A PRACTICAL APPROACH TO FINITE‐DIFFERENCE RESISTIVITY MODELING

Abstract

Highly efficient finite‐difference resistivity modeling algorithms which yield accurate results are put forward. The given medium is discretized and divided into rectangular blocks by using a very coarse system of vertical and horizontal grid lines, whose distance from the source(s) increases logarithmically. Expressions are derived to compute the longitudinal conductance and transverse resistance associated with each of these blocks for a parallel‐layer medium followed by a generalized treatment to accommodate arbitrarily shaped structures. Since the values of Dar Zarrouk parameters are derived from the exact resistivity distribution of the given medium, fine features such as a thin but anomalously resistive bed which ordinarily would be missed entirely in coarse discretization can be taken into account. Further reduction in the size of the model is achieved by making use of a symmetry wherever possible. In most cases the computation of the potential field which involves the inversion of a small sparse matrix requires about 0.5 sec of computer time. Moreover, changes in geology affect neither the size nor the zero structure of the matrix. Therefore, when more than one model is to be computed, the factorization of the matrix can be done symbolically only once for all models, followed by numeric factorization for each individual model. The coarse grid algorithm was applied to a number of horizontally layered models involving a point source. The results obtained for each model were in excellent agreement with the corresponding analytical data. Finite‐difference investigation of the potential field for two‐dimensional structures and a line source dipole indicates that as long as one is interested only in the evaluation of the Schlumberger‐type apparent resistivity curves, the line‐source results may be a much better approximation to the corresponding point‐source data than is commonly believed.