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 methodoriginally proposed by Yang et al. (2003) [26] for acoustic and elastic waves in elasticmedia. This method is based on a truncated Taylor series expansion and interpolationapproximations and it can suppress effectively numerical dispersions caused by the discretizatingthe wave equations when too-coarse grids are used. In the present work, weapply the NADM to simulating acoustic and elastic wave propagations in 2D porousmedia. Our method enables wave propagation to be simulated in 2D porous isotropicand anisotropic media. Numerical experiments show that the error of the NADM for theporous case is less than those of the conventional finite-difference method (FDM) andthe so-called Lax-Wendroff correction (LWC) schemes. The three-component seismicwave fields in the 2D porous isotropic medium are simulated and compared with thoseobtained by using the LWC method and exact solutions. Several characteristics of wavepropagating in porous anisotropic media, computed by the NADM, are also reportedin this study. Promising numerical results illustrate that the NADM provides a usefultool for large-scale porous problems and it can suppress effectively numerical dispersions.