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In-Depth Information
d
(
)
=
8(
A
sin 2
−
B
cos 2
)(
A
cos 2
+
B
sin 2
)
=
0
,
d
d
2
(
)
)
2
)
2
=
16(
A
cos 2
+
B
sin 2
−
16(
A
sin 2
−
B
cos 2
,
d
2
whence
min
R
min
R
A
sin 2
−
B
cos 2
=
0
,
(3
.
10)
min
R
which agrees with (3.7). Thus, the angle
coincides with the regional strike
angle,
0 the (3.8) provides the best approx-
imation to conditions (3.6), which determines the in-phase or anti-phase state in the
columns of the superimposition tensor [
Z
S
].
Practical experience suggests that using the Bahr method we can get the reliable
estimate of the strike angle
R
, defined by (3.8). We see, that at
C
=
R
when
ske
w
B
≤
0
.
15.
R
, we evaluate phases of the principal values of [
Z
R
]. To smooth
noisy data, we use both components in columns of [
Z
S
]. In accordance with (3.1)
With known
arctan
Im
Z
xy
(
arctan
Im
Z
yy
(
R
)
R
)
1
2
R
1
R
1
=
arg
=
R
)
+
Re
Z
xy
(
Re
Z
yy
(
R
)
(3
.
11)
arctan
Im
Z
xx
(
arctan
Im
Z
yx
(
R
)
1
2
R
)
R
2
R
2
=
arg
=
R
)
+
.
Re
Z
xx
(
Re
Z
yx
(
R
)
R
1
R
2
R
1
R
2
Generally the phases
and
are taken in the fourth quadrant. Note that
+
should be close to arg det[
Z
S
].
What about the moduli of the principal values of [
Z
R
]? Let us introduce the
vector components
e
(
x
)
(
e
xx
,
e
(
y
)
(
e
xy
,
e
yy
) of the electric distortion tensor [
e
]
(Fig. 3.1). Their direction is defined by angles
e
yx
)
,
x
and
y
measured clockwise from
the
x
−
axis and
y
−
axis respectively. Thus,
e
xx
+
e
xy
+
e
(
x
)
=
e
(
y
)
=
e
(
x
)
e
(
y
)
=
e
yx
,
=
e
yy
(3
.
12)
Fig. 3.1
Plotting the electric
fields
e
(
x
)
and
e
(
y
)
