A Comparison Study of Explicit and Implicit 3-D Transient Electromagnetic Forward Modeling Schemes on Multi-Resolution Grid

Abstract

This study compares the efficiency of 3-D transient electromagnetic forward modeling schemes on the multi-resolution grid for various modeling scenarios. We developed time-domain finite-difference modeling based on the explicit scheme earlier. In this work, we additionally implement 3-D transient electromagnetic forward modeling using the backward Euler implicit scheme. The iterative solver is used for solving the system of equations and requires a proper initial guess that has significant effect on the convergence. The standard approach usually employs the solution of a previous time step as an initial guess, which might be too conservative. Instead, we test various initial guesses based on the linear extrapolation or linear combination of the solutions from several previous steps. We build up the implicit scheme forward modeling on the multi-resolution grid, which allows for the adjustment of the horizontal resolution with depth, hence improving the performance of the forward operator. Synthetic examples show the implicit scheme forward modeling using the linearly combined initial guess estimate on the multi-resolution grid additionally reduces the run time compared to the standard initial guess approach. The result of comparison between the implicit scheme developed here with the previously developed explicit scheme shows that the explicit scheme modeling is more efficient for more conductive background models often found in environmental studies. However, the implicit scheme modeling is more suitable for the simulation with highly resistive background models, usually occurring in mineral exploration scenarios. Thus, the inverse problem can be solved using more efficient forward solution depending on the modeling setup and background resistivity.

Why the September 2017 geomagnetic storm was stronger at certain locations than the famous Halloween event

“…The geoelectric field can be modeled by coupling ground conductivity models with the measured magnetic field (for an extensive review, see Kelbert (2020)). In recent years, there has been a lot of progress in applying empirical magnetotelluric (MT) impedances (e.g., Bedrosian and Love (2015)) and using first-principle solutions with complex 3D conductivity models (e.g., Gao et al (2021); Marshalko et al (2021Marshalko et al ( , 2023; Rosenqvist et al (2022)). When the geoelectric field is known, calculation of GIC in power grids (Pirjola et al, 2022) or pipelines (Boteler, 2013) is a straightforward task.…”