Quantification of Curvature and Fracture Distributions in Outcrop-Scale Periclines

Fractures are important in understanding the permeability of rocks. They form in response to stresses accumulated within rocks. Numerical studies of both buckle and forced folds show that fold hinges focus stress leading to increased likelihood of fracture. When folding occurs above blind thrusts, hinge-parallel variation in displacement results in non-cylindrical (periclinal) folds with 3D strain fields quantifiable using curvature. In 3-dimensions, curvature is a tensor quantity with two extreme values (principle curvatures). The product of these curvatures, Gaussian curvature, highlights regions of extreme bending in more than one dimension and therefore accommodation of large non-plane strains.
We use terrestrial laser scanning to acquire a digital elevation model for three exemplar periclines, two from Scremerston, Northumberland and one from Bude, Cornwall which should show non-zero Gaussian curvature (Gaussian curvature is 0 for cylindrical or conical folds). The periclines are exposed single bedding surfaces allowing a full 3D survey of the surface. Colouring the point clouds using georeferenced digital photographs enables fracture traces to be picked from the surface of the folds. Principle curvatures are calculated from the smoothed, filtered point clouds. Fracture densities and trace orientations are calculated and these data plotted onto 3D surfaces derived from the triangulated point cloud data. This novel use of precisely georeferenced data allows the spatial variation of surface and fracture attributes to be examined and compared for entire folds with much higher resolution than previously possible.
Curvatures in excess of 0.1 m-1 are observed in one of the folds at Scremerston and correlate with increased fracture density around the hinge zone. Both of the other folds contain a significant amount of fracturing but neither shows a correlation between curvature and fracturing. The two folds at Scremerston show a pattern of minor domes and saddles imposed on the dominant fold. This is interpreted to result from minor undulations in the bedding surface prior to folding. The pericline at Bude shows very low Gaussian curvature (<|0.01|m-2) indicating that the deformation producing the hinge parallel curvature is not distributed. Instead, it is interpreted to be accommodated by several large aperture fractures. This study shows that whilst curvature is a proxy for strain, it is not always a good proxy for fracture density there is no systematic link. Many rocks have fracture densities inherited from early on in their strain history and the densities are not necessarily modified by folding. Structures which show whale-back geometries in the field do not always result from distributed, ductile strain. However, detailed investigation of appropriate field analogues provides limits to the values of fracturing and anisotropy that can be expected in the sub-surface.