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.

中文翻译：

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基于基底滑移的单向冰川流自由表面数据的基岩重建

冰川冰流由多种属性塑造和定义，包括基岩高程剖面和基底滑移分布。这两种基本特性的影响可以以类似的方式呈现在表面上。对于基岩恢复，这使得区分它们成为一个有趣而复杂的问题。本文的结果表明，在一些综合测试案例中，在给定自由表面高程和自由表面速度的情况下，确实可以区分和恢复基岩高程和基底滑移。单向浅冰近似用于计算具有不同基岩剖面和基底滑移分布的许多合成情况的稳态表面数据。将基于牛顿法的简单反演方法应用于已知的表面数据，以返回基岩剖面和基底滑移分布。在每个综合测试案例中，反演成功地恢复了基岩高程剖面和基底滑移分布变量。这些结果意味着存在独特的基岩剖面和基底滑移，这导致了自由表面速度和自由表面高程的独特组合。