Indonesian Journal of Physics Vol 16 No. 4, October 2005

115

Study of Deep Sounding Time-Domain Electromagnetic (TDEM) Method Using Horizontal Electric Dipole to Infer Subsurface Resistivity Structure

Wahyu Srigutomo1), Tsuneomi Kagiyama2), Wataru Kanda3), and Hisashi Utada4) 1)Earth and Computational Physics Research Group, Department of Physics, Institut Teknologi Bandung,

Jl. Ganesa 10 Bandung 40132, Indonesia 2)Institute for Geothermal Sciences,

Graduate School of Science, Kyoto University, Minamiaso, Kumamoto 869-1404, Japan 3)Disaster Prevention Research Institute,

Kyoto University, Sakurajima, Kagoshima 891-1419, Japan 4)Earthquake Research Institute, University of Tokyo, Japan

e-mail: wahyu@fi.itb.ac.id

Abstract

Electromagnetic methods to infer subsurface resistivity structure particularly in volcanic and hydrothermal regions are considered highly effective to apply. Time domain electromagnetic (TDEM) method as one of them, is a robust method utilizing controlled-galvanic source which has higher ability to penetrate deeper structure. This paper tries to elaborate the theoretical formulation of TDEM with a long-grounded current wire for a layered-earth problem, the mathematical inversion algorithm to find the suitable model for interpretation as well as its sensitivity analysis, and the application to synthetic and real measured data.

Keywords: resistivity structure; time domain electromagnetic method.

1. Introduction

Investigations on complete structure of volcanic regions in upper crust play important roles in understanding various volcanic processes such as growth of volcano, history and mechanism of eruptions, formation of hydrothermal system as well as magma supply system and magma degassing process associated with it. Information on magma supply system and degassing process will also provide alternative suggestive answers to question arisen from volcano monitoring and scientific views such as presence of current subsurface activity, type of eruption, location, depth and dimension of main magma chamber, interconnection between magma chamber and deeper magma source, geometrical form of magma propagation to the surface, and possible interaction between volcanic gas and groundwater.

Commonly, volcanic regions are characterized by the presence of high porosity rocks, extremely dry or saturated with ionic hydrothermal fluids and the presence of wet, hot magma reservoir, which exhibit also temperature contrasts in the region1,2). Among other geophysical parameters, electrical resistivity (or its inverse, conductivity, = 1/) is one of the most sensitive to the above composition and temperature, particularly to the presence of fluids in the crust or upper mantle in the form of ion-bearing aqueous phase, or as partial melt distributed along the pores and cracks in the host rock

matrix3). Generally, the bulk conductivity of the host medium follows Arrhenius relation:

kTEe /0= (1)

where 0 is a constant that depends on the number and mobility of charge carrier, E is an activation energy, k is the Maxwell-Boltzman constant, and T is the temperature. At T less than several hundred degrees C, most of dry rocks are essentially resistive insulator, however small amounts of fluids in pores can significantly increase the bulk conductivity according to empirical Archies Law for brine-saturated porous materials, expressed in resistivity:

mfluidbulk a

= , (2) where bulk is the electrical resistivity of the porous medium, fluid is the electrical resistivity of the saturating fluid, a is the coefficient of saturation, m is the cementation factor, and is fractional porosity. The ratio

fluidbulk : is called the formation factor F. For the typical sandstones it was found that the coefficient a was approximately 1 and the exponent m was close to 2. Study with other rocks and sediments shows that this power law is generally valid but with varying coefficients and exponents. Table 1.1 shows brief summary of the coefficients for different materials4).

