The basal speed of valley glaciers: an inverse approach

Geophysical inverse methods are used to calculate the basal motion of a glacier. They are applied to a one-dimensional forward model that can be linearized to make the analysis simpler. The inverse method finds a solution that fits the data within a given error. It selects for smooth solutions to discriminate against unrealistic oscillations. The method is applied to a simple model glacier of uniform shape and thickness to test how well a given basal motion field can be reconstructed. It shows, as expected, that optimizing for smoothness lowers maxima and increases minima of the solution. A step change in basal velocity is drawn out in the inversion over a distance that is given by the half-width of a resolving function. This is typically, about three times the ice thickness, but is also affected by the sampling rate of the data. The method is then applied to two glaciers where suitable data are available: Brown Glacier on Heard Island, southern Indian Ocean, and McCall Glacier in the Brooks Range, Alaska, U.S.A. The McCall results agree well with earlier estimates of basal motion.