TOTAL FIELD RESISTIVITY MAPPING AND SOUNDING OVER HORIZONTALLY LAYERED MEDIA

Abstract

The bipole‐dipole resistivity mapping method has been used extensively in reconnaissance surveys of geothermal areas. Although the method has been used primarily for delineating lateral changes in resistivity, it is shown that significant anomalies can be produced by horizontal layers. Formulas are derived for the calculation of five types of bipole‐dipole apparent resistivities, and a distinction is made between what is defined as: primary field, simple total field, and total field apparent resistivities. It is shown that if the Schlumberger sounding curve for a given horizontally layered medium is known, then the magnitude and direction of the bipole electric field, as well as all types of bipole‐dipole apparent resistivity maps, can be calculated using simple algebraic equations (without having to solve the boundary value problem). Conversely, it is also shown that for each total electric field measurement, two Schlumberger apparent resistivities can be calculated easily, except along the polar axis of the current bipole. In addition, a useful formula is given for extending a symmetric Schlumberger sounding curve using measurements that are made with an asymmetric array. This is illustrated by field examples. Theoretical examples of perpendicular, parallel, primary field, total field, and simple total field apparent resistivity maps (as well as Schlumberger AB profiles and rectangle of resistivity maps) are calculated for a four‐layer earth model to illustrate the type of anomalies that can be obtained over layered media. The characteristic peanut‐shape of simple total field apparent resistivity maps, over horizontally layered media, is illustrated by four field examples from three different geothermal areas. The calculation of residual or “percent‐lateral‐effect” maps or profiles is recommended for the interpretation of all types of bipole-dipole apparent resistivity data, and is also illustrated by a field example.