In 3D seismic interpretation, curvature is a popular attribute that depicts the geometry of seismic reflectors and has been widely used to detect faults in the subsurface; however, it provides only part of the solutions to subsurface structure analysis. This study extends the curvature algorithm to a new curvature gradient algorithm and integrates both algorithms for fracture detection using a 3D seismic test data set over Teapot Dome (Wyoming). In fractured reservoirs at Teapot Dome formed by tectonic folding and faulting, curvature helps define the crestal portion of reservoirs that is associated with strong seismic amplitude and high oil productivity. In contrast, curvature gradient helps define the regional northwest-trending and the cross-regional northeast-trending lineaments that are associated with weak seismic amplitude and low oil productivity. In concert with previous reports from image logs, cores, and outcrops, an integrated seismic curvature and curvature gradient analysis suggests that curvature might help define areas of enhanced potential to form tensile fractures, whereas curvature gradient might help define zones of enhanced potential to develop shear fractures. In fractured reservoirs at Teapot Dome where faulting and fault-related folding contribute dominantly to the formation and evolution of fractures, curvature and curvature gradient attributes can be potentially applied to differentiate fracture mode, to predict fracture intensity and orientation, to evaluate fracture volume and connectivity, and to model fracture networks.