A fast local level set method for inverse gravimetry

Victor Isakov Shing-Yu Leung Jianliang Qian

General Mathematics mathscidoc:1912.43183

Commmun. Comput. Phys., 10, (4), 1044-1070, 2011
We propose a fast local level set method for the inverse problem of gravimetry. The theoretical foundation for our approach is based on the following uniqueness result: if an open set D is star-shaped or x<sub>3</sub>-convex with respect to its center of gravity, then its exterior potential uniquely determines the open set D. To achieve this purpose constructively, the first challenge is how to parametrize this open set D as its boundary may have a variety of possible shapes. To describe those different shapes we propose to use a level-set function to parametrize the unknown boundary of this open set. The second challenge is how to deal with the issue of partial data as gravimetric measurements are only made on a part of a given reference domain . To overcome this difficulty we propose a linear numerical continuation approach based on the single layer representation to find potentials on the boundary of some artificial domain
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  title={A fast local level set method for inverse gravimetry},
  author={Victor Isakov, Shing-Yu Leung, and Jianliang Qian},
  booktitle={Commmun. Comput. Phys.},
Victor Isakov, Shing-Yu Leung, and Jianliang Qian. A fast local level set method for inverse gravimetry. 2011. Vol. 10. In Commmun. Comput. Phys.. pp.1044-1070. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112811100818743.
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