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where
J
H
2
z
(
J
H
1
y
J
H
2
z
J
H
2
y
J
H
1
z
+
−
)
W
zx
=
)
,
1
+
J
H
2
x
+
J
H
1
y
+
(
J
H
2
x
J
H
1
y
−
J
H
1
x
J
H
2
y
J
H
1
z
(
J
H
2
x
J
H
1
z
J
H
1
x
J
H
2
z
+
−
)
W
zy
=
)
.
1
+
J
H
2
x
+
J
H
1
y
+
(
J
H
2
x
J
H
1
y
−
J
H
1
x
J
H
2
y
This relation has been introduced in magnetotellurics by Parkinson (1959)
and Wiese (1965). It is called the
Wiese-Parkinson relation
. The concept of the
Wiese-Parkinson relation has been intensively advanced by Schmucker (1962,
1970, 1979), Jankovski (1972), and Vozoff (1972), as well as by Berdichevsky
(1968),
Lilley
(1974),
Rokityansky
(1975),
and
Gregori
and
Lanzerotti
(1980).
In matrix notation
H
z
=
[
W
]
H
τ
,
(4
.
3)
where
H
x
H
y
[
W
]
=
[
W
zx
W
zy
]
H
τ
=
.
The matrix [
W
] came into play under the name of the
Wiese-Parkinson matrix
or the
tipper matrix
as it acts on the horizontal magnetic field and tips it into the
vertical magnetic field (Vozoff, 1972).
The components
W
zx
,
W
zy
are determined from the vertical anomalous magnetic
field. It is quite evident that they reflect the horizontal asymmetry of the excess cur-
rents of a galvanic and induction nature arising in the Earth due to lateral variations
in the electric conductivity. It follows from Bio-Savart's law that the component
W
zx
defines a contribution of excess current flowing in the
y
direction, while the com-
ponent
W
zy
defines a contribution of excess current flowing in the
x
−
−
direction. Let
us agree to orient
W
zx
,
W
zy
to directions corresponding to their second subscript,
that is, perpendicularly to the contributing current.
Note that the components
W
zx
,
W
zy
reflect not only the lateral conductivity vari-
ations but the vertical conductivity distribution as well. It follows directly from (4.2)
where
W
zx
,
W
zy
depend on convolutions of excess currents with the magnetic Green
tensor which is determined by normal conductivity distribution
N
(
z
).
In the one-dimensional model the excess currents are absent. Here
W
zx
σ
=
W
zy
=
0.
Consider a two-dimensional model with strike along the
x
-axis. Here
J
H
1
x
=
J
H
2
x
=
J
H
2
y
=
J
H
2
z
=
0, hence
W
zx
=
0. Thus,
