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In-Depth Information
It would be interesting to find relations between the principal values of the
impedance tensor [
Z
] and scalar rotationally invariant impedances
Z
eff
and
Z
brd
introduced by (1.30). The effective impedance can be defined as the geometric mean
of the principal impedances:
det [
Z
]
=
Z
xx
Z
yy
−
Z
xy
Z
yx
.
Z
eff
=
1
2
=
(2
.
56)
The Berdichevsky impedance can be defined as the arithmetic mean of the prin-
cipal impedances:
Z
brd
=
1
+
2
2
Z
xy
−
Z
yx
=
.
(2
.
57)
2
The principal impedances give rise to the
principal apparent resistivity
and
prin-
cipal phase
curves:
2
2
1
=
|
1
|
2
=
|
2
|
0
0
(2
.
58)
1
=
arg
1
=
1
2
=
arg
2
=
2
.
1
,
2
-curves are oriented along the principal directions of the
impedance tensor. Unfortunately, their orientation may vary with frequency. There-
fore the principal MT-curves should be considered together with curves of
The
1
,
2
- and
1
,
2
.
In parallel with principal MT-curves we can plot the effective MT-curves
2
eff
=
|
Z
eff
|
eff
=
.
arg
Z
eff
(2
59)
0
and the Berdichevsky MT-curves
2
brd
=
|
Z
brd
|
brd
=
arg
Z
brd
.
(2
.
60)
0
2.6 The La Torraca-Madden-Korringa Method
The method offers a potent alternative to the Swift-Eggers method. It is based on
the SVD (singular value decomposition) theorem of Lanczos (1961). The funda-
mental work in this area was done by LaTorraca et al. (1986) as well as by Yee and
Paulson (1987). Applying the LaTorraca-Madden-Korringa method (
LMK method
),
we look for
EE
and
HH
orthogonal magnetotelluric eigenfields
E
τ
1
,
H
τ
1
and
E
τ
2
,
H
τ
2
, which, according to (2.20), (2.21) and (2.23), (2.24), satisfy equations
