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) Z yy (
) Z yy (
Z xx (
Z xx (
Im
{
)
}=
0
,
Re
{
)
}
< 0
(3
.
40)
or, with account for (1.27),
)( Z 2
Z 3 sin 2
Z 4 cos 2
{
( Z 2 +
Z 3 sin 2
+
Z 4 cos 2
}
Im
)
2Im( Z 2 Z 3 sin 2
Z 2 Z 4 cos 2
=
+
=
,
)
0
)( Z 2
Z 3 sin 2
Z 4 cos 2
( Z 2 +
Z 3 sin 2
Z 4 cos 2
Re
{
+
)
}
< 0
,
where
Z xx +
Z yy
Z xy +
Z yx
Z xx
Z yy
Z 2
Z 3
Z 4
=
,
=
,
=
.
2
2
2
Hence
2 arctan Im Z 2 Z 4
1
=
Im Z 2 Z 3
(3
.
41)
2Im Z yy Z xx
Im( Z xy +
1
2 arctan
L
+ 2
=
Z yy ) =
Z yx )( Z xx +
L
with
>
( Z xy +
Z yx )sin2
( Z xx
Z yy ) cos 2
+
0
.
Z xx +
Z yy
Similarly to the Bahr method, we define the local superficial strike by the simple
analytical formula. It is easy to verify that in the presence of measurement errors
and model discrepancies this formula provides the best approximation to the con-
dition (3.40), which defines the anti-phase state in the diagonal components of the
superimposition tensor [ Z S ].
The Zhang-Roberts-Pedersen method may considerably extend the useful work-
ing range of the Bahr-Groom-Bailey method. Combining both of these methods, we
get not only the strike of a regional structure, but the strike of a near-surface local
structure as well.
Moreover, we can take an advantage of the Zhang-Roberts-Pedersen method and
estimate (at least roughly) the static effect of the superficial local structure and eval-
uate the principal regional impedances. Assume that a local structure is sufficiently
long. Then considering L as a two-dimensional structure, we disregard the galvanic
effect of the longitudinal current (electric charges hardly appear) and take e
1.
Thus, we return to (3.38), we write
Z xx Z xy
Z yx
Z 3
sin 2
Z 1
+
Z 3
cos 2
[ Z S ]
=
,
.
(3
42)
e ( Z 1
Z 3
e Z 3
Z yy
cos 2
)
sin 2
 
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