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172
J. Math. Fun
Received February 20
th
, 2012, 1
st
R 2013.
Copyright © 2013 Published by ITB J
Interpretation o Magnetotelluri
Imran Hilman Moh
1
Earth Phys Faculty of Mathemati Jalan Ga
2
Geophysics, Physics De Sumedang K
3
Applied Geology Rese Institut Teknologi BanE-m
Abstract.
In conventio prospecting, scalar CSA simplicity and low opera complex, the scalar CS The complex conditions or tensor CSAMT, to intinterpretation. A full solu and used to interpret bot constrained inversion interpretations. The resul CSAMT data in complex
Keywords:
1D Occam isolution 1D CSAMT forward
1
Introduction
Controlled-source audio-resolution electromagneti dipole as the source magnetotellurics (MT); th artificial signals. CSA Strangway [1] to solve si sources produce a stable faster time measurement t
. Sci., Vol. 45, No. 2, 2013, 172-188
vision March 4
th
, 2013, 2
nd
Revision April 11
th
, 2013, Accepted April 2
urnal Publisher,ISSN: 2337-5760, DOI: 10.5614/j.math.fund.sci.2013.45.2.
1D Vector Controlled-Source Audio- (CSAMT) Data Using Full Solution Modeling
mmad
1,2
, Wahyu Srigutomo
1
, Doddy Sutarno
1
& Prihadi Sumintadiredja
3
ics and Complex System Research Group, s and Natural Sciences, Institut Teknologi Bandung, esa No. 10, Bandung 40132, Indonesia partment, Universitas Padjadjaran, Jalan Raya Bandung 21, Jatinangor, Sumedang 45363 Indonesia rch Group, Faculty of Earth Sciences and Technology, ung, Jalan Ganesa No. 10, Bandung 40132, Indonesia il: imran.hilman@phys.unpad.ac.id al controlled-source audio-magnetotelluric (CSAMT) MT measurement is usually performed because of its ional cost. Since the structure of earth’s conductivity is MT method can lead to a less accurate interpretation. need more sophisticated measurements, such as vector rpret the data. This paper presents 1D vector CSAMT tion 1D CSAMT forward modeling has been developed vector and scalar CSAMT data. Occam’s smoothness as used to test the vector and scalar CSAMT s indicate the importance of vector CSAMT to interpret geological system.
version; controlled-source audio-magnetotellurics; f modeling; scalar CSAMT; vector CSAMT interpretation.
frequency magnetotellurics (CSAMT) is a hig sounding technique that uses a grounded elect of artificial signals. CSAMT is a variant e main difference with conventional MT is the use T was originally introduced by Goldstein a gnal stability problems in the MT method. Artific signal, allowing high-precision data acquisition a an natural sources.
6
th
,
7
ull
h- ic of of d ial d
Interpretation of 1D Vector CSAMT 173
There are many works on controlled-source electromagnetic modeling for 2D electromagnetic modeling with 3D finite source, such as Unsworth
, et al.
[2], and Mitsuhata [3]. Li and Key [4] developed a 2D marine controlled-source electromagnetic modeling method using an adaptive finite element algorithm. Streich [5] used the finite-difference frequency domain (FDFD) scheme for 3D modeling of marine controlled-source electromagnetic modeling. To avoid effects by the presence of an artificial source, CSAMT data are usually taken at a distance of 3-5 skin depth from the source using the plane wave approach [6]. Yamashita
, et al.
[7] and Bartel and Jacobson [8] proposed a source effect correction and used plane wave approach to interpret the corrected data. Near-field corrections have received serious attention since they are based on a homogeneous earth model and have validity under question in complicated environments [9]. As shown by Routh and Oldenburg, the use of MT inversion for the interpretation of CSAMT data can lead to unexpected results [9]. Hence they introduced a full solution CSAMT inversion to avoid this problem and stated the importance of full solution CSAMT to interpret CSAMT data [9].
Figure 1
Vector CSAMT field setup over a 1D layered earth.
