and Disaster Prevention, Tennôdai 3-1, Tsukuba-shi, Ibaraki-ken, 305-0006, Japan b Tokyo Metropolitan Government, Nishishinjuku 2-8-1, Shinjuku-ku, Tokyo, 163-8001, Japan c Research Center for Seismology, Volcanology and Disaster Mitigation, Graduate School of Environmental studies, Nagoya University, Furo-cho, Chikusa-ku, Nagoya City, Aichi-ken, 464-8602, Japan Received 15 June 2005; received in revised form 13 February 2006; accepted 18 February 2006 Available online 17 April 2006 Editor: R.D. van der Hilst

Abstract A marked magnetic field change exceeding 200 nT was detected by a three-component magnetometer at the beginning of the 2000 Miyakejima eruptive activity. The change in the magnetic field is correlated with an earthquake activity and crustal deformation, which indicate a dike intrusion very close to the observation site. A dike model based on the crustal deformation data shows that the primary cause of the magnetic change was the piezomagnetic effect associated with the dike emplacement, and that the other potential factors, including thermal and electrokinetic effects, were unlikely to be its principal cause. We obtained a new dike model by combining both the crustal deformation and the magnetic field change, which is sensitive to the strong stress changes near the edges of dike. The new dike model shows lateral and upward propagation of the dike during its intrusion, and suggests that shallow cracks induced by the dike intrusion near the ground surface contributed to the changes seen in the magnetic field. © 2006 Elsevier B.V. All rights reserved. Keywords: Miyakejima volcano; piezomagnetic effect; crustal deformation; tiltmeter; GPS; dike

1. Introduction Observations of geomagnetic fields are essential for monitoring volcanic activities, since they provide different kinds of information on magma emplacements from geodetic and seismic observations (e.g., [1–3]). Several causes of magnetic changes during volcanic activity have been proposed: demagnetization ⁎ Corresponding author. Fax: +81 29 851 5658. E-mail address: [email protected] (H. Ueda). 0012-821X/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2006.02.036

or remagnetization due to temperature changes [1], piezomagnetism due to stress changes in the crust [4] and electrokinetic effects [5]. Of these, dike intrusions are presumed to cause geomagnetic field changes due to the piezomagnetic effect as observed during the 2002 Etna eruptive activity [6]. During the 2000 Miyakejima eruptive activity in Japan [7,8], geomagnetic field changes exceeding 200 nT were detected by three-component magnetometers at one of the observation stations on Miyakejima Island during the dike intrusion stage.

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Continuous observation data on crustal deformation and geomagnetic field changes were recorded during the 2000 Miyakejima activity. The dike intrusion process has been successfully modeled on the basis of this crustal deformation data, including ground tilt changes and kinematic GPS analysis [9]. The observation of geomagnetic field changes thus provides an excellent opportunity to study the relationship between large magnetic changes and volcanic activity. The purpose of this study is to investigate possible causes of the observed large geomagnetic changes at Miyakejima and to improve the dike intrusion model proposed by Ueda et al. [9] in consideration of both the geomagnetic changes and crustal deformation data. 2. The 2000 Miyakejima eruptive activity and the dike model Miyakejima is an active basaltic stratovolcano lying 170 km to the south of Tokyo, Japan (Fig. 1). The most

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recent eruptive activity began on June 26, 2000, with an earthquake swarm and anomalous crustal deformation on the island [7,8]. Former studies of earthquake activities [7] and crustal deformation [8] showed that dikes intruded under the island at the beginning of the activity, followed by underground magma migration from Miyakejima toward the northwest until August 2000 [10,11], simultaneously with the caldera formation process [12]. By assuming rectangular dikes, Ueda et al. [9] modeled the source of the crustal deformation observed by the tiltmeters and kinematic GPS analysis from 18:30 LT on June 26 to 06:00 LT on June 27 (Japan Standard Time, UT + 9:00) [13]. The source model consists of three intrusive dikes designated DK1, DK2 and DK3, and one contractive dike, DK4, which were located in the southwestern part of Miyakejima and off the western coast of the island, as shown in Fig. 1a. The active periods of these dikes were 18:30 LT–21:50 LT (DK1), 20:50 LT–01:00 LT (DK2), 00:10 LT–06:00 LT (DK3), and

Fig. 1. (a) Map showing epicenter distribution from June 26 to 29, 2000, and observation stations. Rectangles and thick lines show horizontal projections of the dike model obtained by Ueda et al. [9] and its upper boundary, respectively. The model consists of four dikes that successively intruded or contracted from 18:30 LT on June 26 to 06:00 LT on June 27, 2000. The thin lines depict baselines between GPS stations. (b) Spatiotemporal distribution of the earthquakes as determined by NIED [8].

