An Optimal Nearly Analytic Discrete Method for 2D Acoustic and Elastic Wave Equations

In this article, we present the so-called optimal, nearly analytic, discrete method (ONADM), which is an improved version of the NADM proposed recently (Yang et al., 2003a). We compare numerically the error of the ONADM with those of the NADM and other finitedifference methods for 1D and 2D cases, and give wavefield modeling in 2D isotropic media. We also discuss the validity of the n-times absorbing boundary condition, when absorbing boundary conditions are incorporated in the ONADM. We show that, compared with the original NADM, the ONADM for the 2D case can significantly reduce storage space and computational cost. The temporal accuracy of the optimal method is also increased from second order in the original NADM to fourth order, and spatial accuracy remains the same as that of the original. Promising numerical results suggest that the ONADM is suitable for large-scale numerical modeling, as it can suppress effectively numerical dispersion caused by discretizing the wave equations when too coarse grids are used.