116 IJP Vol. 16 No. 4, 2005

Tabel 1.1 Fractional porosity, coefficient of saturation and cementation factor

Rock a m Weakly cemented, detrital (Tertiary) 0.25 0.45 0.88 1.37 Moderately well cemented (Mesozoic) 0.22 0.35 0.62 1.72 Well cemented (Paleozoic) 0.05 0.25 0.62 1.95 Dense, igneous, metamorphic < 0.05 1.4 1.6 High porosity volcanic 0.2 0.8 3.5 1.4

fluid is inversely proportional to the mobility of ion

contained in the fluid which is proportional to the its radius and viscosity. Increasing temperature will decrease viscosity, hence increasing in mobility which causes decreasing in the total resistivity (or increasing the conductivity). Resistivity also depends on clay content, for materials with high clay contents, when fluid and clay are mixed, concentration of ions is increased in the solution in the vicinity of the clay surface and (2) is modified into5)

+

=s

fluid

bulkF

21

(.3)

where is a length parameter, which is a weighted volume-to-surface-area ratio and s is the surface conductivity.

Geophysical methods to infer electrical resistivity structure down to about 10 km depth or more of active volcanic regions mainly can be classified into two groups: natural source electromagnetic methods such as geomagnetic depth sounding (GDS) method (cf. Gough6)) and the widely used magneto-telluric (MT) method7). Although MT method is more practical because no source instruments needed, it still suffers from several possible drawbacks such as galvanic distortion due near surface heterogeneity, its dependency on the electrodes performance and expected low quality data in areas with highly artificial noise due to power lines or trains. The other group is controlled-source EM methods, which utilize either inductive source such as current loop or galvanic source such as horizontal grounded wire. The inductive types use secondary magnetic field as a source, which decay rapidly in the earth whereas the galvanic types use injected current as a source and hence has higher ability to penetrate into deeper structure. The time domain electromagnetic (TDEM) method is more appropriate than its counterpart, namely frequency domain electromagnetic (FDEM) method. The former only measures secondary signal reflecting the earth responses by switching off the current, while the later measures total field composed by secondary field and primary field from the harmonically oscillating current. The secondary fields of the deeper part are usually several order of magnitude smaller than the primary fields causing separation between them is highly difficult and inaccurate. TDEM method, also called transient electromagnetic (TEM) is good choice for inferring resistivity structure since it is robust against noise, having

best lateral and vertical resolution with regard to highly conductive targets, less influenced by near-surface heterogeneity and less ambiguous compared to other methods.

2. Theoretical background

In this section, the term TDEM will refer to the method in which a time-dependent magnetic field is generated by passing bipolar square waves of current through a grounded wire source. The components of the magnetic fields from the wire are detected at a receiver site using a sensor.

Electromagnetic field is generated by passing a step of current along a cable lying on the surface of the earth. Both ends of the cable are grounded to the earth. The magnetic field from this current circuit can be separated into two parts, one from the current flowing through the cable and the other from the return currents flowing through the earth. The magnetic field from the current in the cable establishes a magnetic field more or less instantaneously within the insulating half-space above the earth. Energy from this magnetic field is refracted nearly vertically into the earth and is scattered back to the surface from any conductive regions within the Earth. For a laterally uniform earth which is the of the main interest in 1-D structure, only a vertical component of magnetic field from the source exists at any observation point on the earths surface. If the Earth is not laterally uniform, a horizontal component of a magnetic field can be contributed by scattering. The magnetic field from return current in the earth spreads very slowly compared to the rate at which the magnetic field above the earth establishes itself.

When current is transmitted, stationary magnetic field is generated due to Amperes law. If the current is shut off at t = 0, the eddy current is induced at the area near the dipole and the earth surface to preserve the existing magnetic fields (Faradays law). This induced current itself generates the secondary magnetic field, and this process is repeated downward and outward to cancel the changes in magnetic field. The magnitude of the induced current decreases with the increasing time. Because of this induction process, the magnetic fields also show diffusive nature. The magnetic field does not disappear soon in the Earth after shutting off the source current but it took a time to diffusive completely. Time constant of the diffusion can be estimated 20 r = , using the typical earths conductivity, the magnetic permeability of free space 0 and the distance between

