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In-Depth Information
arg
Z
yx
for
e
xy
e
yy
>
0
arg
Z
xx
=
arg
Z
yx
+
for
e
xy
e
yy
<
0
(3
.
2)
arg
Z
yy
for
e
xx
e
yx
>
0
arg
Z
xy
=
arg
Z
yy
+
e
xx
e
yx
<
0
.
for
Another peculiarity of the low-frequency truncated decomposition is that the ten-
sor [
Z
S
] has zero
ske
w
B
which can be accompanied with nonzero
ske
w
S
. In virtue
of (1.61), (3.1)
2
Im
e
xx
e
yx
Im
Z
xy
1
e
xy
e
yy
2
Z
yx
2
R
R
+
Z
yy
+
Z
xx
ske
w
B
=
Z
xy
−
Z
yx
=
e
xx
2
=
.
0
R
1
R
+
e
yy
(3
.
3)
and
=
.
Z
xx
+
Z
yy
e
xy
2
−
e
yx
1
w
=
.
ske
(3
4)
S
Z
xy
−
Z
yx
R
1
R
2
e
xx
+
e
yy
In general
e
xy
2
=
e
yx
1
and
ske
w
=
0
.
S
We can say that the departure of
ske
w
S
from 0 characterizes the local asymmetry,
while
ske
w
B
= 0 indicates the regional two-dimensionality (or axially symmetric
three-dimensionality). Condition
ske
w
B
= 0 defines the applicability of the Bahr
method.
In an arbitrary coordinate system,
Z
xx
Z
xy
Z
yx
Z
yy
0
cos
cos
e
xx
e
xy
e
yx
e
yy
1
−
sin
sin
[
Z
S
]
R
R
R
R
=
=
,
−
sin
cos
sin
R
cos
−
2
0
R
R
R
where
R
is an angle between observation and regional coordinate systems, that is,
a regional strike angle. This matrix equation contains nine real unknowns (a strike
angle
R
, four real elements of the electric distortion tensor [
e
], and two complex
principal values of the regional impedance tensor [
Z
R
]) against eight degrees of
freedom of the superimposition tensor [
Z
S
]. So, we can count only on partial sepa-
ration of local and regional effects.
Now we consider the separation technique in some detail. Let
ske
0.
To determine the strike of the two-dimensional regional structure, we rotate
the reference frame trough an angle
w
=
B
so that components
Z
xx
(
,
Z
yx
(
)
) and
Z
xy
(
Z
yy
(
) in columns of the tensor [
Z
S
(
)
,
)] are in-phase or anti-phase. These
phase conditions can be written in the form
Im
Z
xx
(
)
=
)
Z
yx
(
0
(3
.
5)
Im
Z
xy
(
)
=
)
Z
yy
(
0
