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

TL;DR

This paper introduces a high-order finite-difference time-domain method on nonuniform grids for efficient and accurate 3D controlled-source electromagnetic simulations in Earth sciences, overcoming limitations of conventional schemes.

Contribution

The paper develops a high-order FDTD method on nonuniform grids with adaptive coefficients, establishing stability conditions and an optimal grid stretching scheme for improved efficiency and accuracy.

Findings

Achieves high accuracy with arbitrarily high order schemes.

Reduces computational cost by optimal grid stretching along depth.

Demonstrates superior efficiency and accuracy in numerical examples.

Abstract

Simulation of 3D low-frequency electromagnetic fields propagating in the Earth is computationally expensive. We present a fictitious wave domain high-order finite-difference time-domain (FDTD) modelling method on nonuniform grids to compute frequency-domain 3D controlled-source electromagnetic (CSEM) data. The method overcomes the inconsistency issue widely present in the conventional 2nd order staggered grid finite difference scheme over nonuniform grid, achieving high accuracy with arbitrarily high order scheme. The finite-difference coefficients adaptive to the node spacings, can be accurately computed by inverting a Vandermonde matrix system using 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 both 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.