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One of the unresolved questions concerning fault deformation is the degree and cause of localization of shear at depth beneath a fault. Geologic observations of exhumed shear zones indicate that while the motion is no longer planar, it can still be localized near the down-dip extension of the fault; however, the degree of localization is uncertain. We employ simple analytic and numerical models to investigate the structural form of distributed shear beneath a strike-slip fault, and the relative importance of the physical mechanisms that have the potential to localize a shear zone. For a purely depth dependent viscosity, η = η0 exp (-z/z0), we find that a shear zone develops with a half-width δw ~ √z0 for small z0 at the base of the layer, where lengths are non-dimensionalized by the layer thickness (d km). Including a non-linear stress-strain-rate relation (ε ∝ σn) scales δw by 1/√n, comparable to deformation length scales in thin viscous sheet calculations. We find that the primary control on the shear-zone width is the depth dependence of viscosity that arises from the temperature dependence of viscosity and the increase in temperaturewith depth. As this relationship is exponential, scaling relations give a dimensional half-width that scales approximately as where T1/2 (K) is the temperature at the midpoint of the layer, R (J mol-1 K-1) the gas constant, Q (J mol-1) the activation energy and β (K km-1) the geothermal gradient. This relation predicts the numerical results for the parameter range consistent with continental rheologies to within 2-5 per cent and shear-zone half-widths from 2 to 6 km. The inclusion of shear-stress heating reduces δw by only an additional 5-25 per cent, depending on the initialwidth of the shear zone. While the width of the shear zone may not decrease significantly, local temperature increases from shear-stress heating range from 50 to 300 °C resulting in a reduction in viscosities beneath the fault of several orders of magnitude and a concomitant reduction in the stresses needed to drive the motion

Scaling of viscous shear zones with depth-dependent viscosity and power-law stress–strain-rate dependence