3-D inversion of borehole-to-surface electrical data using a back-propagation

1. 3-D inversion of borehole-to-surface electrical data using a back-propagation
neural network
Trong Long Ho ⁎
Graduate School of Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
A B S T R A C T
A R T I C L E I N F O
Article history:
Received 29 May 2008
Accepted 3 June 2008
Keywords:
Mise-à-la-masse (MAM)
3-D MAM inversion
Back-propagation neural network
Takigami geothermal field
“fluid-flow tomography” method
The “fluid-flow tomography”, an advanced technique for geoelectrical survey based on the conventional
mise-à-la-masse measurement, has been developed by Exploration Geophysics Laboratory at the Kyushu
University. This technique is proposed to monitor fluid-flow behavior during water injection and production
in a geothermal field. However data processing of this technique is very costly. In this light, this paper will
discuss the solution to cost reduction by applying a neural network in the data processing. A case study in the
Takigami geothermal field in Japan will be used to illustrate this. The achieved neural network in this case
study is three-layered and feed-forward. The most successful learning algorithm in this network is the
Resilient Propagation (RPROP). Consequently, the study advances the pragmatism of the “fluid-flow
tomography” technique which can be widely used for geothermal fields. Accuracy of the solution is then
verified by using root mean square (RMS) misfit error as an indicator.
© 2008 Published by Elsevier B.V.
1. Introduction
The mise-à-la-masse (MAM) is one of borehole-to-surface DC
resistivity methods, which has already been recognized as a tool for
mapping low resistivity areas. The areas are often encountered in the
highly fractured reservoir zones, where upstream flows of geothermal
fluid found in a hot water-dominated geothermal area (Kauahikaua
et al., 1980, Tagomori et al., 1984; Ushijima, 1989).
The Exploration Geophysics Laboratory at the Kyushu University
has developed an advanced technique which is modified from the
conventional MAM measurement, namely “fluid-flow tomography”
method. The method was firstly implemented at the Sumikawa
geothermal field, Akita, in Japan in 1999 (Ushijima et al., 1999). The
advantages of this method are that this method not only being able to
measure the charged potential but also the streaming potential; and
that the data can be continuously recorded as a function of time.
The Takigami geothermal field, situated in Kyushu Island, is one of
the most important geothermal fields in Japan, where Takigami
geothermal power station with installed capacity at 25 MWe has been
installed and operated since 1996. In order to automatically monitor
the fluid flow behavior during water injection and production
operations, the “fluid-flow tomography” method has been proposed
to apply in this geothermal field. However, the main problem with the
existing method is the enormous data processing time that leads into
the high field costs of exploration and production operations.
An artificial neural network (ANN) can be viewed as a fast
computational technique that makes use of some organizational
principles presented in biological nervous systems (Patterson, 1996).
The ANN processing encompasses a broad range of computer
algorithms that solve several types of problems, which include
procedures of classification, parameter estimation, parameter predic-
tion, pattern recognition, completion, association, filtering and
optimization (Brown and Poulton, 1996). There are numerous kinds
of neural networks, however, the main aim of any research is usually
to find out the network that performs best on presented data. In this
research, I attempt to address the application of ANN for 3-D inversion
of MAM data recorded by the “fluid-flow tomography” method, and
present a case study at the Takigami geothermal field. The aim of this
application is to reduce the data processing time and advance the
pragmatism of the “fluid-flow tomography” method.
2. The Takigami geothermal field
The Takigami geothermal field is located in the Hohi geothermal
region of the northeast of the Kyushu Island (Fig. 1). This is one of the
most active geothermal areas in Japan. The Hohi geothermal region
has an outstanding level of geothermal resources, with many
volcanoes and geothermal manifestations such as hot springs,
fumaroles and hydrothermal alteration halos at the surface. Although
the Takigami field lies within the promising Hohi geothermal region,
there are no surface manifestations in its immediate area. The nearest
hot springs are located within 2 km north and east of the area (Fig. 1).
Thus, it is regarded as a “concealed geothermal system”. Since 1979,
Journal of Applied Geophysics 68 (2009) 489–499
⁎ Fax: +81 92 642 614.
