An efficient solution for the response of electrical well logging tools in a complex environment

Abstract

A symmetrical form of the solution for an electrical source in a multibed well-logging environment is derived. The method uses local reflection and transmission operators of a single-bed boundary and a general recursive algorithm to derive generalized reflection and transmission operators. Using this method, the computation time scales linearly as N, where N is the number of beds in the environment. Hence, the method is much more efficient than the finite-element method for solving the same problem. The solution is presented in a symmetric form so that reciprocity can be readily verified. A computer program was developed to implement the solution. The program is robust and generates accurate results from 20 kHz to 25 MHz, achieving excellent agreement with the finite-element method solution of the same problem.