The neutral lines in buckle folds

The neutral line in a buckle fold, dividing areas of outer-arc extension from areas of inner-arc shortening, is a fundamental concept in structural geology. In the past, folds have been constructed kinematically from a given neutral line geometry using the tangential longitudinal strain pattern. In this study, a mechanical finite element model is used to numerically buckle single-layer folds with Newtonian and power-law viscous rheology. Two neutral lines can be distinguished, the incremental neutral line (zero layer-parallel strain rate) and the finite neutral line (zero finite layer-parallel strain). The former develops first and migrates through the layer from the outer towards the inner arc ahead of the latter. Both neutral lines are discontinuous along the fold and terminate either at the bottom or top interface of the layer. For decreasing viscosity ratio between layer and matrix and for decreasing initial amplitude, the neutral lines develop later during folding and, for some cases, no neutral line develops. The dynamical behaviour of the neutral lines is similar for Newtonian and power-law viscous rheology if the viscosity ratio is large, but substantially different for small viscosity ratios. The results are discussed in light of fold-related structures, such as outer-arc-extension structures and inner-arc-shortening structures.