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is the regional three-dimensional impedance tensor in the absence of sediments
inhomogeneities
.
In order to determine the distortion tensor [
e
], we examine a two-
layered model with the inhomogeneous upper layer of given conductance
S
(
x
,
y
)
and the homogeneous basement of high resisistivity
B
. The model is excited by a
plane wave. Solving the problem in the low-frequency thin-sheet approximation, we
get the model impedance
Z
xx
Z
xy
[
Z
m
]
=
Z
yx
Z
yy
that, similar to (11.13), can be presented as
[
Z
m
]
[
e
m
][
Z
N
]
=
,
(11
.
14)
where [
e
m
]is the tensor of the electric distortion:
e
xx
e
xy
[
e
m
]
=
e
yx
e
yy
and [
Z
N
] is the normal impedance defined by the normal conductance
S
N
:
0
Z
N
1
[
Z
N
]
Z
N
=
=
.
1
Z
N
−
0
S
N
+
√
−
i
o
B
In such an approximation we determine the tensor of the electric distortion as
[
e
m
]
[
Z
m
][
Z
N
]
−
1
=
.
(11
.
15)
Let the
S
−
effect weakly depend on the structure of the highly resistive litho-
sphere. Then
[
e
m
]
[
e
]
≈
,
(11
.
16)
and
[
Z
R
]
[
e
]
−
1
[
Z
]
[
e
m
]
−
1
[
Z
]
[
Z
N
][
Z
m
]
−
1
[
Z
]
=
≈
=
.
(11
.
17)
Thus, we compute the regional impedance tensor, which is supposed to be
free of near-surface distortions caused by the
S
-effect. Now we can solve the
eigenstate problem (say, by the Swift-Eggers method) and define the principal
