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Naturally fractured reservoirs are important targets for exploration and production of hydrocarbons. Past methods to detect fractures included the processing of pre-stack seismic data for velocity and amplitude variation with azimuth, or bi-refringence analysis of multi-component P- and S-wave data. Both methods are expensive. Recent less expensive methods from post-stack 3D seismic data include horizon-based or volumetric curvature indicators. Current volumetric curvature methods compute lagged cross-correlations followed by eigenstructure analysis. These methods are computer-intensive and slow. We present an alternative efficient method that derives curvature from spatial derivatives of phase spectra of laterally separated time-windowed traces. The method detects faults, fractures, ridges and valleys. We used high volumetric curvature as an indicator to detect fractures from 3D post-stack seismic data. A map of high indicator values overlaid on target horizon structure matched with the map of independently picked faults. More significantly the azimuth of the lineament on horizon indicator map at a well location matched with the natural fracture orientation observed from borehole image analysis. Further, the lineament trajectory followed a tight doubly folded ridge. With these supporting observations we used high curvature as a fracture predictor away from the well where hydrocarbons were found in a fractured zone.