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21:20 LT–06:00 LT (DK4). Although no eruptions occurred on the island itself during this dike intrusion process, the upper depths of DK2 (0.5 km) and DK3 (0.1 km) indicate that the dikes reached close to the surface. They concluded that the contractive dike, DK4, is an upper part of a magma chamber that consists of DK4 and a deep seated magma chamber just beneath DK4 from the discussion on a volume balance between the intruded and discharged magma. Based on this source model, Ueda et al. [9] inferred the magma migration process as follows. Magma began to intrude from the upper tip of the dike-like magma chamber DK4 beneath the southwest of Miyakejima into DK1 at 18:30 LT on June 26. At around 21:00 LT, the intrusion of DK1 ceased and DK2 began to intrude from the deep seated chamber; then the dike propagated laterally to DK3 at around 01:00 LT on June 27. Considering the gap between DK2 and DK4, they inferred that the large amount of magma was supplied from the deep chamber to DK2. The DK3 further propagated towards the northwest until late August, with its length reaching 30 km [7,10,11]. 3. Geomagnetic observations NIED (the National Research Institute for Earth Science and Disaster Prevention) has had a volcano observation network in place on Miyakejima since 1998. The observation network consists of borehole seismometers and tiltmeters, broadband seismometers,

GPS receivers and magnetometers [8]. The magnetometers are three-component flux-gate type (Shimazu Co., MB162 type), installed at the bottom of ten-meter boreholes with vinyl chloride casing at three stations (MKA, MKK and MKT in Fig. 1). The data have been continuously telemetered to NIED in Tsukuba at a sampling frequency of 1 Hz. Fig. 2 shows the geomagnetic field differences during the period from June 26 to 29, 2000, between the three sites at Miyakejima and Kakioka Magnetic Observatory (KAK), which is located 250 km to the north of Miyakejima (see the inset in Fig. 1a). Using the differences in the magnetic data allows us to remove common signals due to ionospheric and magnetospheric sources. Significant magnetic changes at MKA began at around 23:00 LT on June 26, about 5 hours after the beginning of the earthquake swarm [14] and crustal deformation [8]. A gradual increase in the downward component seems to begin at 21:00 LT. At around 02:30 LT on June 27, the westward and downward components exceeded the measurement ranges of the telemetry system. The northward component continued to decrease until 07:00 LT with about 150 nT for 8 h (we call this the first event). After a quiet interval of about four hours, the northward component resumed decreasing until 18:00 LT on June 27. The change reached about 60 nT, which we call the second event. After the second event, the northward component of the magnetic change at MKA remained almost constant, intermittently exceeding the measurement range, and then entirely exceeded the range at 06:00

Fig. 2. Minute differences in magnetic fields of MKA, MKT and MKK in comparison with KAK. The westward and downward components of MKA–KAK exceeded their telemetry system measurement ranges at around 02:30 LT on June 26. The northward component exceeded its measurement range at 18:00 LT on June 29. The small arrow indicates the start time of the gradual increase of the downward component.

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LT on June 29 as shown in Fig. 2. Meanwhile, no significant magnetic changes were detected at MKT or MKK during the same period. The large magnetic change at MKA is probably related to the intrusion of dike DK2, since MKA is located very close to the eastern edge of DK2 (Fig. 1) and the start time of the large magnetic change almost

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coincides with the start of the DK2 intrusion. The anomalous magnetic change of the first event were recorded in three components at MKA until around 02:30 LT on June 27. We will therefore focus on this period. The magnetic change recorded in each component at MKA during the period from 23:00 LT on June 26 to 02:30 LT on June 27 was − 84 nT

Fig. 3. Magnetic field and crustal deformation data at the initial stage of the 2000 eruptive activity of Miyakejima. (a) Minute differences in the magnetic field in comparison with KAK. The westward and downward components of MKA–KAK exceeded the telemetry system's measurement range at around 02:30 LT. The small arrow indicates the start time of the gradual increase of the downward component. (b) Baseline length changes between GPS stations [13]. (c) Tilt change at MKA. (d) Volumetric changes in the intrusive dikes DK2 and DK3 [9]. The vertical broken lines at 21:00 LT indicate the time that the dike intrusion began beneath the west coast of Miyakejima. Dotted lines are bounds of the phases defined in the text.

