The optimized expansion based low-rank method for wavefield extrapolation

Handle URI:
http://hdl.handle.net/10754/575704
Title:
The optimized expansion based low-rank method for wavefield extrapolation
Authors:
Wu, Zedong; Alkhalifah, Tariq Ali ( 0000-0002-9363-9799 )
Abstract:
Spectral methods are fast becoming an indispensable tool for wavefield extrapolation, especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain extrapolation operator efficiently. To solve this problem, we evaluated an optimized expansion method that can approximate this operator with a low-rank variable separation representation. The rank defines the number of inverse Fourier transforms for each time extrapolation step, and thus, the lower the rank, the faster the extrapolation. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low-rank representation. As a result, we obtain lower rank representations compared with the standard low-rank method within reasonable accuracy and thus cheaper extrapolations. Additional bounds set on the range of propagated wavenumbers to adhere to the physical wave limits yield unconditionally stable extrapolations regardless of the time step. An application on the BP model provided superior results compared to those obtained using the decomposition approach. For transversely isotopic media, because we used the pure P-wave dispersion relation, we obtained solutions that were free of the shear wave artifacts, and the algorithm does not require that n > 0. In addition, the required rank for the optimization approach to obtain high accuracy in anisotropic media was lower than that obtained by the decomposition approach, and thus, it was more efficient. A reverse time migration result for the BP tilted transverse isotropy model using this method as a wave propagator demonstrated the ability of the algorithm.
KAUST Department:
Earth Science and Engineering Program
Publisher:
Society of Exploration Geophysicists
Journal:
GEOPHYSICS
Issue Date:
Mar-2014
DOI:
10.1190/GEO2013-0174.1
Type:
Article
ISSN:
0016-8033; 1942-2156
Sponsors:
We thank KAUST for its support and the SWAG group for the collaborative environment. We also thank the associate editor Y. Zhang, X. Song, and two anonymous reviewers for their fruitful suggestions and comments. The computational examples in this paper use the Madagascar open-source software package http://www.ahay.org/.
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorWu, Zedongen
dc.contributor.authorAlkhalifah, Tariq Alien
dc.date.accessioned2015-08-24T08:36:11Zen
dc.date.available2015-08-24T08:36:11Zen
dc.date.issued2014-03en
dc.identifier.issn0016-8033en
dc.identifier.issn1942-2156en
dc.identifier.doi10.1190/GEO2013-0174.1en
dc.identifier.urihttp://hdl.handle.net/10754/575704en
dc.description.abstractSpectral methods are fast becoming an indispensable tool for wavefield extrapolation, especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain extrapolation operator efficiently. To solve this problem, we evaluated an optimized expansion method that can approximate this operator with a low-rank variable separation representation. The rank defines the number of inverse Fourier transforms for each time extrapolation step, and thus, the lower the rank, the faster the extrapolation. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low-rank representation. As a result, we obtain lower rank representations compared with the standard low-rank method within reasonable accuracy and thus cheaper extrapolations. Additional bounds set on the range of propagated wavenumbers to adhere to the physical wave limits yield unconditionally stable extrapolations regardless of the time step. An application on the BP model provided superior results compared to those obtained using the decomposition approach. For transversely isotopic media, because we used the pure P-wave dispersion relation, we obtained solutions that were free of the shear wave artifacts, and the algorithm does not require that n > 0. In addition, the required rank for the optimization approach to obtain high accuracy in anisotropic media was lower than that obtained by the decomposition approach, and thus, it was more efficient. A reverse time migration result for the BP tilted transverse isotropy model using this method as a wave propagator demonstrated the ability of the algorithm.en
dc.description.sponsorshipWe thank KAUST for its support and the SWAG group for the collaborative environment. We also thank the associate editor Y. Zhang, X. Song, and two anonymous reviewers for their fruitful suggestions and comments. The computational examples in this paper use the Madagascar open-source software package http://www.ahay.org/.en
dc.publisherSociety of Exploration Geophysicistsen
dc.titleThe optimized expansion based low-rank method for wavefield extrapolationen
dc.typeArticleen
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalGEOPHYSICSen
kaust.authorWu, Zedongen
kaust.authorAlkhalifah, Tariq Alien
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