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Chapter 5
The Recent Developments
5.1 Advancement of the Plane-Wave Model
We have examined the plane-wave model of the inhomogeneous Earth that offers
basic invariant magnetotelluric and magnetovariational response functions: the
impedance tensor [
Z
] and phase tensor
, the Doll and magnetic tensors [
D
] and
[
M
], the Schmucker perturbation tensor [
S
], the Wiese-Parkinson and Vozoff tipper
vectors
W
and
V
.
The condition of existence of these invariant response functions is that the normal
magnetic field allows for the plane-wave (one-dimensional) approximation. This
actually is the case if the horizontal components of the normal magnetic field change
slowly along the Earth's surface and its vertical component is close to zero.
Unfortunately, the question on physical feasibility of the plane-wave model with
its one-dimensional normal magnetic field is poorly studied theoretically. Up to now
we content ourselves with empirical estimates derived from the practical magne-
totelluric experience. There are good grounds to believe that at middle and low
latitudes (far away from the polar field sources) the magnetotelluric and magneto-
variational response functions in a broad range of frequencies (from 10
3
to 10
-4
Hz)
yield to stable determination and give geologically meaningful information on the
structure of the Earth's interior. The more complicated situation is encountered in
the polar zones with their dramatic electromagnetic disturbances caused by events
in the ionosphere and magnetosphere.
Concluding the analysis of magnetotelluric and magnetovariational response
functions, we would like to consider a generalized model taking into account a
source effect which may manifest itself in considerable departure of the normal
magnetic field from the plane wave (specifically, with noticeable vertical magnetic
component).
The model to be examined is presented in Fig. 5.1. It consists of the horizontally
homogeneous Earth of normal conductivity
N
(
z
) and a bounded three-dimensional
inhomogeneous domain V of conductivity
(
x
,
y
.
z
)
=
N
(
z
)
+
(
x
,
y
,
z
), where
,
,
,
,
(
x
y
z
) is an excess conductivity that varies arbitrarily in
x
y
z
.TheEarth
air
=
comes in contact with the nonconducting air,
0. The field is excited by