There are several types of CSAMT data measurement, based on the number of components of measurement, which can be classified as
tensor
,
vector
, or
scalar
measurement [10]. Vector CSAMT is defined as a four- or five-component measurement, which consists of
E
x
, E
y
, H
x
, H
y
and optionally
H
z
,
excited by a single source polarization [10]. Scalar CSAMT only uses a two-component measurement (
E
x
–
H
y
measurement, or the so-called
xy
configuration; and
E
y
–
H
x
measurement, or the so-called
yx
configuration). Usually, conventional 1D CSAMT surveys use scalar CSAMT, which has low operational cost and a high production speed of data acquisition [10]. Since the earth is complex, a more sophisticated configuration could be set up in order to obtain better data, such as
174 Imran Hilman Mohammad,
et al.
a vector and tensor CSAMT configuration. In this study, vector and scalar CSAMT were used to interpret full solution CSAMT data. We have developed a forward modeling of vector and scalar 1D CSAMT based on the full CSAMT solution. The performance of vector CSAMT compared to scalar CSAMT was tested by applying the developed modeling to the smoothness-constrained Occam inversion developed by Constable
, et al.
[11].
2
The EM Field Generated by CSAMT
1D CSAMT data can be considered as electromagnetic field excitation generated by a horizontal electric dipole (HED) over a layered earth. Calculation of the electric and magnetic fields generated by HED has been widely performed and can be found in many works [12-14]. A vector CSAMT configuration usually consists of two electrodes and two magnetic antennas, as shown in Figure 1. Suppose the layered-earth model consists of
n
layers with each layer having conductivity value
σ
ι
and thickness
h
i
(Figure 1). A horizontal electric dipole located on the surface is placed parallel to the
x
axis. A receiver is located at distance r from the dipole. The direction of the receiver is calculated from the dipole center with an angle
φ
, the angle formed between the
x
-axis and the direction of the receiver. The components of the electric and magnetic fields generated by electric dipole excitation sources in cylindrical coordinates measured at the surface expressed as follows [12,13]:
( ) ( )
1100011
ˆsinˆˆ2
R
Idxmm HJmrdmrYJmrdmr mYmY
ϕ π
∞ ∞
−= +
+ +
∫ ∫
(1)
( )
101
cosˆ2
Idxm HJmrdmr mY
ϕ
ϕ π
∞
=
+
∫
(2)
( ) ( )( )
*1110001*1110
1ˆˆcos2ˆ
R
i JmrdmYmJmrdmr mY Idx E r YJmrdmr
ωµ ρ ϕ π ρ
∞ ∞∞
−
+
=
+
∫ ∫∫
(3)
( ) ( )( )
1210001101
ˆˆsin21ˆ
mYJmrdmiJmrdmr mY Idx E r i Jmrdmr mY
ϕ
ρ ωµ ϕ π ωµ
∞ ∞∞
−
+
=
+
+
∫ ∫∫
(4)
Interpretation of 1D Vector CSAMT 175
1
ˆ
Y
and
2
ˆ
Y
are the admittances of the lower half-space, which can be expressed recursively as [12,13]:
( )( )
2111112111
ˆtanhˆˆtanh
YYuhYY YYuh
+=+
(5)
( )( )
**221111*11**221111
ˆˆtanhˆˆtanh
YYuhYY YYuh
σ σ σ σ
+
=
+
(6)
( )( )
11
ˆtanhˆˆtanh
nnnnnnnnn
YYuhYY YYuh
++
+=+
(7)
( )( )
**11***11
ˆˆtanhˆˆtanh
nnnnnnnnnnnnnn
YYuhYY YYuh
σ σ σ σ
++++
+
=
+
(8) with
( ) ( )
nnnnn
nn y xn
nnn
ik k k k k u
uY Y
σ ωµ ε µ ω
λ
−=−=−+=
==
222 / 1222 / 1222*
Eqs. (1)–(4) are usually called
full solution CSAMT equations
, since they describe the field behavior in all zones of radiation (i.e. near field zone, transition field zone and far field zone). The field components in Cartesian coordinates
E
x
, E
y
, H
x
and
H
y
are calculated using the following transformations [12]:
cossinsincoscossinsincos
xr yr xr yr
EEE EEE HHH HHE
ϕ ϕ ϕ ϕ
ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ
= −
= +
= −
= +
(9)

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