New advances in FDTD methods for electromagnetic and elastic waves for probing complex media

For modeling large-scale 3-D problems in electro-magnetic and elastic waves in the probing of complex media, the finite-difference time domain (FDTD) method is widely used. However, there are still challenges in the high-frequency regime and extremely low-frequency regime, as well as in the accurate curved boundary treatment in this method. In this work, we report several new improvements in the FDTD method to address these challenging issues: (a) We have developed a high-order FDTD method for elastic waves to greatly reduce the numerical dispersion errors, and computer memory and CPU time requirements, with a novel treatment of the free ground boundary condition and the fluid-solid interface condition. (b) We have proposed a new numerical method, finite volume method and enlarged cell technique (ECT), to accurately and efficiently implement the free-surface boundary conditions in FDTD elastic wave simulations of an arbitrary ground-surface topography. (c) We have developed an implicit FDTD scheme that allows a time step increment many orders of magnitude beyond the stability condition in the explicit FDTD method for extremely low frequency electromagnetic probing of subsurface, based on the Crank-Nicolson scheme together with the perfectly matched layer. The efficacy of these methods and their large scale applications will be demonstrated in the presentation.