de Hoop, MV;
Kepley, P;
Oksanen, L;
(2018)
Recovery of a Smooth Metric via Wave Field and Coordinate Transformation Reconstruction.
SIAM Journal on Applied Mathematics
, 78
(4)
pp. 1931-1953.
10.1137/17M1151481.
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Abstract
In this paper, we study the inverse boundary value problem for the wave equation with a view towards an explicit reconstruction procedure. We consider both the anisotropic problem where the unknown is a general Riemannian metric smoothly varying in a domain and the isotropic problem where the metric is conformal to the Euclidean metric. Our objective in both cases is to construct the metric, using either the Neumann-to-Dirichlet (N-to-D) map or Dirichlet-to-Neumann (D-to-N) map as the data. In the anisotropic case we construct the metric in the boundary normal (or semigeodesic) coordinates via reconstruction of the wave field in the interior of the domain. In the isotropic case we can go further and construct the wave speed in the Euclidean coordinates via reconstruction of the coordinate transformation from the boundary normal coordinates to the Euclidean coordinates. Both cases utilize a variant of the Boundary Control method, and work by probing the interior using special boundary sources. We provide a computational experiment to demonstrate our procedure in the isotropic case with N-to-D data.
| Type: | Article |
|---|---|
| Title: | Recovery of a Smooth Metric via Wave Field and Coordinate Transformation Reconstruction |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/17M1151481 |
| Publisher version: | https://doi.org/10.1137/17M1151481 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, inverse problem, wave equation, boundary control, Riemannian metric, MULTIDIMENSIONAL INVERSE PROBLEMS, UNIQUE CONTINUATION, BOUNDARY CONTROL, BC-METHOD, EQUATION, MANIFOLDS, STABILITY, ALGORITHM |
| 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/10032203 |
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