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Imaging with the elliptic Radon transform in 3D from an analytical and numerical perspective

Grathwohl, Christine; Kunstmann, Peer Christian; Quinto, Eric Todd; Rieder, Andreas

Abstract:
The three-dimensional elliptic Radon transform (eRT) averages distributions over ellipsoids of revolution. It thus serves as a linear model in seismic imaging where one wants to recover the earth’s interior from reflected wave fields. As there is no inversion formula known for the eRT, approximate formulas have to be used. In this paper we suggest several of those, microlocally analyze their
properties, provide and implement an adapted algorithm whose performance we test by diverse numerical experiments. Our previous results of [Inverse Problems, 34 (2018), 014002 & 114001] are thus generalized to three space dimensions.

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Volltext §
DOI: 10.5445/IR/1000118531
Veröffentlicht am 21.04.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000118531
Verlag KIT, Karlsruhe
Umfang 28 S.
Serie CRC 1173 ; 2020/13
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter generalized Radon transforms, Fourier integral operators, microlocal analysis, seismic imaging
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