Isakov, Victor; Leung, Shingyu; Qian, Jianliang A three-dimensional inverse gravimetry problem for ice with snow caps. (English) Zbl 1264.86012 Inverse Probl. Imaging 7, No. 2, 523-544 (2013). 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. Cited in 11 Documents 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 Keywords:inverse gravimetry; level set method; alternating minimization; weighted essentially non-oscillatory schemes; Green function PDFBibTeX XMLCite \textit{V. Isakov} et al., Inverse Probl. Imaging 7, No. 2, 523--544 (2013; Zbl 1264.86012) Full Text: DOI