Processing and Interpretation of Gravity Data for the ...

Memoirs of the Faculty of Engineering, Kyushu University, Vol.66, No.2, June 2006

Processing and Interpretation of Gravity Data for the Shimabara Peninsula Area, Southwestern Japan

by

Hakim SAIBI*, Jun NISHIJIMA** and Sachio EHARA*** (Received May 8, 2006)

Abstract Shimabara Peninsula is located in southwestern Japan. There are three geothermal areas as well as a volcano on this Peninsula. In this study, we attempt to delineate the subsurface structures of the area using integrated interpretation techniques on gravity data. This study describes data processing and interpretation methods for gravity data. This processing was required in order to estimate the depths to the gravity sources, and to estimate the locations of the contacts of density contrast. The power spectral analysis was used to delineate the regional and the local components of the Bouguer anomaly. A bandpass filter was applied in order to separate the local from the regional Bouguer anomaly. Three methods were used for estimating source depths and contact locations: the horizontal gradient method, the analytic signal method, and the Euler deconvolution method. The depth estimation resulting from the respective methods were compared, and the contact locations combined into an interpretative map showing the direction for some contacts. Keywords: Shimabara Peninsula, Bouguer anomaly, Power spectrum, Euler deconvolution, Horizontal gradient, Analytic signal

1.

Introduction

The Shimabara Peninsula, southwestern Japan (Fig. 1-A), contains of three geothermal areas, from west to east: Obama, Unzen and Shimabara (Fig. 1-B). The topographic map of Shimabara Peninsula (Fig. 1-B) clearly shows that Unzen volcano has been dissected and displaced by many E-W trending faults. An active complex stratovolcano occupies the central part of Shimabara Peninsula. Many geological and geophysical surveys have been carried out in the Shimabara Peninsula to delineate the subsurface structure and its relation to the geothermal reservoirs1) and *

Graduate Student, Department of Earth Resources Engineering

**

Research Associate, Department of Earth Resources Engineering

***

Professor, Department of Earth Resources Engineering

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also a large project named USDP (Unzen Scientific Drilling Project) began in 1999 to study the mechanism of the 1990 eruption of Unzen volcano. The gravity method is one of the best geophysical techniques for delineating subsurface structures and monitoring subsidence as well as estimating mass recharge in geothermal areas during long-term exploitation related to the production/reinjection processes. The aim of this study is to understand if there is any structural/thermal relation among the three major geothermal areas (Obama, Unzen and Shimabara). The present study is based on qualitative and quantitative analysis of the gravity data to delineate both shallow and deep basement structures. For that purpose, the gravity data were first digitized at an interval of 500 m and subjected to spectral analysis2) to distinguish deep sources from shallow sources. The gravity data were transformed to the frequency domain and regional/residual separation was made using bandpass filter based on the power spectrum. In this paper, we present a new perspective on the subsurface structural setting at the Shimabara Peninsula using the existing gravity data. 2.

Geological Setting

The Shimabara Peninsula is located on western Kyushu Island, where no seismisity related to the subducting Philippine Sea Plate is detected. Active Unzen volcano is situated in the middle of the Peninsula, and is being displaced by the E-W trending Unzen graben, an active regional tectonic graben. Rocks produced by Unzen volcano have subsided more than 1000 m beneath sea level inside the graben. The tectonic framework of the Shimabara Peninsula is characterized by the regional tectonic stresses of N-S extension and E-W compression3). Figs. 2 (A) and (B) show the geologic map of Shimabara Peninsula and the tectonic model of Shimabara Peninsula, respectively. 3.

