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Observations on Athabaska Glacier and their relation to the theory of glacier flow Paterson, William Stanley Bryce

Abstract

The objects of the present study were to collect adequate data concerning the distribution of velocity in a typical valley glacier, to relate these to current theories of glacier flow, and if necessary to suggest modifications to these theories. Conventional field methods were used. Surface movement, both horizontal and vertical, was measured by triangulation of markers in the ice from fixed points on bedrock around the perimeter of the glacier. Movement at depth was determined by measurements in boreholes of the change of inclination with time. Seismic and gravity measurements of ice thickness were also available. The methods of measurement and computation are described and their accuracy is assessed. It was observed that the vertical velocity of the top of the pipe in each borehole is equal to that of the ice in its vicinity. Methods of analysing borehole data are critically reviewed in the light of this fact. A correction term for the curvature of the pipe is also used in the analysis. It is shown that, on the Athabaska Glacier, the longitudinal strain rate is not constant with depth, and that, for about 100 metres below the surface, the horizontal velocity is slightly greater than its surface value. Present theory does not cover these cases. Possible modifications are suggested. The assumption, sometimes made in the past, that the width of a valley glacier can be regarded as infinite, is shown to be unjustified. In the absence of a complete stress and velocity solution for the case of finite width, the stress solution is modified by the introduction of the "shape factor" in the stress solution. The relation between the second invariants of the strain rate and stress deviator tensors is compared with the simple power law as determined by laboratory experiments with ice. Comparison is made both for borehole measurements and measurements of change of surface velocity across transverse lines. Agreement is satisfactory, within the limits of experimental error, for all the borehole results and some of the surface movement results. This is interpreted as evidence that the underlying theory is not seriously in error. In particular, the basic assumptions, made by Nye, that the components of strain rate and stress deviator tensors are proportional, that the constant depends only on the second invariant of the stress deviator, and that the shear stress is only a slowly varying function of distance down the glacier, seem to be reasonable approximations. Of three laboratory flow laws, that of Glen for quasi-viscous creep gives the most satisfactory fit to the data. The fit would be improved if the mean temperature of the glacier were about -0.75°C rather than the pressure melting temperature. This point has not been checked because of technical difficulties. The results appear to show that the index in the power law is reduced at low stresses (i.e. less than about 0.5 bar). Other interpretations of the data are possible, however, so the result is not considered to be established.

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