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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Volume 27, Issue 4

Issues

On the travel time tomography problem in 3D

Michael V. Klibanov
  • Corresponding author
  • Department of Mathematics and Statistics, University of North Carolina Charlotte, Charlotte, NC 28223, USA
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Published Online: 2019-07-16 | DOI: https://doi.org/10.1515/jiip-2019-0036

Abstract

Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables are used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator.

Keywords: Global convergence; semi-finite dimensional mathematical model; Carleman weight function; weighted Tikhonov-like functional

MSC 2010: 35R25; 35R30

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About the article

Received: 2019-05-21

Accepted: 2019-06-03

Published Online: 2019-07-16

Published in Print: 2019-08-01


This work was supported by US Army Research Laboratory and US Army Research Office grant W911NF-19-1-0044.


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 27, Issue 4, Pages 591–607, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2019-0036.

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