Seismic characterization of anisotropic in situ stress is of great importance in improving the success of planning drilling and hydraulic fracturing treatment. Shales generally exhibit orthorhombic elastic symmetry due to the presence of vertical fractures and horizontal fine layering. We propose a novel anisotropic extended elastic impedance (AEEI) inversion approach for in situ stress estimates in shale gas reservoirs with weakly orthorhombic symmetry. Considering an orthorhombic model formed by a system of aligned vertical fractures embedded in a vertical transverse isotropic (VTI) background rock, we first derive the in situ stress expression by combining poroelastic Hooke’s law and linear slip theory. Next, we deduce a linearized PP-wave reflection coefficient as a function of fluid bulk modulus, vertical effective stress-sensitive parameter, dry-rock P- and S-wave moduli, density, dry normal and tangential weaknesses of the VTI background, and dry normal and tangential weaknesses of vertical fractures. To estimate in situ stress from the observed seismic data, we derive the AEEI and Fourier coefficients (FCs) expression and establish a three-step AEEI inversion workflow involving (1) Bayesian seismic inversion for intercept impedance, gradient impedance, and curvature impedance estimates; (2) estimating model parameters using the FCs of AEEI; and (3) estimating in situ stress using the inverted model parameters. The synthetic examples demonstrate that in situ stress can be reliably estimated even with moderate noise. Test on a real data set implies that the proposed method can generate reasonable results of in situ stress that are helpful for optimizing the horizontal drilling and hydraulic fracture stimulations of shale gas reservoirs.

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