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  Monochromatic Identities for the Green Function and Uniqueness Results for Passive Imaging

Agaltsov, A. D., Hohage, T., & Novikov, R. G. (2018). Monochromatic Identities for the Green Function and Uniqueness Results for Passive Imaging. SIAM Journal on Applied Mathematics, 78(5), 2865-2890. doi:10.1137/18M1182218.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0003-C8C8-A Version Permalink: http://hdl.handle.net/21.11116/0000-0003-C8C9-9
Genre: Journal Article

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 Creators:
Agaltsov, Alexey D.1, Author
Hohage, Thorsten1, Author
Novikov, Roman G., Author
Affiliations:
1Max Planck Institute for Solar System Research, Max Planck Society, Justus-von-Liebig-Weg 3, 37077 Göttingen, DE, ou_1125546              

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 Abstract: For many wave propagation problems with random sources it has been demonstrated that cross correlations of wave fields are proportional to the imaginary part of the Green function of the underlying wave equation. This leads to the inverse problem to recover coefficients of a wave equation from the imaginary part of the Green function on some measurement manifold. In this paper we prove, in particular, local uniqueness results for the Schrödinger equation with one frequency and for the acoustic wave equation with unknown density and sound speed and two frequencies. As the main tool of our analysis, we establish new algebraic identities between the real and the imaginary part of Green's function, which in contrast to the well-known Kramers--Kronig relations, involve only one frequency.

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Language(s): eng - English
 Dates: 2018
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1137/18M1182218
 Degree: -

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Title: SIAM Journal on Applied Mathematics
Source Genre: Journal
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Publ. Info: Philadelphia, PA : Society for Industrial and Applied Mathematics
Pages: - Volume / Issue: 78 (5) Sequence Number: - Start / End Page: 2865 - 2890 Identifier: ISSN: 0036-1399
CoNE: https://pure.mpg.de/cone/journals/resource/110975500577317