Kinematics of constant arc length folding for different fold shapes

Basic mathematical functions are applied for the two-dimensional geometrical and kinematical analysis of different fold shapes. Relationships between different fold parameters are established and related to the bulk shortening taking place during folding under upper crustal conditions. The bulk shortening taking place during constant arc length folding is mathematically related to the bulk shortening during homogenous pure shear using a particular aspect ratio, which is for folding the ratio of amplitude to half wavelength and for pure shear the ratio of vertical to horizontal length of the deformed, initially square body. The evolution of the fold aspect ratio with bulk shortening is similar for a wide range of fold shapes and indicates that the fold aspect ratio allows a good estimate of the bulk shortening. The change of the geometry of individual layers across a multilayer sequence in disharmonic folding indicates a specific kinematics of multilayer folding, referred to here as “wrap folding”, which does not require significant flexural slip nor flexural flow. The kinematic analysis indicates that there is a critical value for constant arc length folding between shortening values of 30–40% (depending on the fold geometry). For shortening values smaller than the critical value limb rotation and fold amplitude growth are dominating. For shortening larger than this value, faulting, boudinage and foliation development are likely the dominating deformation process during continued shortening. The kinematical analysis of constant arc length folding can be used for estimating the bulk shortening taking place during multilayer folding which is an important component of the deformation of crustal rocks during the early history of shortening. The bulk shortening is estimated for a natural, multilayer detachment fold and the shortening estimates based on the kinematic analysis are compared and supported by numerical finite element simulations of multilayer detachment folding in power-law materials.