Estimation of in situ stresses from PP-wave azimuthal seismic data in fracture-induced anisotropic media

Abstract

Horizontally transverse isotropy (HTI) induced by vertical or subvertical aligned fractures is common for unconventional fractured porous shale oil or gas reservoirs. Compared with the unfractured rocks, the seismic response characteristics of PP-wave azimuthal amplitudes are usually disturbed by the fractures and the in situ stresses. Knowledge of fracture properties, as well as in situ stresses, is required to optimize horizontal well planning and hydraulic fracturing during production, and the seismic inversion for in situ stresses from the PP-wave azimuthal amplitude data in fracture-induced anisotropic media is an essential step. Using the linear-slip theory and the effective stress law, we derive the fluid-saturated effective elastic stiffness tensors parameterized by background elastic moduli, the effective stress coefficient of isotropic host rocks, fluid modulus, porosity, and fracture parameters based on the anisotropic Gassmann’s fluid substitution equation. Combining the perturbations in saturated stiffness tensors and scattering theory, we formulate the reflection coefficient equation of PP-wave data as a function of background porosity-related stress parameter and two (i.e., normal and shear) fracture weakness parameters. Following Bayes’ rule, we estimate the porosity-related stress parameter and fracture weaknesses using the inversion method of azimuthal Fourier coefficients. Finally, we compute the effective horizontal and vertical in situ stresses using the estimated elastic moduli, porosity-related stress parameter, and fracture weaknesses. Synthetic and real data sets demonstrate that our proposed inversion approach based on the derived reflection equation provides us another way to obtain reasonable estimates of in situ stresses in a complex-fractured porous shale reservoir.