CALCULATING THE CURVATURE OF THE WHALEBACK ANTICLINE: DIFFERENTIAL GEOMETRY WITH STRUCTURE-FROM-MOTION PHOTOGRAMMETRY

The Whaleback Anticline is the most prominent structure exposed at the Bear Valley Strip Mine, near Shamokin, PA, on the southern limb of the Western Middle Anthracite Field Synclinorium in the Alleghanian Valley and Ridge Province. The Bear Valley excavation exposes the 100-m long Whaleback and adjacent anticlines on a continuous sandstone bedding surface. As part of a larger multidisciplinary study, we use structure-from-motion photogrammetry to produce a high-resolution, three-dimensional, digital surface model of the folded surface, from which quantitative descriptions of the fold form are generated.

Curvature is a function of the second derivative of position, describing the spatial rate of change in gradient. Curvature and related metrics can thus characterize the shape, and variability in shape, of folds. Previous researchers have sought to evaluate various measures of curvature as proxy for the distribution of strain but have been hampered in part by limited or noisy data or incomplete exposure of secondary structures that record strain. Due to the exceptional exposure at Bear Valley, we can directly compare the complete fold form to the strain recorded in the rock without typical data limitations. Here, we present results of curvature analyses to describe variations in the form of Whaleback Anticline and adjacent folds. Ultimately, these calculations can be compared with observed strain from field observations to directly test the hypothesis that quantitative measures of fold curvature predict strain distribution.