Elastic wave modelling method based on the displacement-velocity fields : an improving nearly analytic discrete approximation

In this paper, we present an improvement to our previously published nearly analytic discrete method (NADM) to solve acoustic and elastic wave equations. We compare the numerical errors of the improved NADM with the original NADM and also the fourth-order Lax–Wendroff correction and present examples of three-component wave fields in 2D transversely isotropic media with strong velocity contrasts. Comparing with the original NADM, we find that the improved method requires significantly less storage space and can increase the time accuracy from second order of the original NADM to fourth order, while the space accuracy remains the same as that of the original one. Theoretical analyses and numerical results suggest that our improved NADM is suitable for large-scale numerical modelling as it can effectively suppress numerical dispersion and source-generated noises caused by discretising wave equations when too-coarse grids are used.