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Table 7.2
Conditions of the quasi-two-dimensionality of elliptic inclusion
m
=
S
1
/
S
1
The
S
1
−
interval
The
h
−
interval
Longitudinal
xy
-curve
Transverse
yx
-curve
Longitudinal
xy
-curve
Transverse
yx
-curve
Resistive inclusion
m
<
1
***
m
=0.5
m
=0.1
m
=0.01
m
=0
e
=6
e
=16
e
= 19.6
e
=20
e
=8.55
e
= 80.1
e
= 939
e
=
∞
e
=9.5
e
= 17.9
e
= 19.8
e
=20
e
=18
e
= 170
e
= 1880
e
=
∞
Conductive inclusion
m
>
1
***
m
=2
m
=10
m
= 100
m
=
e
=5.33
e
= 14.5
e
= 17.6
e
=18
e
=4.27
e
=8.45
e
=9.39
e
=9.5
e
=18
e
= 170
e
= 1880
e
=
e
=9.5
e
= 17.9
e
= 19.8
e
=20
∞
∞
xy
−
are for the longitudinal
curves, observed over a resistive inclusion (
e
does
not exceed 20 in the
S
1
−
and
h
−
intervals), and for the transverse
yx
−
curves,
observed over a conductive inclusion (
e
does not exceed 9.5 in the
S
1
−
interval and
20 in the
h
−
interval). At the same time the longitudinal
xy
−
curves, observed
over a conductive inclusion, and the transverse
curves, observed over a
resistive inclusion, call for elongations
e
which range up to 100 or even 1000.
The different robustness of the longitudinal and transverse apparent-resistivity
curves to the 3D effects generated by the resistive and conductive elliptical inclu-
sions is accounted for by difference in current around-flow and current gathering
mechanisms.
yx
−
7.3.4 The Golubtsova Model
The elliptic-cylinder model exposes the galvanic mechanism of the three-
dimensional near-surface distortions. In addition to this analytic model, it would
be useful to consider a similar numerical model that reflects both the mecha-
nisms, galvanic and induction. Let us examine the model consisting of sediments
(
1
,
1
,
h
1
), the resistive lithosphere (
2
>>
h
2
>>
h
1
), and the conductive man-
tle (
2
). The sediments contain a regional conductive inclusion in the form
of a round cylinder of the radius
a
with resistivity
3
<<
1
(
r
), which decreases mono-
1
at its centre.
The calculations were performed by Debabov's program in the Price-Sheinmann
thin-sheet
S
-approximation (Debabov, 1980; Golubtsova, 1981). So, we have a con-
ductance model with
S
1
1
(
a
)
=
1
at the inclusion edge to
1
(0)
tonically from
=
min
=
h
1
/
1
and
S
1
(
r
)
=
h
1
/
1
(
r
)
,
where
S
1
(
a
)
=
S
1
and
S
1
(0)
=
max
S
1
. Figure 7.37 shows the field profiles, which pass through the
