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Z
xx
+
Z
yy
max
E
min
H
max
H
min
E
w
=
−
=
−
=
Z
xy
.
.
ske
arctan Re
(1
96)
CLM
Z
yx
−
This parameter characterizes the mutual orientation of polar diagrams of the
H-
and
E-
polarized impedances. Here, the angles
mi
H
define the
directions of the maximum and minimum diameters of the polar diagrams. Note
that
ske
max
E
min
E
max
H
,
and
,
0. So, in symmetric and quasi-symmetric models
the diagrams of the
H
- and
E
-polarized impedances are elongated in perpendicular
directions.
Examples of polar diagrams of the
H-
and
E-
polarized impedances typical of 1D,
2D, and 3D-models are presented in Fig. 1.8.
The
Z
H
and
Z
E
diagrams in a 1D-model are circles of the radius
w
CLM
=
0if
ske
w
S
=
|
Z
|
, where
Z
is
the Tikhonov-Cagniard 1D-impedance.
Consider a 2D-model with the strike along the
x
-axis. According to (1.54), we
have
Z
,
Z
⊥
,
Z
xy
=
0
,
Z
xy
=
Z
yx
=−
Z
yy
=
0
,
3D
1D
2D
a
b
x
Z
E
y
x
Z
H
y
Fig. 1.8
Polar diagrams of the
E
-polarized (
Z
E
)and
H
-polarazed (
Z
H
) impedances
1D:
Z
=
4
−
2
i
04
−
2
i
ske
w
=
0
,
ske
w
=
0
S
CLM
2D: [
Z
]
=
,
−
1
+
2
i
0
ske
w
=
0
B
−
0
.
5
−
3
i
4
−
2
i
ske
w
=
0
,
ske
w
=
0
S
CLM
=
,
3D:
a)
[
Z
]
−
1
+
2
i
0
.
5
+
3
i
ske
w
=
0
.
47
B
−
0
.
2
+
0
.
2
i
ske
w
S
=
0
.
63
,
ske
w
CLM
=
20
o
ske
w
B
=
0
.
44
−
1
+
3
i
b)
[
Z
]
=
,
0
.
7
−
0
.
5
i
0
.
5
−
1
.
4
i
