Geology Reference
In-Depth Information
1.0
I
r
B
r
A
0.8
Δ
V
+I
- I
0.6
A
C
D
B
R
A
R
B
0.4
Fig. 8.4
The generalized form of the electrode configuration
used in resistivity measurements.
0.2
Equation (8.6) allows the calculation of the potential
at any point on or below the surface of a homogeneous
half -space. The hemispherical shells in Fig. 8.3 mark
surfaces of constant voltage and are termed
equipotential
surfaces
.
Now consider the case where the current sink is a
finite distance from the source (Fig. 8.4). The potential
V
C
at an internal electrode C is the sum of the potential
contributions
V
A
and
V
B
from the current source at A
and the sink at B
0
0
2
4
6
8
10
L/Z
Fig. 8.5
The fraction of current penetrating below a depth
Z
for a
current electrode separation
L
. (After Telford
et al
. 1990.)
pendent of both electrode spacing and surface location.
When subsurface inhomogeneities exist, however, the
resistivity will vary with the relative positions of the elec-
trodes. Any computed value is then known as the
appar-
ent resistivity
r
a
and will be a function of the form of the
inhomogeneity. Equation (8.9) is the basic equation
for calculating the apparent resistivity for any electrode
configuration.
In homogeneous ground the depth of current pene-
tration increases as the separation of the current elec-
trodes is increased, and Fig. 8.5 shows the proportion of
current flowing beneath a given depth
Z
as the ratio of
electrode separation
L
to depth increases. When
L
=
Z
about 30% of the current flows below
Z
and when
L
= 2
Z
about 50% of the current flows below
Z
. The
current electrode separation must be chosen so that the
ground is energized to the required depth, and should be
at least equal to this depth.This places practical limits on
the depths of penetration attainable by normal resistivity
methods due to the difficulty in laying long lengths of
cable and the generation of sufficient power. Depths of
penetration of about 1 km are the limit for normal
equipment.
Two main types of procedure are employed in resistiv-
ity surveys.
Vertical electrical sounding
(VES), also known as 'electri-
cal drilling' or 'expanding probe', is used mainly in the
study of horizontal or near-horizontal interfaces. The
current and potential electrodes are maintained at the
same relative spacing and the whole spread is progres-
VVV
CAB
=+
From equation (8.6)
I
11
r
2
Ê
Ë
ˆ
¯
V
=
-
(8.7)
C
r
r
AB
Similarly
I
1
1
r
2
Ê
Ë
ˆ
¯
V
=
-
(8.8)
D
RR
A
B
Absolute potentials are difficult to monitor so the poten-
tial difference
D
V
between electrodes C and D is
measured
I
11
1 1
r
2
Ó
Ê
Ë
ˆ
¯
Ê
Ë
ˆ
¯
˛
D
VV V
=-=
-
-
-
CD
r
r
R R
AB
A
B
Thus
2
11
D
V
p
=
r
(8.9)
1 1
Ó
Ê
Ë
ˆ
¯
Ê
Ë
ˆ
¯
˛
I
-
-
-
r
r
R R
AB
A
B
Where the ground is uniform, the resistivity calcul-
ated from equation (8.9) should be constant and inde-
