Defining a 3-dimensional trishear parameter space to understand the temporal evolution of fault propagation folds

The application of trishear, in which deformation occurs in a triangular zone in front of a propagating fault tip, is often used to understand fault related folding. A key element of trishear, in comparison to kink-band methods, is that non-uniform deformation within the triangle zone allows the layer thickness and length to change during deformation. By varying three controlling parameters independently (trishear propagation/slip ratio, trishear apical angle and fault dip), we construct a three-dimensional parameter space to demonstrate the variability of resultant geometry feasible with trishear. We plot published natural examples in this parameter space and identify two clusters and show that the most applicable typical trishear propagation/slip ratio is 2to3, while the trishear apical angle varies from 30° to 100°. We propose that these findings can help estimate the best-fit parameters for natural structures. We then consider the temporal evolution of specific geometric examples and factors that increase the complexity of trishear including: (1) fault-dip changes and (2) pre-existing faults.To illustrate the applicability of the parameter space and complex trishear models to natural examples, we apply our results to a sub-surface example from the Qaidam basin in northern Tibetan Plateau.