A dike intrusion model in and around Miyakejima,

Niijima and Kozushima in 2000

Takeo Ito a,*, Shoichi Yoshioka b

aResearch Center for Earthquake Prediction, Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji,

Kyoto 611-0011, JapanbDepartment 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�109 and 5.4� 108 m3,

respectively. The maximum amount of the dike intrusion and the deflation beneath Miyakejima reached over 3.5� 108 m3

during the period from July 20 to July 28, 2000, and over 1.7� 108 m3 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/m3, the mass would be about 2.75� 109 and 1.35� 109 tons, respectively. We deduced that at least 1.4� 109 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

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

* Corresponding author. Tel.: +81-774-38-4188; fax: +81-774-

38-4190.

E-mail address: take@rcep.dpri.kyoto-u.ac.jp (T. Ito).

www.elsevier.com/locate/tecto

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 northwest-

ward 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 mag-

nitudes 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 Miyake-

jima 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) 171–187172

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 east-

ernmost 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).

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, longitude140.088j 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.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187 173

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 displace-

ments 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 fromMiyakejima 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 (Miya-

kejima4). 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) 171–187174

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–Miyake-

jiam4) increased when the earthquake swarm activity

started, but they turned the trend to the opposite di-

rection, indicating deflation of the volcano on June 28.

The vertical components of GPS data show subsidence

of the western part ofMiyakejima. 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 fromMiyakejima 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 corre-

sponds to source on plane dike and sill-like deflated

planes, is expressed by superposing basis functions.

Therefore, we can deduce the amounts of dike intru-

sions and deflation of magma by determining the

coefficients of each basis function. We used disloca-

tion 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 earth-

quakes with magnitude 5.4 and above (Maruyama,

1964). Here, we can express observation equations

with N observation data as

d ¼ Haþ e ð1Þ

efNð0; r2EÞ

where d, H, a and r2 are data, an N�M dimensional

coefficient matrix, model parameters and unknown

scale factor for the covariance matrix of E, respec-

tively.M is the number of model parameter. We assume

the errors e to be Gaussian, with zero mean and

covariance r2E. The solution a* of Eq. (1) is given by

a* ¼ ðHTE�1HÞ�1HTE�1d 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 inves-

tigated period. Moreover, the observation errors for

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� 104 m3) at Miyakejima

July 9 M6.1 earthquake in the vicinity of Kozushima

July 14–15 Eruption (2.1�106 m3) at Miyakejima

July 15 M6.3 earthquake at Niijima

July 30 M6.4 earthquake in the vicinity of Miyakejima

August 10 Eruption (2.3� 105 m3) at Miyakejima

August 18 Eruption (5.2� 106 m3) at Miyakejima

M6.0 earthquake near Kozushima

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187 175

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* ¼ ðHTE�1Hþ a2GÞ�1HTE�1d ð3Þ

where a2 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 a2 to minimize the

ABIC. Once the value of a2 minimizing the ABIC has

been found, denoting it by a2, we can obtain the best

estimate of r2 as

r2 ¼ sða*Þ=ðN þ P �M Þ ð4Þwith

sða*Þ ¼ ðd�Ha*ÞTE�1ðd�Ha*Þ þ a2a*TGa*

ð5Þwhere P and a* 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 Miya-

kejima. We attempted to determine these fault param-

eters 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 Miya-

kejima and Kozushima, and the location, width,

length, dip and strike of the deflation beneath Miya-

kejima (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) 171–187176

earthquake for each period from distribution of epi-

centers 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 calcu-

lation, 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, contra-

diction 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.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187 177

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 coef-

ficient of the quadratic curve. The larger these values

are, the better the reliabilities are. Tables 2 and 3 re-

present 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 138.5jF 10j, 88.6jF10j, 34.073jF 0.05j, 139.482jF 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 sol-

utions 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

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.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187178

the 4 subfaults of horizontal plane beneath Miyake-

jima, 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:

where ‘‘Calculate’’ and ‘‘Assume’’ are the amounts of

slips obtained by the synthetic inversion and given

slip, respectively. The subscripts represent the distri-

bution 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

the image of the synthetic inversion of the checker-

board, 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 defla-

tion beneath Miyakejima is smaller than 10 cm for all

the periods. Fig. 7 shows the result of the checker-

board test for the dike plane. The resolution is gen-

erally 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 param-

eters 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.

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)

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)

R:M:S: ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðCalculatenormal � AssumenormalÞ2 þ ðCalculatereverse � AssumereverseÞ2Þ

q

2ð6Þ

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187 179

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) 171–187180

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-

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187 181

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) 171–187182

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 move-

ments 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 intru-

sion. 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 defla-

tion, 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� 108 m3.

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� 108 m3 for the period from July 20 to

August 17. The estimated amount of the deflation

beneath Miyakejima in this study is about 1.3� 108

m3 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�109 m3 (Fig. 9). The tem-

poral 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 max-

imum 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 earth-

quakes which occurred for these periods obtained in

this study are 7.06� 1017 and 1.06� 1018 Nm,

respectively. The seismic moment of these earth-

quakes 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).

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187 183

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

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 planeTable 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

(108 m3)

Amount

of the dike

intrusion

(108 m3)

Seismic

moment

(1018 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.

