Formulating an inverse problem to infer the accumulation-rate pattern from deep internal layering in an ice sheet using a Monte Carlo approach

Abstract

Using a Monte Carlo (MC) method, we determine the accumulation-rate profile along a flowband, the influx of ice into the upstream end of the flowband and the age of an internal layer. The data comprise the depth profile of the internal layer, a few velocity measurements at the surface and the average accumulation at one location. The data in our example were collected at Taylor Mouth, a flank site off Taylor Dome, Antarctica. We present three alternative formulations of this inverse problem. Depending on the formulation used, this particular inverse problem can have up to four solutions, each corresponding to a different spatial accumulation-rate pattern. This study demonstrates the ability of a MC method to find several solutions to this inverse problem, and how to use a Metropolis algorithm to determine the probability distribution of each of these different solutions. The only disadvantage of the MC method is that it is computationally more expensive than other inverse methods, such as the Gradient method.