A PARALLEL FINITE-DIFFERENCE APPROACH FOR 3D TRANSIENT ELECTROMAGNETIC MODELING WITH GALVANIC SOURCES

Abstract

A parallel finite-difference algorithm for the solution of diffusive, three-dimensional (3D) transient electro-magnetic field simulations is presented. The purpose of the scheme is the simulation of both electric fields and the time derivative of magnetic fields generated by galvanic sources (grounded wires) over arbitrarily com-plicated distributions of conductivity and magnetic per-meability. Using a staggered grid and a modified DuFort-Frankel method, the scheme steps Maxwell's equations in time. Electric field initialization is done by a conjugate-gradient solution of a 3D Poisson problem, as is common in 3D resistivity modeling. Instead of calculating the ini-tial magnetic field directly, its time derivative and curl are employed in order to advance the electric field in time. A divergence-free condition is enforced for both the magnetic-field time derivative and the total conduction-current density, providing accurate results at late times. In order to simulate large realistic earth models, the al-gorithm has been designed to run on parallel computer platforms. The upward continuation boundary condi-tion for a stable solution in the infinitely resistive air layer involves a two-dimensional parallel fast Fourier transform. Example simulations are compared with an-alytical, integral-equation and spectral Lanczos decom-position solutions and demonstrate the accuracy of the scheme.