ATTENUATION AND DISPERSION OF ELASTIC WAVES IN A POROELASTIC MEDIUM DUE TO RANDOM AND REGULAR DISTRIBUTION OF FLUID PATCHES

Fluid patches in partially saturated poroelastic medium at mesoscopic-scale may cause significant attenuation and dispersion of elastic waves due to wave-induced flow of the pore fluid between more compliant to less compliant areas. Several recent theories describe this phenomenon. The new model based on the multiple scattering theorem assuming randomly distributed spherical inclusions was developed by Ciz et al. (2005). Three other theories based on periodic distribution of inclusions (White, 1975, Johnson, 2000, Pride & Berryman, 2003) are considered for inclusions of spherical shape. This geometry enables the derivation of the exact analytical formulas for the P-wave attenuation and seismic velocity dispersion for all four models. The derived expressions served for the numerical comparisons of analyzed models and for the analytical derivation of the asymptotical behavior. The velocity prediction is consistent with Wood equation at low frequencies and with upper Hill’s law for high frequencies. The frequency dependence of the attenuation has a form of a relaxation peak, with the maximum of the dimensionless attenuation (inverse quality factor) at a frequency at which the wavelength of the Biot’s slow wave is approximately equal to the characteristic size of the inclusion. Attenuation scales with at low frequencies and with-1/2 at high frequencies. For the wide range of rock and fluid parameters all models demonstrate very similar quantitative behavior for velocity dispersion and attenuation. In particular, in contrast to 1-D case, random but isotropic distribution of heterogeneities in a porous medium produces essentially the same attenuation and dispersion as their regular distribution