Fractures, which are common structural heterogeneities in geological folds and domes, impact the charge, seal, and trapping potential of hydrocarbon reservoirs. Because of their effects on reservoir quality, the numerical prediction of fractures has recently been the focus of petroleum geoscientists. A horizon's curvature is commonly used to infer the state of deformation in those strata. It is assumed that areas of elevated calculated curvatures underwent elevated deformation, resulting in a concentration of fractures and faults there. Usually, curvatures are calculated from spatial data after sampling the continuous horizon at discrete points. This sampled geometry of the horizon includes surface undulations of all scales, which are then also included in the calculated curvatures. Including surface undulations of all scales in the curvature analysis leads to noisy and questionable results. We argue that the source data must be filtered prior to curvature analysis to separate different spatial scales of surface undulations, such as broad structures, faults, and sedimentary features. Only those surface undulations that scale with the problem under consideration should then be used in a curvature analysis. For the scale-dependent decomposition of spatial data, we test the suitability of four numerical techniques (Fourier [spectral] analysis, wavelet transform filtering, singular value decomposition, factorial kriging) on a seismically mapped horizon in the North Sea. For surfaces sampled over a regular grid (e.g., seismic data), Fourier (spectral) analysis extracts meaningful curvatures on the scale of broad horizon features, such as structural domes and basins.