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Abstract The electric field on the borehole axis in the presence of a casing can be divided into three zones: the near, intermediate, and far zones. Within the intermediate zone, determination of the second derivative of the potential allows me to define the formation resistivity. Outside the casing, the electric field, at large distances from the borehole, has a radial direction that provides a sufficient depth of investigation in this direction. The measurement requires knowledge of the casing conductance. Application of transmission line theory is based on the fact that the electric field in the formation is radial within the intermediate zone, resulting in the conclusion that the vertical resolution of such a measurement would depend only upon the spacing of the electrodes required to estimate the second derivative of the potential.
Alexander Kaufman (Mon,) studied this question.