Seismic wave propagation in fractured reservoirs exhibits anisotropy and attenuation, which are in turn related to fracture properties (e.g., fracture density) and fluid parameters (e.g., moduli and viscosity). Based on the linear slip theory, stiffness parameters can be determined for fractured and dissipative rocks, from which integrated attenuation factors involving host-rock intrinsic attenuation and fracture-induced attenuation emerge. Using a simplified mathematical form for these stiffness parameters, a linearized mathematical relationship directly relating the reflection coefficient to fracture weaknesses and integrated attenuation factors is available. A two-step inversion approach, involving (1) an iterative damped least-squares algorithm to predict P- and S-wave moduli using seismic angle gathers along the fracture orientation azimuth and (2) an iterative inversion method to estimate fracture weaknesses and integrated attenuation factors from azimuthal amplitude differences, is examined. The objective function for the second step is constructed based on a Bayesian framework. Synthetic testing confirms that fracture weaknesses and integrated attenuation factors are stably determined from seismic amplitudes exhibiting a moderate signal-to-noise ratio. The approach is applied to a field data set from a fractured carbonate reservoir. We observe that geologically reasonable results of fracture weaknesses and integrated attenuation factors are obtained. We conclude that this estimation procedure provides a reliable tool in fracture prediction and inverted attenuation factors appear as additional proofs to identify fluid type in fractured reservoirs.