Papers - Electrical Methods - Interpretation of Three-layer Resistivity Curves

The question of the interpretation of apparent resistivity curves is still a much disputed subject although the discussion has been going on for several years, mainly since Gish and Rooneyl made their first measurements on the Tidal Basin at Washington, D. C. As a first approximation, they interpreted the depth to a horizontal discontinuity in terms of the electrode spacing at which a maximum or a minimum occurs in the resistivity curve. Later on, Lancaster-Jones2 proposed a closer approximation of depth determination by evaluating the depth to a horizontal discontinuity as the two-thirds of the electrode spacing at which a point of inflection occurs in the resistivity curve. An accurate determination of the depth was recently proposed by Tagg3 for a two-layer problem. It is a graphic solution of the problem by means of charts calculated from the formula of the apparent resistivity based on the theory of electrical images. Tagg's method is theoretically sound but the fact that the layers have been assumed to be homogeneous and isotropic must not be overlooked. Abusive use of the method has been made by geologists who have failed to recognize the fact that nature offers only few cases where the conductivity of the rocks may be assumed to be the same parallel and perpendicular to the bedding plane. Actually the ratio of the two resistivities in those directions may take values ranging from one (isotropic medium) to three for shales. In such conditions Tagg's method leads to disappointments. A method recently advocated by Manhart4 and Tattam6 forces Tagg's method to give a solution where manifestly the case under