A Nearly Analytical Discrete Method for Wave-Field Simulations in 2D Porous Media (Communications in Computational Physics, 2006)
The nearly analytic discrete method (NADM) is a perturbation method\roriginally proposed by Yang et al. (2003) [26] for acoustic and elastic waves in elastic\rmedia. This method is based on a truncated Taylor series expansion and interpolation\rapproximations and it can suppress effectively numerical dispersions caused by the discretizating\rthe wave equations when too-coarse grids are used. In the present work, we\rapply the NADM to simulating acoustic and elastic wave propagations in 2D porous\rmedia. Our method enables wave propagation to be simulated in 2D porous isotropic\rand anisotropic media. Numerical experiments show that the error of the NADM for the\rporous case is less than those of the conventional finite-difference method (FDM) and\rthe so-called Lax-Wendroff correction (LWC) schemes. The three-component seismic\rwave fields in the 2D porous isotropic medium are simulated and compared with those\robtained by using the LWC method and exact solutions. Several characteristics of wave\rpropagating in porous anisotropic media, computed by the NADM, are also reported\rin this study. Promising numerical results illustrate that the NADM provides a useful\rtool for large-scale porous problems and it can suppress effectively numerical dispersions.
Keywords: Porous media; nearly-analytic discretization; three-component seismic wavefield; anisotropy; numerical dispersion.