Attenuation and dispersion of compressional waves in porous rocks with aligned fractures

Abstract

Fractures in a porous rock can be modeled as very thin and highly porous layers in a porous background. Elastic moduli of such fractured medium can be obtained using the result of Norris (1993) for wave propagation in periodically layered poroelastic media. When this porous fractured system is dry, it is equivalent to a transversely isotropic dry elastic porous material with linear-slip interfaces. When saturated with a liquid this system exhibits significant attenuation and velocity dispersion due to wave-induced fluid flow between pores and fractures. The characteristic frequency of such attenuation and dispersion depends on the background permeability, fluid viscosity, as well as fracture density and spacing. The theoretical results are in a good agreement with numerical simulations using the reflectivity algorithm generalized to poroelasticity.