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Abstract One of the most accepted geologic models is the relation between reflector curvature and the presence of open and closed fractures. Such fractures, as well as other small discontinuities, are relatively small and below the imaging range of conventional seismic data. Depending on the tectonic regime, structural geologists link open fractures to either Gaussian curvature or to curvature in the dip or strike directions. Reflector curvature is fractal in nature, with different tectonic and lithologic effects being illuminated at the 50-m and 1000-m scales. Until now, such curvature estimates have been limited to the analysis of picked horizons. We have developed what we feel to be the first volumetric spectral estimates of reflector curvature. We find that the most positive and negative curvatures are the most valuable in the conventional mapping of lineations — including faults, folds, and flexures. Curvature is mathematically independent of, and interpretatively complementary to, the well-established coherence geometric attribute. We find the long spectral wavelength curvature estimates to be of particular value in extracting subtle, broad features in the seismic data such as folds, flexures, collapse features, fault drags, and under- and overmigrated fault terminations. We illustrate the value of these spectral curvature estimates and compare them to other attributes through application to two land data sets — a salt dome from the onshore Louisiana Gulf Coast and a fractured/karsted data volume from Fort Worth basin of North Texas.