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E
N
E
A
Z
N
H
N
Z
N
H
A
(
r
)
+
(
r
)
(
r
)
+
(
r
)
E
(
r
)
H
r
(
r
)
=
(
r
)
=
=
Z
N
H
r
(
r
)
+
H
r
H
N
(
r
)
+
H
A
(
r
)
(7
.
118)
E
r
+
E
r
Z
N
H
r
+
Z
N
H
r
E
r
(
r
)
H
(
r
)
=
(
r
)
(
r
)
(
r
)
(
r
)
(
r
)
=−
=−
.
Z
N
H
N
H
A
H
r
(
r
)
H
r
(
r
)
(
r
)
+
+
So, the condition
r
>>
max
defines a zone, in which we can estimate
Z
N
,
using the magnetovariational and magnetotelluric ratios.
Singer and Fainberg believe that these rough estimates can be applied even to
large-scale inhomogeneities. In that event one has to estimate the distance
r
min
from
the nearest edge of the inhomogeneous area.
{
λ
o
,λ
L
}
7.3.3 The Berdichevsky-Dmitriev Model
Let us recall this simple model that gives an analytic image of galvanic distortions
caused by three-dimensional sedimentary structures (Berdichevsky and Dmitriev,
1976). The model is shown in Fig. 7.31. It consists from sediments (
1
,
h
1
), the
resistive lithosphere (
2
=∞
,
h
2
>>
h
1
), and the conductive mantle (
3
=
0). The
1
with
diameters 2
a
,2
b
along
x
,
y
. In the Price-Sheinmann thin-sheet
S
-approximation we
have
sediments contain an inclusion in the form of elliptic cylinder of resistivity
S
1
=
h
1
/
1
outside the inclusion
S
1
=
(7
.
119)
S
1
h
1
/
1
=
inside the inclusion
.
To get an analytic solution to this three-dimensional problem, we ignore the cur-
rent leakage through the
layer and use the hybrid quasistatic method based on
the LR-decomposition. The mathematcs is performed in three stages as shown in
Sect. 1.3.4.
2
−
a
b
ρ
‛
ρ
‛‛
h
1
h
2
Fig. 7.31
The
Berdichevsky-Dmitriev
model
