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, rateand 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 neof 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.