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where
S 1 ( x , y )
= 2
y B x
1
M yy ( x B ,
,
y )
+
[ M xy ( x B ,
y B |
x
,
y ) Z xx ( x B ,
y B )
+
M yy ( x B ,
y B |
x
,
y ) Z xy ( x B ,
y B )] S ( x B ,
y B )
/
2
Z xy ( x , y )
S 1 ( x , y )
2
.
1 M xx ( x B , y B | x , y ) [ M xx ( x B , y B | x , y ) Z yx ( x B , y B ) + M yx ( x B , y B | x , y ) Z yy ( x B , y B )] S ( x B , y B ) / 2
Z yx ( x
=
,
y )
Here
2 S 1
S 1
=
S 1 +
S 1
characterizes the measurement and model errors.
The above technique is a part of more general approach which is referred to as
the Obukhov Z int
transformation . Let us recall this interesting approach which
can be usefull in indentifying the geoelectric structures.
On the surface of the 1D model, the internal magnetic field H int
τ =
H τ /
2
.
In view
of this, we can introduce an “internal” 1D impedanse Z int
as
E x
H int
y
E y
H int
x
Z int
=
=−
=
2 Z
(11
.
39)
int
and an “internal” apparent resistivity
as
Z int
2
2
o =
|
Z
|
int
=
o =
.
(11
.
40)
A
4
int coincide
respectively with the doubled Tikhonov-Cagniard impedance Z and the Tikhonov-
Cagniard apparent resistivity
In the 1D model, the impedance Z int
and apparent resistivity
A .
Similarly we can introduce an “internal”-impedance tensor in the 2D and 3D
models. To this end, we turn to (1.13) and replace H x ,
H y for H int
H in y :
,
x
E x
E x
H x o J E2
J E1
x
E x =
+
=
+
H y o ( Z N
+
)
a
x
E y
E y
J E2
y
H y o J E1
E y =
+
=
H x o (
Z N
+
)
+
b
y
(11
.
41)
H int
x
5 H x
H x
J H2
x
H y o J H1
x
=
0
.
+
=
H x o (0
.
5
+
)
+
c
H int
y
5 H y
H y
H x o J H2
J H1
y
=
0
.
+
=
+
H y o (0
.
5
+
)
.
d
y
Eliminating H x o ,
H y o from (11.41 c,d ) and substituting these values in (11.41 a,b ),
we establish
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