Migration in transversely isotropic media using implicit operators

Ristow, D.; Rühl, Thomas

doi:10.1190/1.1885756

Cited by 14 publications

(10 citation statements)

References 5 publications

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“…Furthermore, the implicit FD methods are good at handling strong velocity variations. Therefore, implicit FD methods received increased attention recently in imaging VTI media, either as independent methods or as high-order corrections to the phase-shift method (Ristow, 1999;Han and Wu, 2005;Zhang et al, 2005b;Hua et al, 2006;Fei and Liner, 2008;Bakker, 2009;Shan, 2009;Zhang, 2009;Amazonas et al, 2010;Pedersen et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, the global optimization scheme is independent of tables and is suitable for all possible models (e.g., Lee and Suh, 1985;Xie and Wu, 1999;Huang and Fehler, 2000;Zhu et al, 2008;Zhang et al, 2010;Zhang and Yao, 2011). Ristow (1999) designs an implicit FD scheme using the analytic Taylor-series expansion under the assumption of weak anisotropy. He also suggests a local optimization scheme, but the resulting accuracy is only 70°for the sixth-order FD method.…”

Section: Introductionmentioning

confidence: 99%

“…For strong anisotropy, Shan (2009) designs a second-order implicit FD scheme by the analytic Taylor-series expansion and estimates a simplified form of the fourth-order FD method. Shan's optimized FD method is accurate to 60°for the second-order operator and to 80°for the fourthorder operator, which is more accurate than the method devised by Ristow (1999). Based on the local optimization scheme, their optimized coefficients are functions of Thomsen anisotropy parameters (Thomsen, 1986), which can be calculated before wavefield extrapolation and stored in a table.…”

Section: Introductionmentioning

confidence: 99%

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Globally optimized finite-difference extrapolator for strongly VTI media

Zhang

Yao

2012

GEOPHYSICS

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Implicit finite-difference (FD) migration is unconditionally stable and is popular in handling strong velocity variations, but its extension to strongly transversely anisotropic media with vertical symmetric axis media is difficult. Traditional local optimizations generate the optimized coefficients for each pair of Thomsen anisotropy parameters independently, which can degrade results substantially for large anisotropy variations and lead to a huge table. We developed an implicit FD method using the analytic Taylor-series expansion and used a global optimization scheme to improve its accuracy for wide phase angles. We first extended the number of the constant coefficients; then we relaxed the coefficient of the time-delay extrapolation term by tuning a small factor such that error is less than 0.1%. Finally, we optimized the constant coefficients using a simulated annealing algorithm by constraining that all the error functions on a fine grid of the whole anisotropic region did not exceed 0.5% simultaneously. The extended number of the constant coefficients and the relaxed coefficient greatly enhanced the flexibility of matching the dispersion relation and significantly improved the ability of handling strong anisotropy over a much wider range. Compared with traditional local optimization, our scheme does not need any table and table lookup. For each order of the FD method, only one group of optimized coefficients is enough to handle strong variations in velocity and anisotropy. More importantly, our global optimization scheme guarantees the accuracy for various possible ranges of anisotropy parameters, no matter how strong the anisotropy is. For the globally optimized second-order FD method, the accurate phase angle is up to 58°, and the increase is about 18°-22°. For the globally optimized fourth-order FD method, the accurate phase angle is up to 77°, and the increase is about 22°-27°.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Globally optimized finite-difference extrapolator for strongly VTI media

Zhang

Yao

2012

GEOPHYSICS

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“…This method improves the accuracy with the same computational cost. Under the weak anisotropy assumption, Ristow and Ruhl (1997) design an implicit scheme for VTI media. Liu et al (2005) apply a phase-correction operator (Li, 1991) after the finite-difference operator for VTI media and improve the accuracy.…”

Section: Introductionmentioning

confidence: 99%

Optimized implicit finite‐difference migration for TTI media

Shan

2007

SEG Technical Program Expanded Abstracts 2007

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I develop an implicit finite-difference migration algorithm for tilted transversely isotropic (TTI) media. I approximate the dispersion relation of TTI media with a rational function series, whose coefficients are estimated by least-squares optimization. The dispersion relation of TTI media is not a symmetric function, so an odd rational function series is required in addition to the even one. These coefficients are functions of Thomsen anisotropy parameters. They are calculated and stored in a table before the wavefield extrapolation. Similar to the isotropic and VTI media, in 3D a phase-correction filter is applied after the finite-difference operator to eliminate the numerical error caused by two-way splitting. I generate impulse responses for this algorithm and compare them to those generated using the phase-shift method.

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“…Failure to account for anisotropy in seismic modeling and imaging leads to large traveltime and position errors. One-way operators such as the implicit finite-difference [Ristow, 1999], explicit filtering [Uzcategui, 1995;Zhang et al, 2001a], non-stationary phase-shift [Ferguson and Margrave, 2002], and wideangle screen [Han and Wu, 2005] have been proposed for imaging 2D VTI (or TI) media. The generalized-screen operators [Le Rousseau and de Hoop, 2001a] were developed to model one-way wavefields in 2D and 3D weak VTI media.…”

Section: Introductionmentioning

confidence: 99%

Optimum split‐step Fourier one‐way operators for seismic modeling and imaging in 3D VTI media

Liu¹,

Zhang²

2006

Geophysical Research Letters

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[1] One-way operators are proposed for modeling wideangle wave propagation in 3D heterogeneous, transversely isotropic media with a vertically symmetric axis (VTI). The operators are built in the wavenumber-space domain such that the terms in the space domain and in the wavenumber domain are separable. This means that the resulting algorithm can be implemented alternately in the space and wavenumber domains using the fast Fourier transforms. The proposed one-way operators can accommodate a wide range of anisotropy rather than the weak anisotropy. An optimization scheme is used to determine the coefficients in the operators by directly matching to spatially varying, exact anisotropic phase-shift operators over a prescribed angular range of wave propagation. We demonstrate the accuracy of the one-way operators by a comparison with the two-way elastic anisotropic finite-difference modeling in the presence of severe lateral variations. Citation: Liu, L., and J. Zhang (2006), Optimum split-step Fourier one-way operators for seismic modeling and imaging in 3D VTI media, Geophys. Res. Lett., 33, L09308,

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Migration in transversely isotropic media using implicit operators

Cited by 14 publications

References 5 publications

Globally optimized finite-difference extrapolator for strongly VTI media

Globally optimized finite-difference extrapolator for strongly VTI media

Optimized implicit finite‐difference migration for TTI media

Optimum split‐step Fourier one‐way operators for seismic modeling and imaging in 3D VTI media

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