Gravity and Well Data

The gravity data set used for this study contains land gravity data acquired by several institutions (NEDO, GSJ and Nagoya University) 4), 5). We have transformed the coordinates of the gravity stations positions using software TKY2JGD6), which supports the revision of Japanese national geodetic datum from Tokyo datum (with Bessel ellipsoid) to Japanese Geodetic Datum 2000 (JGD 2000=ITRF94), with GRS80 ellipsoid7). The Shimabara Peninsula is about 816 km2 in area. The total number of gravity stations was up to 1007, and average distribution of the stations was approximately 3 to 4 per km2. The basement rocks in the study area were reached by many boreholes; five boreholes are selected: T-3, UZ-1, UZ-4, UZ-5 and UZ-7 as the control points to aid in gravity forward modeling. These depths are listed in Table 1. Table 1 Borehole depths at the Shimabara Peninsula area1). Well name

Well head altitude above sea level

Bottom depth below sea

Depth from the head to

(m)

level (m)

the basement (m)

UZ-4

117

1385

682.1

UZ-7

383

1073

483.5

UZ-5

606.4

595.7

595.4

UZ-1

297.8

659.57

908.4

T-3

53.2

351.06

248.1

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A

B

1 UNZEN

Fugendake

Unzen Graben

SHIMABARA OBAMA

2

3

0 1500 Elevation Fig. 1 A) Location map of the Shimabara Peninsula in Kyushu Island and B) the elevation map of Shimabara Peninsula. 1=Chijiwa fault; 2=Kanahama fault; 3=Futsu fault.

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A

B

Fig. 2 A) Simplified geologic map of the Shimabara Peninsula; B) Tectonic model of Shimabara Peninsula 8).

The gravity data is compiled from different institutions. Some differences may exist when surveying or measuring. A correlation plot between the gravity data of GSJ and Nagoya Univ. is shown in Fig. 3. We observe a good correlation between these gravity data sets (Fig. 3). Thus, the gravity data does not require any kind of transformation.

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979550

Gravity of Nagoya Univ. (mgal)

979500

979450

979400

979350

979300

Gravity Correlation Y=1.25X-247322.46, R=0.936

979250

979200 979400

979450

979500

979550

979600

979650

Gravity of GSJ (mgal)

Fig. 3 Correlation between the gravity data of GSJ and Nagoya Univ.

The gravity data of GSJ and NEDO are positively correlated with the station altitude due to the effect of the topographic masses in the short-wave range which can be described by a linear regression (Figs. 4 and 5). The Bouguer density is the slope deduced from the correlation between the Bouguer anomaly and topography. From Fig. 4, the Bouguer density is 2,300 kg/m3 for the GSJ gravity data and 2,200 kg/m3 from NEDO gravity data (Fig. 5). These values are not so far from the value of Bouguer density of 2,400 kg/m3 estimated by Murata (1993)9).

Normal gravity - Absolute gravity (mgal)

Normal gravity - Absolute gravity (mgal)

300

GSJ gravity data 2 H=0.2296X - 20.741, R =0.8656

150

100

50

0

-50

NEDO gravity data 2 H=0.2184 X - 15.531, R =0.9868

250

200

150

100

50

0

-50

-200

0

200

400

600

Altitude (m)

Fig. 4 Correlation between gravity data of GSJ and altitude.

800

0

200

400

600

800

1000

1200

Altitude (m)

Fig. 5 Correlation between gravity data of NEDO and altitude.

3.1 Bouguer anomaly A terrain correction was applied for the raw gravity data using the program GKTC8710) with a mesh of 250 m. A density of 2,400 kg/m3 9) was used to yield the Bouguer anomaly map shown in Fig. 6. The map is characterized by a low Bouguer gravity in the central part of this area less than 20 mGal, and a high north-to-south trending contour greater than 30 mGal which may reflect the volcano-tectonic depression zone. The Bouguer anomaly (△gB) is the difference between the

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observed value (gobs), properly corrected, and a value at a given base station (gbase), such that:

 g B  g base   corr   g obs

(1)

With

 corr    g

L

  g F   g B    g TC   g D

(2)

where the subscripts refer to the following corrections: L: latitude; F: free-air; B: Bouguer; TC: terrain correction; D: drift (including Earth tides). 4.

