Information Technology Reference
In-Depth Information
Here [
W
R
] and [
W
L
] are the regional and local Wiese-Parkinson matrices distorted
by local anomalies of the horizontal magnetic field:
[
W
R
]
[
h
][
Z
R
]
[
W
R
][
h
]
−
1
[
W
R
]
}
−
1
=
=
{
[
I
]
+
,
(4
.
76)
[
W
L
]
[
h
z
][
e
]
−
1
[
Z
S
]
=
.
(4
.
77)
Decomposition (4.75) has been suggested in the excellent paper by Zhang et al.
(1993). It reveals three significant properties of the Wiese-Parkinson matrix that
manifest themselves in the superimposition model:
1. The regional and local Wiese-Parkinson matrices [
W
R
] and [
W
L
]involve
the impedances [
Z
R
] and [
Z
S
] and it is just this that can explain why the tipper
reflects not only the horizontal conductivity contrasts but the vertical contrasts as
well.
2. Let the local near-surface inhomogeneities be much smaller than the induct-
ion scale length defined by the skin-depth. Then their electromagnetic excitation
can be described in the direct-current approximation, so that the distortion matri-
ces [
e
]
[
h
z
] are real-valued and frequency-independent. Hence, in the low-
frequency range, the local Wiese-Parkinson matrix assumes the form
[
h
]
,
,
[
W
L
]
[
t
][
Z
S
]
=
,
(4
.
78)
where [
t
]
[
h
z
][
e
]
−
1
[
t
zx
t
zy
]. Thus,
=
=
W
zy
=
t
zx
Z
xx
+
t
zy
Z
yx
(4
.
79)
W
zy
=
t
zx
Z
xy
+
t
zy
Z
yy
.
As is seen, the components of the local Wiese-Parkinson matrix are linear combina-
tions of the impedance tensor components. The coefficients
t
zx
,
t
zy
of these combi-
nations are real and frequency-independent, so that
W
zx
,
W
zy
reflect the frequency
W
zx
and
W
zy
mix the
dependence of
Z
xx
,
Z
yx
and
Z
xy
,
Z
yy
, while the phases of
phases of
Z
xx
,
Z
yy
.
3. Let us assume that [
Z
R
] and [
Z
S
] in (4.76) and (4.77) go down with lowering
frequency. In this case the distorting effects of local near-surface inhomogeneities
attenuate at large periods, so that [[
W
L
]
Z
yx
and
Z
xy
,
=
0 and the Wiese-Parkinson matrix
[
W
S
]
=
[
W
R
] carries undistorted information on deep regional structures.
Below we consider three methods which separate the local and regional
effect in the magnrtovariational response functions. The main difficulty on this
