Anisotropic P-SV-wave attenuation and dispersion in finely layered porous media

Rocks often show a finely layered structure with randomly distributed medium properties. An understanding of anisotropic attenuation and dispersion is significant for characterizing and identifying finely layered rocks with applications especially in geomechanics, exploratory geophysics, and hydrogeology. Previous analytical studies on seismic attenuation and dispersion in randomly layered poroelastic rocks are restricted to the normal incidence of P waves. We develop a frequency-dependent anisotropic effective medium model for quasi-P and SV waves. Derivations follow the generalized O’Doherty-Anstey approach, and the solutions are validated by comparing with the global matrix method. Unlike most existing models that focus on only one kind of attenuation mechanisms, the present model incorporates all of interlayer flow, elastic scattering, and Biot’s global flow together and can be regarded as a unified model valid over a broad frequency range. At interlayer-flow-dominated frequencies, an equivalent vertically transversely isotropic medium is developed. Sensitivity analysis indicates that the fluctuation in fluid bulk modulus has the greatest effect on the interlayer-flow attenuation of the quasi-P wave, whereas only the fluctuation in shear modulus influences the interlayer-flow attenuation of the quasi-SV wave. Moreover, we find that the spatial correlation structures also have effects on attenuation even if the variances of medium fluctuations are kept the same. Numerical examples indicate that the model can be used to remove the misfit at zero offset to obtain the amplitude-variation-with-offset intercept of higher accuracy at interlayer-flow/elastic-scattering-dominated frequencies.