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Fig. 3.11
Illustrating the
Zhang-Roberts-Pedersen
method
local strike
regional strike
R
1
R
2
R
1
R
2
=
+
=
−
Z
1
Z
3
,
.
2
2
It follows from the symmetry of a two-dimensional structure L that in the local
coordinates the real-valued electric distortion tensor is diagonal:
e
xx
e
0
0
e
⊥
0
[
e
]
=
=
.
(3
.
37)
0
e
yy
e
⊥
,
are aligned with and against the local strike. Thus, in the local coordinate system
the superimposition impedance [
Z
S
] assumes the form
e
and
e
yy
=
Here the positive longitudinal and transverse components,
e
xx
=
Z
xx
Z
xy
Z
yx
Z
yy
e
0
0
e
⊥
Z
3
Z
1
Z
3
sin 2
+
cos 2
[
Z
S
]
=
=
Z
1
Z
3
Z
3
−
+
cos 2
−
sin 2
e
Z
3
e
(
Z
1
Z
3
sin 2
+
cos 2
)
=
,
e
⊥
(
Z
1
Z
3
e
⊥
Z
3
−
−
cos 2
)
−
sin 2
(3
.
38)
where the diagonal components,
Z
xx
and
Z
yy
, are anti-phase:
arg
Z
xx
=
arg
Z
yy
+
.
(3
.
39)
0 in the high
frequency range (we observe only the local symmetrical effect) and
ske
A distinguishing feature of [
Z
S
] is that
ske
w
=
0
,
ske
w
=
S
B
w
=
0
,
S
ske
0 in the low frequency range (we observe an asymmetrical superimposi-
tion of local and regional effects).
Now take a tensor [
Z
S
] measured on arbitrary axes
x, y
. Using the Bahr or
Groom-Bailey decomposition, we determine the regional strike. To determine the
local strike, we rotate [
Z
S
] trough a clockwise angle
w
B
=
so that components
Z
xx
(
)
and
Z
yy
(
) satisfy (3.39). This condition can be written as
