An all‐at‐once approach to full waveform inversion in the viscoelastic regime. (25th February 2021)

• Record Type: Journal Article
• Authors: Rieder, Andreas
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 8(2021)
• Page Start: 6376
• Page End: 6388
• Publication Date: 2021-02-25
• Subjects: adjoint state method -- all‐at‐once method -- full waveform inversion -- viscoelastic wave equation -- wavefield reconstruction inversion; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7190
• Languages: English
• ISSNs: 0170-4214

Abstract

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.