Fracture characterization is fundamental to the reliable prediction of fractured reservoirs; however, it is difficult and expensive to obtain detailed fracture information required for reservoir prediction due to the lack of direct observational data in the subsurface. Here we develop seismic analysis methods to characterize fractured reservoirs based on reflection geometry related to bending and shearing of reservoir formations. Among various geometric attributes, we focus on extreme curvature and extreme flexure that are considered effective at detecting fractures. Extreme curvature refers to the signed absolute maximum curvature at a specific azimuth where the curve shape is the tightest, whereas extreme flexure refers to the signed absolute maximum gradient of curvature at a specific azimuth where the curve shape changes the most. We implement new algorithms based on analytical equations to calculate extreme curvature and extreme flexure along with the corresponding azimuth from 3D seismic data. Results from 3D seismic surveys demonstrate that the new algorithms help resolve structural details that are otherwise not easily discernible from regular amplitude and conventional attributes. Most importantly, the algorithms hold the potential to volumetrically detect and visualize fractures in an automatic and quantitative manner. We conclude that extreme curvature and extreme flexure attributes have important geologic implications for predicting fundamental fracture properties that are critical to fractured reservoir characterization in the subsurface.