Fast frequency‐domain electromagnetic modeling of a 3‐D earth using finite differences

Abstract

A numerical modeling code has been developed to simulate the electromagnetic response of a general three-dimensional (3-D) earth. The problem is solved using the numerical finite difference approximation of either the coupled, first-order Maxwell`s equations for both the electric and magnetic fields, or the second-order vector Helmholtz equation for the electric fields. The resulting matrix system of equations is sparse and is solved using either a bi-conjugate gradient (BiCG) or quasi-minimal residual (QMR) technique with Jacobi preconditioning. The scheme been tested against a host of other numerical models including 1-D routines and 3-D integral equation codes. Here numerical results calculated with the 3-D code are compared to a set of scale model data that were collected in a simulated crosswell EM experiment. The results show the accuracy of the 3-D code to be excellent. Because the ultimate goal in the development of this numerical model is to incorporate it into a 3-D imaging scheme, a large emphasis has been placed on solution speed. In certain situations time savings of an order of magnitude or greater can be achieved by using a half space background model rather than a whole space solution. Recent experience with the QMR solver indicates that itmore » tends to be faster than the BiCG routine. Finally the code is currently being implemented on a massively parallel (MP) machine with a matrix solution-software package that includes several previously untested methods of preconditioning the matrix as well as various different Krylov subspace methods for arriving at a solution.« less