An iterative scheme for determining glacier velocities and stresses

There are no direct methods to measure the boundary condition at the base of a glacier. Here, we propose a method that works by iteratively changing boundary conditions until a satisfactory fit to surface observations is obtained. The method is an accelerated version of one known as Kozlov–Maz’ya iteration. We apply it to the problem of ice flow through a transverse cross-section, and show it to be effective by solving the inverse problem for a sequence of synthetic data. We also apply the method to two real glaciers, Athabasca and Perito Moreno, one of which has a known basal velocity distribution.