Abstract: Hydraulic fracturing is a crucial technology for improving permeability and production of shale reservoirs. The precise estimation of the stress distribution has a significant guidance for optimizing the placement of hydraulic fracturing. Assuming that the shale gas reservoir is a weakly anisotropic medium with orthorhombic symmetry, a new stress indicator parameterized by rock mechanical parameters and fracture parameters is firstly presented to predict the differential horizontal stress ratio in shale gas reservoirs. Then, we derive a novel simplified P-to-P reflection coefficient and a logarithmic normalized elastic impedance (EI) as a function of Young's modulus, Poisson's ratio, Thomsen's WA parameter δb and normal excess compliance ZN. Next, we adopt azimuthal EI inversion in a Bayesian framework to estimate rock mechanics parameters and fracture parameters directly on a fractured shale gas field seismic data. Finally, the stress indicator is determined by utilizing four inverted parameters. Synthetic examples demonstrate that the proposed approach produces stable parameter estimates even with moderate noise, verifying the feasibility and effectiveness of the method. Test on a field data set illustrates that the inversion results can be reasonably estimated, and the stress indicator derived by the inversion accords with the geomechanics result. Compared with the previous method, the new stress indicator has a higher capability to describe stress characteristics in the shale reservoir. We conclude that this stress evaluation procedure can provide reliable guidance for well location deployment and hydraulic fracturing reformation.