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Frequency-dependent anisotropy in porous rocks with aligned cracks containing compressible fluid–a model based on poroelastic spring condition and exact solution of scattering by a circular crack at oblique incidence


 Thorough understanding of seismic signatures in cracked rocks is essential to estimate rock physical properties. Wave-induced fluid flow (or diffusion), scattering and Biot's global flow are three major mechanisms in controlling frequency-dependent attenuation and dispersion. To shed light on how those mechanisms and their interference affect the anisotropic features in cracked porous rocks, we develop an analytic model to estimate the angle-dependent attenuation and dispersion in such media. The most noteworthy feature of the model is that it is developed upon the exact solution of the problem of elastic wave scattered by a crack at oblique incidence. In particular, the poroelastic spring condition is applied to describe the influences of crack thickness and crack-filling fluid elasticity on wave scattering. Regardless of its complexity, we have showed that the model agrees with many benchmark theories under corresponding conditions, demonstrating its reasonability. It is found that the key factors that dominate anisotropic attenuation and dispersion are different in separating frequency regimes. At diffusion-dominated frequencies, the frequency-dependent anisotropic properties are mainly determined by the normal stress on the crack faces. In contrast, in Rayleigh scattering regime, they are greatly determined by the applied shear stress. At higher frequencies (Mie scattering regime), affected by the wave reflections between the crack edges, the frequency-dependent anisotropy becomes complex. The angle-dependent velocity can largely deviate from elliptic-shaped profile. As a result, the material properties cannot be described within the framework of the transversely isotropic medium model. Moreover, it is found that the attenuation is sensitive to the fluid compressibility and crack thickness, showing evidences that it is possible to invert fluid saturation and permeability from seismic attenuation. We also conclude that using a simple linear superposition of the attenuations due to wave-induced fluid flow and elastic scattering from their corresponding equivalent medium models will leads to an overestimation of the total attenuation. Our results demonstrate it is necessary to account for the mechanism interference to allow for an adequate estimation of the intrinsic attenuation of cracked porous rocks.