Kinematic strain localization

Deformation within a steady-state compressional orogen, i.e., where tectonic accretion is, on geological time scales, balanced by surface erosion, can best be described by a stationary velocity field. Instantaneous deformation results from spatial gradients in the velocity field, whereas total accumulated strain results from the integration of this instantaneous deformation along material paths following the flow lines defined by the velocity field. We have synthesized the net strain distributions for rocks exposed at the surface of such an orogenic system using simple, linear velocity fields corresponding to (a) simple shear within a dipping shear zone and (b) pure vertical shear. In both cases we demonstrate the development of surface patterns of finite strain accumulation that do not reflect the geometry of the assumed velocity field in a simple manner. Large gradients in finite strain arise as a consequence of the geographic variation in particle residence time imposed by the surface boundary, even for the limiting case where no instantaneous strain gradient exists. Such patterns of deformation are often recognised in exhumed orogenic systems, but have commonly been assumed to reflect more complex velocity fields resulting from nonlinear, localizing crustal rheologies. We therefore demonstrate that caution should be exercised in interpreting observed strain patterns because a proportion of the observed strain localization must be attributed to this purely kinematic (or geometric) effect - and this proportion may be significant in many systems. Such kinematic effects should be quantified, and subtracted from observed strain distributions before they are used to infer the rheological behavior of crustal rocks. We also suggest that in a simple shear (thrust) setting, kinematic strain localization may in fact nucleate strain softening on the side of the deforming region that is stable or fixed with respect to the Earth's surface and thus be responsible for the asymmetry that characterizes the large majority of thrust systems.