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Inversion of seismic amplitude variation with incident angle and azimuth (AVAZ) data for estimating fracture and fluid indicators is an important task. We first express reflection coefficient and azimuthal elastic impedance (AEI) in terms of fracture and fluid indicators, and based on the reflection coefficient and AEI, we proposed a two-stage inversion method of using azimuthal seismic data to estimate fracture and fluid indicators. To improve the accuracy of multi-parameter inversion, we consider establishing good initial models of multiple unknown parameters to constrain the inversion. We propose a novel method of employing pre-stacked seismic attributes (AVA intercept, isotropic and anisotropic gradients) to obtain initial models of fracture and fluid indicators. To further improve the multi-parameter inversion, we propose to employ Hessian matrix calculated using the first- and second-order derivatives of AEI to compute the perturbation in unknown parameter vector in the second stage of the proposed inversion method. We finally apply the proposed method to noisy synthetic and real data, which verifies that the proposed inversion method is robust and is capable of generating reliable fracture and fluid indicators that match well logging data. We conclude the proposed inversion method is a promising tool for predicting potentially hydrocarbon-bearing fractured reservoirs.