A unified description of localization for application to large-scale tectonics

[1] Localized regions of deformation such as faults and shear zones are ubiquitous in the Earth's lithosphere. However, we lack a simple unified framework of localization that is independent of the mechanism or scale of localization. We address this issue by introducing the effective stress exponent, ne, a parameter that describes how a material responds to a local perturbation of an internal variable being tested for localization. The value of ne is based on micromechanics. A localizing regime has a negative ne, indicating a weakening behavior, and localization is stronger for more negative 1/ne. We present expressions for the effective stress exponent associated with several mechanisms that trigger localization at large scale: brittle failure with loss of cohesion, elastoplasticity, rate- and state-dependent friction, shear heating, and grain-size feedback in ductile rocks. In most cases, localization does not arise solely from the relation between stress and deformation but instead requires a positive feedback between the rheology and internal variables. Brittle mechanisms (failure and friction) are generally described by ne of the order of −100. Shear heating requires an already localized forcing, which could be provided by a brittle fault at shallower levels of the lithosphere. Grain size reduction, combined with a transition from dislocation to diffusion creep, leads to localization only if the grain size departs significantly from its equilibrium value, because either large-scale flow moves rocks through different thermodynamic environments or new grains are nucleated. When shear heating or grain-size feedback produce localization, 1/ne can be extremely negative and can control lithospheric-scale localization.