E-mail address: htlong@mine.kyushu-u.ac.jp.
0926-9851/$ – see front matter © 2008 Published by Elsevier B.V.
doi:10.1016/j.jappgeo.2008.06.002
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journal homepage: www.elsevier.com/locate/jappgeo

2. Fig. 1. Map of the northeast Kyushu, showing the Takigami geothermal field.
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3. various research studies in geology, geochemistry, hydrogeology and
geophysics have been conducted by Idemitsu Geothermal Co. Ltd.
2.1. Geological settings
The subsurface geology of the area was studied from drill cores and
cuttings by Furuya et al. (2000). The central Kyushu Island is cut by a
volcano–tectonic depression that developed within a tensile stress
field since the Neogene time, resulting in volcanism since the Pliocene
time. A schematic cross-sectional model of the geothermal system in
the southwest–northeast of the Takigami area is shown in Fig. 2. The
area is mainly covered by Quaternary volcanic rocks overlying the
Tertiary Usa Group. The oldest volcanic rock is Mizuwake andesite
(Pliocene) exposed in the northern part of the area. The formations
developed in the Takigami area consist of the thick Pliocene to
Pleistocene age dacitic to andesitic lavas and pyroclastics, which are
interfingered with lacustrine sediments.
Resistivity structures of the area were obtained by two-dimensional
(2-D)inversionof MT data (Phoenix,1987) and CSAMT data (West Japan
Engineering Consultants,1994). The resistivity model is characterized by
a low resistivity reservoir (from 10 to 12 Ωm) beneath an impermeable
and rather high resistivity layer (from 100 Ωm to 105 Ωm) (Fig. 3).
The conceptual geological model of the area is illustrated in Fig. 3.
There are twotypes of fault/fracture system,i.e. the east-to-west and the
north-to-south striking faults, which are identified mainly from studies
of lineaments using remote sensing data and correlations of subsurface
stratigraphy. The east-to-west striking faults are estimated to have
smaller vertical displacements than that of the north-to-south striking
faults. The north-to-south trending of the Noine fault zone is not
observed from the surface, but is important because it stratigraphically
Fig. 2. Geological cross-section of the Takigami geothermal system (after Takenaka and Furuya, 1991).
Fig. 3. Three-dimensional structural model of the Takigami area, constructed from 2-D inversion of MT and CSAMT data.
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4. divides the area into the eastern and the western parts. The Takigami
geothermal system is best described ashaving two parts, the eastern and
western reservoirs. The eastern part of the reservoir is shallower (700–
1100 m in depth) and has dominated fractures with a high permeability
(50–100 m-darcy). The strata temperature varies from 160 °C to 210 °C.
On the other hand, the western part of the reservoir is deeper (1500–
2000 m in depth) and has a lower permeability (5–10 m-darcy) and
higher temperature (230 °C–250 °C).
The Takigami geothermal power station has been jointly developed
by Idemitsu Geothermal Co. Ltd with Kyushu Electric Power Co. Ltd.,
and operated since November 1996 with the capacity of 25 megawatts
(MW). It is important to keep stability of the Takigami geothermal
power plant by having proper understanding of the subsurface
structure, reservoir characteristics with possibility of its extension,
the proper location of re-injection area; and reservoir monitoring is
necessary during water injection or steam production operations.
3. The “fluid-flow tomography” method
The “fluid-flow tomography” method has been developed by Geo-
physics Laboratory, Kyushu University since 1999 (Ushijima et al., 1999).
The method is used tomonitorthe transientphenomena of dynamic fluid-
flow behavior during water injection and production operations of a
geothermal field. In this method, two potentials (charged and streaming)
are measured on the ground surface as a function of time. By multiplying
with geometric factor of the MAM method, the charged potentials can be
converted to the apparent resistivity (Ushijima, 1989). The resistivity
changes express the fluid distribution; meanwhile the self potentials (SP)
due to streaming potentials show the anisotropic permeability.
