Time-lapse waveform inversion regularized by spectral constraints and Sobolev space norm
KAUST DepartmentEarth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Seismic Wave Analysis Group
Online Publication Date2018-08-27
Print Publication Date2018-08-27
Permanent link to this recordhttp://hdl.handle.net/10754/631145
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AbstractImperfect illumination from surface seismic data due to lack of aperture and frequency content leads to ambiguity and resolution loss in seismic images and in full-waveform inversion (FWI) results. The resolution of time-lapse velocity updates can, however, be improved enforcing the sparsity of the parameter changes. Edge-preserving regularizations and constraints are typically used to promote sparsity. However, different choice of regularization parameters leads to different inversion results and optimal parameters are hard to identify, especially for real data. In particular it is not straightforward to balance the inversion between sparsity constraint and data fit. Fortunately, it is possible to estimate local spatial wavenumbers in a velocity model that are best illuminated by the data. We propose to constrain part of the model difference spectrum that is well illuminated by the data and optimize the rest of the spectrum to enhance sparsity. We approximate correctly retrieved model wavenumbers by simply picking large enough values in the inverted spectrum and constrain that part of model spectrum. Then we adjust the rest of the wavenumbers to reduce the value of a Sobolev space norm (SSN). SSN reduction promotes sparsity of time-lapse updates, while spectral constraints ensure that the part of the modeled spectrum retrieved from the data is completely retained. Application to synthetic noisy data for a perturbation of the Marmousi II model shows that the model resolution can be improved by using our method to extrapolate the model spectrum.
CitationKazei V, Alkhalifah T (2018) Time-lapse waveform inversion regularized by spectral constraints and Sobolev space norm. SEG Technical Program Expanded Abstracts 2018. Available: http://dx.doi.org/10.1190/segam2018-w12-04.1.
SponsorsWe thank KAUST for support and computational resources. Vladimir Kazei is also grateful to Jonathan Edgar of Total and Celine Ravaut of Statoil for helpful discussions at the EAGE 2017 meeting in Paris.
PublisherSociety of Exploration Geophysicists
Conference/Event name88th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2018