Effective properties of a poroelastic medium containing a distribution of aligned cracks

Abstract

We simulate the effect of fractures by considering them to be thin circular cracks in a poroelastic background. Using the solution of the scattering problem for a single‐crack and multiple‐scattering theory, we estimate the attenuation and dispersion of elastic waves in a porous medium containing a sparse distribution of cracks. When comparing with a similar model, in which multiple‐scattering effects are neglected, we find that there is agreement at high frequencies and discrepancies at low frequencies. We conclude that the interaction between cracks should not be neglected at low frequencies, even in the limit of weak crack density. Since the models only agree with each other at high frequencies, when the time available for fluid diffusion is small, we conclude that the interaction between cracks, which is a result of fluid diffusion, is negligible at high frequencies. We also compare our results with a model for spherical inclusions and find that the attenuation for spherical inclusions has exactly the same dependence upon frequency but a difference in magnitude, which depends upon frequency. Since the attenuation curves are very close at low frequencies, we conclude that the effective medium properties are not sensitive to the shape of an inclusion at wavelengths that are large compared with the inclusion size. However, at frequencies such that the wavelength is comparable to or smaller than the inclusion size, the effective properties are sensitive to the greater compliance of the flat cracks, and more attenuation occurs at a given frequency as a result.