American Institute of Mathematical Sciences

May  2013, 7(2): 523-544. doi: 10.3934/ipi.2013.7.523

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

 1 Wichita State University, 1845 Fairmount, Wichita, KS 67260-0033 2 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.
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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