Inversion of flow Measurements for Stress and Rheological Parameters in a Valley Glacier

• Published in: Journal of Glaciology
• Main Author: Raymond, Charles F.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 1973
• Subjects: Earth-Surface Processes; Paterson; Journal of Glaciology
• Online Access: http://dx.doi.org/10.1017/s0022143000022681; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000022681

Abstract Methods are developed for determining the distributions of stress and effective viscosity in a glacier, under the assumptions: the ice is quasi-viscous, the flow is time independent, and acceleration forces are negligible. Measurements of the three-dimensional distribution of velocity are needed for their application. The differential equations of mechanical equilibrium, expressed in terms of viscosity, strain-rate components, mean stress, and their gradients, are viewed as equations to be solved for viscosity and mean stress subject to boundary conditions at the free upper surface. For certain rectilinear flow patterns, unique distributions of stress and effective viscosity can always be derived. For more complicated flow this is not necessarily so. However, it is still possible to choose the best values of rheological parameters in any trial flow law based on the requirement that the residuals to the equations of equilibrium be minimized in a mean-square sense. The techniques are applied to measurements of internal deformation made in nine bore holes on the Athabasca Glacier. At the center line the magnitude of the surface-parallel shear stress increases with depth more slowly than would be expected from a standard shape factor correction or the theoretical distribution of Nye. Correspondingly the lateral distribution of lateral shear stress shows the opposite relationships. In the lower one- to two-thirds of the depth corresponding to a range in effective stress from about 0.5 to 1.2 bars, the gross rheology of the ice is not distinguishably different from the experimentally determined flow law of Glen ( n = 4.2, T = 0.02° C) as generalized by Nye. The results do not support the conclusion that the effective viscosity is higher than would be expected from Glen’s experiments as indicated by the more limited measurements of Paterson and Savage. Power-law parameters derived for the different bore holes considered separately show a spread, which suggests some rheological inhomogeneity. However, no ...