Controlled-source electromagnetic modeling using a high-order finite-difference time-domain method on a nonuniform grid

Abstract

Simulation of 3D low-frequency electromagnetic (EM) fields propagating in the earth is computationally expensive. We have developed a fictitious wave-domain high-order finite-difference time-domain (FDTD) modeling method on nonuniform grids to compute frequency-domain 3D controlled-source EM data. The method overcomes the inconsistency issue widely present in the conventional second-order staggered-grid finite-difference scheme over a nonuniform grid, achieving high accuracy with an arbitrarily high-order scheme. The finite-difference coefficients adaptive to the node spacings can be accurately computed by inverting a Vandermonde matrix system using an efficient algorithm. A generic stability condition applicable to nonuniform grids is established, revealing the dependence of the time step and these finite-difference coefficients. A recursion scheme using fixed-point iterations is designed to determine the stretching factor to generate the optimal nonuniform grid. The grid stretching in our method reduces the number of grid points required in the discretization, making it more efficient than the standard high-order FDTD with a densely sampled uniform grid. Instead of stretching in vertical and horizontal directions, better accuracy of our method is observed when the grid is stretched along the depth without horizontal stretching. The efficiency and accuracy of our method are demonstrated by numerical examples.