Modeling low-frequency electrode-type resistivity tools in 2-D formations

Abstract

In this work, we derive the low-frequency approximation of the Maxwell's equations to obtain the partial differential equation for the potential field. We then formulate and implement a numerical mode-matching (NMM) method to solve this two-dimensional potential field in order to model electrode-type resistivity tools in invaded thin beds. The new NMM program is validated by comparing the numerical results with those obtained from other DC programs. It is found that this new program is much faster than the program using the finite-element method (FEM), and hence is useful for routine interpretation of resistivity logs. We illustrate one application of the NMM program with an inversion of multiple field logs.