Overthrusts due to easy-slip/poor-slip transitions at the bed: the mathematical singularity with non-linear isotropic viscosity

Abstract

AbstractThere are several cases in which large overthrusts and sub-horizontal faults appear to have occurred in temperate or cold glaciers. As a contribution to solving the problem of their origin, the stress field when there is an abrupt change in the bottom boundary conditions is determined, assuming ice to be isotropic, third-power-law viscous. Deviatoric stresses vary with the distance r to the singularity as r−1/4, and strain rates as r−3/4. They are computed numerically to a multiplicative factor, which is determined by the conditions at a large distance, but not computed here. Although the apparent viscosity varies as r1/2 times a function of the polar angle, the stress field around the singularity is not essentially different from that obtained assuming a constant viscosity. Some considerations on the apparition of faults follow, but at the scale of the microrelief the adopted model becomes oversimplified.