Block Preconditioning Techniques for Geophysical Electromagnetics

Abstract

Geophysical electromagnetic (EM) methods are an important technique for investigating the subsurface of the Earth, particularly when exploring for metallic ore deposits but also when delineating hydrocarbon reserves and in hydrological and geotechnical applications. Geophysical EM methods provide information on subsurface structure from depths of meters to hundreds of kilometers. Quantitative interpretation of the data from such EM methods, whether via trial-and-error forward modeling or inversion, requires the solution of many forward problems, simulating EM fields in candidate models of the Earth's subsurface. In this paper, we consider the solution of the linear systems of equations that arise from finite-element discretization of such forward problems, in the setting where the Helmholtz decomposition of the electric field intensity is needed for the inversion process. In particular, a block preconditioning framework is proposed for the equivalent real form of the resulting modeling equations. Particular attention is paid to the interaction between inner and outer Krylov iterations in the resulting preconditioner, and numerical results are presented that explore the balance between time-to-solution and iterations of the outer Krylov method.