The application of an optimal transport to a preconditioned data matching function for robust waveform inversion

Bingbing Sun, Tariq Ali Alkhalifah

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Scopus citations

Abstract

Full Waveform Inversion updates the subsurface model iteratively by minimizing a misfit function, which measures the difference between observed and predicted data. The conventional l norm misfit function is widely used as it provides a simple, sample by sample, high resolution misfit function. However it is susceptible to local minima if the low wavenum-ber components of the initial model are not accurate. A deconvolution of the predicted and observed data offers an extend space comparison, which is more global. The matching filter calculated from the deconvolution has energy focussed at zero lag, like a Dirac Delta function, when the predicted data matches the observed ones. We use the Wasserstein distance to measure the difference between the matching filter and a Dirac Delta function. Unlike data, the matching filter can be easily transformed to a distribution satisfying the requirement of optimal transport theory. Compared with the conventional normalized penalty applied to non-zero lag energy in the matching filter, the new misfit function is a metric and has solid mathematical foundation based on optimal transport theory. Both synthetic and real data examples verified the effectiveness of the proposed misfit function.
Original languageEnglish (US)
Title of host publicationSEG Technical Program Expanded Abstracts 2018
PublisherSociety of Exploration Geophysicists
Pages5168-5172
Number of pages5
DOIs
StatePublished - Aug 27 2018

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