Modeling of pseudoacoustic P-waves in orthorhombic media with a low-rank approximation

Song, Xiaolei; Alkhalifah, Tariq

doi:10.1190/geo2012-0144.1

Cited by 68 publications

(26 citation statements)

References 42 publications

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“…To test the accuracy of our modeling approach, we compare the wavefield solution from equation 9 with the low-rank approximation (Song and Alkhalifah, 2013), as well as with the traveltimes from the eikonal solution (Waheed et al, 2014). Figure 2a and 2b shows wavefield snapshots in an orthorhombic medium with the homogeneous model parameters…”

Section: Forward Modelingmentioning

confidence: 99%

“…In the orthorhombic case, this yields the cubic polynomial (Song and Alkhalifah, 2013) −Φ 3 þ aΦ 2 þ bΦ þ c ¼ 0; (A-2)…”

Section: Appendix a The Phase Operatormentioning

confidence: 99%

“…The phase operator can be obtained from the dispersion relation using the Christoffel equation (Alkhalifah, 2003). In the orthorhombic case, this yields the cubic polynomial (Song and Alkhalifah, 2013):…”

Section: Forward Modelingmentioning

confidence: 99%

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Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

Masmoudi

Alkhalifah

2018

GEOPHYSICS

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Full-waveform inversion (FWI) in anisotropic media is challenging, mainly because of the large computational cost, especially in 3D, and the potential trade-offs between the model parameters needed to describe such media. By analyzing the trade-offs and understanding the resolution limits of the inversion, we can constrain FWI to focus on the main parameters the data are sensitive to and push the inversion toward more reliable models of the subsurface. Orthorhombic anisotropy is one of the most practical approximations of the earth subsurface that takes into account the natural horizontal layering and the vertical fracture network. We investigate the feasibility of a multiparameter FWI for an acoustic orthorhombic model described by six parameters. We rely on a suitable parameterization based on the horizontal velocity and five dimensionless anisotropy parameters. This particular parameterization allows a multistage model inversion strategy in which the isotropic, then, the vertical transverse isotropic, and finally the orthorhombic model can be successively updated. We applied our acoustic orthorhombic inversion on the SEG-EAGE overthrust synthetic model. The observed data used in the inversion are obtained from an elastic variable density version of the model. The quality of the inverted model suggests that we may recover only four parameters, with different resolution scales depending on the scattering potential of these parameters. Therefore, these results give useful insights on the expected resolution of the inverted parameters and the potential constraints that could be applied to an orthorhombic model inversion. We determine the efficiency of the inversion approach on real data from the North Sea. The inverted model is in agreement with the geologic structures and well-log information.

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Section: Forward Modelingmentioning

confidence: 99%

“…In the orthorhombic case, this yields the cubic polynomial (Song and Alkhalifah, 2013) −Φ 3 þ aΦ 2 þ bΦ þ c ¼ 0; (A-2)…”

Section: Appendix a The Phase Operatormentioning

confidence: 99%

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Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

Masmoudi

Alkhalifah

2018

GEOPHYSICS

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“…From this point on, we denote |k| as k for convenience. A second-order time-marching scheme with a multidimensional inverse Fourier transform leads to the familiar expression (Soubaras & Zhang 2008;Wards et al 2008;Etgen & Brandsberg-Dahl 2009;Zhang & Zhang 2009;Fomel et al 2010;Chu & Stoffa 2011;Song & Alkhalifah 2013;Liu et al 2014):…”

Section: O P T I M I Z E D E X Pa N S I O N B a S E D L O W-r A N K Mmentioning

confidence: 99%

The optimized gradient method for full waveform inversion and its spectral implementation

Alkhalifah

2016

Geophys. J. Int.

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“…To derive the governing equation for P-waves in acoustic orthorhombic media, we need to find the root of the cubic polynomial (Song & Alkhalifah 2013),…”

Section: Acknowledgmentsmentioning

confidence: 99%

Efficient anisotropic quasi-Pwavefield extrapolation using an isotropic low-rank approximation

Zhang

Liu

Alkhalifah

et al. 2017

Geophysical Journal International

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2 SUMMARYThe computational cost of quasi-P wave extrapolation depends on the complexity of the medium, and specifically the anisotropy. Our effective-model method splits the anisotropic dispersion relation into an isotropic background and a correction factor to handle this dependency. The correction term depends on the slope (measured using the gradient) of current wavefields and the anisotropy. As a result, the computational cost is independent of the nature of anisotropy, which makes the extrapolation efficient. A dynamic implementation of this approach decomposes the original pseudo-differential operator into a Laplacian, handled using the low-rank approximation of the spectral operator, plus an angular dependent correction factor applied in the space domain to correct for anisotropy. We analyze the role played by the correction factor and propose a new spherical decomposition of the dispersion relation. The proposed method provides accurate wavefields in phase and more balanced amplitudes than a previous spherical decomposition. Also, it is free of SVwave artifacts. Applications to a simple homogeneous transverse isotropic medium with a vertical symmetry axis (VTI) and a modified Hess VTI model demonstrate the effectiveness of the approach. The Reverse Time Migration (RTM) applied to a modified BP VTI model reveals that the anisotropic migration using the proposed modeling engine performs better than an isotropic migration.

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Modeling of pseudoacoustic P-waves in orthorhombic media with a low-rank approximation

Cited by 68 publications

References 42 publications

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

The optimized gradient method for full waveform inversion and its spectral implementation

Efficient anisotropic quasi-Pwavefield extrapolation using an isotropic low-rank approximation

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