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Bedrock reconstruction from free surface data for unidirectional glacier flow with basal slip

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Abstract

Glacier ice flow is shaped and defined by several properties, including the bedrock elevation profile and the basal slip distribution. The effect of these two basal properties can be present in similar ways in the surface. For bedrock recovery, this makes distinguishing between them an interesting and complex problem. The results of this paper show that in some synthetic test cases it is indeed possible to distinguish and recover both bedrock elevation and basal slip given free surface elevation and free surface velocity. The unidirectional shallow ice approximation is used to compute steady-state surface data for a number of synthetic cases with different bedrock profiles and basal slip distributions. A simple inversion method based on Newton’s method is applied to the known surface data to return the bedrock profile and basal slip distribution. In each synthetic test case, the inversion was successful in recovering both the bedrock elevation profile and the basal slip distribution variables. These results imply that there are a unique bedrock profile and basal slip which give rise to a unique combination of free surface velocity and free surface elevation.

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Acknowledgements

We would like to thank the reviewer for their thoughtful comments and efforts towards improving our manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

    Elizabeth K. McGeorge & Miguel Moyers-Gonzalez

  2. Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand

    Mathieu Sellier

  3. School of Mathematics and Statistics, University of Canterbury and Te Pūnaha Matatini, Christchurch, New Zealand

    Phillip L. Wilson

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McGeorge, E.K., Sellier, M., Moyers-Gonzalez, M. et al. Bedrock reconstruction from free surface data for unidirectional glacier flow with basal slip. Acta Mech 232, 305–322 (2021). https://doi.org/10.1007/s00707-020-02845-x

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