Velocity and attenuation of elastic waves in finely layered porous rocks

Abstract

SUMMARY We perform a theoretical study of the effect of fine layering on the compressional-wave velocities and attenuation coefficients in fluid-saturated rocks. This effect in a permeable rock differs from that in a purely elastic solid because of the local flow of the pore fluid across the interfaces, which is caused by the passing wave. For analytical calculations. Biot theory is applied to non-homogeneous (randomly and periodically layered) porous media leading to Biot's equations with variable coefficients. By analysing these equations with the help of a statistical perturbation technique we obtain the velocity and normalized attenuation 1/Q of the fast compressional wave as a function of frequency f. Both attenuation and velocity dispersion are found to obtain their maximum values near some frequency f0, at which the Biot slow-wave attenuation length equals the mean inhomogeneity size (mean layer thickness or characteristic length). In the low-frequency limit, 1/Q is proportional to f1/2 for random and to f for periodic layering. At frequencies higher than f0, attenuation decreases with increasing frequency as f−1/2, regardless of the particular type of layering. The results for periodic layering are in a good agreement with recently published exact results. The results for the more realistic case of random layering with exponential correlation reveal more gradual changes of velocity and attenuation versus frequency than those for a periodically layered medium.