Seismic modeling using the phononic lattice solid method

Accurate methods for modeling seismic waves are required if the goal of inverting seismic data for rock properties is to be attained. But how can seismic waves be modeled in rocks with a high degree of inhomogeneity or containing microscopic features such as fractures and fluid filled pore spaces? The "phononic lattice solid" is an alternative to advanced present day approaches such as finite-differences, which may handle these important cases. Unlike finite-differences which is based on a discretization of the continuous equations of physics (the wave-equation), the phononic lattice solid is a cellular automaton for simulating seismic waves which models the microscopic "quanta" of an elastic lattice. These quanta, called phonons, represent lattice vibrations. They move and "collide" on the discrete lattice exactly conserving momentum and energy from a probabilistic viewpoint. At the macroscopic scale, the phonon distributions behave like compressional seismic waves. Because the method is based on the microscopic process underlying wave propagation, it is well suited to simulations of waves in media with microscopic features. The lattice solid method directly models a physical equation (the wave-equation) and consequently fits perfectly onto massively parallel computer architectures such as that of the 65,536 processors Connection Machine. Considering the massively parallel computer revolution is progressing in leaps and bounds, the yet expensive lattice solid method is rapidly becoming more feasible.