Geology Reference
In-Depth Information
where a current
I
flows between current electrodes at A and B and the
voltage electrodes are at M and N (Figure 6.1a), and the quantities in square
brackets represent inter-electrode distances. These distances are always the
actual distances between electrodes, whether or not they lie in a straight
line. The quantity in brackets is often denoted by 1
/
K
, and the apparent
resistivity can then be calculated from the
basic array equation
:
ρ
a
=
2
π
K
(
V
/
I
)
where
V
and
I
are measured and
K
is the
geometric factor,
expressed in
metres, which is determined by the electrode arrangement.
Geometric factors are not affected by interchanging current and voltage
electrodes, but voltage electrode separations are normally kept small to
minimise the effects of natural potentials.
6.1.2 Electrode arrays
Figure 6.2 shows some common electrode arrays and their geometric factors.
The names are those in general use and may upset pedants. A dipole, for
example,
should
consist of two electrodes separated by a distance that is
negligible compared to the distance to any other electrode. Application of
the term to the dipole-dipole and pole-dipole arrays, where the distance to
the next electrode is usually only between one and six times the 'dipole'
spacing, is thus formally incorrect. Not many people worry about this.
The distance to a fixed electrode 'at infinity' should be at least 10, and
ideally 30, times the distance between any two mobile electrodes. The long
cables required can impede field work, and can also act as aerials, picking up
stray electromagnetic signals that can affect the readings (
inductive noise
).
6.1.3 Array descriptions (see Figure 6.2)
Wenner array
: Very widely used, and supported by a vast amount of inter-
pretational literature and computer packages. The 'standard' array against
which others are often assessed.
Two-electrode (pole-pole) array
: Theoretically interesting since it is possible
to calculate from readings taken with it along a traverse the results that
would be obtained from any other type of array, providing coverage
is adequate. However, the noise that accumulates when large numbers
of results obtained with closely spaced electrodes are added together
prevents any practical use being made of this fact. The array is very
popular in archaeological work because it lends itself to rapid one-man
operation. As the
normal
array, it is one of the standards in electrical
well-logging.
