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⎧
⎨
⎫
⎬
⎧
⎨
⎫
⎬
2
1
2
1
−
1
a
3
3
=
=
1
+
2
(7
.
11)
1
1
⎩
3
⎭
⎩
⎭
|
y
|
1
+
2
1
+
2
which, according to (7.6), characterize the magnitude of the static shift.
Let us compare the static shifts observed in the 3D-model with a hemisphere and
in the 2D-model with a semicylinder of the same relative resistivity. Reasoning from
(7.5) and (7.11), we can show that
⎧
⎨
⎫
⎬
3
log
1
1
+
⎩
⎭
2
(3
D
)
log
⎧
⎨
⎫
⎬
(2
D
)
=
<
1
,
(7
.
12)
log
2
log
1
⎩
⎭
1
+
1
1
>
1
1
<
1
. Thus,
which is valid for resistive and conductive inclusions,
and
the three-dimensional
effect is less expressive than two-dimensional one. This
can be accounted for by the redistribution of currents that flow around a 3D resis-
tive inclusion and inflow from each side into a 3D conductive inclusion. The three-
dimensional
−
effect is exemplified in Fig. 7.3. We see here the same pattern as in
Fig. 7.1, but the static shift over the near-surface inclusion is noticeably reduced.
In models under consideration the total conductance
S
1
of the upper layer varies
but little. Now we have to examine models with significant variations in the sedi-
ments conductance.
−
7.2 Two-Dimensional Conductance Models
The distortions caused by variations in the sediments conductance will be referred
to as
S-effect
. Let us begin our analysis with the two-dimensional S-effect.
7.2.1 The Tikhonov-Dmitriev Basic Model
We will examine several models that are essential for understanding the nature of the
near-surface distortions caused by variations in the conductance
S
1
of the sediments
underlaid with resistive basement.
Here we consider a pioneering model devised by Tikhonov and Dmitriev (1969).
This two-dimensional model consists of three layers (Fig. 7.4). The upper layer of
uniform resistivity
1
=
const
simulates the sediments. It contains an infinitely
