Seismic attenuation in porous rocks with random patchy saturation

Saturation of porous rocks with a mixture of two fluids has a substantial effect on seismic-wave propagation. In particular, partial saturation causes significant attenuation and dispersion of the propagating waves due to the mechanism of wave-induced fluid-flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. Most models of attenuation and dispersion due to mesoscopic heterogeneities imply that fluid heterogeneities are distributed in a regular way. However, recent experimental studies show that mesoscopic heterogeneities have less idealized distributions and that the distribution itself affects attenuation and dispersion. Based on an approximation for the coherent wavefield in random porous media, we develop a model which assumes a continuous distribution of fluid heterogeneities. As this continuous random media approach assumes that there will be a distribution of different patch sizes, it is expected to be better suited to modelling experimental data. We also show how to relate the random functions to experimentally measurable parameters.