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In-Depth Information
Applying the rotation method to a real asymmetric medium, we look for direc-
tion, in which the tensor
Z
xx
(
)
Z
xy
(
)
[
Z
]
=
Z
yx
(
)
Z
yy
(
)
is best approximated by the tensor
0
0
Z
xy
(
)
1
[
Z
]
=
=
.
Z
yx
(
)0
−
2
0
The error of approximation can be evaluated using Euclidean norms of matrices
Z
] and [
Z
]:
[
Z
−
Z
=
||
Z
−
||
(
)
||
Z
||
M
(
2
2
|
Z
xx
(
)
|
+|
Z
yy
(
)
|
)
=
=
)
.
(2
2
2
2
2
+
|
Z
xx
(
)
|
+|
Z
xy
(
)
|
+|
Z
yx
(
)
|
+|
Z
yy
(
)
|
1
M
(
.
39)
So, the physical basis for this method is the approximation of a real asymmetric
medium by the two-dimensional or axially symmetric medium. Such an approxima-
tion is justified if
2).
It is not unusual to receive large values for (for instance,
is sufficiently small (say,
≤
0
.
5). In that event
we hardly can approximate the medium by two-dimensional or axisymmetric model.
So, the physical basis for the rotation method is ruined and its application may lead
to information losses.
To remove these limitations, we turn to the Swift-Eggers method or the
LaTorraca-Madden-Korringa method. These methods are modifications of the stan-
dard methods of matrix algebra.
>
0
.
2.5 The Swift-Eggers Method
This method has been proposed by Swift (1967) and advanced by Eggers (1982).
The Swift-Eggers method (
SE method
) can be considered as a modification of the
classical approach shown in Sect. 2.1. Here we look for
EH
quasi-orthogonal mag-
netotelluric eigenfields,
E
τ
1
,
H
τ
1
and
E
τ
2
,
H
τ
2
, which, according to (2.34), satisfy
equation
E
xm
H
xm
+
E
ym
H
ym
=
0
,
m
=
1
,
2
.
(2
.
40)
Assume that
