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

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    optimal_transport_matching_filter_modified_now_tariq_clean_compressed (2) (2).pdf
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    PDF
    Description:
    Accepted manuscript
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    Type
    Article
    Authors
    Sun, Bingbing
    Alkhalifah, Tariq Ali cc
    KAUST Department
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Seismic Wave Analysis Group
    Date
    2019-08-26
    Online Publication Date
    2019-10-28
    Print Publication Date
    2019-11-01
    Submitted Date
    2018-05-29
    Permanent link to this record
    http://hdl.handle.net/10754/661527
    
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    Abstract
    Full-waveform inversion (FWI) promises a high-resolution model of the earth. It is, however, a highly nonlinear inverse problem; thus, we iteratively update the subsurface model by minimizing a misfit function that measures the difference between the measured and the predicted data. The conventional [Formula: see text]-norm misfit function is widely used because it provides a simple, high-resolution misfit function with a sample-by-sample comparison. However, it is susceptible to local minima if the low-wavenumber components of the initial model are not accurate. Deconvolution of the predicted and measured data offers an extended space comparison, which is more global. The matching filter calculated from the deconvolution has energy focused at zero lag, like an approximated Dirac delta function, when the predicted data matches the measured one. We have introduced a framework for designing misfit functions by measuring the distance between the matching filter and a representation of the Dirac delta function using optimal transport theory. We have used the Wasserstein [Formula: see text] distance, which provides us with the optimal transport between two probability distribution functions. Unlike data, the matching filter can be easily transformed to a probability distribution satisfying the requirement of the optimal transport theory. Though in one form, it admits the conventional normalized penalty applied to the nonzero-lag energy in the matching filter, the proposed misfit function is metric and extracts its form from solid mathematical foundations based on optimal transport theory. Explicitly, we can derive the adaptive waveform inversion (AWI) misfit function based on our framework, and the critical “normalization” for AWI occurs naturally per the requirement of a probability distribution. We use a modified Marmousi model and the BP salt model to verify the features of the proposed method in avoiding cycle skipping. We use the Chevron 2014 FWI benchmark data set to further highlight the effectiveness of the proposed approach.
    Citation
    Sun, B., & Alkhalifah, T. (2019). The application of an optimal transport to a preconditioned data matching function for robust waveform inversion. GEOPHYSICS, 84(6), R923–R945. doi:10.1190/geo2018-0413.1
    Sponsors
    We thank the associate editor S. Operto for the constructive comments that helped to improve the paper. The authors also thank the SWAG group for the useful discussion and the resources of the SHAHEEN supercomputing laboratory at KAUST. We appreciate Chevron for the 2014 FWI benchmark data set.
    Publisher
    Society of Exploration Geophysicists
    Journal
    GEOPHYSICS
    DOI
    10.1190/geo2018-0413.1
    Additional Links
    http://mr.crossref.org/iPage?doi=10.1190%2Fgeo2018-0413.1
    ae974a485f413a2113503eed53cd6c53
    10.1190/geo2018-0413.1
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program

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