Geology Reference
In-Depth Information
(a)
300
(b)
0
100 m
Alluvium
100
0
Fig. 8.19
(a) The observed Wenner
resistivity profile over a shale-filled sink of
known geometry in Kansas, USA. (b) The
theoretical profile for a buried hemisphere.
(After Cook &Van Nostrand 1954.)
50
250
m
Limestone
Ω
m
15
Shale
Plan
source, the optical analogue indicates that light would be
received only after transmission through the mirror, re-
sulting in a reduction in intensity by a factor correspond-
ing to the transmission coefficient.The only contributor
to the potential
V
P¢
at P¢ is the current source reduced in
intensity by the factor (1 -
k
). From equation (8.6)
X
Conductor
Equipotentials
I
1
2
-
k
r
(
)
r
2
V
=
(8.21)
P
¢
p
3
Equations (8.20) and (8.21) may be used to calculate
the measured potential difference for any electrode
spread between two points in the vicinity of the interface
and thus to construct the form of an apparent resistivity
profile produced by longitudinal constant separation
traversing. In fact, five separate equations are required,
corresponding to the five possible configurations of a
four-electrode spread with respect to the discontinuity.
The method can also be used to construct apparent resis-
tivity profiles for constant separation traversing over a
number of adjacent discontinuities. Albums of master
curves are available for single and double vertical con-
tacts (Logn 1954).
Three-dimensional resistivity anomalies may be ob-
tained by contouring apparent resistivity values from
a number of CST lines. The detection of a three-
dimensional body is usually only possible when its top is
close to the surface, and traverses must be made directly
over the body or very near to its edges if its anomaly is to
be registered.
Three-dimensional anomalies may be interpreted by
laboratory modelling. For example, metal cylinders,
blocks or sheets may be immersed in water whose resis-
tivity is altered by adding various salts and the model
moved beneath a set of stationary electrodes. The shape
Conductor
Section
Fig. 8.20
The mise-à-la-masse method.
of the model can then be varied until a reasonable
approximation to the field curves is obtained.
The mathematical analysis of apparent resistivity vari-
ations over bodies of regular or irregular form is complex
but equations are available for simple shapes such as
spheres or hemispheres (Fig. 8.19), and it is also possible
to compute the resistivity response of two-dimensional
bodies with an irregular cross-section (Dey & Morrison
1979).
Three-dimensional anomalies may also be obtained
by an extension of the CST technique known as the
mise-à-la-masse method
. This is employed when part of a
conductive body, for example an ore body, has been lo-
cated either at outcrop or by drilling. One current elec-
trode is sited within the body, the other being placed a
large distance away on the surface (Fig. 8.20). A pair
of potential electrodes is then moved over the surface