Spectral Analysis and Filtering of Gravity Data

4.1 Analysis of the energy spectrum The power spectral analysis yield the depths of significant density contrasts in the crust, where there is little information on the crustal structure. Spector and Bhattacharyya (1966)11) studied the energy spectrum calculated from different 3-D model configurations; Spector and Grant (1970)12) studied the statistical ensemble of 3-D maps. They concluded that the general form of the spectrum displays contributions from different factors and can be expressed as:

E r ,    H h, r  S a, b, r ,   C t , , r 

(3)

where E: Total energy; r= 2ð(f2x+f2y)1/2 : Radial wave number (r= 2ðf, where frequency f can be measured in any direction in the x-y plane); è= tan-1(fx/fy): Azimuth of the radial wave number; ‹›: Express ensemble average; h: Depth; H: Depth factor; S: Horizontal size (width) factor; C: Vertical size (thickness or depth extent) factor; a, b: Parameters related to the horizontal dimensions of the source; t, Ô: Parameters related to the vertical depth extent of the source. It is clear that only three factors (H, S, and C) are functions of the radial frequency r ; thus in the case of profile form, Equation (3) can be written as:

ln E q   ln H h , q   ln S a , q   ln C t , , q   Constant

(4)

Processing and Interpretation of Gravity Data for the Shimabara Peninsula Area, Southwestern Japan

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UNZEN

B

A

SHIMABARA

OBAMA

Fig. 6 Bouguer anomaly map of the Shimabara Peninsula area with the location of the gravity stations. ñ=2,400 kg/m3.

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where

h , a , t : The average depth, half width and thickness of a source ensemble. This equation demonstrates that contributions from the depths, widths and thickness of a source ensemble can affect the shape of the energy spectral decay curve. The effect of each factor has been discussed in the literature. The result of the spectral analyses of Bouguer anomaly of Shimabara Peninsula is shown in Fig. 7. The distinguishing feature of the logarithmic decay energy curve shows the rapid decrease of the curve at low wavenumbers, which is indicative of response to deeper sources. The gentler decline of the remainder of the curve relates to the near-surface sources. The spectrum consists essentially of two components: a very steep part at low wavenumbers (0 km-1  wavenumber  0.2 km-1) and a less steep part at high wavenumbers. This negative asymptotic character shows that the gravity data has two components: 1. 2.

a regional component of long wavelength from deep-seated sources, a local component caused by sources at shallow depth, e.g., volcanic rock.

Between 0.1 km-1 and 2 km-1, the contribution of the regional component decreases as the wavenumber value increases at the near-surface component. At wavenumber equal to 8 km-1, the curve approaches the Nyquist frequency; which describes the noise, produced by the digitization errors and finite sample interval, as fluctuations about a constant level of energy. The depth of the gravity sources can be estimated and the field components can be separated by bandpass filtering of the field. 15

10

Log(Power)

5

0

Nyquist

-5

-10

-15 -2

0

2

4

6

8

10

12

Wavenumber (1/km)

Fig. 7 Radially averaged power spectrum of the Bouguer anomalies of the Shimabara Peninsula.

4.1.1 Effect of the source depth The depth to the source ensemble H ( h , q) is the main factor which controls the shape of the energy spectral decay curve. It is expressed as:

H h , q  e 2 h q

 

(5)

Depths to deeper and shallower sources are described by the decay slopes of the curve at lower and higher frequencies, respectively. The slope of a line fitted to any linear segment of the curve

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can be used to compute either the depth to the causative source or the mean depth to a corresponding group of sources having comparable depths. It is clear from Equation (4) that if S= C= 1 (a > h and t < h ), then the equation will be reduced to:

ln E q   ln H h , q   Constant

(6)

but from Equation (5)

ln H h , q    2 h q

(7)

Hence the depth to the top of the source ( h ) can be computed from the slope as follows: h = -s / 2 if E is plotted against q or h = -s / 4ðif E is plotted against f.

