DOES CURVATURE CORRESPOND TO FOLD-RELATED STRAIN IN THE ANTICLINES AT BEAR VALLEY, SHAMOKIN, PA, USA?

Tangential longitudinal strain (TLS) is a primary mechanism of folding that involves stretching of the outer arc of a fold, concentrating maximal strain along the fold hinge that diminishes towards the inflection points of the limbs. Curvature quantitatively describes fold form: regions of highest curvature indicate the location of a fold’s hinge, and the magnitude of the curvature describes a fold’s tightness. If TLS is a dominant mechanism of folding, high curvature should correlate with regions of greatest fold-related strain and secondary structures. However, this correlation is not consistently observed, possibly due to the inability to quantitively define fold form or insufficient exposure of secondary structures and/or the third dimension. At Bear Valley, coal mining exposed a fold train in sandstone that provides an opportunity to capture fold form in 3D and measure well-exposed secondary structures that record strain during fold development. Does strain distribution on this fold train correspond to tangential longitudinal strain?

To model the shape of the folds, we used a carefully cleaned structure-from-motion-generated point cloud of the exposure, consisting of points recording only the folded surface. We selected NURBS (non-uniform rational basis splines) to create a smoothed model of the sandstone surface from the point cloud. NURBS are appropriate for interpolating geologic structures like folds because they are mathematically operable and can model smooth, continuous geometries that single-variable polynomials cannot describe (e.g., an overturned fold limb). A curvature analysis of the NURBS surface identified regions of greatest curvature along the fold crests, as expected. Observations of meso- and microscale structures show strain consistent with early layer-parallel shortening and later-stage layer-parallel extension during fold tightening. Contrary to predictions from TLS, the later-stage extensional structures are distributed across the folds, rather than concentrated in regions of high curvature. Despite our ability to model fold form with high fidelity and access to secondary structures coeval with folding, curvature and fold-related strain do not correspond. Thus, the traditional 2D model of TLS does not adequately describe the folding mechanism at Bear Valley.