Characteristic Responses of Resistivity Tools in Elliptical Boreholes

The solution for the potential created by a point-electrode current source in an elliptical borehole is obtained. This solution is applied to the computation of the responses of two typical shallow-investigation resistivity logging tools. These computations cover a range of contrasts between borehole-fluid and formation resistivities encompassing all cases normally encountered in well-logging practice. The effect of the finite size of the electrodes is approximately accounted for by first determining a circular borehole giving the same point-electrode resistivity response as the elliptical hole, and then making the same correction for electrode size to the elliptical-hole results as would apply in the circular-hole case.