h is the depth, s is the slope of the log (energy) spectrum and q is the wavenumber at frequency f (spatial frequency). where slope= ln E (q) and q= 2ðf. Two different approaches can be used to interpret the gravity depth: 1) the linear segments of the energy decay curve, with distinguishable slopes, that are attributed to contributions in the gravity data from sources at various depths; 2) the point average calculation from the slope of the energy curve, which is used in this paper. Five points moving average window “triangular” filters with weighting factors of 1/9, 2/9, 3/9, 2/9 and 1/9 was used to trace the gravity depths at the Shimabara Peninsula. Fig. 8 shows the gravity depth estimated from the power spectral analyses of Bouguer anomaly of the Shimabara Peninsula. Two different layers can be separated, the first layer is characterized by the near surface contribution, the depth may vary from 0 to 1 km; the second layer is characterized by the deep-seated contribution, the depth is from 1 to 4 km depth.

4

deep-seated contribution

Depth (km)

3

2

near-surface contribution 1

0

-1 0

2

4

6

8

10

Wavenumber (1/km)

Fig. 8 Gravity depth estimation based on five point averages of the slope of the energy spectrum.

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4.2 Bandpass filter of gravity data The Bouguer anomaly of Shimabara Peninsula was separated into residual and regional gravitational anomalies according to the results of the power spectral analyses using bandpass filter technique. All wavenumbers between certain values would be saved or passed (r0 < r < r1), while the rest would be cut as shown in Fig. 9. The filter function L(r) will be: L(r) =0 for r < r0

or

r > r1; L(r) =1 for r0 ≤ r ≤ r1.

where r0 (=0.2): The low wavenumber cutoff in 1/km. r1 (=8): The high wavenumber cutoff in 1/km.

1.0 Reject

0.5

L r 

Pass

Reject

0.0

ro

r1

Wavenumber 1 / km  Fig. 9 Schematic of the Bandpass filter.

5.

Gravity Gradient Interpretation Techniques

5.1 Horizontal gradient The horizontal gradient method has been used intensively to locate boundaries of density contrast from gravity data or pseudogravity data stated that the horizontal gradient of the gravity anomaly caused by a tabular body tends to overlie the edges of the body if the edges are vertical and well separated from each other13), 14). The greatest advantage of the horizontal gradient method is that it is least susceptible to noise in the data, because it only requires the calculations of the two first-order horizontal derivatives of the field15). The method is also robust in delineating both shallow and deep sources, in comparison with the vertical gradient method, which is useful only in identifying shallower structures. The amplitude of the horizontal gradient14) is expressed as:

2

g g     HG g   x y

2

(8)

where (∂g/∂x) and (∂g/∂y) and are the horizontal derivatives of the gravity field in the x and y

Processing and Interpretation of Gravity Data for the Shimabara Peninsula Area, Southwestern Japan

139

directions. The amplitude of the horizontal gradient for the regional data of the Shimabara Peninsula area was calculated in the frequency domain and is illustrated in Fig. 10. High gradient values were observed around the low gravity of the Shimabara Peninsula. It is observed that the pattern of the high gradient anomalies is broad, not like the sharp anomalies of ideal vertical boundaries of contrasting density. One explanation of this pattern is that the boundaries in the Shimabara area are not vertical and are relatively deep, and/or the anomalies are produced by several boundaries. Grauch and Cordell (1987)16) discussed the limitations of the horizontal gradient method for gravity data. They concluded that the horizontal gradient magnitude maxima can be offset from a position directly over the boundaries if the boundaries are not near-vertical and close to each other. Figure 10 shows a tentative qualitative interpretation of the horizontal gradient data. Generally, the area may be dissected by major faults striking in the E-W, NE-SW direction. The most interesting result is that the locations of the geothermal fields are well correlated with the horizontal gradient anomalies. This indicates that the geothermal fields in Shimabara Peninsula region are structurally controlled, especially by the deep gravity sources. This result indicates that the selection of new areas for geothermal exploration can be made based on the horizontal gradient map.

mgal / m

Obama

Unzen

Shimabara

0.0063 0.0061 0.0059 0.0057 0.0055 0.0053 0.0052 0.0051 0.0049 0.0048 0.0046 0.0045 0.0044 0.0043 0.0042 0.0041 0.0040 0.0038 0.0037 0.0036 0.0034 0.0033 0.0031 0.0030 0.0028 0.0026 0.0024 0.0022 0.0017 0.0014 0.0010 0.0000

Fig. 10 Horizontal gradient of the regional gravity data of Shimabara Peninsula. The dashed lines indicate the location of the interpreted faults.

