Validity of the thin viscous sheet approximation in models of continental collision

摘要

The two-dimensional thin viscous sheet approximation is widely used to describe large-scale continental deformation. It treats the lithosphere as a fluid layer in which deformation results from a balance between buoyancy forces and tectonic boundary conditions. Comparisons between two-dimensional thin sheet and full three-dimensional solutions of a simple indenter model show that appreciable differences exist, especially when the indenter half width, D, is of the same order as the thickness of the deforming layer, L (i.e., D/L= 1). These differences are amplified by increasing the power law exponent of the viscous constitutive law (n) but decrease as the Argand number (Ar) is increased. The greatest differences between two-dimensional and three-dimensional solutions are found at the indenter corner, where the thin sheet consistently overestimates vertical strain rates. Differences between strain rates at the corner may be 50% or greater for small Argand numbers. Other differences arise because a lithospheric root zone is formed in the three-dimensional solutions and vertically averaged strain rate is decreased in regions close to the indenter. This effect is absent from thin sheet calculations since the thickness of the load-bearing layer is assumed constant. In general, the thin viscous sheet approximation provides a reasonably accurate estimate of long wavelength deformation for D/L as low as 1 if n is less than —3. However, even at large D/L the solutions may be inaccurate close to strain rate concentrations at the indenter corners where horizontal gradients of deformation are large.