The phononic lattice solid by interpolation for modeling P-waves in heterogeneous media

The phononic lattice solid (PLS) approach based on a finite difference scheme to solve a transport equation has been developed recently for modeling compressional waves in hetroge-neous media. The significant problems of the method are that it requires a small lattice spacing and cannot handle sharp interfaces. We develop an improved phononic lattice solid approach by interpolation for modeling P--waves in heterogeneous media by simulating underlying microscopic proccsscs - transportation, scattering and collision of quasi- -particles carrying pressure rather than solving the Boltzmann equation for the PLS by a finite--difference scheme. The transportation step of particles in the method has high precision using an interpolation algorithm while the transmission and reflection processes arc exact for any velocity or impedance contrasts. In the macroscopic limit, we obtain the Boltzmann equation for the PLS which leads to the wave equation for inhomogeneous acoustic media. Because the PLS by interpolation can handle sharp interfaces, we hope that it, will enable numerical experiments to be conducted of wave propagation through complex rocks (e.g. fractured, porous) to study the causes of anisotropy and attenuation.