The analysis of charged potential obtained from the “fluid-flow
tomography” method can also recognize the presence and boundary
of an anomalous body. If the conductivity of the anomalous body is
very high, there is a relatively little potential drop across the body and
the buried body can therefore be mapped.
Fig. 4 illustrates a field layout of the “fluid-flow tomography”
method. A charged current electrode (C1) is connected to the conductor
casing of the well. A distant electrode (C2) is fixed at distance 3 km away
from the charged well. A base potential electrode (P2) is also fixed 3 km
away from the well and on the opposite side of the C2 cable line to
minimize electromagnetic coupling effects. A potential electrode (P1) is
moved along a traverse line for the conventional MAM survey, while
multiple potential electrodes are used for the “fluid-flow tomography”
survey. An electric current of 1–5 A at a frequency of 0.1 Hz is introduced
into the earth by a transmitter used for a conventional electrical
resistivity surveys. Potential distributions on the ground surface are
continuously measured by a digital recording system controlled by a
personal computer on the survey site, and time series data are stored in
the computer's memory with a sampling rate of 1800 runs/h. By doing
so, fluid-flow fronts and the distribution of fluid flow can be
continuously imaged as a function of time on the survey site. Practical
images of fluid-flow behavior can be obtained by making contour maps
and a comparison of two data sets between an arbitrary time lag and an
initial time (a base time). These contour maps could be continuously
obtained before and during stimulations of reservoirs such as hydraulic
fracturing, production and re-injection operations.
I have carried out the “fluid-flow tomography” method in the
northern part of the Takigami area by utilizing the anchor casing of the
re-injection wells of TT-19 (Fig. 5).
The current electrode C1 was connected to the wellhead part of a
casing pipe of TT-19 (1500 m in length) and 160 of multiple potential
electrodes were radially set along the survey lines from A to P with an
interval of 150 m as shown in Fig. 5. The data processing included 3-D
inversion of MAM resistivity data and 3-D inversion of spontaneous
potential (SP) data. Because of the long period of the monitoring
operation and high sampling rate, a large quantity of measured data was
obtained. Unfortunately, the data processing of the “fluid flow tomo-
graphy” method had a drawback due to the limitations in computational
speed and high data processing costs. Therefore, here I introduced the
usingof neural network techniquetosolvethe problem. Within thescope
of this study, I will present an application of ANN for quick 3-D inversion
of MAM resistivity data in the Takigami geothermal field.
4. MAM 3-D forward problem
The 3-D forward problem of resistivity method is a common issue in
recent years. In this study, I used the algorithm proposed by Mizunaga
and Ushijima (1991), who used a singularity removal that provided
with a high accuracy in numerical modeling. A full description of the
program can be found in Mizunaga and Ushijima (1991).
The forward numerical modeling was carried out according to the
scheme illustrated in Fig. 6. The mathematical basis of this method is
as follows:
The relationship between electric current density (
Y
J), electric field
intensity (
Y
E) and isotropic conductivity (σ) is given by
Y
J = σ
Y
E ð1Þ
Y
E = − ∇ϕ; ϕ; electric potential: ð2Þ
Substitution of the Eq. (1) and Eq. (2) to the Poisson's equation
gives
j σ x; y; z
ð Þj/ x; y; z
ð Þ
½ = − Iδ x − xs
ð Þδ y − ys
ð Þδ z − zs
ð Þ ð3Þ
where, xs, ys, zs: coordinates of the source, I: current in amperes.
The volume integration of Eq. (3) was carried out, where the
electric potential φi,j,k is unknown
Z
Vi;j;k
∇ σ∇ϕ
ð Þdv = −
Z
Vi;j;k
Iδ xi − xs
ð Þδ yj − ys
δ zk − zs
ð Þdv ð4Þ
Using Green theorem, the volume integral becomes
Z
Si;j;k
∇σ
∂ϕ
∂η
ds = − I xs; ys; zs
ð Þ ð5Þ
where η is the outward normal and Si,j,k consists of six sub-surface
enclosing the elemental volume ΔVi,j,k. The interior node in the
discretization grid was derived by approximation ∂φ/∂η value by
central difference and integrating of each bounding face of each
elemental volume ΔVi,j,k. Therefore, from combination of Eqs. (4), (5)
Fig. 4. Field survey of the “fluid-flow tomography” method (Ushijima et al., 1999).
