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Theory of Deformations within Ice Sheets due to Bottom Undulations

Published online by Cambridge University Press:  30 January 2017

Sigfus J. Johnsen ,
Kjeld Rasmussen  and
Niels Reeh
Sigfus J. Johnsen
Affiliation:
Geophysical Isotope Laboratory, University of Copenhagen, Haraldsgade 6, DK-2200 Copenhagen N, Denmark
Kjeld Rasmussen
Affiliation:
Geophysical Isotope Laboratory, University of Copenhagen, Haraldsgade 6, DK-2200 Copenhagen N, Denmark
Niels Reeh
Affiliation:
Geophysical Isotope Laboratory, University of Copenhagen, Haraldsgade 6, DK-2200 Copenhagen N, Denmark
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Abstract

Bedrock undulations of glaciers and ice sheets cause undulations of the ice surface and of internal layers. Models are constructed, that describe this phenomenon, using perturbation techniques and utilizing the stress function as harmonic solution to the full biharmonic equation. This approach is an extension of a previous treatment of the problem, which was based on the solution of the Laplace equation. This solution is shown to be inadequate. Two types of ice flow, with and without bottom sliding, are considered. Furthermore, in order to cope with the variation of viscosity with depth, semi-analytical multi-layer models have been constructed.

Type
Abstracts of Papers Accepted for the Symposium but not Presented
Information
Journal of Glaciology , Volume 24 , Issue 90 , 1979 , pp. 512
Copyright
Copyright © International Glaciological Society 1979

For the models considered, transfer functions, relating amplitudes of surface and bottom undulations, phase angles, and variation with depth of perturbational stress and velocity components, and in particular of the amplitude of internal isochronic layers, are presented. The predictions of the models presented show significant differences mutually as well as compared with those of previous theories. This opens up the possibility of using field data to check the models and possibly draw conclusions regarding flow conditions at the ice-rock interface and regarding viscosity variations with depth.