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Let us compare both modificatons.
1. The SE method does not impose any limitation on the medium under con-
sideration. However, the LMK method assumes that the Earth is locally passive (it
can only absorb the electromagnetic energy) and the real Pointing vector defined by
the eigenfields everywhere points down. This limitation removing the
-ambiguity
in phases of principal values of the impedance tensor is a weak point of the LMK
method because nobody has proved that near-surface local inhomogeneities cannot
emit the energy back into the air. Note that Yee and Paulson (1987) have proposed
another modification of SVD approach with unitary matrices expressed in terms
of polarization parameters
and this SVD version has no need of some limita-
tions. But here we obtain the phases of principal impedances that are not rotationally
invariant, and practical usefulness of this version is questionable.
2. The SE method provides the determination of the principal values
,
1
,
2
in a
wide class of geoelectric media including horizontally homogeneous medium. At
the same time the LMK method in horizontally homogeneous medium delivers only
|
1
|
,
|
2
|
ς
2
are undefined).
3. The principal values,
(arg
ς
1
,
arg
1
,
2
, found by the SE and LMK methods, coincide
in the 1D-, 2D- and axisymmetric 3D-models, but differ in the asymmetric 3D-
models. The LMK method is more sensitive to the geoelectric asymmetry than the
SE method. Let
S
m
,
=
,
m
1
2 be the principal values obtained by the Swift-Eggers
method. In virtue of (2.47)
+
E
ym
2
2
|
E
xm
|
m
SE
m
=
1
,
2
=
2
,
(2
.
87)
H
ym
2
|
H
xm
|
+
where
E
τ
m
and
H
τ
m
are the quasi-orthogonal eigenfields envolved in the Swift-
Eggers procedure. Take into account that
E
τ
m
=
[
Z
]
H
τ
m
and expand the magnetic
eigenfield with respect to basis
h
1
,
h
2
formed by normalized magnetic eigenfields
envolved in the La Torraca-Madden-Korringa procedure:
H
τ
m
=
1
m
h
1
+
2
m
h
2
.
Then, according to (2.70), (2.77) and (2.80),
+
E
ym
2
E
xm
E
xm
+
E
ym
E
ym
=
2
|
E
xm
|
=
H
τ
m
[
Z
][
Z
]
H
τ
m
=
¯
2
m
h
2
[
C
H
] (
¯
1
m
h
1
+
1
m
h
1
+
2
m
h
2
)
2
m
h
2
h
2
=
¯
1
m
LM
1
h
1
+
2
m
LM
2
2
2
¯
1
m
h
1
+
2
LM
1
2
LM
2
2
2
= |
1
m
|
+ |
2
m
|
,
H
ym
2
H
xm
H
xm
+
H
ym
H
ym
2
|
H
xm
|
+
=
=
¯
2
m
h
2
(
¯
2
2
1
m
h
1
+
1
m
h
1
+
2
m
h
2
)
= |
1
m
|
+ |
2
m
|
,
(2
.
88)
