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

Eller, Matthias; Rieder, Andreas

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 Lipschitz stable, in particular, it is conditionally well-posed.

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Volltext §
DOI: 10.5445/IR/1000130168
Veröffentlicht am 02.03.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 01.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000130168
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 14 S.
Serie CRC 1173 Preprint ; 2021/9
Externe Relationen Siehe auch
Schlagwörter tangential cone condition, Lipschitz stability, full waveform seismic inversion, acoustic wave equation
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