IJP Vol. 16 No. 4, 2005 117

the dipole and the receiver r. If the time after shutting off the current is small enough (t

118 IJP Vol. 16 No. 4, 2005

Kaufman & Keller8) make use of the vector potential A, such that

ii = , (11) substituting (11) to (10) yields:

( ) 00 =+ ii s (12) Electric fields can be expressed by introducing the arbitrary scalar potential U as:

iii Us = 0 (13) from (6):

iiiiii

ii

Us ===

02 (14)

Defining a gauge condition as:

iii U= (15) and apply it to the last equations of (15), then: ( ) 022 =+ iik (16) where, ii sk 02 = . Without loss of generality, we can define that the y component of the vector potential is equal to zero, that is:

( )iii zx = ,0, (17) Then, we have: ( ) 022 =+ ii xk (18) ( ) 022 =+ ii zk (19) We have to solve equations (18) and (19) under the appropriate boundary conditions, which continuity of tangential components of the electric and magnetic fields at the layer interface. Making use the definition for vector potential (equations (12) and (13)), we have:

=

yx

xz

zx

yz iiii

i ,, (20)

=

zUzs

yU

xUxs iioiiioi ,, (21)

where ii U= . Continuity of tangential EM fields component is assured, if ix , ,, ii zz

x and Ui, are

continuous. For the boundary at z = zi, it requires that:

1+= ii xx (22) 1+= ii zz (23)

zAx

zAx ii

=

+1 (24)

+=

+

++ z

Azx

Axz

Azx

Ax iii

ii

i

1

1

11 (25)

Consequently, we solve equations (18) and (19) under the condition of (22) - (25) in the source free region (z > 0).

In the upper half-space (z < 0), labeled the zero-th layer, the vector potential component can be written as sum:

000 xxxsp += (26)

000 zzzsp += (27)

where 0xp and 0zp are the components of vector

potential for an electric dipole source in a uniform full-space, and 0x

s and 0zs are the vector potential terms representing the effect of the secondary fields. For convenience, we assume for the time being that the upper half-space is also the conducting full-space has only a single component, which is perpendicular to the direction of the dipole, and has cylindrical symmetry. Therefore, the vector potential has only one component, 0x

p in the present case, and we have 00 = zp . Kaufman and Keller8) give appropriate expressions for 0x

p at the point (r,0,z) for the dipole situated at (0,0,-h):

( ) drJemIdx

Redxx hzm

Rikp

00 0

00

0

44+== (28)

where r is the distance from the dipole source, J0 is the Bessel function of the first kind of order O, and;

( )( ) ,22 hzrR += 00

220

20 skm +== (29)

0xp is only the function of the coordinate r and z, so

that we can represent the vector potential for the secondary and total fields as function of yet to be determined from the boundary condition of the equation (25), the expression for 0z

s can be written as:

( ) ( ) drJeCmIdxx zms 00

0 00

0

4

= (30)

where C0 () is unknown function of () yet to be determined from the boundary condition. Taking into account that we have to calculate div A for the boundary condition of the equation (25), the expression for Asz0 can be written:

( ) ( ) drJeDxIdxz zms 0

000

0

4

= (31)

where D0 () is also to be determined. From the equation (26) and (27), the vector potential in the upper half-space can be written as:

( )[ ] ( ) drJeCemIdxx zmhzm 00

00

000

4 + += (32)

( ) ( ) drJeDxIdxz zm 1

000

0

4

= (33)

Similarly solutions of the equations (18) and (19) can be written by using the coordinate r and z only. Taking into account for similarity to the equations (32) and (33), and for the boundary conditions, we can write them for the i-th layer ( Ni 1 ) as:

IJP Vol. 16 No. 4, 2005 119

( ) ( ) ( ) ( )[ ] ( ) drJeceCIdxx iiii zzmizzmii 00

11

4

+=

(34)

