A rational Krylov subspace method for 3D modeling of grounded electrical source airborne time-domain electromagnetic data

Abstract

The rational Krylov subspace method enables the time integration required to calculate responses directly in the time-domain to be computed accurately and more efficiently than by regular time-stepping methods. In this study, the optimal rational Krylov subspace approach is used for the forward modeling of data from the grounded electric source airborne time-domain electromagnetic (GREATEM) method. The space dependence of Maxwell's equations is discretized using a mimetic finite-volume (MFV) technique, which allows strongly discontinuous conductivities to be treated properly. One advantage of an MFV approach is that the initial magnetic problem for the grounded electric source can be solved using the same discrete operators. The optimal rational Krylov subspace approach is then used for the time integration to efficiently model the full spectrum with fewer solutions of a large system of equations. A concise optimization algorithm is presented to select a single repeated pole parameter, which results in convergence under an a priori given error independent of mesh grid and electrical structure. The direct solver 'PARDISO' and right preconditioning are used to further accelerate solution performance of solving the large asymmetrical linear system of equations. The accuracy and efficiency advantages are demonstrated by a large conductivity contrasts layered model and in a 3D benchmark model. A deeply buried massive sulfide model was also built up to evaluate the deep detection capability of the GREATEM method, which shows one can expect to detect a significant response from the deep target in the airborne measurements.