Fracture characterization is critical to reliable prediction of fractured reservoirs. Fractures formed by folding and/or shearing of reservoir formations, can be detected using seismic curvature and flexure analysis. Previous curvature and flexure analysis methods often have limitations in accuracy and efficiency in the presence of structural dip. We have developed new algorithms for volumetric curvature and flexure analysis based on 3D surface rotation using the local reflector dip to improve the accuracy and efficiency for curvature and flexure analysis in structurally complex settings. Among the various measures of curvature and flexure in 3D space, we have focused on signed maximum curvature and flexure that are considered to be most effective for predicting intensity and orientation of faults and fractures in fractured reservoirs. The application of the algorithms to a 3D seismic survey from Teapot Dome (Wyoming) demonstrated that the new methods help resolve subtle structural details that are otherwise not easily discernible from regular amplitude and conventional attributes, thus enhancing our capability to visualize and understand the structural complexity of fractured reservoirs.