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On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map

de Hoop, MV; Kepley, P; Oksanen, L; (2016) On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map. SIAM Journal On Applied Mathematics , 76 (2) pp. 805-825. 10.1137/15M1033010. Green open access

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Abstract

We introduce a new algorithm to construct travel time distances between a point in the interior of a Riemannian manifold and points on the boundary of the manifold, and describe a numerical implementation of the algorithm. It is known that the travel time distances for all interior points determine the Riemannian manifold in a stable manner. We do not assume that there are sources or receivers in the interior, and use the hyperbolic Neumann-to-Dirichlet map, or its restriction, as our data. Our algorithm is a variant of the boundary control method, and to our knowledge, this is the first numerical implementation of the method in a geometric setting.

Type: Article
Title: On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map
Open access status: An open access version is available from UCL Discovery
DOI: 10.1137/15M1033010
Publisher version: http://doi.org/10.1137/15M1033010
Language: English
Additional information: Copyright © 2016, Society for Industrial and Applied Mathematics. All rights reserved. First Published in SIAM Journal On Applied Mathematics, in 76 (2), 2016. Published by the Society for Industrial and Applied Mathematics (SIAM).
Keywords: Boundary control method, Travel time distances, Wave equation
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/1508484
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