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(northward), 133 nT (westward), and 136 nT (downward), giving a total change of 208 nT. This corresponds to a total magnetic intensity increase of about 60 nT, if we assume that original magnetic field at MKA is the same as that at KAK (total intensity, 46371 nT; inclination, 49.58°; declination, 7.02°) [15]. Fig. 3 shows a comparison of the temporal changes in the magnetic field at MKA (Fig. 3a), the crustal deformation data (Fig. 3b and c) and the volume changes of DK2 and DK3 (Fig. 3d) for a one day period from 12:00 LT on June 26. Fig. 3b shows two baseline lengths between the GPS stations (IGYA-AKTD and MYK1-RJIN) crossing the modeled dikes as shown in Fig. 1. The GPS station at MYK1 belongs to the Geographical Survey Institute, those at IGYA and RJIN to Tokyo University and that at AKDT to the Japan Coast Guard. Fig. 3b and c indicate that the anomalous crustal deformation in the southwestern part of Miyakejima started at 21:00 LT on June 26 with the earthquake swarm activity in the same region (Fig. 1b). It is noticeable that the tiltmeters at MKA recorded a major ground tilt change amounting about 160 μrad, suggesting proximity of the intruding dike to the MKA site. The crustal deformation is modeled as DK2 by Ueda et al. [9] in Figs. 1a and 3d. The horizontal distance from MKA to the surface trace of DK2 is less than 1 km. A close look at the temporal change in the magnetic field at MKA (arrows in Figs. 2 and 3a) indicates that the anomalous change began with a gradual increase in the downward component from 21:00 LT to 23:00 LT, and that the change rate increased at 23:00 LT and continued until 07:00 LT on June 27. The start time of the gradual increase in the downward component (21:00 LT) is the same as the start time of the anomalous crustal defor-

Fig. 4. Magnetic field change caused by the thermal demagnetization effect calculated from the dike model (rectangles) of Ueda et al. [9]. Arrows and counter lines show horizontal and downward magnetic changes, respectively. The predicted magnetic field change at MKA is 3 nT toward the northeast.

mation in the western part of Miyakejima (Fig. 3b and c), and the start time of the intrusion of DK2 (Fig. 3d). 4. Modeling 4.1. Mechanisms of geomagnetic change In considering the former studies on the piezomagnetic effect (e.g., [3,4,16]) and the proximity of the dike (DK2) to MKA, the piezomagnetic effect is the most probable cause of the larger geomagnetic changes during the dike intrusion process than for the other candidates, that is, the demagnetization or remagnetization effect due to temperature changes and the electrokinetic effect. To examine the possibility of the

Table 1 Dike parameters and physical properties Period

Lat. (°N)

Lon. (°E)

Depth (km)

Strike (°)

Dip (°)

Length (km)

Width (km)

Open (m)

Open of DK4 (m)

Phase 1 (21:00 LT–23:00 LT) Phase 2 (23:00 LT–01:00 LT) Phase 3 (01:00 LT–02:30 LT)

34.074

139.48 9 139.48 7

0.5

N102.4 E N102.4 E

90

0.9

9.8

0.92

− 1.43

90

2.7

9.6

0.59

− 0.13

Phase 3 (01:00 LT–02:30 LT)

34.075

Dike model 34.072 139.49 9 Dike + crack model 34.081 139.45 1 34.077 139.49 6

0.2

2.7

N102.4 E

90

0.4

9.4

4.84

− 4.71

0.0

N102.4 E N102.4 E

90

3.0

3.9

0.55

− 2.45

90

0.5

0.5

3.16

1.7

Magnetization 10.3 A/m. Inclination 49.58°. Declination 7.02°. Stress sensitivity 3 × 10− 3 MPa− 1, and Curie depth 5 km.

