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or
[
Z
S
]
G
[
T
][
S
][
A
][
Z
R
]
=
(3
.
25)
where
1
G
=
g
(1
+
s
2
)(1
+
t
2
)(1
+
a
2
)
and
1
1
1
−
t
s
+
a
0
[
T
]
[
S
]
[
A
]
=
,
=
,
=
.
t
1
s
1
01
−
a
0
1
[
Z
R
]
=
.
2
−
0
A peculiarity of decomposition (3.25) is that
G
and [
A
] cannot be determined
separately from [
Z
R
]. So, we actually deal with apparent regional impedance [
Z
R
]
absorbing
G
[
A
]:
0
˜
R
1
G
[
A
][
Z
R
]
[
Z
R
]
=
=
,
(3
.
26)
˜
R
2
−
0
where
˜
˜
1
1
2
2
=
G
(1
+
a
)
,
=
G
(1
−
a
)
.
The principal impedance values
˜
and
˜
2
preserve the true phases, but their ampli-
tudes differ from the true amplitudes by real-valued frequency-independent scalar
factors
G
(1
1
+
a
) and
G
(1
−
a
), which characterize the static effect of near-surface
local inhomogeneities.
Substituting (3.26) in (3.25), we get
[
T
][
S
][
Z
R
]
[
Z
S
]
=
.
(3
.
27)
Pass now from the regional coordinate system to a measurement coordinate sys-
tem. At arbitrary orientation of the
x
,
y
-axes
R
)]
−
1
[
T
][
S
][
Z
R
][
R
(
[
Z
S
]
=
[
R
(
R
)]
(3
.
28)
where
R
is the regional strike angle measured clockwise from the
x
-axis. This
matrix equation enables the determination of regional strike angle,
R
, along with
apparent regional impedance, [
Z
R
], and shear and twist parameters,
t
and
s
.
.
On
simple though cumbersome algebra we obtain
