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A new phase space method for recovering index of refraction from travel times

Chung, Eric and Qian, Jianliang and Uhlmann, Gunther and Zhao, Hongkai (2007) A new phase space method for recovering index of refraction from travel times. Inverse Problems, 23 (1). pp. 309-329. ISSN 0266-5611. doi:10.1088/0266-5611/23/1/017.

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We develop a new phase space method for reconstructing the index of refraction of a medium from travel time measurements. The method is based on the so-called Stefanov–Uhlmann identity which links two Riemannian metrics with their travel time information. We design a numerical algorithm to solve the resulting inverse problem. The new algorithm is a hybrid approach that combines both Lagrangian and Eulerian formulations. In particular the Lagrangian formulation in phase space can take into account multiple arrival times naturally, while the Eulerian formulation for the index of refraction allows us to compute the solution in physical space. Numerical examples including isotropic metrics and the Marmousi synthetic model are shown to validate the new method.

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Additional Information:Copyright © Institute of Physics and IOP Publishing Limited 2007. Received 17 October 2006, in final form 1 December 2006. Published 12 January 2007. Print publication: Issue 1 (February 2007). Jianliang Qian is supported by NSF #0542174. The research of Gunther Uhlmann is partially supported by NSF and a Walker Family endowed Professorship. The work of Hongkai Zhao is partially supported by NSF DMS 0513073, ONR Grant #N00014-02-1-0090, DARPA Grant #N00014-02-1-0603 and Sloan Foundation Fellowship.
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Deposited On:14 Jan 2007
Last Modified:12 Jul 2022 19:48

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