A Contribution to the Theory of the Interpretation of Resistivity Measurements Obtained from Surface Potential Observations

IN an earlier paper, Ehrenburg and Watson1 published the develop-ment for a potential function by which it is possible to obtain the electric potential at points on the surface of the ground when a current I passes between two electrodes and the subsoil is composed of parallel, homo-geneous layers. In view of the continued interest in the resistivity method of electrical prospecting, the author has considered it desirable to publish the results of a number of theoretical studies making use of this potential function, and also the results of a considerable number of tests with models designed to show the soundness of the mathematical theory. It is hoped that these results will prove how erroneous the various empirical rules for depth determination may be. It has always seemed puzzling to the author that one can find, in papers published comparatively recently, statements upholding empirical rules for depth determination, and attributing most of the irregularities of resistivity curves to vertical discontinuities in resistivity in the subsoil. It would indeed be fortunate for the geophysical investigator if such a simple rule held. However, numerous investigators have proved both theoretically and by the success of their field work that such a rule does not hold, even by a" rough approximation" in many cases. On the other hand, as is shown in the development to follow; if the underground conditions are favorable it is possible for such empirical rules to give a satisfactory depth determination. Authors should be more careful about making such sweeping state-ments about the accuracy of these empirical rules because the relative simplicity of the field work places the method in the hands of any inter-ested experimenter, and he is likely to become completely disgusted with the method after he has made several obviously wrong interpretations by empirical rules.