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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 ]:
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