492 T.L. Ho / Journal of Applied Geophysics 68 (2009) 489–499

5. and approximation ∂φ/∂η value, the set of simultaneous equations
is given as
C
½ /
½ = S
½ ð6Þ
where, C is a function of medium geometry and physical property
distribution in the grid of LMN×LMN matrix, ϕ is the unknown
solutions of the total potential at all nodes and S is the source term of
charge injection.
5. Neural network recognition
Nowadays, ANN has become a well-known subject. In this section,
the neural network recognition will be briefly presented. More
detailed illustrations of the neural network recognition can be seen
in Hu and Hwang (2002).
In recent years, ANN has been successfully applied in solving many
geophysicalproblems(TaylorandVasco,1990;Wieneretal.,1991;Poulton
Fig. 5. Location of the “fluid-flow tomography” survey in the Takigami area.
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6. et al.,1992; Winkler,1994; Ashida,1996; Spichak and Popova, 2000; Salem
et al., 2000, El-Qady and Ushijima, 2001; Aristodemou et al., 2005).
Particularly, most of the successful studies of geophysical problems used
the multilayer perceptron (MLP) neural network model which is the most
popular among all the existing techniques. The MLP is a variant of the
original perceptron model proposed by Rosenblatt (1958) in the 1950s.
The model consists of a feed-forward, layered network of McCulloch and
Pitts' neurons (McCulloch and Pitts,1943). Each neuron in the MLP model
has a nonlinear activation function that is often continuously differenti-
able. Some of the most frequently used activation functions for MLP model
are the sigmoid and the hyperbolic tangent functions.
A key step in applying the MLP model is to choose the weighted
matrices. Assuming a layered MLP structure, the weights feeding into
each layer of neurons form a weight matrix of the layer. Values of these
weights are found using the error back-propagation method. This
leads to a nonlinear least square optimization problem to minimize
the error. There are numerous nonlinear optimization algorithms
available to solve this problem, and some of the basic algorithms are
the Steepest Descend Gradient method, the Newton's method and the
Conjugate-Gradient method.
There are two separate modes in which the gradient descent
algorithm can be implemented: the incremental mode and the batch
mode (Battiti, 1992). In the incremental mode, the gradient is
computed and the weights are updated after each input is applied
to the network. In the batch mode, all the inputs are applied to the
network before the weights are updated. The gradient descent
algorithm with momentum converges faster than gradient descent
algorithm with non-momentum. Two powerful techniques of gradient
descent algorithm with momentum in incremental and batch modes
are online back-propagation and batch back-propagation,
respectively.
Some researches proposed high-performance algorithms that can
converge from ten to one hundred times faster than conventional
descend gradient algorithm, for example the Quasi-Newton algorithm
(Battiti, 1992), the Resilient Propagation algorithm — RPROP (Ried-
miller and Braun, 1993), the Levenberg–Marquardt algorithm (Hagan
Fig. 6. (a) 3-D numerical modelingof the forward problem (b) Apparent resistivityat the grid points onthe surface (excepted wellhead point) (c) Grid discretization around current source.
Fig. 7. The generation of (a) training data set and (b) testing data set for the neural network.
494 T.L. Ho / Journal of Applied Geophysics 68 (2009) 489–499

7. and Menhaj, 1999) and the Quick Propagation algorithm (Ramasu-
bramanian and Kannan, 2004). The disadvantage of the Quasi-Newton
algorithm and the Levenberg–Marquardt algorithm is long time
training due to complex calculations in computing the approximate
of the Hessian matrix (Battiti, 1992; Hagan and Menhaj, 1999).
In this study, I have considered the mathematical basis of four
training techniques, including the online back-propagation, the batch
back-propagation, the RPROP and the Quick propagation algorithm, as
they are the most suitable techniques. The main difference among these
techniques is on the method of calculating the weights and their
updating (Werbos, 1994).
The training process starts by initializing all weights with small
non-zero values. Often they are generated randomly. A subset of
training samples (called patterns) is then presented to the network,
one at a time. A measure of the error incurred by the network is made,
and the weights are updated in such a way that the error is reduced.
Table 1
RMS errors of training process with different numbers of hidden neurons.
Hidden layer RMS error vs. training time (epochs)
1000
epochs
5000
epochs
10,000
epochs
30,000
epochs
50,000
epochs
10 neurons 3.34927 2.34985 1.95743 1.800345 1.783045
30 neurons 3.02836 1.238736 0.465372 0.228475 0.196982
45 neurons 1.59503 0.143918 0.094006 0.027905 0.0196439
70 neurons 2.03857 1.034759 0.320564 0.175873 0.146573
Fig. 8. Training RMS errors of the neural network with various algorithms: (a) The Resilient propagation algorithm — RPROP, (b) The Online backpropagation algorithm, (c) The Batch
backpropagation algorithm, (d) The Quick propagation algorithm.
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T.L. Ho / Journal of Applied Geophysics 68 (2009) 489–499

8. One pass through this cycle is called an epoch. This process is repeated
as required until the global minimum is reached.
In the online back-propagation algorithm, the weights are updated
after each pattern is presented to the network, otherwise the batch
back-propagation with weight updates occurring after each epoch
(Battiti, 1992). The weights are updated as follows;
Δwij t
ð Þ = − β
∂MSE t
ð Þ
∂wij t
ð Þ
+ αΔwij t − 1
ð Þ ð7Þ
where Δwij is the change of the synaptic connection weight from
neuron i to neuron j in the next layer, MSE is the least mean square
error, β is the learning rate, t is the time of training and α is the
momentum that pulls the network out of small local minima. And
then,
wij t + 1
ð Þ = wij t
ð Þ + Δwij t
ð Þ ð8Þ
The RPROP algorithm is an adaptive learning rate method, where
weight updates are based only on the signs of the local gradients, not
their magnitudes (Riedmiller and Braun, 1993). Each weight (wij) has
its own step size or update value (Δij), which varies with step (t)
according to the following equations;
Δij t
ð Þ =
βþ
Δij t − 1
ð Þ; if
AMSE
wij
t − 1
ð Þ
AMSE
wij
t
ð Þ N 0
β
−
Δij t − 1
ð Þ; if
AMSE
wij
t − 1
ð Þ
AMSE
wij
t
ð Þb0
Δij t − 1
ð Þ; else
8
:
ð9Þ
where, 0 b β− b 1 b β+, and the weights are updated according to:
Δwij t
ð Þ =
−Δij t
ð Þ; if
AMSE
wij
t
ð Þ N 0
+ Δij t
ð Þ; if
AMSE
wij
t
ð Þb0
0 else
8
:
ð10Þ
The Quick propagation is a training method based on the following
assumptions (Ramasubramanian and Kannan, 2004):
1. MSE(w) for each weight can be approximated by a parabola that
opens upward, and
2. The change in slope of MSE(w) for this weight is not affected by all
other weights that change at the same time.
The weights update rule is
Δwij t
ð Þ =
Q t
ð Þ
Q t − 1
ð Þ − Q t
ð Þ
Δwij t − 1
ð Þ − βQ t
ð Þ ð11Þ
where Q t
ð Þ = AMSE
Awij
t
ð Þ is the derivative of the error with respect to the
weight and Q t − 1
ð Þ − Q t
ð Þ
Δwij t − 1
ð Þ is its finite difference approximation. Together
theseapproximate, Newton's method for minimizinga one-dimensional
function f(x) is applied as Δx = −f ′ x
ð Þ
f W x
ð Þ
.
In general, too low learning rate makes the network learning very
slowly, whereas too high learning rate makes the weights and error
function diverge, so there is no learning at all. In this view, I used fixed
values of 0.1 and 0.5 for the learning rate β and the momentum α,
respectively. Although using these relatively low values may be time-
consuming, they give accurate results.
The activation function used at each hidden layer and the output
layer is logistic, and that is a sigmoid function with smooth step. This is
expressed by
Oj =
1
1 + e−u ð12Þ
where, u is the output of any neuron in the network.