( ) ( ) ( ) ( )[ ] ( ) drJedeDxIdxz iiii zzmizzmii 00

11

4

+=

(35) where Ci (), ci (), Di (), di (), are unknown to be determined, and:

iii skm 0222 +== (36) Since EM fields must vanish with z , in the lowest (N-th) layer we have:

( ) ( ) 0== NN DC (37) We solved the sequential equations (32) and (34)

under the boundary condition (22) and (24). From the straight forward algebraic calculations, we have following regressive expressions for Ci()and ci():

( )( ) iiiii

iiii

ii

i

n

i mhmmhimmm

CcCic

tanhtanh

1

1

++

++=+

= ,

( )11 Ni (38) NN m= (39)

where hi is the thickness of the i-th layer, that is:

1= iii zzh (40) At the surface of the Earth (z=0) the same boundary conditions are applied, we have:

( ) hmhm oem

YmeRC +==

10

100

0 (41) If the dipole is located on the surface ( )0h , we have:

[ ] ( ) ( ) drJemIdxdrJeRmIdxx zmzm 00 10

00 0

000

24

14

+=+=

(42) We have to solve equations (33) and (36) under the

boundary conditions (23) and (25) to seek for the expressions for Az. This time equations to be solved are a bit complicated because of the boundary conditions (25). However, by replacing Di() and di() with the following regressive expressions, they result in the similar equations which we solved to determine Ci() and ci(), that is:

( ) ( ) ( ) iiii cmFd 2+= (43)

( ) ( ) ( ) iiii cmGD 2= (44)

Then we have following expressions for Fi () and Gi (): ( )( ) iiiii

iiiii

ii

iii nhmZn

hmnZnGFGFZ

tanhtanh

1

1

+++

+=+= ,

( )11 Ni (42)

,n

nNN

mnZ == ii

imn = (46)

For the boundary condition at the surface:

( ) ( ) [ ] hmhm eRReZnZnCD 00 ||

10

1000

11

+=

++= (47)

In accord with (41) and with 0h , we have:

[ ] ( ) dJeRRxIdxAz zm

+=

00||0

01

4 (48)

With the obtained expression of vector potential, we can write expressions for the magnetic field components at the surface (z = 0). Taking into account for the symmetry, we drive them in cylindrical coordinates (r, , z):

[ ] ( ) ( ) ( )

++=

00

01|| 1

1sin4

drJRrdrJRRrIdxHr

(49)

[ ] ( ) ( ) ( )

+++=

00||

01|| 1

cos4

drJRrdrJRRrIdxH

(50)

( ) ( ) drJRmIdxH z 1

0 01sin

4

+= (51)

At this moment, we recognize that the upper half-space is an insulator, namely 00 . Then with 1|| R and

0m , we have:

( ) ( ) ( ) ( )

+=

001

00 ,, drJsQrdrJsRrHH rr

(52)

( ) ( ) drJsRrHH 10

0 ,

= (53)

( ) ( ) ( ) drJsRrHshHH zzzz 10

200 ,

== (54)

where Jk (k = 0 or 1) is the Bessel function of the first kind of order k and:

( ),sin4 200

rIdxHH rz ==

( ) cos4 20 rIdxH = (55)

( ) ,2,1+

= sR ( )

1

12, +=

sQ (56) In Cartesian, the magnetic field intensity on the

surface and in the earth can be expressed as

120 IJP Vol. 16 No. 4, 2005

( )( ) ( ) = drJeDrxyIdxHx zm 10 030 02

4

( )( ) ( ) drJeDrxyIdx zm 020 02 04

(57a)

( ) ( ) ( ) ( )[ ] ( ) += drJedeDrxyIdxHx iiii zzmizzmii 10 11324 ( ) ( ) ( ) ( )[ ] ( ) drJedeDrxyIdx iiii zzmizzmi 020 1124

+ (57b)

( )[ ] ( ) ++= + drJeCmemmIdxHy zmhzm 00 00000 004( ) ( ) +

drJeDr

xr

Idx zm1

003

20

214

( ) ( ) drJeDrxIdx zm

02

002

20

4

(58a)

