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An all-at-once approach to full wavefrom seismic inversion in the viscoelastic regime

Rieder, Andreas ORCID iD icon


Full waveform seismic inversion (FWI) in the viscoelastic regime entails the task of identifying parameters in the viscoelastic wave equation from partial waveform measurements. Traditionally, one frames this nonlinear problem as an operator equation for the parameter-to-state map. Alternatively, in an all-at-once approach one augments the nonlinear operator by the viscoelastic wave equation as an additional component and considers the states as additional variables. Hence, parameters and states are sought-for simultaneously. In this article, we give a mathematically rigorous all-at-once version of FWI in a functional analytical formulation. Further, the corresponding nonlinear map is shown to be Fréchet differentiable and the adjoint operator of the Fréchet derivative is given in an explicit way suitable for implementation in a Newton-type/gradient-based regularization scheme.

Volltext §
DOI: 10.5445/IR/1000119758
Veröffentlicht am 26.05.2020
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: 1000119758
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 14 S.
Serie CRC 1173 Preprint ; 2020/16
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter all-at-once method, full waveform inversion, wavefield reconstruction inver- sion, viscoelastic wave equation, adjoint state method, nonlinear inverse and ill-posed problem
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