Detection of Natural Tilted Fractures From Azimuthal Seismic Amplitude Data Based on Linear-Slip Theory

Tilted transverse isotropy (TTI) is common for naturally fractured reservoir when the fractures exist a tilted axis of symmetry. Seismic characterization of natural tilted fractures from observable azimuthal reflected amplitude data, however, is quite difficult. We focus on the detection of natural tilted fractures from azimuthal seismic amplitude data, especially for low- and high-angle tilted fractures. Using the linear-slip theory, we first express the effective elastic stiffness matrix of a TTI medium as a function of background elastic moduli, fracture density, and three angles, including the incident angle, the azimuth angle, and the tilt angle. Based on the scattering function and the first-order perturbations in stiffness components across a weak-contrast reflection interface separating two weak-anisotropy TTI media, we then derive a weak-anisotropy and linearized PP-wave reflection coefficient containing the tilt angle and fracture density. For low- and high-angle aligned fracture sets, we formulate the low- and high-angle approximate PP-wave reflection coefficient equations, respectively, and propose a Bayesian seismic inversion approach to estimate the tilt angle and the corresponding fracture densities using the azimuthal differences in seismic reflected amplitude data. Synthetic and real datasets are used to demonstrate the feasibility and reliability of the proposed inversion approach. Test results make us believe that our proposed inversion approach allow us to obtain the tilted fracture properties of hydrocarbon reservoirs in a more accurate manner than previous cases of vertically transverse isotropy (VTI) or horizontally transverse isotropy (HTI).