Modeling P-waves in complex rock structures with the phononic lattice solid method

The Phononic Lattice Solid method is a Lattice Gas and Lattice Boltzmann based approach to simulate macroscopic wave phenomena in complex solids. It models number densities of wave-like particles propagating and interacting on a discrete lattice. The particles are partially reflected and transmitted at boundaries between lattice links with different properties (i.e. particle speed and medium density). In the macroscopic limit, the phononic lattice solid simulates compressional acoustic waves in inhomoge-neous media. The 2-D section of a fractured rock can thus be modeled by specifying values of the particle speed and density for the rock itself or for the inside of fractures at each grid node. About 50 grid nodes per wavelength are necessary to reach the macroscopic limit (where numerical convergence and isotropy are ensured). The simulation shows that the P-wavespeed stays isotropic while the length and amplitude of the codas are anisotropic. These results are in qualitative agreement with laboratory measurements of P-waves in thin fractured plexyglass. This approach could potentially be used to investigate the causes of seismic anisotropy and attenuation which are thought to be controlled by the microscopic geometry of rock matrices, micro-fractures, and their coupling to pore fluids. Generalisation of the Phononic Lattice Solid method for full elastic waves (i.e. P-waves and S-waves in 3-D) is however required for such studies.