( ) ( ) ( ) ( )[ ] ( ) += drJecmeCmIdxHy iiii zzmiizzmiii 00

11

4

( ) ( ) ( ) ( )[ ] ( ) ++

drJedeDrx

rIdx

iiii zzmi

zzmi 1

0

113

2214

( ) ( ) ( ) ( )[ ] ( ) drJedeDrxIdx iiii zzmizzmi 020 1122

4

+ (58b)

( )[ ] ( ) drJeCemryIdxHz zmhzm 00

00

000

4 + += (59a)

( ) ( ) ( ) ( )[ ] ( ) drJeceCryIdxHz iiii zzmizzmii 10

11

4

+= .(59b)

Similar expression for vertical and horizontal electric fields can be obtained by using (21).

To calculate the related Hankel transform integral, digital linear filtering based on the works of Chave12) and Anderson13-15) algorithm is used. To obtain the response value in the time domain, the inverse Laplace transform is applied to all components of the desired data at any given location. The field to be inversed is the total value and it has the form of

( ) ( ) dtssFi

t stc

c

+

= 21h . (60)

The numerical integration of the above equation is carried out using the Gaver-Stehfest approximate inversion formula16,17)

=

=L

lll sFKt

th1

)(2ln)( , t

lsl2ln= (61)

and

( ) ( )( )( )( )

+=

+

=

2,min

21

22

21!!2

!21

Ll

lk

LLl

llkkllkkL

kkK (62)

where L is the number of the coefficient which depends on the computer used to calculate the inverse. Since we are interested in the transient response after the current is switched-off at t = 0, the magnetic field measured as a function of time can be expressed as:

( ) ( ) 0= tthhth DC , (63) where hDC is the induced magnetic field at t or 0 due to HED source, calculated in the same manner as h(t) for the stratified Earth except that the value of the Laplace variable s is set to zero.

4. Sensitivity calculation

Actual geophysical problems mainly are inverse problems, in which one has to develop such a mathematical process by which data are used to generate a model that is consistent with the data. Inverse problem requires calculation of sensitivity, which correlates changed in a proposed model to the resulting changes in the forward modeled data. Comparative study of several methods for calculating the sensitivity of non-linear problems involving perturbation or brute force approach, sensitivity equation approach, and adjoint equation approach was discussed by McGillivray and Oldenburg18) and Furquharson and Oldenburg19). The layered conductivity structure in Figure 1 can be described in terms of linear combination e.g., 20,21):

( ) ( )zz Nj

jj=

=1

, (64)

where j is the basis function that equals to unity within the jth layer zero everywhere else. The coefficient j denotes conductivity of the jth layer. If this coefficient is changed by a small amount, the resulting value of hz value measured at the surface can be expressed by a Taylor series expansion about the original conductivity structure:

[ ] [ ] [ ] 21

=

++=+

N

jj

jOhhh

, (65)

where ( )TN ,,1 = is a vector of original conductivity structure, whereas

( )TN ,,1 = represents the changes in the coefficients, and the first order partial derivatives are the sensitivities, and represents the l2 norm. Based on the principle of linearity, the sensitivity calculation is started with the expression of A. For vertical magnetic field hz, the equation (18) can be written in a form of

HEDsourceAiudzd

x

N

jjj =

=00

202

2 (66)

which is valid for - < z < . Differentiation with respect to j and realizing that

the source is independent of j will yield

IJP Vol. 16 No. 4, 2005 121

xjj

xN

jjj Ai

Aiudzd 000

202

2

''' =

=

(67)

which is the inhomogeneous ordinary differential equation for the sensitivity.

