Modeling techniques commonly exhibit errors of 3 to 10 percent or more in the calculation of apparent resistivities over earth models for which analytic solutions are easily available. A singularity occurs in the solution of any elliptic partial differential equation for which the forcing function is not smooth. The inability to adequately represent in discrete space a discontinuous function (in this case, the delta function describing the introduction of current at a point) commonly results in numerical error near the source of a modeled singularity.Inspection of an integrated finite-difference method for modeling the de resistivity geophysical technique indicates much of the error encountered is of singular origin. A procedure is herein detailed by which the singularity is mathematically removed from the modeling process and reintroduced as a last step, thus preventing it from contributing to the numerical error. Using this procedure, the average error in apparent resistivity values for a model of a polar-dipole traverse over a nonconducting sphere is reduced by 40 percent. For a dipole-dipole traverse of a two-layer model the error decreases by 75 percent, and in the case of a Wenner profile of a model of a vertically faulted earth, the average error is diminished by 90 percent.

The Bristow method, an electrical resistivity technique employing a pole‐dipole measurement array in conjunction with a simple graphical method of interpretation, has proven an effective means of locating subsurface cavities. There have been questions, however, regarding the limits of the method and whether the Bristow method is indeed the most suitable of the various electrical resistivity techniques for cavity detection. In hopes of resolving some of the controversy surrounding Bristow’s method, resistivity traverses are numerically modeled over spherical and cylindrical cavities given a variety of circumstances. Using a slight variation of Bristow’s original interpretive technique on modeled data, the size and location of subsurface cavities can be determined with surprising accuracy. However, when the simulation is altered to incorporate geologic noise, the maximum depth at which a cavity can be detected is found to be far less than has been reported in field investigations. In this instance the presence of a cylindrical cavity cannot be discerned beyond a depth to the top approximately equal to the diameter of the cavity, and spherical cavities are indistinguishable at depths much greater than the radius. One should note that the noise field generated for this model may not be representative of what would normally be found in the real earth. In the field, the maximum achievable depth of detection will vary depending on the actual geologic conditions and whether some technique is employed to reduce the effects of noise. In any case, a comparison of traverses using various electrode arrays confirms that the Bristow method is the most satisfactory of the applicable electrical resistivity techniques.

A companion paper (this issue) describes a method for producing three‐dimensional simulations of physical properties for different geologic situations. Here we create a simulation for a particular case, which is a near‐surface (<80 ft deep) description of a karst environment. We simulate seismic velocity, density, resistivity, and the dielectric constant for this situation. We then conduct (in the computer) hypothetical geophysical surveys at the surface of the model. These surveys are seismic refraction, microgravity, dc resistivity, and ground‐probing radar. Physical properties appropriate for cavities are then entered in the model. Repeating the geophysical surveys over the model with cavities provides a convenient method of evaluating their potential for cavity detection. Anomalies produced by normal variations in physical properties may simulate or obscure anomalies from target features. More data about the correlation of physical properties, particularly in the horizontal directions, will be required to evaluate this problem properly.

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