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A three-dimensional inverse gravimetry problem for ice with snow caps. (English) Zbl 1264.86012

Summary: 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 its known (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 \(g\) for the inverse problem. We design and test two algorithms for finding \(D\) and \(g\). One is based on a standard regularized 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.

MSC:

86A22 Inverse problems in geophysics
86A05 Hydrology, hydrography, oceanography
86-08 Computational methods for problems pertaining to geophysics
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
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