An improved nearly analytical discrete method: an efficient tool to simulate the seismic response of 2-D porous structures

Abstract

The nearly analytic discrete method (NADM) for acoustic and elastic waves in porous elastic media is a perturbation method recently proposed by Yang et al (2006a Commun. Comput. Phys. 1 528–47). This method uses the truncated Taylor series expansion to approximate the time derivatives and the local high-order interpolation to approximate the spatial high-order derivatives by simultaneously using the displacements and its gradients and the velocity. As a result, it can suppress effectively numerical dispersions caused by the discretizing the wave equations when too-coarse grids are used. In this paper, we present an improved nearly-analytic discrete method (INADM) for the porous case. We compare numerically the error of the INADM with those of the original NADM and the so-called Lax–Wendroff correction (LWC) schemes for 1-D and 2-D cases, and give the wave-field modelling in 2-D porous isotropic and anisotropic media. We show that, compared with the original NADM, the INADM for the 2-D case can reduce significantly the storage space and increase time accuracy, while the space accuracy remains the same as that of the original one. Numerical experiments show that the error of the INADM for the porous case is less than those of the NADM and the fourth-order LWC scheme. The three-component seismic wave-fields in the 2-D porous isotropic medium are compared with those obtained by using the NADM, the LWC method, and exact solutions. Several characteristics of waves propagating in porous anisotropic media, computed by the INADM, are also reported in this study. Promising numerical results illustrate that the INADM provides a useful tool for large-scale porous problems and it can effectively suppress numerical dispersions.