Curvature measures are widely used as fault delineators and fracture indicators in seismic data. Recently, there is an interesting discussion in the literature about the efficacy of such measures in seismic data, and why they are able to catch relevant seismic features. However, as far as we know, there are no works in literature that explain, in a mathematical point of view, why seismic curvature detects faults. For that reason, this paper aims to elucidate the meaning of curvature attributes, demonstrating their mathematical relationship with discontinuity measures. We show that curvature can be understood as a second-order directional derivative, that is, in fact, an oriented edge-detection filter. In order to assess the theoretical explanation, our results are presented both in synthetic and real datasets.
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