Strain patterns in an ice cap and implications for strain variations in shear zones

Glacier flow is a form of gravity tectonics in thin sheets, characterized by the development of large strains, foliation and folds. Strain is difficult to measure in ice, but numerical methods provide a good means of estimating cumulative strains. In simple terms, flow in an ice cap involves vertical flattening at the center with bottom-parallel shear increasing in intensity downwards and outwards. In steady state, cumulative strains will be plane if flow is two-dimensional, as in parts of many valley glaciers and some ice caps, and of flattening type if lateral extension occurs normal to the flow direction, as in many ice sheets. In both radial and plane flow, strain gradients will be large vertically and low horizontally outwards. Cumulative strain magnitude can be extremely large near the base and at the margin. Z is everywhere sub-vertical. If flow is unsteady, more complex strain patterns develop, even if changes in the flow field are slight. Over bedrock ridges, flow perturbations can lead locally to rotations greater than those of the quasi-simple shear acting near the base in steady state flow. This may cause the X-direction of the cumulative strain to rotate through the 'shear plane' in the neighborhood of the perturbation, in which case strain magnitudes subsequently diminish, leading to low or zero strains in plane flow, and to constrictional strains in radial flow. In the latter case, X lies horizontal and perpendicular to the flow direction, and we have local constrictional strain in an overall flattening field. The zones of perturbed strain tend to be associated with the inverted limbs of recumbent folds. Shear zones in rocks are expected to show similar patterns of strain perturbation.