Table 5

The rate of the deflation beneath Miyakejima, the dike intrusion,

and observation error

Periods Rate of

the deflation

beneath

Miyakejima

(107 m3/day)

Rate of the

dike intrusion

(107 m3/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.

Fig. 9. Temporal change of the amounts of the dike intrusion and the deflation beneath Miyakejima.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187184

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 Septem-

ber. 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 Qp

zone exists at shallow depth (0–32 km) around

Kozushima region. Moreover, Pn velocity near

Kozushima is low (Hashida, 1989). Therefore, a

magma chamber would exist beneath Kozushima. In

this study, the amount of the dike intrusion corre-

sponds 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 mid-

dle 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/m3, the mass would

be about 2.75� 109 and 1.35� 109 tons, respectively,

for all the periods. Hence, we find that the magma of

1.4� 109 tons came from a sub-crustal magma

pocket. Moreover, we estimated rate (m3/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

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.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187 185

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� 108 m3, 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 defor-

mation 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 nec-

essarily correct that the hypocentral distribution cor-

responds to the plane of the dike intrusion. In our

result, the southeastward crustal deformation at Shi-

kinejima 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 Miya-

kejima, 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�109 and 5.4� 108 m3, respectively. The spatial

distribution of the dike intrusion is concentrated in the

area between Kozushima and Miyakejima. The max-

imum amount of the dike intrusion and the deflation

beneath Miyakejima reached over 3.5� 108 m3 dur-

ing the period from July 20 to July 28, 2000 and over

1.7� 108 m3 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 Kozush-

ima 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: Bernar-

do, 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 Pn 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

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187186

swarm off the east coast of the Izu peninsula, Japan. J. Seismol.

Soc. Jpn. 34, 481–493 (in Japanese with English abstract).

Ishida, M., 1987. Recent seismic activity in and around the Izu pen-

insula. Proc. Symp. Earthquake Prediction Res., Seismological

Society of Japan, pp. 51–60 (in Japanese with English abstract).

Japan Meteorological Agency, 2000. Recent seismic activity in

Miyakejima and Nii-kozushima region, Japan?—the largest

earthquake swarm ever recorded. Earth Planets Space 52, i–viii.

Kaizu, M., Nishimura, T., Murakami, M., Ozawa, S., Sagiya, T.,

Yarai, H., Imakiire, T., 2000. Crustal deformation associated

with crustal activities in the northern Izu-islands area during

the summer, 2000. Earth Planets Space 52, ix–xviii.

Kumagai, H., Ohminato, T., Nakano, M., Ooi, M., Kubo, A., Inoue,

H., Oikawa, J., 2001. Very-long-period seismic signals and Cal-

dera formation at Miyake Island, Japan. Science 293, 687–690.

Maruyama, T., 1964. Statical elastic dislocations in an infinite and

semi-infinite medium. Bull. Earthq. Res. Inst. Univ. Tokyo 42,

289–368.

Nakamura, K., 1980. Tectonics in the Izu Peninsula and plate bend-

ing. Mon. Earth 2, 94–102 (in Japanese).

Sekiguchi, S., 1991. Tree-dimensional Q structure beneath the

Kanto-Tokai district, Japan. Tectonophysics 195, 83–104.

Seno, T., Stein, S., Gripp, A.E., 1993. A model for the motion of the

Philippine Sea plate consistent with NUVEL-1 and geological

data. J. Geophys. Res. 98, 17941–17948.

Seno, T., Sakurai, T., Stein, S., 1996. Can the Okhotsk plate be

discriminated from the North American plate? J. Geophys.

Res. 101, 11305–11315.

Shimazaki, K., 1988. Dike intrusion hypothesis for the crustal ac-

tivity in Izu peninsula. Progr. Abstr. Seismol. Soc. Jpn. 1, 330

(in Japanese).

Tada, T., Hashimoto, M., 1991. Anomalous crustal deformation in

the Northeastern Izu Peninsula and its tectonic significance—

Tension Crack Model. J. Phys. Earth 39, 197–218.

Tsukuda, E., Ito, J., Yamazaki, T., 2000. Tectonics around Izu is-

lands, history earthquake and volcano activity. Mon. Earth 22,

12, 828–846 (in Japanese).

Wessel, P., Smith, W.H.F., 1995. New version of the generic map-

ping tools released. EOS Trans. Am. Geophys. Union 76, 329.

Yabuki, T., Matsu’ura, M., 1992. Geodetic data inversion using a

Bayesian information criterion for spatial distribution of fault

slip. Geophys. J. Int. 109, 363–375.

Yamaoka, K., Kimata, F., Fujii, N., Kubo, T., Takai, K., Kato, T.,

Tabei, T., Nakao, S., 2000. Long-lasting dike intrusion causing

large crustal deformation and active earthquake swarm in Izu

volcanic islands, Japan. AGU 2000 Fall Meeting.

Zhao, D., Hasegawa, A., Horiuchi, S., 1992. Tomographic imaging

of P and S wave velocity structure beneath northeastern Japan. J.

Geophys. Res. 97, 19909–19928.

T. Ito, S. Yoshioka / Tectonophysics 359 (2002) 171–187 187