Numerical experiments for elastic wave propagation: analyses for accuracy and partially saturated fluid effects

Abstract

Summary Two-dimensional elastic wave propagation simulation using staggered pseudo-spectral (PS) and high-order finitedifference (FD) methods are studied and the results are compared with each other. Our numerical modeling shows that, although the PS methods given less spatial dispersions than the high-order FD method, they generate more spatial noises because of its global operators. This is true even for staggered PS method in a homogeneous formation; while the high-order FD method does not possess this feature. For strong heterogeneous formations, the high-order FD balances the lower-order FD and infinite-order FD or pseudo-spectral procedure and does a better job. Furthermore, based on Biot’s porous elastic models, elastic wave propagation in rock samples with three-phase fluids is calculated with the high-order FD method. The rocks are assumed to be partially saturated with water, oil and gas. A random function is used to form uniform random pore fluid distributions. The numerical experiment shows some interesting features of variation in P-wave and slow P-wave velocity and attenuation with variation of saturation (oil and gas) and source center frequencies. The saturations of the two phases strongly affect the P-wave velocity and attenuation in some special situation, which is an important clue on seismic exploration and acoustic logging interpretation. The wave modes in the fluids-filled porous media are converted back and forth that attenuate gradually, especially for heterogeneous pore fluids.