Abstract
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.
Highlights
We propose a model for the gravitational field of a floating iceberg D with snow on its top
We will assume that μ is zero outside D ⊂ Ω, D is some bounded open set, Ω is a given open set in R3, and Γ0 ⊂ ∂Ω
When Ω is a sphere of radius R and D is a concentric sphere of radius r these singular values behave like the exponential powers of r R
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. The second one applies the level set method to our problem. Level set method, alternating minimization, weighted essentially non-oscillatory schemes, Green function. The (compact) linear operator mapping μ into the data (2) has exponentially fast decreasing singular values. This decay is growing with the distance from Γ0 to D. When Ω is a sphere of radius R and D is a concentric sphere of radius r these singular values behave like the exponential powers of r R
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