Unsteady transpression: How progressive variations in kinematic vorticity influence finite strain in shear zone evolution

Abstract

Natural shear zones usually follow unsteady deformation histories. Concerning transpression zones, it is expected that the vorticity of the flow will vary not only in space but also in time. This work presents a study of unsteady flows that considers two ideal extreme cases: one, here named Type i, in which the vorticity increases with time, from virtual pure to simple shearing (W_k = 0.01 to 0.999), and another, Type d, in which vorticity decreases with time, from virtual simple to pure shearing (W_k = 0.999 to 0.01). To tackle the issue of vorticity changes during progressive strain, we modeled the evolution of a vertical transpression zone with left lateral movement and vertical extrusion, considering four basic types of shear zone growth. The results show that, in many cases, the resulting fabrics are difficult to distinguish from those of a steady flow. There are situations, however, in which the pattern of foliations, the orientation of stretching lineations, or an abnormally high magnitude of local non-coaxiality may be criteria to identify the unsteady character of the flow. Under Type i flows, the spin undergone by the instantaneous stretching axes, antithetic to the rotation imposed by the vorticity vector, should have consequences in an exceptionally high non-coaxiality of the fabric, and can induce an antithetic rotation of the foliation. In some cases, the resulting foliation pattern can be sigmoidal, whose tips indicate the direction of relative displacement of the adjacent blocks. Other pieces of evidence detected in the fabric patterns that may indicate unsteadiness in the flow are: a) zones with low deformation intensity that nevertheless show lineations parallel to the extrusion direction; b) local zones of very high non-coaxiality (reflected in rock fabrics - high asymmetric porphyroclasts or CPOs), higher than that imposed by the total vorticity; and c) the coexistence of mutually orthogonal stretching lineations without evidence of steady deformation trajectories to justify it. Our model also suggests that, when temporal strain partitioning is identified in a shear zone, the main evidence of unsteadiness of the flow would be found in bands where the non-coaxial component is eventually concentrated. For the rest of the shear zone, the variations in strain trajectories are so small compared to those of steady flows that the assumption that the flow is steady may be considered valid. We have tested the model into two natural shear zones: one where vorticity increase has been already noticed (Balaram Shear Zone in the northwestern part of the Indian Peninsula) and another one where unsteady transpression is presented as a simpler explanation than the provided steady analytic models (a high strain zone in Cap de Creus, Eastern Pyrenean Axial Zone).