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Z
1
Z
2
= −
st
=
t
+
s
Z
3
=
(
−
st
)cos 2
R
−
(
t
+
s
)sin 2
R
(3
.
29)
Z
4
=−
(
t
+
s
) cos 2
R
−
(
−
st
)sin 2
R
,
where
Z
xy
−
Z
yx
Z
xx
+
Z
yy
Z
1
Z
2
=
=
2
2
Z
xy
+
Z
yx
Z
xx
−
Z
yy
Z
3
Z
4
=
=
2
2
and
˜
˜
˜
˜
R
1
R
2
R
1
R
2
−
+
=
=
.
2
2
This is a system of eight equations formed by real and imaginary parts of
(3.29) for seven unknowns:
t
. The system is slightly
overdetermined. It can be solved by a least squares fitting procedure with the
,
s
,
,
Re
,
Im
,
Re
,
Im
R
/2-
ambiguity in the regional strike angle
R
.
The final findings of Groom-Bailey's method are:
˜
1
,
˜
2
,
R
R
1
R
1
R
R
2
R
2
=
arg
,
=
arg
,
,
t
,
s
.
(3
.
30)
R
Similarly to the Bahr method, the Groom-Bailey method may give reasonable
results if transverse and longitudinal regional impedances,
1
and
2
, have signifi-
2
the system of equations
(3.29) falls into two linearly dependent systems and becomes undetermined.
1
cantly different phases. The point is that at arg
=
arg
3.2.3 Final Remarks on the Bahr and Groom-Bailey Methods
Intuitively it seems that the Bahr and Groom-Bailey methods yield closely related
characteristics of the local and regional structures. Let us examine the relationships
between these two methods in more detail.
To begin with, we compare the deflection angles
x
and
y
, determined by Bahr's
equations (3.16), with the twist and shear angles
t
=
arctan
t
and
s
=
arctan
s
,
determined by Groom-Bailey's equations (3.29). By virtue of (3.27)
[
T
][
S
][
Z
R
]
[
Z
S
]
=
1
1
s
0
−
˜
t
)
˜
st
)
˜
1
2
1
−
t
(
s
−
(1
−
(3
.
31)
=
=
,
˜
st
)
˜
t
)
˜
R
2
R
2
R
1
t
1
s
1
−
0
−
(1
+
(
s
+
