Seismic theory 3: Discrete grid methods wednesday morning, November 13th lattice boltzman phononic lattice solid (PLS) to model seismic P-waves

The phenomena of seismic anisotropy and attenuation are thought to be due to small scale features in rocks such as such as microfractures, the intrinsic Theological behaviour of the grains and nonlinear behaviour including wave induced fluid motions through porous media. The lattice Boltzman phononic lattice solid (PLS) could provide a direct numerical approach to model such effects. This approach is based on the phononic lattice solid method (Mora and Maillot (1990, 1991a)) which models elastic wave packets (phonons) propagating and colliding on a discrete lattice using a lattice gas-like cellular automaton. Rather than dealing with the phonon "particles" themselves, the lattice Boltzman approach deals with the particle number densities, propagating them with a finite-difference approximation to the Boltzman transport equation and modeling their interactions with one another and the medium using a modified "collision term" (Mora and Maillot (1991b)). All calculations are floating-point and hence the lattice Boltzman approach is better suited to floating-point computer architectures than the boolean method which requires calculations to be performed on large grids in order to achieve precise results. Comparisons between numerical results obtained by the lattice Boltzman PLS and a classical finite-difference scheme to model seismic P-waves in an inhomogeneous medium verify the approach. Future research is required to introduce SI and S2 phonons and one-or multi-phase pore fluids in order exploit the approach for seismic anisotropy and attenuation studies.