3-D time-domain electromagnetic modeling based on multi-resolution grid with application to geomagnetically induced currents

Abstract Time-domain electromagnetic modeling in 3-D requires the solution of partial differential equations discretized on a grid. The finer grid resolution is usually required to describe rapid variations of the electromagnetic field in the near-surface, where the source and small-scale anomalies present. Since the electromagnetic field diffuses in the lossy medium, its variations become smoother with depth. The conventional finite-difference modeling approach using the staggered grid extends the fine grid resolution (needed for shallow layers) to all depths. It results in over-discretization of the problem and redundant computational costs. Here, we apply the multi-resolution (MR) grid approach to the time-domain electromagnetic modeling (TDEM). The MR grid allows us to decrease the grid resolution with depth and consequently reduce the number of degrees of freedom without compromising the accuracy of the solution. We implement a way of treating the loop source in TDEM modeling such that the definition of the source term is based on the Biot-Savart law; this allows separation of the loop source from the grid, making the source simulation more flexible. To verify our new TDEM modeling, we perform several synthetic tests. We also apply the algorithm to model the geomagnetically induced electric field (GIE). Such modeling is an essential part of estimating hazards caused by geomagnetically induced currents (GIC). In contrast to frequency-domain modeling primarily used in previous studies, the time-domain GIE modeling allows us to consider the time variability of the source in the ionosphere in real-time. For more realistic simulations, we use a large-scale 3-D resistivity model of Fennoscandia. An example of the MR grid GIE modeling highlights the areas of high GIE contrasts and shows that the real inhomogeneous 3-D resistivity distribution and realistic source geometry are necessary for a better estimation of GIC.