Seismic attenuation due to wave-induced fluid flow in a porous rock with spherical heterogeneities

Most natural porous rocks have heterogeneities at nearly all scales. Heterogeneities of mesoscopic scale that is, much larger than the pore size but much smaller than wavelength can cause significant attenuation and dispersion of elastic waves due to wave induced flow between more compliant and less compliant areas. Analysis of this phenomenon for a saturated porous medium with a small volume concentration of randomly distributed spherical inclusions is performed using Waterman-Truell multiple scattering theorem, which relates attenuation and dispersion to the amplitude of the wavefield scattered by a single inclusion. This scattering amplitude is computed using recently published asymptotic analytical expressions and numerical results for elastic wave scattering by a single mesoscopic poroelastic sphere in a porous medium.This analysis reveals that attenuation and dispersion exhibit a typical relaxation-type behavior with the maximum attenuation and dispersion corresponding to a frequency where fluid diffusion length (or Biot's slow wave length) is of the order of the inclusion diameter. In the limit of low volume concentration of inclusions the effective velocity is asymptotically consistent with the Gassmann theory in the low-frequency limit, and with the solution for an elastic medium with equivalent elastic inclusions (no-flow solution) in the low-frequency limit. Attenuation (expressed through inverse quality factor ) scales with frequency in the low frequency limit and with in the high frequency limit. These asymptotes are consistent with recent results on attenuation in a medium with a periodic distribution of poroelastic inclusions, and in continuous random porous media