Longitudinal Variations in Glacial Flow: Theory and Test Using Data from the Byrd Station Strain Network, Antarctica

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Abstract
A theory advanced by Budd (1970) for ice-flow variation due to bed effects is improved and applied to the flow of the ice sheet leading to Byrd Station, Antarctica. Linear viscous rheology is used and a biharmonic equation for stress and strain-rate variation is solved. Basal boundary conditions include an undulating bottom topography and longitudinal variations in basal sliding and shear stress. Near Byrd Station it is found that variations in basal sliding and shear stress have more important direct effects than does the bed topography. This result is important to considerations on the stability of glacial flow. Distortions of internal layers are calculated and these closely match the distortions observed in the internal layers detected by the NSF-SPRI-TUD radar. The phase relationship between internal layer distortion and surface topography provides a positive test for the theory. The theory does not predict a spectral power maximum in surface topographic relief at a wavelength of three ice thicknesses. Such wavelengths however dominate and we speculate that this may be due to the dynamics of glacial erosion and deposition or with subglacial water motion.