An iterative finite element time-domain method for simulating three-dimensional electromagnetic diffusion in earth

Abstract

An iterative finite element time-domain (FETD) method has been developed for simulating transient electromagnetic fields in 3-D diffusive earth media and has been verified through comparisons with analytic and finite-difference time-domain solutions. The adaptive time step doubling (ATSD) method plays an important role in reducing solution run-time by allowing large time steps in late time when high-frequency electric fields are increasingly attenuated in the Earth. We demonstrate that for the ATSD method to work effectively, the conductivity of the air and a drop tolerance of a preconditioner should be carefully selected. The conductivity of the air should not be too large for accurate simulations but also not too small for avoiding ill conditioning that results in error amplification in the ATSD method. A proper drop tolerance keeps the eigenvalues of the preconditioned FETD matrices clustered when a time step size is successively doubled during the ATSD processes, resulting in the convergence of iterative solutions with the reasonable number of iterations. A rule of thumb for determining the conductivity of the air and the drop tolerance has been presented. We also present the simultaneous multiple-sources modelling (SM 2) approach. The SM 2 approach simultaneously advances the electric fields excited by multiple individual sources in a single time stepping loop. This approach allows multiple sources to share the same preconditioner in the time stepping loop and improves the simulation efficiency per a survey line. © 2012 The Authors Geophysical Journal International © 2012 RAS.