Information Technology Reference
In-Depth Information
where the bars denote the complex conjugation. With account for (1.27),
Im
Z
2
+
−
=
Z
1
+
Z
3
Z
4
Z
3
Z
4
sin 2
+
cos 2
cos 2
−
sin 2
0
Im
Z
1
+
Z
2
−
=
Z
3
cos 2
Z
4
sin 2
Z
3
sin 2
Z
4
cos 2
−
−
0
.
Expanding and simplifying these equations, we obtain
A
sin 2
−
B
cos 2
+
C
=
0
,
A
sin 2
−
B
cos 2
−
C
=
0
,
(3
.
6)
where
Im
Z
xx
Z
yy
+
Z
xy
Z
yx
A
=
Im
Z
yx
Z
xx
+
Z
xy
Z
yy
B
=
Im
Z
xy
Z
yy
+
Z
xx
Z
yx
=
B
Z
xy
−
Z
yx
2
C
=
ske
w
.
=
w
=
Taking into account that
C
0 when
ske
0, we write
B
A
sin 2
−
B
cos 2
=
0
,
(3
.
7)
whence
2
arctan
Im
Z
yx
Z
xx
+
Z
xy
Z
yy
1
2
B
A
=
1
R
Im
Z
xx
Z
yy
+
Z
xy
Z
yx
=
=
arctan
(3
.
8)
+
2
,
R
where
R
is a strike angle of the regional two-dimensional structure. Applying the
Bahr method, we specify the principal directions,
R
and
+
/
2, of the regional
R
impedance [
Z
R
].
Let
ske
0 because of measurement noises and asymmetry of regional struc-
ture. In that event
w
=
B
A
sin 2
−
B
cos 2
+
C
=
0
,
A
sin 2
−
B
cos 2
−
C
=
0
.
Departure of these equations from 0 can be characterized by the quadratic deviation
C
)
2
C
)
2
(
)
=
(
A
sin 2
−
B
cos 2
+
+
(
A
sin 2
−
B
cos 2
−
.
(3
.
9)
At a minimum of
) we have the least disagreement between phases in columns
of the tensor [
Z
S
]. Solving the equation
d
(
/
=
0 with
d
2
/
2
>
(
)
d
(
)
d
0, we
min
R
find an angle
which minimizes
(
). By virtue of (3.9)
