gravity procesing

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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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130 H. SAIBI, J. NISHIJIMA and S. EHARA

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

(m)

Bottom depth below sea

level (m)

Depth from the head to

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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Processing and Interpretation of Gravity Data for the Shimabara Peninsula Area, Southwestern Japan 131

Fig. 1A) 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.

0 1500

Elevation

A

B

OBAMA

UNZEN

SHIMABARA

1

2 3

Unzen

Graben

Fugendake


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Fig. 2A) 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.

A

B


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979400 979450 979500 979550 979600 979650

979200

979250

979300

979350

979400

979450

979500

979550

GravityofNagoyaUniv.

(mgal)

Gravity of GSJ (mgal)

Gravity Correlation

Y=1.25X-247322.46, R=0.936

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)

.

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

Fig. 4 Correlation between gravity data of GSJ

and altitude.

Fig. 5 Correlation between gravity data of

NEDO and altitude.

-200 0 200 400 600 800

-50

0

50

100

150

Normalgravity-Absolutegravity(mgal)

Altitude (m)

GSJ gravity data

H=0.2296X - 20.741, R2=0.8656

0 200 400 600 800 1000 1200

-50

0

50

100

150

200

250

300

Normalgravity-Absolutegravity(mgal)

Altitude (m)

NEDO gravity data

H=0.2184 X - 15.531, R2=0.9868


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

obsbaseB gcorrgg (1)

With

DTCBFL gggggcorr (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:

rtCrbaSrhHrE ,,,,,,, (3)

where

E: Total energy;

r= 2(f2x+f

2y)

1/2 : Radial wave number (r= 2f, where frequency f can be measured in any

direction in thex-y plane);

= 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, : 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:

qtCqaSqhHqE ,,ln,ln,lnln Constant (4)


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Fig. 6 Bouguer anomaly map of the Shimabara Peninsula area with the location of the gravity stations.

=2,400 kg/m

3

.

OBAMA

UNZEN

SHIMABARAA

B


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where

tah ,, : 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 negativeasymptotic character shows that the gravity data has two components:

1. a regional component of long wavelength from deep-seated sources,

2. 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.

-2 0 2 4 6 8 10 12

-15

-10

-5

0

5

10

15

Nyquist

Log(Power)

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:

qheqhH 2, (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 ifS=

C= 1 (a > h and t


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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 functionL(r) will be:L(r) =0 for r < r0 or r > r1;L(r) =1 for r0rr1.

where

r0 (=0.2): The low wavenumber cutoff in 1/km.

r1 (=8): The high wavenumber cutoff in 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 inthe 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:

22

y

g

x

gHGg (8)

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

Reject Pass Reject

or 1r

0.0

0.5

1.0

rL

kmWavenumber /1


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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

0.00630.00610.00590.00570.00550.00530.00520.0051

0.00490.00480.00460.00450.00440.00430.00420.00410.00400.00380.00370.00360.00340.00330.00310.00300.00280.00260.00240.00220.00170.0014

0.00100.0000

ObamaUnzen Shimabara

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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222

,

z

g

y

g

x

gyxA

g(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.

1112

10

9

23

2221

8

20

19

3

4

5

6

7

1

2

15

16

13

14

17

18

0.01670.01570.01470.01390.01330.01290.01220.01170.01120.01080.01040.01000.0098

0.00920.00890.00850.00810.00780.00740.00710.00670.00630.00600.00570.00530.00490.00450.00420.00380.00330.00300.00250.00200.00140.00090.0002-0.0008-0.0015

-0.0025-0.0043

mgal / m2

ObamaUnzen Shimabara

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)

:

22 xh

khAg

(10)

where: kis 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):

2

122

1

xh

xA

(11)

where: |A (x)| is the analytic signal and 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)

:

25

22

22

2

22

xh

hx

xd

xAd

(12)

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.

-200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

0.00

0.01

0.02

0.03

0.04

0.05

Inflection point Inflection point

AnalyticSignal(mgal/m

2)

Distance (m)

Profile 1

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




8 1471.7 North Shimabara

9 1145 Northern part of Obama

10 931.4 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







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:

gnz

gzz

y

gyy

x

gxx

000 (14)

Equation (14) can be rewritten as:

nz

gz

y

gy

x

gxgn

z

gz

y

gy

x

gx

000 (15)

where (x0, y0, z0) is the position of a source whose total gravity is detected at (x, y, z), 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 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.

0 5000 10000 15000 20000 25000 30000

0

5000

10000

15000

20000

25000

30000

35000

200 - 500

500 - 750

750 - 1000

Depth in m:

m

m

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.

Obama

Unzen

Shimabara


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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.

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.

ShimabaraUnzen

Obama

A B

Calculated

1

23

4 5

Measured

Density contrast: -300 kg/m3


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7. 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.

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