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In the two-dimensional model with the strike along the
y
-axis, we have
W
zy
=0
(2D,a). Here
|
|
=
|
|
.
W
zx
(
)
W
zx
cos
(4
.
38)
Similarly, in the two-dimensional model with the strike along the
x
-axis, we have
W
zx
= 0 (2D,b). Here
| =
W
zy
sin
.
|
W
zx
(
)
(4
.
39)
Thus, the two-dimensional polar diagrams are shaped as a figure-eight oriented per-
pendicularly to the strike. The diagram of the same shape is characteristic of any
axisymmetric model. Here the figure-eight is oriented radially. It is remarkable that
the figure-eight diagram is also characteristic of any real-valued Wiese-Parkinson
matrix no matter what the structure of the medium (3D,a).
The polar diagrams in the form of an regular oval with more or less narrow waist
characterizes a three-dimensional asymmetric model (3D,b).
We have considered three graphical representations of the Wiese-Parkinson
matrix. The most efficient (most convenient, most informative) technique may be
chosen depending on the conditions of survey, target structures and used period
range.
4.4 Magnetic Tensors
Now we will consider the magnetic tensors, which define relation between the mag-
netic fields
H
at two sites: at an observation site and at a base (reference) site B. The
concepts of the magnetic tensors came from the pioneering works of Schmucker
(1970) and Berdichevsky (1968). The analysis of the magnetic tensors has been
advanced by Varentsov (2004, 2005).
4.4.1 The Horizontal Magnetic Tensor
Coming back to the model of inhomogeneous medium presented in Fig. 1.1, we
direct our attention to (1.13), and write
H
x
(
r
)
=
H
x
+
H
x
(
r
)
=
H
x
o
[1
+
J
H
2
x
(
r
)]
+
H
y
o
J
H
1
(
r
)
,
x
(4
.
40)
H
y
H
y
(
r
)
H
x
o
J
H
2
J
H
1
y
H
y
(
r
)
=
+
=
(
r
)
+
H
y
o
[1
+
(
r
)]
,
y
H
x
H
x
J
H
2
x
H
y
o
J
H
1
H
x
(
r
B
)
=
+
(
r
B
)
=
H
x
o
[1
+
(
r
B
)]
+
(
r
B
)
,
x
(4
.
41)
H
y
(
r
B
)
=
H
y
+
H
y
(
r
B
)
=
H
x
o
J
H
2
(
r
B
)
+
H
y
o
[1
+
J
H
1
y
(
r
B
)]
.
y
