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

TL;DR

This paper demonstrates that it is possible to uniquely recover both bedrock elevation and basal slip distribution in glaciers from surface data using a Newton-based inversion method, validated on synthetic cases.

Contribution

It introduces a novel inversion approach that successfully distinguishes and reconstructs bedrock and basal slip from surface measurements in synthetic glacier models.

Findings

Successful recovery of bedrock and slip in synthetic tests

Unique solutions for bedrock and slip distributions

Validation of method with different synthetic profiles

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 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 is a unique bedrock profile and basal slip which give rise to a unique combination of free surface velocity and free surface elevation.