On  Curvature and Fracturing in Some Periclinal Folds

Fractures are important to understanding the permeability of rocks. They form in response to stresses imposed on rock bodies. Since folding also occurs as a result of imposed stress it has been hypothesised that the strain accumulated by folding may also result in elevated fracture densities. Numerical models of 2-dimensional similar folding show increased maximum tensile stress around the outer arc of the fold hinge which increases the probability of tensile failure in this region (e.g. Casey and Butler, 2004).These hinge zones are the sites of high curvatures, an intrinsic surface property which may be used as a proxy for strain. 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-planar strains.

We use terrestrial laser scanning to acquire a digital elevation model for three examples of 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). These 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.

At Scremerston one of the folds shows curvatures in excess of 0.1 m-1 and increased fracture density around the hinge zone. Neither of the other folds shows a correlation but still have a significant amount of fracturing. Both of the Scremerston folds 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) so the deformation which produces 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. Casey, M., and R. W. H. Butler, 2004, Modelling Approaches to Understanding Fold Development: Implications for Hydrocarbon Reservoirs, Oil and Gas in Compressional Belts, Marine and Petroleum Geology 21, 933-946.