The derivative of this function has a Gaussian shape, which helps to
stabilize the network and to compensate forovercorrection of theweights.
5.1. Training and testing data
To generate the training data set, I considered a geological model
which the subsurface condition is isotropic and homogeneous
(Fig. 6). As a reference from the resistivity structures of the area
which were obtained by 2-D inversion of MT data (Phoenix, 1987)
and CSAMT data (West Japan Engineering Consultants, 1994),
the resistivity values assigned to the model are 100 Ωm and
10 Ωm. The background resistivity is 100 Ωm and an anomalous
block of 10 Ωm moving to all the model mesh elements (see Figs. 6
and 7).
To simplify the problem, I placed the anomalous block in different
positions within a blocks matrix (12×12×5) which was in survey
area and upper 2500 m in depth (Figs. 6 and 7a). As a result, 720
patterns of training data set were generated.
The competence of the neural network was manifested by a
testing data set. The testing set corresponded to a model which
has been used only for testing the performance of the network,
not for the training. I chose the anomalous block in the testing
set consisting of four element blocks instead of one element block
in the training set. This block moved in the whole lowest
layer (layer 5 from the surface) of the blocks matrix (12×12×5)
(see Figs. 6 and 7b); the testing set had 36 patterns. This model
was chosen because it was close to the structural model of the
Takigami field shown in Fig. 3, where the geothermal reservoir
exists in considerable depth.
Fig. 9. RMS error vs. pattern of training data set.
496 T.L. Ho / Journal of Applied Geophysics 68 (2009) 489–499

9. 5.2. Comparison of ANN algorithms
The architecture of three layers feed-forward neural network is used
in this study. The input layer has 168 neurons representing apparent
resistivity values and the output layer has 720 neurons representing
resistivity of element blocks in the subsurface (see Fig. 6).
The number of neurons in the hidden layer affects the efficiency in
the training network. It has been proven that with a sufficient number
of hidden neurons, the capability of neural network will be achieved
(Huang and Huang, 1991). Therefore, I tried several network models
with different numbers of hidden neurons to find out the optimal one.
Root mean squares (RMS) error parameter is calculated as the square
root of squared difference between the desired output and the actual
output of a neural network. Table 1 presents the RMS errors of
network models with the hidden layer of 10; 30; 45; 70 neurons.
These numbers were selected according to heuristic method. The
neural network having 45 neurons in the hidden layer is the most
efficient one in this work and its training time was about 4 days.
The network was run and trained with many kinds of learning
algorithms to reduce the error. Four algorithms I considered are the
online back-propagation algorithm, the batch back-propagation
algorithm, the RPROP algorithm and the Quick propagation algorithm.
From the errors behavior, I found that the resilient propagation
algorithm (Fig. 8a) is the most suitable for the training data set. The
error was initially high, and then decreased as the iteration proceeded.
It reached 0.0196439 after 50,000 epochs and it attained an almost
constant value of 0.0194422 after 87,409 epochs. The RMS errors for all
720 patterns of training data and 36 patterns of testing data are shown
in Figs. 9 and 10, respectively. Otherwise, in the models of other
algorithms, the errors are almost constant at 3.35 with the online
back-propagation mode, 3.36 with the batch back-propagation mode
and not stable with big rough errors around 3.56 of the Quick
propagation mode (Fig. 8).
6. 3-D ANN inversion result
The achieved neural network is used for a quick 3-D inversion of
MAM data measured from the “fluid-flow tomography” method in
the Takigami geothermal field (so is called 3-D ANN inversion,
according to Spichak and Popova, 2000). Fig. 11 shows the contour-
map of the apparent resistivities that are interpolated by Kriging
method (see details in Cressie, 1990) from apparent resistivities data
set of the survey measurement. Hence, the apparent resistivities at
168 mesh points of the survey area which are formed according to
the numerical model of the 3-D forward problem were specified. The
set of these 168 apparent resistivities was utilized as input data of
Fig. 11. Apparent resistivities distribution.
Fig. 10. RMS error vs. pattern of testing data set.
