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the tippers can be explained by considerable impact of oceanic currents flowing
around the Kamchatka peninsula on the south.
4.3 Polar Diagrams of the Wiese-Parkinson Matrix
This representation was originated by Berdichevsky (1968). Polar diagrams show
the dependence of the components of the Wiese-Parkinson matrix upon orienta-
tion of the measurement axes. They characterize the dimensionality of geoelectric
structures and outline their strike.
Plot a value
|
W
zx
(
)
|
on the
x
-axis rotated clockwise through an angle
.As
, the resultant point describes a closed curve called the
polar
diagram of the Wiese-Parkinson matrix.
Its equation is deduced from (4.7):
goes from 0 to 2
+
W
zy
2
sin
2
W
zy
sin
2
cos
2
|
W
zx
(
)
| =
|
W
zx
|
+
2Re
W
zx
cos
.
(4
.
33)
Find an angle
that provides extreme values of
|
W
zx
(
)
|
. From the extremum
condition
d
|
W
zx
(
)
|
=
0
d
we derive
W
zy
2Re
W
zx
tan 2
=
2
.
(4
.
34)
−
W
zy
2
|
W
zx
|
Solving this equation, we obtain two maxima and two minima of
|
W
zx
(
)
|
that alter-
nate in
/2. Obviously, the polar diagram may appear as a symmetric oval (with or
without “waist”) or as a figure-eight.
According to (4.33) and (4.34), the major and the minor semiaxes of the polar
diagram of the Wiese-Parkinson matrix are
|
(
+
W
zy
−
W
zy
2
2
)
2
W
zy
2
2
4Re
2
W
zx
W
zx
|
+
|
W
zx
|
+
a
WP
=
2
(4
.
35)
|
(
+
W
zy
−
W
zy
2
2
)
2
W
zy
2
2
4Re
2
W
zx
W
zx
|
−
|
W
zx
|
+
b
WP
=
,
2
whence
W
zy
2
a
WP
+
b
WP
= |
W
zx
|
2
2
+
=
W
.
.
(4
36)
