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.

In order to test the theory of glacier flow over bedrock undulations presented by S. J. Johnsen, K. Rasmussen, and N.Reeh in the accompanying abstract, data from the E.G.I.G. and the Dye-3 flow lines on the Greenland ice sheet have been analysed. The data comprise surface profiles measured by conventional techniques, and ice thicknesses and depths of internal isochronic layers obtained by the Technical University of Denmark by means of radio echo-soundings.