Spectral-element modeling of the time-domain electromagnetic field in 3D geophysical anisotropic media

The transient electromagnetic method is widely used in diverse fields, including mineral and groundwater exploration, environmental studies, geothermal investigations, and near-surface surveys. The subsurface is often assumed to be isotropic; however, it becomes essential to consider electrical anisotropy when dealing with complex media like layered or fractured models. Fortunately, the progress in computational power and advanced algorithms have significantly enhanced our ability to improve forward modeling in complex media. The Spectral Element Method (SEM) has been very successful for seismic modeling, and its suitability for other geophysical methods has been the focus of recent research. We investigate the applicability of SEM to model three-dimensional transient electromagnetic fields on isotropic and anisotropic geophysical media; we also test the explicit finite-difference method for time stepping. We compare in our experiments nodal basis functions of up to order 8 for different scenarios using \(\varvec{x}\) $\mathit{x}$ - and \(\varvec{z}\) $\mathit{z}$ -polarized electric dipoles as sources. We find that using higher-order polynomial basis functions and finite-difference time stepping yields accurate results. Specifically, 2nd and 4th-order basis using coarse meshes provide better results than a finer mesh with first-order polynomials. The finite-difference method is conditionally stable and computationally efficient since it does not require solving a system of linear equations.