A rectangular-grid lattice spring model for modeling elastic waves in Poisson’s solidsRectangular LSM to model elastic waves

Lattice spring model (LSM) combined with the velocity Verlet algorithm is a newly developed scheme for modeling elastic waves propagation in solid media. Unlike conventional wave equations, LSM is established on the basis of micro-mechanics of the subsurface media, which enjoys better dynamic characteristics of elastic systems. We present a rectangular grid LSM scheme for elastic waves simulation in Poisson solids, and the direction-dependent elastic constants are deduced to keep the isotropy of the discrete grid. The stability condition and numerical dispersion properties of LSM are discussed and compared with other numerical methods. Two- and three-dimensional numerical simulations are carried out using the rectangular grid LSM, as well as the second and fourth order accuracy staggered finite difference method (FDM). Wavefields obtained by LSM are fairly similar with those by analytical solution (ANA) and FDM, which demonstrates the correctness of the proposed scheme and its capability of modeling elast...