Prestack anisotropic (orthotropic symmetry) AVAz inversion of full-azimuth 3D seismic data for fracture characterization of the upper Najmah Formation in northern Kuwait was conducted. This formation comprises a thin, tight, naturally fractured carbonate overlying a kerogen-rich shale source rock. The inversion methodology uses an orthotropic system of symmetry that is appropriate for analysis of vertical transverse isotropic (VTI) anisotropic rock layers containing swarms of aligned vertical fractures. Measured seismic amplitudes show good agreement with synthetic models created at different well locations, indicating reliable representation of fractures in amplitude data. Inversion results show good agreement with well and drilling data. Rock-physics modeling shows a relationship between elastic properties and seismic anisotropy and between elastic properties and reservoir properties, such as porosity and fracture density.