VELOCITY AND ATTENUATION OF ELASTIC-WAVES IN FINELY LAYERED POROUS ROCKS

We perform a theoretical study of the effect of fine layering on the c ompressional wave velocities and attenuation coefficients in fluid-sat urated rocks. This effect in a permeable rock differs from that in a p urely elastic solid because of the local flow of the pore fluid across the interfaces, which is caused by the passing wave. For analytical c alculations, Blot theory is applied to non-homogeneous (randomly and p eriodically layered) porous media leading to Blot's equations with var iable coefficients. By analysing these equations with the help of a st atistical perturbation technique we obtain the velocity and normalized attenuation 1/Q of the fast compressional wave as a function of frequ ency f. Both attenuation and velocity dispersion are found to obtain t heir maximum values near some frequency fo, at which the Blot slow-wav e attenuation length equals the mean inhomogeneity size (mean layer th ickness or characteristic length). In the low-frequency limit, 1/Q is proportional to f(1/2) for random and to f for periodic layering. At f requencies higher than f,, attenuation decreases with increasing frequ ency was f(-1/2), regardless of the particular type of layering. The r esults for periodic layering are in a good agreement with recently pub lished exact results. The results for the more realistic case of rando m layering with exponential correlation reveal more gradual changes of velocity and attenuation versus frequency than those for a periodical ly layered medium.