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from which
Z
yy
Z
xx
e
⊥
≈
(3
.
43)
and
Z
xy
−
Z
xy
−
Z
yx
e
⊥
Z
xx
Z
yy
1
2
1
2
Z
1
Z
yx
≈
≈
Z
xy
+
Z
xy
+
Z
yx
e
⊥
Z
xx
Z
yy
1
1
Z
3
Z
yx
≈
≈
2 cos 2(
L
−
R
)
2 cos 2(
L
−
R
)
(3
.
44)
or
,
1
+
Z
xy
−
1
−
Z
yx
Z
xx
Z
yy
1
2
1
cos 2(
1
2
1
cos 2(
R
1
=
Z
1
+
Z
3
≈
−
R
)
−
R
)
L
L
,
1
−
Z
xy
−
1
+
Z
yx
Z
xx
Z
yy
1
2
1
cos 2(
L
−
R
)
1
2
1
cos 2(
L
−
R
)
R
2
=
Z
1
−
Z
3
≈
(3
.
45)
where
Z
xx
,
Z
yy
are components of the superimposition tensor [
Z
S
]
expressed in local coordinates, and
Z
xy
,
Z
yx
,
1
,
2
are principal values of the regional
impedance.
Note that the findings of the Zhang-Roberts-Pedersen procedure are stable if the
phase difference in the longitudinal and transverse regional impedances is rather
large (say, 15-20
◦
). In this point the Zhang-Roberts-Pedersen method is similar to
the Bahr and Groom-Bailey methods.
3.4 The Chave-Smith Method
Chave and Smith (1994) considered not only the local electric distortions but the
magnetic distortions as well and suggested a method based on the full local-regional
decomposition (1.74). On this way we significantly extend the frequency range
favorable for the local-regional decomposition. Recall, for instance, that in the
case of a three-layered K-type medium we apply the truncated Bahr-Groom-Bailey
decomposition beginning with
T
which far exceeds a period
T
max
for the maximum
of the
A
-curve. With Chave-Smith's technique we can come down to
T
close to
T
max
.
Return to the local-regional decomposition (3.25) underlying the Groom-Bailey
method and rewrite it together with the magnetic distortion tensor [
h
]: