Low-frequency dispersion and attenuation in partially saturated rocks

A theory is developed for the attenuation and dispersion of compressional waves in inhomogeneous fluid-saturated materials. These effects are caused by material inhomogeneity on length scales of the order of centimeters and may be most significant at seismic wave frequencies, i.e., on the order of 100 Hz. The micromechanism involves diffusion of pore fluid between different regions, and is most effective in a partially saturated medium in which liquid can diffuse into regions occupied by gas. The local fluid flow effects can be replaced on the macroscopic scale by an effective viscoelastic medium, and the form of the viscoelastic creep function is illustrated for a compressional wave propagating normal to a layered medium. The wave speeds in the low- and high-frequency limits are associated with conditions of uniform pressure and of uniform “no-flow,” respectively. These correspond to the isothermal and isentropic wave speeds in a disordered thermoelastic medium.