Pan, X.P., Zhang, G.Z., Chen, H.Z. and Yin, X.Y., 2018. Elastic impedance parameterization and inversion in a vertical, rotationally invariant fractured HTI medium. Journal of Seismic Exploration, 27: 227-254. Seismic wave propagating in a purely isotropic background medium containing a single set of vertically aligned fractures exhibits a long-wavelength effective transversely isotropy (HTI) with a horizontal symmetry axis. The estimation of fracture weaknesses is significant for the characterization of anisotropy in a fracture-induced HTI medium. Our goal is to demonstrate an azimuthal elastic impedance inversion approach for fracture characterization by utilizing the observable wide-azimuth seismic reflection data in a vertical, rotationally invariant fractured reservoir. Under the assumption of weak contrast across the interface and weak anisotropy, we first derive the perturbations in elastic stiffness parameters of a weakly HTI medium. Then we derive a linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, and fracture weaknesses for the case of a weak-contrast interface separating two weakly HTI media based on the perturbation matrix and scattering function. Using the least square ellipse fitting (LSEF) method to calculate the azimuth of fracture normal, we build a perfect linear relationship between the reflection coefficient and fracture weaknesses. Finally, we propose a novel parameterization method for fracture weaknesses, and derive the elastic impedance variation with angles of incidence and azimuth (EIVAZ) equation. In order to refine the inversion stability and lateral continuity, we implement the EIVAZ inversion in a Bayesian framework incorporating the Cauchy-sparse regularization and the low-frequency information regularization, and the nonlinear iteratively reweighted least squares (IRLS) strategy is employed to solve the linear inversion problem. A test on a real data set indicates that the estimated results agree well with the well log interpretation, and the proposed method appears to generate reliable results for the characterization of fractured reservoirs.