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In-Depth Information
.
This generalized model characterizes the typical geoelectric structure of the upper
Earth's layers. The first layer represents conductive sedimentary strata, the second
layer relates to the resistive lithosphere, and the third layer simulates the highly
conductive mantle.
Solving the Riccati equation, we get
Let us consider a three-layered K-type model with
2
>>
1
,
h
2
>>
h
1
,
3
=
0
tan h
ik
1
h
1
+
tan h
ik
2
h
2
E
y
E
x
H
y
=−
H
x
=−
o
tan h
−
1
k
1
k
2
Z
=
,
(1
.
43)
k
1
where
k
1
=
√
i
o
/
1
and
k
2
=
√
i
0 (Berdichevsky and Dmitriev,
2002). The apparent-resistivity and impedance-phase curves,
o
/
2
,Im
k
>
A
and
, calculated
for
3
= 0 are shown
in Fig. 1.4. Examine the informativeness of different portions of these curves.
The low-frequency asymptotics of the impedance
Z
gives
1
=10Ohm
·
m,
h
1
=1km,
2
= 10000 Ohm
·
m,
h
2
=49km,
i
o
h
1
o
S
1
h
1
,
Z
=−
o
S
1
h
2
,
when
2
>>
1
,
h
2
>>
h
1
and
<<
(1
.
44)
1
−
i
where
S
1
=
h
1
/
1
and
h
=
h
1
+
h
2
. Here two frequency intervals are of specific
interest.
If
o
S
1
h
2
>>
1, then
1
S
1
.
Z
=
(1
.
45)
This frequency interval corresponds to the ascending branch of the
A
-curve. It con-
tains information on the conductance
S
1
of the upper layer. Its title is the
S
1
-interval.
Within the
S
1
-interval the
A
-curve merges with the
S
1
-line, while the impedance
phase nears to zero. According to (1.45), equation for the
S
1
-line is
(
√
T
)
2
2
A
=
o
S
1
.
In bilogarithmic coordinates, this is
2log
√
T
o
S
1
.
=
−
log
log2
A
43
o
to the axis of
√
T
.
Evidently, the
S
1
-line is tilted at an ang
le o
f arctan 2
=
63
.
mat
T
S
1
, from which we can determine
It intersects the line
A
=
1Ohm
·
T
S
1
356
T
S
1
(second)
1
√
2
S
1
=
or
S
1
(siemens)
=
.
o
