An Efficient 3-D Electromagnetic Forward Modeling based on A Nested Integral Equation Approach

Abstract:

Most of the existing Cartesian 3-D electromagnetic (EM) modeling solvers based on integral equation (IE) approach exploit 2-D fast Fourier transform (FFT) to accelerate the matrix-vector multiplication. Use of FFT in turn requires a laterally-uniform (LU) discretization of the modeling domain which might lead to excessive computational loads (in both memory and computational time). For example, it happens when a large region has to be modeled, but there is a need to properly account for the local small-scale inhomogeneities coming from topography and bathymetry. To address this problem, we developed a 3-D EM IE forward modeling tool based on the nested LU grids. Within this approach, the IE modeling at a large volume is first performed on a coarse grid. Then the results in the local region of interest are refined by conducting modeling at a smaller volume and on a denser grid, exploiting the coarse-grid solution. The usage of nested LU grids at both steps allows us to preserve the efficacy of FFT-based IE solutions. Tests on three 3-D conductivity models were performed to validate the accuracy and efficiency of the developed tool. We demonstrate that the tool is an order of magnitude more efficient – in terms of memory and CPU time – than one of the most advanced conventional IE solvers.