RESISTIVITY METHODS - Field Geophysics - page 125

Figure 6.8 Construction of a complete Schlumberger depth-sounding curve
(dashed line) from overlapping segments obtained using different inner-
electrode separations. Current electrode separation = 2 L .

require exact logarithmic spacing. The sequences for five and six readings
to the decade are 1.58, 2.51, 3.98, 6.31, 10.0, 15.8

...

and 1.47, 2.15, 3.16,
4.64, 6.81, 10.0, 14.7 ... respectively. Curves drawn through readings at
other separations can be resampled but there are obvious advantages in
being able to use the field results directly.
Schlumberger apparent resistivities are usually calculated from the ap-
proximate equation of Figure 6.2c, which strictly applies only if the inner
electrodes form an ideal dipole of negligible length. Although more accurate
apparent resistivities can be obtained using the precise equation, interpreta-
tions are not necessarily more reliable, because all type curves are based on
the ideal dipole.
As the Schlumberger array is expanded (by moving the outer electrodes),
the voltage will eventually become too small to be accurately measured
unless the inner electrodes are also moved farther apart. The sounding curve
will thus consist of a number of separate segments (Figure 6.8). Even if the
ground actually is divided into layers that are perfectly internally homo-
geneous, the segments will not join smoothly because the approximations
made in using the dipole equation change each time the inner-electrode sep-
aration is changed. This effect is generally less important than the effect of
ground inhomogeneities around the potential electrodes, and the segments
may be linked for interpretation by moving them in their entirety parallel
to the resistivity axis to form a continuous curve. To do this, overlap read-
ings must be made. Ideally there should be at least three of these at each
change, but two are more usual (Figure 6.8), and one is unfortunately the
norm.