Chapter 6 3-D EM Forward Modeling Using Integral Equations

Abstract

This chapter is devoted to the volume integral equation and the surface integral equation (IE) method. As a rule the surface IE method assumes that the conductivity does not change within each anomalous volume and therefore it imposes very strong limitations on the complexity of the models under consideration. Three-dimensional (3-D) electromagnetic (EM) modeling is based on various methods for numerical solution of Maxwell equations. One usually uses the finite-difference (FD), finite-element (FE), or IE methods to solve Maxwell equations numerically. The FD and FE methods also produce systems of linear equations. From a computational point of view the key difference between these methods is due to the difference in properties of the system matrices. The modified iterative dissipative method (MIDM) encouraged great interest and advances in the IE approach. As it is an extension of an iterative dissipative method the method was originally presented by Singer for quasi-static EM fields and for isotropic media.