5.2 Analytic signal The function used in the analytic method is the analytic signal amplitude of the gravity field, defined by Marson and Klingele (1993)17):

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2

2

g g g        A g x, y    x y z 

2

(9)

where |Ag (x, y)| is the amplitude of the analytic signal at (x, y), g is the observed gravity field at (x, y), and (∂g/∂x, ∂g/∂y and ∂g/∂z) are the two horizontal and vertical derivatives of the gravity field, respectively. The analytic signal amplitude peaks over isolated density contacts. As with the horizontal gradient method, the assumption of thick sources leads to minimum depth estimates. Because the analytic signal method requires the computation of the vertical derivative (using Fourier transforms18)), it is more susceptible to noise than the horizontal gradient method. The analytic signal method has been applied to the Shimabara Peninsula gravity data in order to estimate the contact locations and the minimum depths to gravity sources. The analytic signal method was calculated without Bandpass filtering. The analytic signal of the Shimabara Peninsula is shown in Fig. 11.

mgal / m2

20

21

19 1

8

22 9 23

3

2

4 11

12

10

Obama

Shimabara

Unzen 5 6 15

7

13 16 14 18

17

0.0167 0.0157 0.0147 0.0139 0.0133 0.0129 0.0122 0.0117 0.0112 0.0108 0.0104 0.0100 0.0098 0.0092 0.0089 0.0085 0.0081 0.0078 0.0074 0.0071 0.0067 0.0063 0.0060 0.0057 0.0053 0.0049 0.0045 0.0042 0.0038 0.0033 0.0030 0.0025 0.0020 0.0014 0.0009 0.0002 -0.0008 -0.0015 -0.0025 -0.0043

Fig. 11 Analytic signal of the Bouguer gravity data of Shimabara Peninsula. Lines 1-23 are the selected profiles that were used to estimate the depths.

5.2.1 Depth calculation In a manner identical to that used in the horizontal gradient method, the crests in the analytic signal amplitude are located by passing a 500 m by 500 m window over a grid we set on the analytical area and searching for maxima. When a crest is found, the local strike direction within

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the window is determined. The minimum source depth and its standard error are estimated by a least squares fit to the equation for a two-dimensional analytic signal19):

k

Ag h  

h

2

 x2

(10)



where: k is the amplitude factor related to the radius and density contrast of the source. The analytic signal anomaly over a 2-D magnetic contact located at x and at depth h is described by the expression19):

1

A x   

h

2

 x2



1

(11) 2

where: |A (x)| is the analytic signal and á is the amplitude factor. The analytic signal described by Equation (11) is a simple bell shaped function. The shape of the analytic signal is dependant only on depth. For a contact, taking the second derivative of Equation (11) with respect to x produces the following results20):

d 2 A x  d x2



2 x2  h2

h

2

x

2

5



(12) 2

After rearranging Equation (12), we obtain20): xi= 21/2 h.

(13)

where: h is the depth to the top of the contact and xi is the width of the anomaly between the inflection points (Fig. 12). To estimate the depth to the contacts from the analytic signal method, twenty three profiles were selected over the Shimabara Peninsula especially around the three main geothermal areas (Obama, Unzen and Shimabara) in which some contrasts could be found. Equation (13) was used to calculate the depth for each profile at the top of the contacts. Table 2 shows the depth values.

