Implicit finite-difference time-domain schemes for TDEM modeling in three dimensions

Geophysical exploration methods that use controlled electromagnetic sources in time domain are becoming ubiquitous because of their ease of deployment and data coverage capabilities. Although these prospecting methodologies have evolved significantly, most computational numerical modeling techniques have been developed in the frequency domain. Given this evolution, it is pertinent to ask whether some known advantages of implicit finite-difference (FD) modeling techniques, which are common among other disciplines, apply to the time-domain electromagnetic (TDEM) problem in geophysics. To explore the potential advantages of 3D time-domain modeling for TDEM, we have analyzed the differences between two implicit FD formulations: a single-order backward Euler scheme and a second-order Crank-Nicolson scheme. To validate our algorithms, we tested them with existing analytical solutions for simple geometries and performed detectability tests for various electromagnetic sources. The results find an acceptable match of both numerical schemes to the analytical solutions and higher accuracy of the second-order discrete operator without a significant difference in computing time.