In unconventional resources such as the Haynesville Shale, a proper understanding of natural fracture patterns is essential to enhancing the economic success of petroleum extraction. The spatial density of naturally occurring fracture sets affects drainage area and optimal drilling location(s), and the azimuth of the strike of the predominant fracture set affects the ideal orientation of wells. In the absence of data to directly determine these fracture characteristics, such as Formation Microimaging (FMI) logs, these natural fracture patterns can be analyzed by examining the seismic anisotropy present in the reservoir. Anisotropy introduced from aligned fracture sets creates predictable azimuthal variations in the seismic wavefield. This allows the reservoir anisotropy, and thus the fracturing present in the reservoir, to be studied indirectly through the azimuthal analysis of industry standard 3D seismic data. The work presented here outlines three distinct methodologies, which utilize azimuthal amplitude variations (AVAZ) present in 3D seismic data, to infer fracture characteristics without the need for substantial well log information. Two of these methods have been previously established and assume the reservoir to be characteristic of Horizontally Transverse Isotropic (HTI). The last method is novel and assumes orthorhombic anisotropy when inverting for fracture density and is able to unambiguously invert for fracture azimuth. All methodologies used in this work produced similar results, increasing confidence in the accuracy of these results through statistical repeatability. Fracture density inversion results indicate spatially varying fracture density throughout the area, with a distinct area of higher fracture density present in the Northwestern corner of the area analyzed. Spatially varying fracture density and localized pockets of fracturing is consistent with expectation from analyzing production data and FMI logs from other areas of the Haynesville. Fracture azimuth inversion results showed some variability; however, the novel method presented in this thesis indicates that the azimuth of the predominant fracture set is oriented at a compass bearing of approximately 82 degrees -- rotated slightly counterclockwise from an east-west orientation. Fracture azimuth results agree well with expectations from a regional stress analysis and from examining comparable formations with known fracture patterns in the surrounding area.