0.05

Profile 1

2

Analytic Signal (mgal/m )

0.04

0.03

0.02

Inflection point

Inflection point

0.01

0.00 -200

0

200

400

600

800

1000 1200 1400 1600 1800 2000

Distance (m)

Fig. 12 Amplitude of the analytic signal of profile 1 of the study area.

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Table 2 Estimated depths from the analytic signal method at the contacts of Shimabara Peninsula. Number of profile

Depth (m)

Region

1

1278.6

Shimabara region

2

1274.4

Shimabara region

3

1650

Unzen region

4

944.1

Unzen region

5

837.4

Unzen region

6

1505.7

Unzen region

7

777.9

Unzen region

8

1471.7

North Shimabara

9

1145

Northern part of Obama

10

931.4

Central part of Obama

11

1014.9

Central part of Obama

12

1570.9

Central part of Obama

13

996.5

Southern part of Obama

14

1027.6

South Shimabara

15

1321

South Unzen

16

837.4

South Unzen

17

1570.8

South Shimabara

18

1629.5

South Shimabara

19

820.4

North Shimabara

20

1015.6

North Shimabara

21

705.6

North Shimabara

22

1081.33

North Shimabara

23

594.5

Northern part of Obama

5.3 Euler deconvolution The Euler deconvolution method is applied for the residual gravity data of the Shimabara Peninsula from the range 0 to 1 km of depth. Euler deconvolution is used to estimate depth and location of the gravity source anomalies. The 3D equation of Euler deconvolution given by Reid et al. (1990)21) is:

x  x0   g   y  y 0   g  z  z 0   g x

y

z

 n   g 

(14)

Equation (14) can be rewritten as:

x

g g g g g g y z  n g  x0  y0  z0  n x y z x y z

(15)

where (x0, y0, z0) is the position of a source whose total gravity is detected at (x, y, z), â is the regional value of the gravity, and n is the structural index (SI) which can be defined as the rate of attenuation of the anomaly with distance. The SI must be chosen according to prior knowledge of the source geometry. For example, SI=2 for a sphere, SI=1 for a horizontal cylinder, SI=0 for a fault, and SI=-1 for a contact22). The horizontal (∂g/∂x, ∂g/∂y) and vertical (∂g/∂z) derivatives are

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used to compute anomalous source locations. By considering four or more neighboring observations at a time (an operating window), source location (x0, y0, z0) and â can be computed by solving a linear system of equations generated from Equation (15). Then by moving the operating window from one location to the next over the anomaly, multiple solutions for the same source are obtained. In our study, Euler deconvolution has been applied to the gravity data using a moving window of 0.5 km X 0.5 km (grid space is 50 m). We have assigned several structural indices values, and found that SI= 0 gives good clustering solutions. Reid et al. (1990; 2003)21), 23), and Reid (2003)24) presented a structural index equal to zero for the gravity field for detecting faults. Results of the Euler deconvolution for gravity data are shown on Fig. 13. The Unzen region is the most folded area in the Shimabara Peninsula. This is due to the volcanic activity of Unzen volcano. The Euler solutions (Fig. 13) indicate that the E-W and NE-SW trends characterize the shallower structure setting of Shimabara Peninsula.

m 35000

30000

25000

20000

Shimabara Unzen Obama

15000

10000

Depth in m: 200 - 500

5000

500 - 750 750 - 1000 0 0

5000

10000

15000

20000

25000

30000

Fig. 13 Euler solutions from the residual gravity data of Shimabara Peninsula. Structural Index=0; tolerance=15%; number of solutions=162,169; window size=500mX500m.

m

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6.

