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

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 sec-ond-order staggered-grid finite-difference scheme over a nonuniform grid, achieving high accuracy with an arbitrarily high-order scheme. The finite-difference coefficients adap-tive to the node spacings can be accurately computed by inverting a Vandermonde matrix system using an efficient algorithm. A generic stability condition applicable to non-uniform 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, mak-ing it more efficient than the standard high-order FDTD with a densely sampled uniform grid. Instead of stretching in ver-tical and horizontal directions, better accuracy of our method is observed when the grid is stretched along the depth with-out horizontal stretching. The efficiency and accuracy of our method are demonstrated by numerical examples.

Automated summary

Researchers have developed a fictitious wave-domain high-order finite-difference time-domain (FDTD) modeling method to calculate frequency-domain 3D controlled-source electromagnetic data on nonuniform grids. The method accurately computes finite-difference coefficients adaptive to node spacings by inverting a Vandermonde matrix system using an efficient algorithm. Grid stretching in this method reduces the number of grid points required for discretization, making it more efficient.