Length scales for continental deformation in convergent, divergent, and strike-slip Environments: Analytical and approximate solutions for a thin viscous sheet model

The deformation of a thin viscous layer that has a moving boundary is investigated for comparison with zones of deformation in the continental lithosphere. Exact analytical solutions, for the case of a Newtonian fluid, and approximate solutions, for the case of fluid with power law rheology, show that: When the imposed velocity vector is normal to the boundary (congressional or extensional regime) the deformation field decays away from the boundary with a characteristic length scale 1/3 to 1/10 the wavelength of the imposed boundary velocity distribution for n between 1 and 10, where n is the stress-strain exponent in the rheology; in contrast, when the imposed velocity vector is parallel to the boundary (transcurrent regime), the length scale of the deformation field is approximately 4 times smaller. In each case these length scales decrease approximately as n^-½. The difference in length scales arises even in the absence of any buoyancy forces acting on thickened or thinned crust; such forces would modify the ratio of length scales, but not sufficiently to affect this result.