Rheological controls on the shapes of single-layer folds

Abstract

Information about rheology can potentially be gained from analyzing the shapes of folds in isolated buckled layers. We employ two-dimensional finite element models of incompressible flow in power-law viscous fluids to investigate this. We first show that the shape of the initial perturbation has relatively little effect on the final shape of the folds when the buckling instability is high. We find that the most significant factor affecting the shapes of single-layer folds is the stress exponent, n L, in the flow law of the layer. The hinges of outer arcs become sharper as n L increases and the limbs become relatively longer and straighter. These differences can be expressed quantitatively by defining a curvature index, ki, which has a value of 0 for a fold formed by circular arcs and 1 for a chevron fold. Results show a dependence of ki on n L that is well-defined for L/ h > 10, with ki increasing with n L. Data for experimentally-produced folds are consistent with the numerical results. Limb dip, ki and L/h can all be readily measured on natural folds and provide a basis for comparing the shapes of natural and computer-simulated folds. The data for small folds in siltstone layers in shales in the central Appalachians are consistent with highly non-linear flow of the stiff siltstone layers during buckling.