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Tangential cone condition and Lipschitz stability for the full waveform forward operator in the acoustic regime

Eller, Matthias; Rieder, Andreas ORCID iD icon 1
1 Karlsruher Institut für Technologie (KIT)


Time-domain full waveform inversion (FWI) in the acoustic regime comprises a parameter identification problem for the acoustic wave equation: pressure waves are initiated by sources, get scattered by the earth's inner structure, and their reflected parts are picked up by receivers located on the surface. From these reflected wave fields the two parameters, density and sound speed, have to be reconstructed. Mathematically, FWI reduces to the solution of a nonlinear and ill-posed operator equation involving the parameter-to-solution map of the wave equation. Newton-like iterative regularization schemes are well suited and well analyzed to tackle this inverse problem. Their convergence results are often based on an assumption about the nonlinear map known as tangential cone condition. In this paper we verify this assumption for a semi-discrete version of FWI where the searched-for parameters are restricted to a finite dimensional space. As a byproduct we establish that the semi-discrete seismic inverse problem is locally Lipschitz stable, in particular, it is conditionally well-posed.

Verlagsausgabe §
DOI: 10.5445/IR/1000137071
Veröffentlicht am 31.08.2021
DOI: 10.1088/1361-6420/ac11c5
Zitationen: 3
Web of Science
Zitationen: 3
Zitationen: 4
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 08.2021
Sprache Englisch
Identifikator ISSN: 0266-5611, 1361-6420
KITopen-ID: 1000137071
Erschienen in Inverse problems
Verlag Institute of Physics Publishing Ltd (IOP Publishing Ltd)
Band 37
Heft 8
Seiten Art.-Nr.: 085011
Vorab online veröffentlicht am 27.07.2021
Schlagwörter tangential cone condition, Lipschitz stability, full waveform seismic inversion, acoustic wave equation
Nachgewiesen in Scopus
Web of Science
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