Non-planar fault models: complexities induced by crustal layering in transcurrent faulting processes

Crack models suitable to describe transcurrent faulting in presence of a softer shallow layer are presented. We employ the asymptotic theory of generalised Cauchy kernel equations in order to study the singular behaviour of a strike-slip crack crossing the welded interface between two different media. If a planar crack cuts vertically across a material discontinuity, the dislocation density is bounded at the interface, but a stress drop discontinuity condition must be met, in which the stress drop is proportional to the local rigidity. Such a condition cannot be fullled in several cases. Two antiplane strain models are proposed to avoid this difficulty. In the first model (Fault bending model), the fault surface is affected by a sharp change of the dip angle at the intersection with the interface. An unbounded singularity in the dislocation density distribution (and in the stress field) appears at the interface and its dependence from model parameters is studied. A generalized stress drop condition is obtained which can be interpreted in terms of the interaction of the crack with the welded boundary condition. In the second model (Fault branching model), the crack is split into three interacting sections, with the lower section vertical and the other two sections inclined with respect to the vertical. In this case the order of the singularity at the interface remains undetermined. This result may be interpreted in terms of the further degree of freedom introduced by the presence of a second fracture in the upper layer. In the case of branching, two conditions are obtained for the stress drop on the three sections. According to both models, the generalised stress drop conditions may account for a stress drop ratio, between the soft layer and the hard basement, lower than the rigidity ratio.