Fault spacing in continental strike-slip shear zones

Strike-slip shear zones with sub-parallel arrays of evenly-spaced faults are widely observed in nature, but the controls on the spacing between major faults are unclear. We analyze a 2-D model and develop a scaling law relating the fault spacing to structural and rheological parameters in the continental crust. We find that fault spacing positively correlates with brittle-layer thickness, viscous lower crust thickness, and strength contrast between active faults and surrounding intact blocks; and is inversely correlative with lower crust viscosity. This is corroborated for either a zero-shear traction (decoupled) or a prescribed velocity (coupled) basal boundary condition in the 2-D analytical solution. The zero-shear traction boundary condition represents low viscosities in the lowermost crust or the topmost mantle that may decouple deformations from mantle flow. The prescribed velocity boundary condition emphasizes basal drag tractional forces imparted on the lower crust by a strong mantle. For a viscous layer that is thicker than half of its average fault spacing, models with either of the boundary conditions produce the same results. Otherwise, a thinner, viscous layer with a linear-velocity condition tends to produce smaller fault spacings than a no-shear model, all else being equal. These theoretical models are comparted to data from shear zones in California, the Marlborough Fault Zone in New Zealand and central Tibet. Modeling indicates that the effective viscosity of the viscous layer underlying the brittle layer in all of the selected areas is 2×10²⁰ to 4×10²¹ Pa⋅s. The subducted oceanic plate attached to the lower crust of the eastern Marlborough Fault Zone also appears to influence fault spacing in the overriding plate.