  A key parameter in ice flow modelling is basal slipping at the ice-bed
interface as it can have a large effect on the resultant ice thickness.
Unfortunately, its contribution to surface observations can be hard to
distinguish from that of bed undulations. Therefore, inferring the ice
thickness from surface measurements is an interesting and non-trivial inverse
problem. This paper presents a method for recovering dually the ice thickness
and the basal slip using only surface elevation and speed measurements. The
unidirectional shallow ice approximation is first implemented to model steady
state ice flow for given bedrock and basal slip profiles. This surface is then
taken as synthetic observed data. An augmented Lagrangian algorithm is then
used to find the diffusion coefficient which gives the best fit to
observations. Combining this recovered diffusion with observed surface
velocity, a simple Newton's method is used to recover both the ice thickness
and basal slip. The method was successful in each test case and this implies
that it should be possible to recover both of these parameters in
two-dimensional cases also.
