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1
g
2
(
y
)
d
1
d
2
dy
2
v
(
y
)
dy
d
v
(
y
)
dy
−
−
=
0
,
whence on some substitutions we obtain
R
2
d
2
E
y
H
x
,
dy
2
S
1
(
y
)
Z
⊥
(
y
)
Z
⊥
(
y
)
Z
⊥
=−
−
=
i
o
h
,
which coincides with low-frequency asymptotics of Tikhonov-Dmitriev's equation
(7.18).
Evidently the Dmitriev-Barashkov model can be considered as a three-
dimensional generalization of the two-dimensional Tikhonov-Dmitriev model.
7.3.2 The Singer-Fainberg Model
Now we review another three-dimensional generalization of the Tikhonov-Dmitriev
model suggested by Singer and Fainberg (1985) and Fainberg and Singer (1987).
The Singer-Fainberg model gains a better insight into the physical mechanism of
anomalies caused by the
S
1
-variations and allows for estimating their long-range
action.
The model is shown in Fig. 7.30. It has the same normal background as in the
Tikhonov-Dmitriev model, but its upper layer contains a closed anomalous domain
V
bounded by arbitrary cylindrical surface:
S
1
=
1
=
const
outside
V
const
outside
V
1
=
S
1
=
1
(
x
,
y
)
inside
V
S
1
(
x
,
y
)
inside
V
(7
.
98)
2
>>
1
h
2
>>
h
1
R
2
>>
R
1
3
=
0
,
where
S
1
=
h
1
/
1
is the conductance of the upper layer, and
R
1
=
h
1
1
,
R
2
=
h
2
2
are the resistances of the upper and intermediate layers.
Fig. 7.30
The
Singer-Fainberg model
