The direct numerical solution of resistivity data for the case of horizontal layering is presented as the solution of a set of nonlinear algebraic equations. Two specific methods, Newton and Steepest Descent, were set up for three-layer analyses on a digital computer. These were applied to field data and to data derived theoretically for three- and four-layer cases.
The case of a thin second layer was found to display a special kind of indeterminacy. It was found that the analyses do not and cannot theoretically be expected to yield the actual values of resistivity and thickness for these thin layers, but, rather, a good value for their ratio (conductive layer) or product (resistive layer) can be obtained. The question of ultimate resolubility of this type of information in the presence of measurement error is discussed quantitatively. It was found that, as the resistivity of the third (lowermost) layer increases, it becomes increasingly difficult to detect a thin, resistive second layer. When the second layer is not thin relative to the first, the resistivities and thicknesses are determined with reasonable accuracy. These solutions do not appear to be unique, but alternate solutions differ sufficiently for the true solution to be easily distinguished.