One of the first arrays used in the 1920 and still popular today is the Schlumberger array shown below with its formula for apparent resistivity. It is another variant of the pole-dipole, again with the second current electrode placed symmetrically opposite the first. The voltage difference is consequently doubled and so the apparent resistivity is the same as that for the general pole-dipole with a factor of 1/2 in the geometric factor. In a Schlumberger sounding the voltage electrodes are usually kept small and fixed while only the “b” spacing is changed.
Further, it is conventional to consider the spacing “b” to be the distance from the center of the array to the outermost electrodes. In this case “b” in the above expressions becomes AB/2. If a << AB/2 the above formulas for Roa are changed:
Roa = V/I*PI* b^2/a if a<<b
Data from a Schlumberger sounding is plotted vs. spacing in the same manner as the Wenner data of figure.