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∞
H
o
y
(
y
o
)
y
1
π
W
zy
(
y
)
H
o
y
(
y
)
+
dy
o
=−
W
zy
(
y
)
.
(5
.
80)
−
y
o
−∞
In the closing stage of the synthesis, it is a simple matter to apply (5.69) and
translate the anomalous magnetic field into the anomalous electric field.
Summing up, we arrive at a conclusion that the Wiese-Parkinson matrices given
at all points of the Earth's surface carry complete information on magnetotelluric
anomalies. Using this information with a knowledge of the normal field and the
normal impedance, we can reconstruct the magnetotelluric field and the impedances.
Thus, considering a two-dimensional model and taking into account (5.58), we have
(Vanyan et al.,1997):
y
E
o
x
−
H
o
z
(
y
o
)
dy
o
,
E
o
x
(
y
)
=
i
o
(5
.
81)
−∞
whence
y
E
o
x
(
y
)
H
o
y
(
y
)
=
1
H
o
y
(
y
)
H
o
z
(
y
o
)
dy
o
}
.
Z
(
y
)
=
1
{
Z
N
−
i
o
(5
.
82)
+
−∞
5.2.4 Synthesis of the Magnetic Field from the Generalized
Impedance Tensors
Let the normal field in the generalized impedance model contain three independent
modes: two plane-wave modes with polarization in the orthogonal directions and
the source-effect mode with vertical magnetic component. In that model we have
the generalized impedance tensor
Z
xx
Z
xy
Z
xz
[
Z
]
=
,
Z
yx
Z
yy
Z
yz
which
transforms
the
magnetic
field
H
(
H
x
,
H
y
,
H
z
)
into
the
electric
field
E
(
E
x
,
E
y
):
Z
xx
H
x
+
Z
xy
H
y
+
Z
xz
H
z
,
E
x
=
Z
yx
H
x
+
Z
yy
H
y
+
Z
yz
H
z
.
E
y
=