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T.L. Ho / Journal of Applied Geophysics 68 (2009) 489–499

10. the ANN inversion. The output data as a result of the inversion is
a set of resistivity values of all mesh element blocks of the numerical
model, and the processing time is just a few seconds. Fig. 12
shows the inversion result of the MAM data set at the well TT-19
at the Takigami geothermal field with depth sliced contour maps of
0–500 m, 500–1000 m, 1000–1500 m and 1500–2500 m. The RMS
misfit that is calculated between the forward modeling result for the
constructed model and the field data is presented in Fig. 13. Although
the RMS misfit from 0.1 to 0.5 is rather high compared to other direct
inversion methods, the solution time reduction is the contribution of
this study to enhance the capacity of the “fluid-flow tomography”
method.
7. Discussions and conclusions
This paper has presented the application of a back-propagation
neural network to 3-D inversion of mise-à-la-masse data measured
from the “fluid-flow tomography” method in the Takigami geothermal
field. The study includes the architecture of the neural network, the
selection of training and testing data and the efficiency of learning
algorithms.
As the most popular and successful solution in solving geophysical
problems, a feed-forward neural network has been adopted. A number
of neurons in the hidden layer were selected according to heuristic
method. The model of 45 hidden neurons provably was the most
efficacious with the RMS error reached 0.0196439 after 50,000
epochs. Among various high-performance learning algorithms, four
algorithms were considered to test the convergence of RMS error: the
online back-propagation, the batch back-propagation, the RPROP and
the Quick propagation. As a result, the RPROP technique produced the
lowest error of 0.0194422 after 87,409 epochs and was considered as
the most suitable for training the data set.
The 3-D inversion of MAM data in the Takigami field was
implemented by using the trained neural network. I calculated the
RMS misfit error between the forward modeling results for the
constructed model and the field data with the range from 0.1 to 0.5.
Because of limitation of the training data set, the RMS misfit error
could not provide a comprehensive evaluation. However, the study
Fig. 12. a. Inversion result of 0–500 m. b. Inversion result of 500–1000 m. c. Inversion result of 1000–1500 m. d. Inversion result of 1500–2500 m.
498 T.L. Ho / Journal of Applied Geophysics 68 (2009) 489–499

11. illustrated a feasibility of neural network technique for quick 3-D
inversion of MAM data, particularly concerning the reduction of data
processing costs in the “fluid-flow tomography” method.
The result of applying 3-D ANN inversion in the Takigami
geothermal field has indicated that, in the near surface of the survey
area, a low resistivity (10–20 Ωm) was widely distributed in the east
and central of the well TT-19 at the depth 0–500 m. On the contrary,
the high resistivity zones were mostly located in the west and
southwest. The low resistivity was almost distributed in the east in the
deeper parts of the area (Fig. 12). In the survey, it was identified that a
gap that divided the area into two zones: northeastern and south-
western. The gap was considered as a fault extending from the
southeast to the northwest (Fig. 12).
Therefore, the result of 3-D MAM inversion can be used not only for
monitoring reservoirs by adopting the “fluid-flow tomography”
method, but also for controlling and developing of the Takigami
geothermal field, taking into account other geological and geophysical
data, which was confirmed by the drilling data.
Acknowledgments
This work is strongly supported by all staffs of Geophysics
Laboratory, Kyushu University during performance of the “fluid-flow
tomography” method. The author expresses his sincere appreciation
to the Idemitsu Oita Geothermal Co., Ltd for the permission to
publishing this paper. I am thankful to Ass. Prof. Hideki Mizunaga and
Dr. Yutaka Sasaki of the Earth Resources Engineering Department,
Kyushu University for their valuable advises. Many thanks to Dr.
Viacheslav Spichak of Geoelectromagnetic Research Institute RAS,
Russia and to anonymous reviewer for their constructive criticisms,
which helps to improve the manuscript to its present form. Moreover,
the author would like to gratefully acknowledge the support of Japan
International Cooperation Agency (JICA) by awarding the author a
doctoral scholarship.
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Fig. 13. The RMS misfit between the forward modeling result and the field data.
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