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In-Depth Information
with
1
f
=
√
1
Re
f
>
0
−
i
o
S
1
h
2
(7
.
21)
1
√
S
1
R
2
=
1
h
1
h
2
2
.
g
=
The parameters
f
and
g
have a simple physical meaning.
According to (1.48) and (1.49),
1
1
1
J
1
J
,
f
≈
1
≈
1
≈
−
(7
.
22)
J
1
J
3
i
T
max
T
+
−
where
T
max
is a period relating to the maximum of the normal apparent-resistivity
curve
N
,
J
is the total current induced in the normal model,
J
1
and
J
3
are the
currents induced in the upper layer and at the surface of the perfectly conductive
basement (Berdichevsky and Dmitriev, 2002). It is seen that
f
reflects the distri-
bution of the currents induced in the layered Earth. Due to the skin effect it varies
from rather small complex values within the
S
1
-interval to 1 within the
h
-interval.
This parameter will be referred to as the
induction parameter.
The parameter
g
characterizes the galvanic coupling between the upper layer
and the basement. It can be considered as a measure of transparency of the resistive
intermediate layer or, in other words, as a measure of percolation of the excess
currents through the intermediate layer. The smaller the longitudinal conductance
S
1
of the upper layer and the smaller the transverse resistance
R
2
of the intermediate
layer, the larger the parameter
g
and the larger the exchange of excess currents
between the upper layer and the basement. This parameter is referred to as
galvanic
parameter
(Berdichevsky and Dmitriev, 1976).
Figure 7.6 shows the normalized amplitude of the Green function calculated for
h
2
/
h
1
=
49 and
2
/
1
=
1000, 10
0 with
λ
1
/
h
1
=
25
,
50 (
S
1
-interval) and
λ
1
/
h
1
=
π
√
2
100 (
h
-interval). Here
1
/
o
is the wavelength in the upper layer of
the normal model. The Green function plays the role of a spatial filter. The degree of
filter locality depends on
λ
1
=
2
2
/
1
and
λ
1
/
h
1
.Thelower
2
/
1
and the less
λ
1
/
h
1
,the
narrower the filter pass-band. In the
S
1
-interval (
λ
1
/
h
1
=
25,
|
f
| =
0
.
4) the degree
of filter locality is much higher than in the
h
-interval (
λ
1
/
h
1
=
100,
|
f
| =
0
.
97).
It would be interesting to make some asymptotic estimates.
Let
0. Here the galvanic coupling between the upper layer
and the conductive basement is violated (no leakage through the intermediate layer)
and the Green function tends to zero. Consequently, the contribution of the integral
term becomes negligibly small. Thus, with account for (7.19) and (7.20),
2
/
1
→∞
and
g
→
