A three-dimensional inverse gravimetry problem for ice with snow caps

We propose a model for the gravitational field of a floating iceberg D with snow on its top.The inverse problem of interest in geophysics is to find D and snow thickness g on itsknown (visible) top from remote measurements of derivatives of the gravitational potential.By modifying the Novikov's orthogonality method we prove uniqueness of recovering D and g forthe inverse problem. We design and test two algorithms for finding D and g. One is based on a standardregularized minimization of a misfit functional. The second one applies the level set method to our problem.Numerical examples validate the theory and demonstrate effectiveness of the proposed algorithms.