ELECTROMAGNETIC INDUCTION IN A GENERALIZED 3D ANISOTROPIC EARTH, PART 2: THE LIN PRECONDITIONER

Abstract

A practical limitation in the use of generalized 3D forward modeling algorithms for inversion of electromagnetic data is the high computational cost of solving large, ill-conditioned systems of linear equations arising from the discretization of the governing Maxwell equations. To address this problem, a new class of preconditioners has recently been proposed which is based on a Helmholtz decomposition of the electric field in the low induction number (LIN) regime. This paper further develops that idea and introduces a LIN preconditioner which can be applied to problems characterized by a fully generalized anisotropic medium. Included are sample calculations demonstrating a reduction by two orders of magnitude in the number of "quasi-minimal residual" iterates and a speedup by a factor of approximately four in the solution time for one forward calculation. Also included are results previously unobtainable by standard Jacobi preconditioning for simulating multicomponent induction sonde response in a horizontal well within a crossbedded formation.