Three-dimensional transient electromagnetic modeling in the Laplace Domain

Abstract

In modeling electromagnetic responses, Maxwell's equations in the frequency domain are popular and have been widely used (Nabighian, 1994; Newman and Alumbaugh, 1995; Smith, 1996, to list a few). Recently, electromagnetic modeling in the time domain using the finite difference (FDTD) method (Wang and Hohmann, 1993) has also been used to study transient electromagnetic interactions in the conductive medium. This paper presents a new technique to compute the electromagnetic response of three-dimensional (3-D) structures. The proposed new method is based on transforming Maxwell's equations to the Laplace domain. For each discrete Laplace variable, Maxwell's equations are discretized in 3-D using the staggered grid and the finite difference method (FDM). The resulting system of equations is then solved for the fields using the incomplete Cholesky conjugate gradient (ICCG) method. The new method is particularly effective in saving computer memory since all the operations are carried out in real numbers. For the same reason, the computing speed is faster than frequency domain modeling. The proposed approach can be an extremely useful tool in developing an inversion algorithm using the time domain data.