A geometry guided image denoising scheme
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May 2013, 7(2): 523-544. doi: 10.3934/ipi.2013.7.523
A three-dimensional inverse gravimetry problem for ice with snow caps
Victor Isakov 1, , Shingyu Leung 2, and Jianliang Qian 2,
Wichita State University, 1845 Fairmount, Wichita, KS 67260-0033
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China, China
Received September 2012 Revised February 2013 Published May 2013
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.
Keywords: alternating minimization, Inverse gravimetry, Green function., weighted essentially non-oscillatory schemes, level set method.
Mathematics Subject Classification: 65N21, 65N06, 65N8.
Citation: Victor Isakov, Shingyu Leung, Jianliang Qian. A three-dimensional inverse gravimetry problem for ice with snow caps. Inverse Problems & Imaging, 2013, 7 (2) : 523-544. doi: 10.3934/ipi.2013.7.523
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Victor Isakov Shingyu Leung Jianliang Qian