Page 141 - Petroleum Geology

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Fig. 6-4. The electrical resistivity of a block of material can be measured by passing a known
current between one pair of electrodes and measuring the voltage (potential drop) between
another pair.

as would be generated by the rotation of Fig. 6-5 about the axis through the
electrodes. Since each path begins at the same potential and each path ends
at the same potential, surfaces exist in the conductor on which all paths have
the same potential. These, as with fluid flow, are called equipotential sur-
faces. Flow paths are everywhere normal to the equipotential surfaces be-
cause this is the direction of maximum potential gradient. The pattern in the
field depends on the resistivity of the conductor.
In the immediate vicinity of the lower electrode, the current flows radially
inwards from all directions, and the equipotential surfaces approximate
spheres. If we now insert another electrode in an arbitrary fixed position, the
potential between this electrode and another on any point of a sphere rela-
tively close to the lower current electrode A would be the same (very nearly)
whether to one side or vertically above or below. Any of these electrode
devices could be calibrated to give the resistivity of the conductor directly.
When, therefore, we put a current electrode down a borehole filled with a
resistive mud (the volume of the borehole being negligible relative to the
volume of rock around it) and pass a current to it from an electrode near the
surface, a potential field is set up in the rocks around the borehole (Fig. 6-6).
If a pair of measuring electrodes is now inserted into the borehole, one being
close to the current electrode A, the potential between the two measuring
electrodes is related to the resistivity of the rocks in the neighbourhood of
electrode A. This potential will be very similar to the potential that would
have been obtained if it had been possible to put M into the rocks a lateral
distance AM from A. The spacing AM is therefore regarded as a measure of