Contact microphysics and viscous relaxation in sandstones

We present a microphysical model for acoustic attenuation and dispersion in sedimentary materials. The theory governs the response of two grains in contact to small sinusoidal loadings. Surface energy and fluid saturation are included explicitly. Grain surfaces are microscopically rough and irregular. We postulate that contact between grains forms numerous small solid‐solid contacts and that narrow interconnected gaps remain between the surfaces. The stress relaxation is hydrodynamic. As the grains oscillate, liquid must be squeezed out of and sucked back into the gaps. The theory offers a unified explanation of several heretofore apparently unrelated observations. The resulting equations predict the stiffness and loss as a function of frequency, effective pressure, fluid adsorption, saturation, viscosity, and temperature. Insofar as the micromechanical predictions relate to continuum acoustic properties, the agreement with observation is excellent.