Forward modeling of non-steady-state deformations and the ‘minimum strain path’

Structural analyses of shear zones often rely on an assumption of steady-state behavior, i.e. that the ratio of pure shear strain rate(s) to simple shear strain rate(s) remains fixed throughout deformation. However, geological deformations are not necessarily steady state. Non-steady-state deformation paths can be theoretically modeled if certain deformation parameters, such as strain or offset, are specified. We have analyzed a two-dimensional case of specified offset and geometry, termed the minimum strain path. The minimum finite strain needed to produce a fixed offset across a shear zone is neither simple shear nor pure shear, but a combination of the two (the minimum strain path). If this deformation accumulates with a steady-state deformation, the kinematic vorticity number (Wk) of the minimum strain path varies with the amount of finite offset, although Wk approaches 0.7 at high offset values. Because of this relation between Wk and finite offset, the minimum strain path is better modeled as a non-steady-state deformation, in which case deformation history starts close to simple shear but rapidly changes to a more pure shear dominated deformation. It is expected that the minimum strain path is applicable to geological deformation zones with relaxed boundary conditions, such as basal parts of spreading nappes or extensional detachment systems.