Dispersion and attenuation of acoustic waves in randomly heterogeneous media

We derive the effective displacement relation for acoustic waves in a spati ally random heterogeneous one-dimensional medium. This relationship is expr essed in terms of parameters sigma(R) and sigma(A) which represent the stan dard deviations of the randomly varying density rho(x) and the randomly var ying Young's modulus alpha(x), of the medium. In this way we build the cont ributions into the total displacement relationship for the spatially random heterogeneous medium and apply this result to determine the dispersion and attenuation of acoustic waves propagating in the random heterogeneous medi um. Attenuation and dispersion of waves propagating in media with randomly varying properties has been the subject of much study. Most of this work ha s neglected the effects of intrinsic dispersion and attenuation in order to concentrate on the effects of the medium inhomogeneities. We demonstrate h ow intrinsic attenuation may be easily included in the theoretical developm ent, and explore the combined effects of scattering-based and intrinsic att enuation and dispersion on wave propagation. We apply the solution to model interwell acoustic waves propagating in the Kankakee formation at the Buck horn Test Site, IL. The modeling results show that the strong dispersion in the frequency range of 500-2000 Hz is due to the reservoir heterogeneity. Alternatively, the velocity dispersion for frequencies greater than 2000 Hz corresponds to the intrinsic properties of the reservoir. (C) 1999 Elsevie r Science B.V. All rights reserved.