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Tangential cone condition for the full waveform forward operator in the viscoelastic regime: the non-local case

Eller, Matthias; Griesmaier, Roland 1; Rieder, Andreas 1
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract:

We discuss mapping properties of the parameter-to-state map of full waveform inversion and generalize the results of [M. Eller and A. Rieder, Inverse Problems 37 (2021) 085011] from the acoustic to the viscoelastic wave equation. In particular we establish injectivity of the Fréchet derivative of the parameter-to-state map for a semi-discrete seismic inverse problem in the viscoelastic regime. Here, the finite dimensional parameter space is restricted to functions having global support in the propagation medium (the non-local case) and that are locally linearly independent. As a consequence we deduce local conditional wellposedness of this nonlinear inverse problem. Furthermore, we show that the tangential cone condition holds, which is an essential prerequisite in the convergence analysis of a variety of inversion algorithms for nonlinear illposed problems.


Volltext §
DOI: 10.5445/IR/1000155827
Veröffentlicht am 10.02.2023
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 02.2023
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000155827
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 20 S.
Serie CRC 1173 Preprint ; 2023/8
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter nonlinear illposed problem, tangential cone condition, Lipschitz stability, full waveform seismic inversion, viscoelastic wave equation
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