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Fig. 7.2
Two-dimensional
-effect of the outcropped
small-scale conductive prism;
model parameters:
1
=
10 Ohm
·
,
h
1
=
,
1
=
m
1km
·
,
h
=
,v
=
1Ohm
m
10 m
20 m
,
2
=
100000 Ohm
·
m
,
h
2
=
The
observation site is located in
the middle of the prism
(
y
124 km
,
3
=
0
.
=
0)
7.1.2 The Three-Dimensional
ρ
-Effect of the Hemisphere
Let us take the same layered model as in the previous subsection and replace the
semicylinder by a small hemisphere (Fig. 7.3). Assuming that the effective pen-
etration depth is many times larger than the hemisphere radius
a
, we neglect the
induction effects as well as the influence of the lithosphere and mantle and solve the
problem in direct-current approximation.
Introduce a spherical coordinate system
r
,
,
with origin at the centre of the
hemisphere (
is polar distance counted off from the
z
−
axis and
is longitude
counted off from the
yz
plane). Following (Groom and Bailey, 1991), we define
the scalar potential of the electric field in the Earth as
−
