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Balise, M.J., 1988

The relation between surface and basal velocity variations in glaciers, with application to the mini-surges of Variegated Glacier

Bibliographic Reference

Balise, M.J., 1988, The relation between surface and basal velocity variations in glaciers, with application to the mini-surges of Variegated Glacier: University of Washington, Seattle, Ph.D. dissertation, 205 p., illust.


The relation between surface and basal velocity variations in glaciers is systematically studied, so that basal velocities of glaciers can be determined from measured surface velocities. Linear viscous, visco-elastic, and non-linear power law rheologies are used. For the forward problem (prescribed basal velocity anomaly), the surface response depends on the length scale of the basal velocity anomaly as compared to the thickness of the ice. Four different length scales are defined: very short, short, intermediate, and long. At short and intermediate scales (anomaly lengths between 1 and 10 ice thicknesses) a cross-component effect allows normal motions at the surface to be caused by longitudinal motions at the base, and the spatial form of the longitudinal component at the surface may be very different from the component at the bed. The magnitude of the surface response increases as the length scale increases. These length scales apply to both the linear and non-linear rheologies, although the magnitude of the surface response is less and the scales shift towards longer wavelengths for the non-linear rheology. Importantly, the anomalous solution is coupled to the steady-state solution for the non-linear rheology. The inverse problem (prescribed surface velocity anomaly) is solved exactly for linear rheology. The solution for the basal velocity anomaly becomes infinite in amplitude as the wavelength of the prescribed surface anomaly goes to zero. This is dealt with by reducing the short wavelength components of the surface velocity. The non-linear inverse problem is solved numerically. When data from Variegated Glacier are used for the surface velocity anomalies, the calculated basal velocities have greater amplitude than the surface velocities. The structure is of similar roughness between surface and bed, but the velocity maxima and minima are often in different spatial positions. Multiple peaks in the surface velocity may be associated with only a single peak in the basal velocity. Substantial normal motions at the bed are calculated, but the uncertainties of the solution process do not allow definite conclusions about basal cavitation. Better spatial-resolution surface data is necessary to more accurately calculate the basal velocity anomalies.

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