Geometric attributes such as coherence and curvature have been very successful in delineating faults in sedimentary basins. While not a common exploration objective, fractured and faulted basement forms important reservoirs in Venezuela, USA (Southern California), Brazil, Libya, Algeria, Egypt, Russia, and Vietnam (Landes, 1960; Canh, 2008). Because of the absence of stratified, coherent reflectors, illumination of basement faults is more problematic than illumination of faults within the sedimentary column. In order to address these problems, it is important to carefully analyze alternative forms of the 3D seismic data, which in this dissertation will be primarily combinations of one or more seismic attributes, and interpret them within the context of an appropriate structural deformation model. For that purpose, in this research, I concentrate on analyzing structural dip and azimuth, amplitude energy gradients, and a large family of attributes based on curvature to better illuminate fracture `sweet spots' and estimate their density and orientation. I develop and calibrate these attribute and interpretation workflows through application to a complexly folded and faulted, but otherwise typical, geologic target in the Chicontepec Basin of Mexico. I then apply this calibrated workflow to better characterize faults and build fracture models in the granite basement of the Cuu Long Basin, Vietnam, and the granite and rhyolite-metarhyolite basement of Osage County, Oklahoma, USA. In the Cuu Long granite basement, it forms an important unconventional reservoir. In Osage County, we suspect basement control of overlying fractures in the Mississippian chat deposits.