Papers - Theoretical Studies - Mathematical Theory of Electrical Flow in Stratified Media with Horizontal, Homogeneous and Isotropic Layers (With Discussion)

During the earlier period of electrical prospecting, the search for orebodies was by far the most important application of this method of geophysical prospecting. In the past few years, however, increasing attention has been paid to the possibilities of this method in the investigation of subsurface structures. Not only have fault zones been located, but attempts have been made to determine the depth to certain strata and thus contouring on some bed which proves to be a good "electrical marker." Many workers have published the results of field tests showing how their particular interpretations have agreed with the actual field conditions, but very few have stated their method of interpretation. Weaver, Hummel and Stefanesco and Schlumbergerl have given a more theoretical discussion of the resistivity methods. Hummel and Stefan-esco and Schlumberger have published mathematical solutions for the flow of electricity in a medium involving four layers. In this paper the authors present a solution for the flow of electricity in a medium of any number of horizontal strata. By means of this solution, curves showing the relationship between the apparent resistivity and the electrode spacing can be computed for ideal cases. Point-source in an Infinite Homogeneous Medium In resistivity measurements the current is conveyed to the earth by means of two electrodes, which can be mathematically treated as point-sources of equal and opposite strength. A point-source of strength I is defined as a point at which electricity is being generated at the constant rate of I coulombs per second, or I