2-D Gravity Forward Modeling

The Bouguer anomaly is calculated using the algorithm of Talwani et al. (1959)25). Using available drilling information from T-3, UZ-1, UZ-4, UZ-5 and UZ-7, we present a conceptual structure model (Fig. 14) through Obama to Shimabara geothermal field (location of the model-line is labeled A-B in Fig. 6). In this model, two layers are used for representing the basement and its overlaying volcanic layer. The density of the Quaternary-Neogene units varies with the facies. The density of the volcanic rocks is higher than that of the pyroclastic or sedimentary rocks. A density contrast of -300 kg/m3 was used and the model was constrained with the borehole data (core density diagram26)). 2-D forward modeling of the gravity indicates the basement depth is about 700 m at the borders of the geothermal areas, and gets deeper at its trough to reach 2 km. The observed structure is presented by half grabens in Shimabara and Obama, and a typical graben at Unzen, which is bounded by normal faults to the east and west.

A

B

Obama

1

2

3

Unzen

Shimabara

4 5

Measured Calculated Density contrast: -300 kg/m3

Fig. 14 2-D conceptual structural model based on forward modeling of the gravity data at Shimabara Peninsula along the line A – B. 1=T-3; 2=UZ-4; 3=UZ-5; 4=UZ-7; 5=UZ-1.

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Conclusion

In this paper, we attempted to give new insights on the structural setting of the Shimabara Peninsula using existing gravity data. The regional and residual components of the Bouguer gravity are detected by the application of the power spectral analysis of gravity data and then the regional and residual components are separated using the effective bandpass filtering as an anomaly isolation tool. The horizontal gradient method was applied to the regional gravity component and residual component was studied using the Euler deconvolution method. The regional structural setting of the area is characterized by two major faults striking mainly in the E-W and NE-SW direction. Horizontal gradient analysis indicates that the existing geothermal areas in the Shimabara Peninsula are structurally controlled. As a result, the horizontal gradient of the regional component of gravity is useful for locating new areas for further geothermal exploration. Acknowledgements The first author would like to thank As. Prof. Y. Fujimitsu and Dr. K. Fukuoka (Faculty of Engineering, Kyushu University, Japan) for their suggestions and comments. We also thank Ms. K. Kovac (Energy and Geoscience Institute, USA) for suggesting a number of improvements in this manuscript. We would like to thank two anonymous reviewers, as well as the Editor, for their detailed and useful comments which improved the paper. Gratefully acknowledges the financial support of the Ministry of Education, Culture, Science and Technology, Government of Japan in the form of Scholarship. References 1) New Energy Development Organization (NEDO) (1988): Geothermal development research document, Unzen Western Region, New Energy Development Organization, No. 15. 2) Spector, A., and Grant, F.E. (1970): Statistical models for interpreting aeromagnetic data, Geophysics, 35, 293-302. 3) Yamashina, K., and Mitsunami, T. (1977): Stress field in the Unzen volcanic area, Kyushu, Japan. Bull. Volcanol. Soc. Japan. 22, 13-25 (in Japanese). 4) Geological Survey of Japan (ed.) (2000): Gravity CD-ROM of Japan, Digital Geoscience Map P-2, Geological Survey of Japan. 5) Shichi, R. and Yamamoto, A. (Representatives of the Gravity Research Group in Southwest Japan), (2001): Gravity Database of Southwest Japan (CD-ROM), Bull. Nagoya University Museum, Special Rept. No.9. 6) Tobita, M. (2000): “TKY2JGD”, Coordinate Transform Program for JGD2000 In: Technical Report of GSI, F-2. 7) Murakami, M. and Ogi, S. (1999): Realization of Japanese Geodetic Datum 2000 (JGD2000) In: Bulletin of GSI, 45, 1-10. 8) Nakada, S. (1995): Geologic background of Unzen Volcano. Volcano Research Center (VRC), University of Tokyo and Shimabara Earthquake and Volcano Observatory (SEVO), Kyushu University. 9) Murata, Y. (1993): Estimation of optimum average surficial density from gravity data: an objective Bayesian approach, Journal of Geophysical Research, 98, N. B7, 12,097-12,109. 10) Katsura, I., Nishida, J. and Nishimura, S. (1987): A computer program for terrain correction of gravity using KS-110-1 Topographic Data, Butsuri-Tansa, 40, No.3, 161-175. (in Japanese with

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