An inverse problem in glacial geology: The reconstruction of glacier thinning in glacier bay, alaska between A.D. 1910 and 1960 from relative sea-level data

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Abstract
Inverse theory is applied to relative sea-level data to reconstruct a glacial history that is consistent with the emergence data near Glacier Bay, Alaska over the past half century. A comparison between the predicted glacial thinning and observed thinning indicates that a combination of elastic uplift of the ground and a fall in the geoid defining the ocean surface, causes 25% to 35% of the observed emergence of the coast line. Because of errors in the sea-level data, inverse theory cannot provide a unique solution in terms of glacier response, and, in fact, the least-squares fit is very inaccurate. However, by considering (1) the error of fit to the data, (2) the accuracy of the model, (3) the variation in the model, and (4) the model resolution, a physically realistic glacial history can be deduced. The advantage of inverse calculations is not only in its efficient means of finding a model that fits the data, but more importantly, it provides a means of assessing the reliability of the model by indicating the accuracy of the model and the range of other glacial histories that also fit the data. This approach also allows an estimate of the extent to which each data point constrains the model, independent of the actual data values. From this information, the most useful areas for additional data collection may be delimited.

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