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Fig. 5. Comparison between the best-fit dike model (thick lines) and the total changes in three different observations during the period from 21:00 LT to 23:00 LT on June 26 (Phase 1). (a) Magnetic field change. The calculated magnetic change is due to the piezomagnetic effect associated with the dike opening. The contour line shows total magnetic intensity change in nT as calculated from the model. The model parameters and physical properties used in the calculation are shown in Table 1. When the dike intrusion began, the magnetic field change was still minor at MKA. (b) Tilt change. (c) Displacement.

piezomagnetic effect, we calculated the geomagnetic change at MKA due to the piezomagnetic effect, provisionally using the dike parameters of DK2 [9]. This preliminary calculation using Sasai's formulation

[4] shows that the total magnetic intensity increase is 91 nT in the west and down direction. The calculated change is approximately 1.5 times the observed value in intensity and is almost in the same direction,

Fig. 6. Comparison between the best-fit dike model (thick lines) and the total changes of three different observations during the period from 23:00 LT on June 26 to 01:00 LT on June 27 (Phase 2). (a) Magnetic field change. The dike expanded beside Phase 1, causing the large magnetic field change at MKA. (b) Tilt change. (c) Displacement.

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Fig. 7. Comparison between the best-fit dike model (thick lines) and the total changes of three different observations during the period from 01:00 LT to 02:30 LT on June 27 (Phase 3). (a) Magnetic field change. (b) Tilt change. (c) Displacement. The dike model fits the magnetic field change at MKA but does not explain the tilt changes and displacements.

confirming that the piezomagnetic effect due to the dike intrusions is the primary cause of the large observed geomagnetic change. We examined the possibilities of other mechanisms. Fig. 4 shows magnetic changes due to the thermal demagnetization associated with the dike intrusion as modeled by Ueda et al. [9]. In this calculation, we assumed that the magnetization of rock with the thickness

of the intruded dikes was completely lost. The rock magnetization, which was the average for Miyakejima [17], and the Curie depth used here are listed in Table 1. The calculated result at MKA is 3 nT toward the northeast, markedly smaller than the observed change, indicating that the demagnetization effect is not a suitable mechanism for the observed magnetic changes at Miyakejima.

Fig. 8. Comparison between the best-fit dike model with a tensile crack model (thick lines) and the total changes of three different observations during the period from 01:00 LT to 02:30 LT on June 27 (Phase 3). (a) Magnetic field change. (b) Tilt change. (c) Displacement. The dike model more or less explains not only the magnetic field change at MKA but also the crustal deformation.

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Fig. 9. Schematic illustration of a cross section of the estimated dike intruded beneath the west coast of Miyakejima. Thick arrows show the magma movements.

The electrokinetic effect of the magmatic fluid flow is also an unsuitable mechanism for the observed magnetic change, since the observed magnetic change exhibits a permanent effect at least until the end of observations on August 18, 2000. If the electrokinetic effect were the main source, the flow would have had to maintain its velocity for the unrealistically long time of one month or more. Displacement and tilt of the magnetometer due to crustal deformation did not affect seriously the magnetic observations, since the calculated magnetic change from the dike model is less than 1 nT. Since no eruption occurred until a small submarine eruption took place off the west coast at about 08:30 LT on July 27 [18] (see Fig. 1a for its location), eruptions could not have contributed to the magnetic change. We conclude that the piezomagnetic effect associated with the dike intrusion is the only possible cause of the large observed magnetic change. 4.2. Improvement of the dike model by magnetic data Although the dike model of Ueda et al. [9] basically explains the observed geomagnetic field changes, the difference between the calculated and observed results is still very large. This difference probably comes from the difference in the sensitivity of the model parameters to the observations between crustal deformation and geomagnetic field change due to the piezomagnetic effect, that is, the piezomagnetic effect is sensitive to stress changes rather than displacements or tilt changes. Below we model the source in a way that explains both the crustal deformation and the geomagnetic changes during the dike intrusion stage.