The boundary conditions are

zA

jx ,0 . This boundary value problem

can be solved using the adjoint Greens function method22):

( ) ( ) ( ) ( )dzzzGzAzizA xx

xjj

x ';' 0

= , (68)

where the adjoint Greens function ( )'; zzG satisfies ( ) ( )'';

00

202

2

''' zzzzGiu

dzd N

jjj =

=

(69) and

( ) 0', zzG as z . (70) Two linear independent solutions of eq. (69) are

necessary to construct the adjoint Greens function. One is for boundary condition for z - and the other is for z . In the region - < z < z = 0, where the conductivity is zero, the adjoint Greens function has the form exp(u0z). In the region z < z = 0

122 IJP Vol. 16 No. 4, 2005

we follow the idea of Occams inversion24,25). The use of Occam's inversion produces a smooth model that fits a data set within certain tolerances, although a smooth model might not be the best fit to the data. In addition to surface data, borehole data inversion from large magnetic loop as inductive source was conducted by Zhang and Xiou27), whereas in this study we use long grounded wire as galvanic source, which formulation has been describe in the previous section.

The TDEM non-linear inverse problem is formulated as

min Lm and ( ) WG m - Wd (75) where L is a finite difference approximation of a first or second derivative and

1 1 1, , ,

1 2diag

N =

W L ,

a diagonal matrix consisting the uncertainty i in the i-th datum. We assume that the measurement errors in d are independent and normally distributed. The goodness of fit of model predictions to the actual values is measured by

the misfit criterion, ( )( )22

21

N d Gi ii

i

= =m

.

Given a model m, we use Taylors theorem to obtain the approximation

( )G(m + m) G(m) + J m m , (76) where J(m) is the Jacobian matrix (see the previous section of sensitivity)

( )( ) ( )

( ) ( )

1 1

1

N N

1

m mM

m mM

=

G m G m

J mG m G m

L

L L L

L

(77)

N is the number of data points (value of magnetic field for each time step) and M is the number of model parameters (resistivity value assigned to each layer).

Under this linear approximation, the damped least squares problem in equation (75) becomes

min ( ) ( )( ) ( )2 22+W G m + J m m - d L m + m (78)

where the variable is m and m is a constant. In practice, it is easier to formulate this as a problem in which the variable is actually mm + which yields min ( )( ) ( ) ( )( ) ( )2 22+WJ m m +m - Wd - WG m + WJ m m L m +m

(79) The solution is given by24,26)

( ) ( )( ) ( ) ( )12 T TT +m + m = WJ m WJ m L L WJ m Wd m , (80)

by letting ( ) ( )d m = d - G m + J(m)m and assuming that J(m) and d are constants.

This method is similar to the GaussNewton method applied to the damped least squares problem. Convergence could be improved by using line search to pick the best solution along the line from the current model to the new model given by (80). This iteration can be used to solve (75) for a number of values of , and then pick the largest value of for which the corresponding model satisfies the data constraint

( ) WG m - Wd . Alternative approach can be use to solve (74) much faster in practice. At each iteration of the algorithm, we pick the largest value of which keeps the data 2 value of the solution within its bound. If this can not be obtained, we pick the value of that minimizes the 2. The above algorithm can be summarized by beginning with a solution m0 using the formula

( ) ( ) ( ) ( )11 2 T Tk k k k k + = + Tm WJ m WJ m L L WJ m Wd m , and then picking the largest value of such that ( ) 212 +km . If the value does not exist, then pick the value of which minimizes ( )22 1km + . 6. Inversion results and discussion

The inversion scheme was tested with synthetic data. The model resistivity structure is shown in Figure 4. The total depth of the model is 10 km and is divided into 40 layers. The resistivity varies between 10 m and 500 m with rather sharp boundary in the deeper part. The scheme is also intended to invert resistivity structure from borehole data. In addition to individual inversion of surface data and borehole data, joint inversion is also performed. The surface data have a higher S/N at early time channels whereas the borehole data have higher S/N ratio at late time channels. Consequently the surface data can be inverted to better resolve shallow structures, and the borehole data can better detect deep structures. One of the purposes of this scheme is to explore the merit of joint inversion in TDEM 1-D problem. 3 % Gaussian noise is added to all magnetic field data. The longest time channel involved is 2.123 s.

