Azimuthal variations of wavefield characteristics, such as traveltime or reflection amplitude, play an important role in the identification of fractured media. A transversely isotropic medium with a horizontal symmetry axis (HTI medium) is the simplest azimuthally anisotropic model typically used to describe one set of vertical fractures. There exist many techniques in industry to recover anisotropic parameters based on moveout equations and linearized reflection coefficients using such a model. However, most of the methods have limitations in defining properties of the fractures due to linearizations and physical approximations used in their development. Thus, azimuthal analysis of traveltimes based on normal moveout ellipses recovers a maximum of three medium parameters instead of the required five. Linearizations made in plane-wave reflection coefficients (PWRCs) limit the amplitude-versus-offset (AVO) analysis to small incident angles and weak-contrast interfaces. Inversion based on azimuthal AVO for small offsets encounters nonuniqueness in the resolving power of the anisotropy parameters. Extending the AVO analysis and inversion to and beyond the critical reflection angle increases the amount of information recovered from the medium. However, well-accepted PWRCs are not valid in the vicinity of the critical angle and beyond it, due to frequency and spherical wave effects. Recently derived spherical and effective reflection coefficient (ERC) methods overcome this problem. We extended the ERCs approach to HTI media to analyze the potential of near- and postcritical reflections in azimuthal AVO analysis. From the sensitivity analysis, we found that ERCs are sensitive to different sets of parameters prior to and beyond the critical angle, which is useful in enhancing our resolution of the anisotropy parameters. Additionally, the resolution of the parameters depends on a sufficient azimuthal coverage in the acquisition setup. The most stable AVO results for the azimuthal acquisition setup with minimum number of lines (three) are achieved when the azimuthal angle between lines is greater than 45°.