We divided the period into three phases, taking into account the geomagnetic changes in Fig. 3a: 21:00 LT– 23:00 LT on June 26 (Phase 1), 23:00 LT on June 26– 01:00 LT on June 27 (Phase 2) and 01:00 LT–02:30 LT on June 27 (Phase 3). Since the geomagnetic change rate accelerated at 23:00 LT, we divided the interval of DK2 into two phases. Because of the clipping of data at 02:30 LT due to its exceeding the measurable range, we analyzed the data up to this time only. Phases 1 and 2 correspond to the period of DK2, and Phase 3 to DK3. We searched for the best-fit dike model for each phase, employing the following assumptions. (1) We considered only magnetic field changes caused by the piezomagnetic effect due to the DK2 and DK3 dike intrusions, because the other factors show far smaller effects on the magnetic field at MKA. (2) We assumed a vertical dike in a homogeneous elastic half-space, and the synthetic crustal deformation and magnetic change are calculated using the analytical expressions of Okada [19] and Sasai [4], respectively, because Ueda et al. [9] estimated that the dikes have steep dip angles. (3) In the context of the topographic slope of Miyakejima, we assumed a half-space with an inclined surface whose inclination was 10° toward the west, and used only stations in the western part of Miyakejima. (4) We assumed that dikes were situated on the same plane, as estimated from the total changes in Phases 1 and 2. (5) We assume the contraction of DK4 to have the same geometry as the dike model of Ueda et al. [9]. The closing displacement of DK4 is estimated simultaneously with the parameters of the intruded dikes. (6) The assumed physical properties are listed in Table 1.

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The best-fit dike parameters are estimated by the same method with a genetic algorithm as used in Ueda et al. [9], which homes in on the fittest model by minimizing the sum of the squared residuals between the observed and calculated changes. Since each data set has different accuracy, we weighted the squared residuals by the inverse of the square of the standard errors (magnetic change, 10 nT; tilt, 5 μrad; horizontal displacement, 2 cm; vertical displacement, 6 cm), following the method of Menke [20]. The resulted best-fit dike models for Phases 1, 2 and 3 are plotted in Figs. 5-7, respectively, and their dike parameters are listed in Table 1. The length of the modeled dike in Phase 1 is considerably reduced for DK2 to about one third of that of the original. This model effectively explains the tilt change and displacements and concurs with the small geomagnetic field change at MKA in this phase (Fig. 5). We obtained a dike model similar to DK2 for Phase 2. The length of the dike is three times longer that of the dike in Phase 1. This model can explain the large observed geomagnetic field changes as well as the large tilt changes and displacements (Fig. 6). The results show that DK2 propagated laterally and upward during Phases 1 and 2. The contour lines in Figs. 5a and 6a show the predicted total intensity change in the magnetic field on the ground surface, demonstrating that the total intensity change is much greater near both edges of the dike due to stress concentration. The large magnetic field change observed at MKA is explained by its proximity to the dike edge as modeled in Phase 2. The dike model also explains why no significant total intensity change was observed by a proton-type magnetometer at ENK (Fig. 5a and 6a) [21], where the total intensity change was expected to be about 1 nT. Unlike the results for Phases 1 and 2, the best-fitting dike model for Phase 3 does not explain the tilt changes and the displacements, despite its concordance with the magnetic field change at MKA as shown in Fig. 7. The obtained solution for Phase 3 is a vertically elongated dike with a horizontal length of 0.4 km and vertical width of 9.4 km (Table 1 and Fig. 7). The geometry of this dike is considerably different from DK3 (Fig. 1a), which is located to the west, off the coast. Because of the large distance between DK3 and MKA, DK3 cannot explain the magnetic change observed at MKA during Phase 3. Moreover, the northward component of the geomagnetic field at MKA kept changing until 18:00 LT on June 27 (Fig. 2), showing different changes with time from the tilt changes at MKA (Fig. 3a and c). The discrepancy between the geomagnetic change and the

