The distributions of slip rate and ductile deformation in a strike-slip shear zone

A simple mechanical model and dimensional analysis are used to derive a scaling law for the partitioning between slip rate on a strike-slip fault and distributed deformation in the far-field. The depth of the fault, the distributions of stress, strain rate and slip rate are solved for a given far-field force or displacement in a 2-D medium with a linear temperature-dependent viscous rheology. At the shear zone axis, a mixed boundary condition is used to account for the presence of both an active fault and a ductile zone below. Over the vertical extent of the fault, the boundary condition is one of a fixed shear stress distribution dictated by a friction law. In the ductile zone below, the boundary condition is one of zero velocity. A deep fault or large vertical rheological variations are required to localize deformation on the fault with small amounts of regionally distributed deformation. In this model without thermal or strain softening, strain localization occurs naturally beneath the fault. For large rheological variations, the slip rate remains approximately constant over half the fault vertical extent and progressively decreases to zero below. Thus, there is a thick transition zone between block motion at the surface and distributed ductile deformation at depth. The near-surface deformation field depends weakly on stress and strain in the lower ductile region and the key controlling parameter is the vertical rheological variation over the depth of the fault. A scaling law relates the far-field strain rate to the slip rate and depth of the fault independently of frictional strength. For typical parameter values, the far-field strain rate is found to be 10(-15) s(-1) or less, showing that strike-slip faults separate blocks that can be considered rigid for all practical purposes. For the large vertical rheological variations of relevance to geological examples, shear heating is mostly a result of friction on the fault plane and is maximum at a small distance above the base of the fault.