3‐D implicit finite‐difference migration by multiway‐splitting

Ristow, D.; Rühl, Thomas

doi:10.1190/1.1887608

Cited by 22 publications

(32 citation statements)

References 4 publications

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“…Various approximations and discretizations, such as screen propagators, the double square-root, and splitting methods, have been proposed (Wu, 1994;Collino and Joly, 1995;Biondi and Palacharla, 1996;Ristow and Ruhl, 1997). For brevity, a migration scheme based on the one-way wave equation is called one-way migration.…”

Section: Introductionmentioning

confidence: 99%

A comparison between one‐way and two‐way wave‐equation migration

2004

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Results for wave-equation migration in the frequency domain using the constant-density acoustic two-way wave equation have been compared to images obtained by its one-way approximation. The two-way approach produces more accurate reflector amplitudes and provides superior imaging of steep flanks. However, migration with the two-way wave equation is sensitive to diving waves, leading to low-frequency artifacts in the images. These can be removed by surgical muting of the input data or iterative migration or high-pass spatial filtering. The last is the most effective.Iterative migration based on a least-squares approximation of the seismic data can improve the amplitudes and resolution of the imaged reflectors. Two approaches are considered, one based on the linearized constantdensity acoustic wave equation and one on the full acoustic wave equation with variable density. The first converges quickly. However, with our choice of migration weights and high-pass spatial filtering for the linearized case, a real-data migration result shows little improvement after the first iteration. The second, nonlinear iterative migration method is considerably more difficult to apply. A real-data example shows only marginal improvement over the linearized case.In two dimensions, the computational cost of the twoway approach has the same order of magnitude as that for the one-way method. With our implementation, the two-way method requires about twice the computer time needed for one-way wave-equation migration.

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Section: Introductionmentioning

confidence: 99%

A comparison between one‐way and two‐way wave‐equation migration

2004

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“…This one-way equation involves the non-local square root operator. In order to obtain an efficient numerical scheme for spatially varying background velocity and to compute the wave field step by step along the preferred direction with a marching approach, a first possibility is to approximate the square root operator with local operators, for instance with Padé fractions leading to the classic 15 • , 45 • or 60 • approximation scheme (see [3,[7][8][9]). A second possibility is to first extrapolate the wave field in the frequency-wavenumber domain assuming a constant velocity model and then to apply a correction using Born approximation.…”

Section: Introductionmentioning

confidence: 99%

Improved amplitude multi-one-way modeling method

et al. 2005

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“…Consequently, the two-way splitting technique leads to large position errors, especially for steep dips in diagonal directions (Claerbout 1985). Several methods have been proposed to reduce the azimuthal anisotropy, including the phase-correction operation (Graves and Clayton 1990), the error-compensation equation (Li 1991), and the multi-way splitting technique (Ristow and Rühl 1997). These methods obtain more circular impulse responses with significantly increasing computational cost.…”

Section: Introductionmentioning

confidence: 99%

3D Fourier finite‐difference migration by alternating‐direction‐implicit plus interpolation

Zhang

Wang

et al. 2007

Geophysical Prospecting

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A B S T R A C TConventional two-way splitting Fourier finite-difference migration for 3D complex media yields azimuthal anisotropy where an additional phase correction is needed with much increase of computational cost. We incorporate the alternating-directionimplicit plus interpolation scheme into the conventional Fourier finite-difference method to reduce azimuthal anisotropy. This scheme retains the high-order remnants ignored by the two-way splitting in the form of a wavefield interpolation in the wavenumber domain. The wavefield interpolation for each step of downward extrapolation is implemented between the wavefields before and after the conventional Fourier finite-difference extrapolation. As the Fourier finite-difference migration is implemented in the space and wavenumber dual space, the Fourier transforms between space and wavenumber domain that were needed for the alternating-directionimplicit plus interpolation in frequency domain (FD) migration are saved in Fourier finite-difference migration. Since the azimuth anisotropy in Fourier finite-difference is much less than that in FD, the application of the alternating-direction-implicit plus interpolation scheme in Fourier finite-difference migration is superior to that in FD migration in handling complex media with large velocity contrasts and steep dips. Impulse responses show that the presented method reduces the azimuthal anisotropy at almost no extra cost. I N T R O D U C T I O NWith 3D surveys becoming standard practice, fast and accurate 3D imaging algorithms are in demand; hence many effective methods in 2D practice should be extended to 3D cases. The Fourier finite-difference method (Ristow and Rühl 1994) can handle complex media with large velocity contrasts and steep dips. Unfortunately, its full 3D extension involves huge computational cost because of the finite-difference correction attached to the phase screen method. A practical way is to split the finite-difference correction into two cascaded 2D operators sequentially along the in-line and cross-line directions. This method is called the two-way splitting technique (Brown 1983) or alternating-direction-implicit scheme (Douglas 1962). * E-mail: zjh@mail.igcas.ac.cn While the two-way splitting technique affords high computational efficiency, it introduces extensive phase errors, the socalled azimuthal anisotropy or splitting error. The azimuthal anisotropy causes the impulse response in a depth slice being not a perfect circle but a smoothed diamond. In addition, the azimuthal anisotropy becomes apparent with increasing dip angles and velocity contrasts. Consequently, the two-way splitting technique leads to large position errors, especially for steep dips in diagonal directions (Claerbout 1985). Several methods have been proposed to reduce the azimuthal anisotropy, including the phase-correction operation (Graves and Clayton 1990), the error-compensation equation (Li 1991), and the multi-way splitting technique (Ristow and Rühl 1997). These methods obtain more circular impulse responses...

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3‐D implicit finite‐difference migration by multiway‐splitting

Cited by 22 publications

References 4 publications

A comparison between one‐way and two‐way wave‐equation migration

A comparison between one‐way and two‐way wave‐equation migration

Improved amplitude multi-one-way modeling method

3D Fourier finite‐difference migration by alternating‐direction‐implicit plus interpolation

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