ONE-DIMENSIONAL RANDOM PATCHY SATURATION MODEL FOR VELOCITY AND ATTENUATION IN POROUS ROCKS

Abstract

Existing models for seismic wave velocity dispersion and attenuation in porous rocks containing a mixture of two pore fluids are based on the assumption of a regular distribution of the fluid phases. However, in reality fluids are distributed in a random fashion forming fluid patches of varying shape and size. We develop a model to predict velocity dispersion and attenuation of such random structures based on the theory of statistical wave propagation. We demonstrate that the assumption of random fluid distribution results in a significantly different behavior of velocity and attenuation as functions of frequency and saturation. Specifically, the randomly layered patchy model predicts a much more gradual increase of P-wave velocity with frequency. This means that the effects of patchy saturation can be observed in a broader frequency range than previously assumed.