Frequency-dependent anisotropy due to non-orthogonal sets of mesoscale fractures in porous media

Abstract

The monoclinic medium with a horizontal symmetry plane is gradually being studied for seismic anisotropy characterization. The principle goal of this paper is to investigate the effect of fracture parameters (azimuth angle, density, aspect ratio, scale) on the exact and approximate monoclinic anisotropy parameters. We derive the monoclinic porous media based on the Chapman model which accounts for the wave-induced fluid flow and give the expressions of the Thomsen-style anisotropy parameters (nine orthorhombic anisotropy parameters: V_P0, V_S0, ε₁, ε₂, γ₁, γ₂, δ₁, δ₂, δ₃, three exact monoclinic parameters: ζ₁, ζ₂, ζ₃, and three approximate monoclinic parameters:|$\widetilde{\zeta _{1}}, \widetilde{\zeta _{2}}, \widetilde{\zeta _{3}}$|⁠). The dependence of Thomsen-style anisotropy parameters associated with azimuth angle between two fracture sets is analyzed. The orthorhombic anisotropy parameters and monoclinic anisotropy parameters have the same period (π) on the azimuth angle between two fracture sets. The exact and approximate monoclinic anisotropy parameters responsible for the rotation of the P-wave NMO ellipse have a similar trend versus the azimuth angle, while those responsible for the rotation of the S1- and S2-wave NMO ellipses have significant discriminations. The influence of fracture density, aspect ratio, and scale on the monoclinic parameters are also analyzed. The monoclinic anisotropy parameters responsible for the rotation of the P-wave NMO ellipse decrease with fracture density and aspect ratio increasing from 0 to 0.1, while those responsible for the rotation of S1- and S2-wave NMO ellipses increase with the fracture parameters. The fracture density has a bigger influence on the monoclinic anisotropy parameters than the fracture aspect ratio. When saturated with different fluids (water and CO₂), the monoclinic parameters have a similar behavior versus the azimuth angle between two fracture sets.