Full-model wavenumber inversion: An emphasis on the appropriate wavenumber continuation

Type
Article

Authors
Alkhalifah, Tariq Ali

KAUST Department
Earth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Seismic Wave Analysis Group

Online Publication Date
2016-04-06

Print Publication Date
2016-05

Date
2016-04-06

Abstract
A model of the earth can be described using a Fourier basis represented by its wavenumber content. In full-waveform inversion (FWI), the wavenumber description of the model is natural because our Born-approximation-based velocity updates are made up of wavefields. Our objective in FWI is to access all the model wavenumbers available in our limited aperture and bandwidth recorded data that are not yet accurately present in the initial velocity model. To invert for those model wavenumbers, we need to locate their imprint in the data. Thus, I review the relation between the model wavenumber buildup and the inversion process. Specifically, I emphasize a focus on the model wavenumber components and identified their individual influence on the data. Missing the energy for a single vertical low-model wavenumber from the residual between the true Marmousi model and some initial linearly increasing velocity model produced a worse least-squares fit to the data than the initial model itself, in which all the residual model wavenumbers were missing. This stern realization validated the importance of wavenumber continuation, specifically starting from the low-model wavenumbers, to higher (resolution) wavenumbers, especially those attained in an order dictated by the scattering angle filter. A numerical Marmousi example determined the important role that the scattering angle filter played in managing the wavenumber continuation from low to high. An application on the SEG2014 blind test data set with frequencies lower than 7 Hz muted out further validated the versatility of the scattering angle filtering.

Citation
Full-model wavenumber inversion: An emphasis on the appropriate wavenumber continuation 2016, 81 (3):R89 GEOPHYSICS

Acknowledgements
I thank KAUST for its support. I am also grateful to Z. Wu and Y. Choi for useful discussions and some of the numerical examples. I thank Chevron for the SEG2014 data set. I also thank the associate editor and the reviewers for their outstanding review of the paper.

Publisher
Society of Exploration Geophysicists

Journal
GEOPHYSICS

DOI
10.1190/geo2015-0537.1

Additional Links
http://library.seg.org/doi/10.1190/geo2015-0537.1

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