dike model based on the crustal deformation data for Phase 3 suggests the presence of a source of the magnetic change other than DK2 and DK3. In the following section, we discuss other potential causes of the geomagnetic changes at MKA. 5. Discussion A possible source that can contribute to the magnetic field change at MKA other than the dike intrusion beneath the west coast is small-scale cracks near the ground surface. On June 27, 2000, many tensile cracks and graben structures with strikes of N50°–60° W were found on the ground surface near the west coast of Miyakejima [22]. These cracks were probably induced by the strong extensional stress caused by the dike intrusions, because they are located near DK2 and DK3, and the strikes of the cracks coincide with those of the dikes. The shallow small-scale cracks do not contribute to the overall pattern of crustal deformation on Miyakejima, but probably significantly affect the local magnetic field near the cracks due to the piezomagnetic effect. Fig. 8 shows the reconstructed best-fit dike model for Phase 3, to which is added a shallow tensile crack near MKA. We obtained our dike model using the same method in the previous section, assuming the cracks to have a size of 500 × 500 m and the same strike as the dike. The obtained dike parameter is shown in Table 1. This dike model more or less explains not only the magnetic field changes at MKA but also the crustal deformation in Phase 3. Akaike's information criterion (AIC) [23] for the shallow crack model is 67.8, which is far smaller than that for the dike model (82.5) obtained in the previous section. If AIC parameter of a model is lower than that of another model, we can judge that the former model is better. Hence, we confirmed that the observed magnetic changes during the period of the DK3 intrusion can be attributed to the very shallow small cracks near DK2. The best-fit dike model is located west off the west coast, and is similar to DK3 of Ueda et al. [9]. The dike model is consistent with the lateral dike propagation towards the northwest as indicated by the earthquake distribution (e.g., [7]) and the crustal deformation (e.g., [9]). Fig. 9 schematically shows a cross section of the estimated dikes intruding beneath the west coast of Miyakejima at the beginning of the 2000 eruptive activity. The previous study based on the crustal deformation data showed that two dikes, DK2 and DK3, respectively, intruded in Phases 1 and 2, then Phase 3, beneath the west coast. Adding the magnetic

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field data to the crustal deformation data reveals that DK2 rapidly extended and its edge propagated to near MKA, suggesting that the shallow crack openings continued to form near the upper edge of DK2 even after the DK2 intrusion. The magnetic field data thus allowed elucidation of the details of the dike intrusion process. The model may seem to be complex, but the model adequately represents the complex behavior of dike including the westward propagation associated with the shallow crack opening. However, the connecting part of the dikes with the magma chamber is still not clear, because a vicinity of the magma chamber is not so magnetized due to the high temperature that the crustal stress change cannot affect the magnetic field. The magnetic field changes seen in the second event after 12:00 LT on June 27 are also probably due to the shallow cracks. The spatio-temporal distribution of earthquakes (Fig. 1) shows that earthquakes continued to occur near MKA until the end of June 27, which corresponds to the duration of the magnetic field change. The earthquake activity indicates that brittle fracture of the shallow crust continued near MKA even after the intrusion of DK2. After the data of MKA scaled out of the range on June 29, Sasai et al. [24] began an observation of magnetic field by a proton-type magnetometer at an observation site TJM near MKA on July 1, 2000. TJM recorded a gradual magnetic intensity increase of 20 nT until September, 2000, which is almost explained by the summit collapse of Miyakejima during July and August, 2000. The record does not contradict the data of MKA, which do not show a significant magnetic change after June 28. The data of TJM are other evidence that the dike intrusion and the crack opening ceased at the west coast of Miyakejima before July 1, 2000. 6. Conclusions During the dike intrusion stage of the 2000 Miyakejima eruptive activity, a major change in the geomagnetic field that exceeded 200 nT was observed by means of a three-component magnetometer at MKA station located in the southwestern part of the island. The dike model based on the crustal deformation by Ueda et al. [9] indicates that the piezomagnetic effect due to the dike intrusion is a primary cause of the observed magnetic change at MKA, and that other potential factors including thermal effects and electrokinetic effects are unlikely to be its principal cause. Our new dike model, which combines the crustal deformation data and the geomagnetic field change is applied to three intervals between 21:00 LT on June

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26 and 02:30 LT on June 27 using a genetic inversion algorithm. Owing to the high sensitivity of geomagnetic change to stress changes at the edges of the dike, the results indicate the lateral and upward propagation of the dike which is located close to MKA. The fact that geomagnetic changes at MKA lasted longer than the tilt change at the same site is explained by the shallow small cracks which were formed after the intrusion of the main dike. Acknowledgements We are grateful to the Japan Meteorological Agency for providing us with geomagnetic data from Kakioka Magnetic Observatory. We thank anonymous reviewers for their thorough reviews and helpful comments.

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