Estimating fluid term and anisotropic parameters in saturated transversely isotropic media with aligned fractures
Pan, X.P., Zhang, G.Z., Liu, JX. and Ren, Z.Y., 2020. Estimating fluid term and anisotropic parameters in saturated transversely isotropic media with aligned fractures. Journal of Seismic Exploration, 30: 65-84. The Gassmann’s equation and general linear-slip model can be combined to characterize the effective elastic properties of a fluid-saturated transversely isotropic medium with aligned fractures. Such a medium represents a saturated fractured porous rock with orthorhombic symmetry. Combining the analysis of orthorhombic anisotropic poroelasticity, we first propose the derivation for the weak-anisotropy stiffnesses of a saturated fractured porous medium with orthorhombic symmetry in terms of the moduli of the background homogeneous isotropic rock, Thomsen-type anisotropy parameters, fracture weaknesses, and fluid modulus. Compared with the exact stiffness components, the approximated components of saturated fractured porous media with orthorhombic symmetry satisfy the actual demands in practical use. Using the approximately linearized expressions of the stiffness components of saturated orthorhombic model with the assumption of small Thomsen-type anisotropic parameters and small fracture parameters, we then derive a linearized PP-wave reflection coefficient in such an orthorhombic model, including a fluid term, a rigidity term, a density term, two Thomsen-type anisotropy terms, and three fracture-weakness terms. With a novel parameterization for Thomsen-type anisotropy parameters and fracture weaknesses, we derive an azimuthal elastic impedance equation with decoupled fluid term and anisotropic parameters. Synthetic and real data sets are used to illustrate the proposed approach in fluid saturated fractured porous rocks with orthorhombic symmetry, Sichuan Basin, China.
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