Scattering-angle based filtering of the waveform inversion gradients

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Abstract

Full waveform inversion (FWI) requires a hierarchical approach to maneuver the complex non-linearity associated with the problem of velocity update. In anisotropic media, the non-linearity becomes far more complex with the potential trade-off between the multiparameter description of the model. A gradient filter helps us in accessing the parts of the gradient that are suitable to combat the potential non-linearity and parameter trade-off. The filter is based on representing the gradient in the time-lag normalized domain, in which the low scattering angle of the gradient update is initially muted out in the FWI implementation, in what we may refer to as a scattering angle continuation process. The result is a low wavelength update dominated by the transmission part of the update gradient. In this case, even 10 Hz data can produce vertically near-zero wavenumber updates suitable for a background correction of the model. Relaxing the filtering at a later stage in the FWI implementation allows for smaller scattering angles to contribute higher-resolution information to the model. The benefits of the extended domain based filtering of the gradient is not only it's ability in providing low wavenumber gradients guided by the scattering angle, but also in its potential to provide gradients free of unphysical energy that may correspond to unrealistic scattering angles.
Original languageEnglish (US)
Pages (from-to)363-373
Number of pages11
JournalGeophysical Journal International
Volume200
Issue number1
DOIs
StatePublished - Nov 21 2014

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