Seismic properties of rocks with distributions of small cracks

Abstract

SUMMARY Hudson's theory of multiple scattering for the dynamic properties of cracked rock is applied to media containing cracks of varying orientation, radius and aspect ratio. Angular variation of velocity and attenuation due to parallel and nearly parallel cracks and cracks with normals at a fixed angle to a given axis are presented. Anisotropy gradually decreases as the distribution of orientations is widened from exactly parallel to random. Increasing the aspect ratio of thin saturated cracks generally causes the elastic properties to approach those due to dry (gas-filled) cracks. For fluid-filled cracks the line singularity where the birefringent shear waves have equal velocity moves closer to the symmetry axis as either the distribution of orientations is widened or the aspect ratio is increased. Calculated attenuations due to Rayleigh scattering and viscous dissipation in crack-filling fluids are many orders of magnitude less than reported attenuations in the Earth. Viscous dissipation varies linearly with frequency and aspect ratio of thin fluid-filled cracks. A power-law distribution of crack radii, intended to represent that found in the Earth's crust, has no effect on the angular variations of seismic velocities or viscous attenuation but scattering attenuation is sensitive to the power-law exponent. Lognormal distributions of aspect ratio, also corresponding to observations in real rock, affect velocity as well as attenuation. Velocities derived from the theory are compared with those measured in laboratory specimens with known geometries of cracks.