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

Rieder, Andreas

Abstract:
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.

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Verlagsausgabe §
DOI: 10.5445/IR/1000130522
Veröffentlicht am 19.03.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Fakultät für Mathematik (MATH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0170-4214, 1099-1476
KITopen-ID: 1000130522
Erschienen in Mathematical Methods in the Applied Sciences
Verlag Wiley
Schlagwörter adjoint state method; all‐at‐once method; full waveform inversion; viscoelastic wave equation; wavefield reconstruction inversion
Nachgewiesen in Scopus
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