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

Liu, Linong; Zhang, Jianfeng

doi:10.1029/2006gl025849

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…Like other local optimization schemes (Ristow, 1999;Liu and Zhang, 2006), however, Shan's method also produces optimized Table 1. Coefficients of implicit FD method using the analytic Taylor-series expansion and using the global optimization scheme (indicated by *).…”

Section: Comparison To Traditional Optimizationsmentioning

confidence: 99%

“…The optimization schemes of seismic migration can be categorized into two classes: the local optimization scheme and the global optimization scheme. The local optimization scheme is table-driven and has very high accuracy because it is tailor-made for a given model (e.g., Ristow and Rühl, 1994;Liu and Zhang, 2006;Shan, 2009). 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).…”

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: Comparison To Traditional Optimizationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Globally optimized finite-difference extrapolator for strongly VTI media

Zhang

Yao

2012

GEOPHYSICS

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“…The dual domain (wavenumber and space) wave equation based migration methods such as split-step Fourier [4] , Fourier finite-difference [5] , generalized-screen [6,7] and optimum split-step Fourier [8∼11] have been widely used because of their many desirable properties. Many scholars have attempted to study on the generalization from isotropic media to anisotropic media of the dual domain one-way wave equation operators methods such as generalized-screen [7] , wide-angle screen [12] and optimum split-step Fourier (OSP) [10,11] . However, the approximation to the anisotropic dispersion relation introduced in the generalized-screen limits the range of anisotropy, and the finite-difference correction [5,13] used in the wide-angle screen yields the same problem, i.e.…”

Section: Introductionmentioning

confidence: 99%

Wave Equation Prestack Depth Migration Method in 3D VTI Media

Liu¹,

Zhang²

2011

Chinese J of Geophysics

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Based on the 3‐D dispersion equation for the transversely isotropic media with a vertical symmetry axis (VTI), we proposed one‐way operators in the wavenumber‐space domain such that the terms that contain spatial coordinates and the terms that contain wavenumbers are separated. The coefficients in one‐way operators are determined using an optimization scheme for more accurately matching to the exact phase‐shift operator with a wide‐angle. The resulting 3‐D VTI wave equation prestack migration algorithm can accommodate a wide range of anisotropy rather than the weak anisotropy. For its practical aspects, we also present a frequency‐dependent varying‐step depth extrapolation scheme for reducing the computational cost of wavefield depth extrapolation and an anti‐alias one‐way propagator aiming at imaging the steep dipping structures with 3‐D sparsely sampling dataset in 3‐D VTI media. The proposed 3‐D VTI wave equation prestack migration scheme is demonstrated by SEG 2‐D Hess VTI dataset and a 3‐D migration impulse response with its layout resulting from the 3‐D field data.

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Frequency‐Dependent Varying‐Step Depth Extrapolation Scheme for Wave Equation Based Migration

Zhang¹,

Lu²,

Liu³

2008

Chinese J of Geophysics

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We propose a frequency‐dependent varying‐step depth extrapolation scheme and a table‐driven, one point wavefield interpolation technique for the wave equation based migration methods. The former reduces the computational cost of wavefield depth extrapolation, and the latter reconstructs the extrapolated wavefield with an equal, desired vertical step with high computational efficiency. The proposed varying‐step depth extrapolation plus one‐point interpolation scheme results in 2/3 reduction in omputational cost when compared to the conventional equal‐step depth extrapolation of wavefield, but gives the almost same imaging. We present the scheme using the optimum split‐step Fourier method on the 2‐D Marmousi dataset and 3‐D field dataset. The results demonstrate the high computational efficiency of the scheme in the absence of loss of accuracy. The proposed scheme can also be used by other wave equation based migration methods of the frequency domain.

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

Cited by 4 publications

References 20 publications

Globally optimized finite-difference extrapolator for strongly VTI media

Globally optimized finite-difference extrapolator for strongly VTI media

Wave Equation Prestack Depth Migration Method in 3D VTI Media

Frequency‐Dependent Varying‐Step Depth Extrapolation Scheme for Wave Equation Based Migration

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