Rl. Mackie et al., 3-DIMENSIONAL ELECTROMAGNETIC MODELING USING FINITE-DIFFERENCE EQUATIONS - THE MAGNETOTELLURIC EXAMPLE, Radio science, 29(4), 1994, pp. 923-935
We have developed a robust and efficient finite difference algorithm f
or computing the magnetotelluric response of general three-dimensional
(3-D) models using the minimum residual relaxation method. The differ
ence equations that we solve are second order in H and are derived fro
m the integral forms of Maxwell's equations on a staggered grid. The b
oundary H field values are obtained from two-dimensional transverse ma
gnetic mode calculations for the vertical planes in the 3-D model. An
incomplete Cholesky decomposition of the diagonal subblocks of the coe
fficient matrix is used as a preconditioner, and corrections are made
to the H fields every few iterations to ensure there are no H divergen
ces in the solution. For a plane wave source field, this algorithm red
uces the errors in the H field for simple 3-D models to around the 0.0
1% level compared to their fully converged values in a modest number o
f iterations, taking only a few minutes of computation time on our des
ktop workstation. The E fields can then be determined from discretized
versions of the curl of H equations.