A new method for calculating anomaly patterns and type curves of apparent resistivity and apparent chargeability over three‐dimensional bodies imbedded in a half‐space is practicable. The solution of the boundary‐value problem for a point source of current near a body of arbitrary shape in the form of an inhomogeneous integral equation is solved numerically by the method of least squares. The solution is then used to construct the apparent resistivity and apparent chargeability functions for three and four‐electrode arrays in the vicinity of the body in a straightforward manner. Type curves show the application to an actual field example. Finally, some simple, direct aids for interpreting anomalies over mineralized zones of compact (i.e. roughly spherical) shape result. This study represents the results of the first phase of a continuing program of research into resistivity and IP interpretation theory.

All boundary conditions of the problem discussed by Dieter et al cannot be satisfied by the solution given in equations (8) and (9). It is not adequate to consider just one image in the manner illustrated by Figure 2. There will be a series of higher order images: [Formula: see text] and [Formula: see text] will be reflected on S giving the next image. This image in turn will be reflected on [Formula: see text]; and so on. Equations (8) and (9), therefore, represent an approximation—not a very good one—and will hold approximately only under very restricted conditions (see, for instance, “Interpretation Theory in Applied Geophysics” by F. S. Grant & G. F. West, p. 425, McGraw‐Hill Book Company, N. Y.). They do not constitute “a perfectly suitable form” for the potential due to a closed conducting body in a half‐space.