Numerical simulation of wave propagation in strongly heterogeneous media using a lattice solid approach

Strongly heterogeneous media such as those with fine layers and/or aligned heterogeneities and/or empty pores can pose problems for classical finite-difference methods to simulate wave propagation. This is due to the difficulties of handling sharp interfaces in these media and total reflections from boundaries of empty pores in a porous medium. The phononic lattice solid by interpolation (PLSI) is a microscopic approach to P wave propagation in strongly heterogeneous media. The method is capable of handling sharp interfaces and, therefore, provides a powerful tool to simulate wave propagation in such media. Numerical simulations by the PLSI to simulate P wave propagation in these media are presented. Anisotropy induced by fine layers and aligned heterogeneities is observed. Numerical results demonstrate that the scattering effect of empty pores is much stronger than non-empty heterogeneities. Ultimately, the approach could enable numerical experiments to be conducted to study the microscopic mechanisms responsible for anisotropy and attenuation of seismic waves. This would require the approach to be extended to the elastic case.