Stresses and velocities in orogenic wedges with power-law rheology and linearly varying longitudinal strain rate

A two-dimensional analytical solution for stress, strain rate, and velocity is obtained for parallel-sided and wedge-shaped blocks with generalized viscous rheology (linearly viscous and power-law) deforming in plane strain. The main assumptions used in the derivation of the solution are that the material is incompressible, the longitudinal gradient in shear stress is much less than the vertical gradient of vertical normal stress, and the longitudinal strain rate varies linearly in the horizontal direction. Velocity boundary conditions are specified at the top of the block, and shear stress boundary conditions at the base of the block. In the one-dimensional case (where stress and strain rate do not vary in the longitudinal direction), the solution reduces to a well-known solution for the deformation of parallel-sided ice sheets [Nye, J. F. (1957) The distribution of stress and velocity in glaciers and ice sheets. Proceedings of the Royal Society of London A-239, 113–133]. The stress equilibrium for tapered wedges [Platt, J. P. (1986) Dynamics of orogenic wedges and the uplift of high-pressure metamorphic rocks. Geological Society of America Bulletin 97, 1037–1053] is a special case of the present stress solution. Implementation of the solution requires the subdivision of the wedge into vertical segments, and yields the tectonic normal and shear stresses that must be applied to the rear of a block with specified rheology in order to maintain a given longitudinal strain rate. The solution makes it possible to model deformation patterns analytically with longitudinally varying strain rate (including coeval compression and extension) and with vertical components of velocity reflecting the effects of underplating.