Figure 3 shows the surface synthetic and calculated data for the model as an example. Acceptable agreement can be seen, however resolution decreases in the late time. Figure 4 shows the model and the corresponding inverted model from the surface data, borehole data, and lastly from the joint inversion of both the surface and borehole data. It can be seen that at borehole depth of 200 m, the discrepancy among the inverted models from individual inversions and joint is not so obvious. The discrepancy between the true model and the inverted ones is rather large in the shallow structure, this is because the synthetic data is too short in early times. It is clearly shows that the structure is better recovered by the joint inversion of surface data and borehole at 600 m. The results suggest that joint inversion

IJP Vol. 16 No. 4, 2005 123

will give better resolution to recover the resistivity structure. The rate of convergence can be seen in the Figure 5. At the early number of iteration the rms-misfit is large for joint inversion of surface data and the deeper borehole data and appears constantly beyond 14-th iteration.

The inversion scheme was applied to the actual data taken from the eastern part of Unzen volcanic area, Simabara peninsula, Kyushu, Japan in 2001 and 200211). An approximately 1.4 km long grounded-wire transmitter was deployed to generate EM signal and the earths transient responses were recorded using fluxgate magnetometer with sampling rate of 32 and 128 Hz. Robust stacking and deconvolution procedures were applied to enhance the S/N ratio as well as removing the effects of measurement system to the data. The vertical magnetic data to be inverted then were normalized by their DC values as discussed in the previous section. The longest time channel was 5 seconds for this measurement, hopefully longer enough to recover the structure of the deeper part. . Example of the observed and calculated data from four stations is shown in Figure 6. The inverted model of the complete resistivity structure in the area is shown in Figure 7. The existence of low resistive (or conductive) layer at shallow depth over dominantly high resistive layer at depth was revealed This conductive layer corresponds with the existence of water saturated layer which also characterizes the eruption mechanism and the hydrothermal system in the area28).

Figure 4. Comparison of synthetic data (dots) from model in Figure 4 and the calculated data from inversion (continuous line).

The above examples clearly show the usefulness and effectiveness of TDEM method particularly in volcanic and hydrothermal area as well as other fields such as deep groundwater study and hydrocarbon. As for Indonesia, a country whose, according to DVGHM29) website has about 129 volcanoes and 241 geothermal areas, the application of transient EM methods still few. To name one of it, only Merapi volcano that has been more ore less studied by using the long-offset transient electromagnetic (LOTEM) method from surveys in 1998, 2000 and 2001e.g.,30). By this condition the scientific

challenge is still widely open, and TDEM study, together with other methods will also enrich the knowledge toward a better understanding of volcano related system particularly in Indonesia.

1

10

100

1000

10000

1 10 100 1000 10000D epth (m )

Res

istivity

(oh

m.m

)

modelsurfacebore200joint200joint400joint600

Figure 5. The inverted model for surface data; borehole at 200 m depth; joint inversion of data from surface and 200 m, 400 m and 600 m depth respectively.

Figure 6. Rms misfit vs. iteration number.

Figure 7. Comparison of the observed and inverted data for vertical magnetic fields data recorded at four different stations.

124 IJP Vol. 16 No. 4, 2005

Figure 8. Resistivity structure revealed from TDEM data in the western part of Shimabara peninsula, Japan.

Acknowledgement

We wish to express our thanks and high appreciation to all members of Earth and Computational Physics Research Group and the Physics Department executives of ITB and also members of Earthquake Research Institute, Tokyo University for all the support and encouragement for this study.

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9. Ward, S. H., and Hohman, G. W., Electromagneic theory for geophycial applications, in Nabighian, M. N., Ed., Electromagnetic method in applied geophysics, Vol. 1 - Theory: Soc. Expl. Geophys (1988).

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