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Chapter 6
Two Classic Models of the Distortion Theory
In the subsequent chapters we will consider how the near-surface and deep inho-
mogeneities distort the magnetotelluric and magnetovariational response functions
observed on the Earth's surface. We are going to examine a number of models with a
view to find the characteristic evidences of two-dimensional and three-dimensional
galvanic and induction distortions and look for ways of their recognition. All mod-
els to be examined are excited by a plane monochromatic wave vertically incident
on the Earth's surface. We have to analise the informativeness of MT- and MV-
soundings and provide the background necessary for qualitative interpretation of
experimental data and identification of objective geoelectric structures.
As a preliminary we would like to review two, now classic, models put forward
by Obukhov (1962), d'Erceville and Kunetz (1962) and Rankin (1962) at dawn of
magnetotellurics. A special feature of these two-dimensional models is that they
offer analytical solutions for the TM-mode.
6.1 The Vertical-Interface Model
We start with a vertical-interface model shown in Fig. 6.1. Meaningful analysis of
this model can be found in works by Weaver (1963, 1994), Berdichevsky (1968),
Jones and Price (1970) and Fischer et al. (1992). The model consists of the noncon-
ductive air and the conductive Earth that includes two quarter-spaces of different
resistivities,
, divided by the infinite vertical interface
y
≤∞
.
The problem for the TM-mode has been solved independently by Obukhov (1962)
and d'Erceville and Kunetz (1962). Following these pioneering works, we write
and
=
0, 0
≤
z
⎧
⎨
H
N
H
A
x
(
z
)
+
x
(
y
,
z
)
y
≤
0
,
z
≥
0
H
x
(
y
,
z
)
=
(6
.
1)
⎩
H
x
(
z
)
H
x
(
y
+
,
z
)
y
≥
0
,
z
≥
0
,
H
x
are the normal and anomalous magnetic fields within
the left and right quarter-spaces.
H
x
,
H
x
H
x
,
where
and
