Eliminating Nearly All Dispersion Error from FD Modeling and RTM with Minimal Cost Increase

Stork, Christof

doi:10.3997/2214-4609.20130478

Cited by 52 publications

(46 citation statements)

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“…For seismic imaging, the time dispersion might cause mispositioning of reflectors, especially deep reflectors with high frequency that are imaged from long-offset data. Numerous approaches have been proposed in the literature to cope with time dispersion in wave propagation, such as using high-order FD schemes in time (Chen, 2007), the rapid expansion method (Tal-Ezer et al, 1987;Tessmer, 2011), low-rank methods (Song et al, 2013), and correction methods based on filter and interpolation (Li et al, 2013;Stork, 2013;Dai et al, 2014). One popular wavefield simulation scheme by FD is the second-order scheme (Stoffa and Pestana, 2009), which requires very fine time steps to minimize the numerical errors.…”

Section: Introductionmentioning

confidence: 99%

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Finite-difference time dispersion transforms for wave propagation

Wang¹,

Xu²

2015

GEOPHYSICS

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The finite-difference (FD) wave equation is widely implemented in seismic imaging for oil exploration. But the numerical dispersion due to discretization of time and space derivatives can introduce severe numerical errors. We have investigated time dispersion, which might distort the phase and introduce severe artifacts to the data and images, especially for long-time propagation. We first studied precisely how the time dispersion was produced, and then we developed an efficient approach -the time dispersion transforms -to cope with time dispersion errors in wave propagation. The proposed forward time dispersion transform can predict or simulate the time dispersion errors, and it can be applied to remove time dispersion errors in reverse time migration. The inverse time dispersion transform can be used to eliminate time dispersion errors from synthetic data after modeling. The proposed method is general and works for low-and high-order time FD schemes. By using this method, large time steps were allowed in wave propagation; thus, we can remove the time dispersion errors at a negligible numerical cost, and the efficiency is not affected. To test the effectiveness and robustness of the proposed time dispersion transforms, we used isotropic and anisotropic examples, as well as modeling and imaging examples.

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Section: Introductionmentioning

confidence: 99%

“…Thus, time dispersion could be handled separately from space dispersion. Stork (2013) proposes to fix the time dispersion by applying a timevariant filter and interpolation. For RTM, the inverted procedure is performed on data before backward propagation.…”

Section: Introductionmentioning

confidence: 99%

Finite-difference time dispersion transforms for wave propagation

Wang¹,

Xu²

2015

GEOPHYSICS

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“…Consequently, non-linear gradient inversion methods, like the non-linear steepest-descent method, can iteratively minimise the objective function using the gradient. This leads to the second scheme, NLLSRTM (Yao and Jakubowicz, 2012c;2013).…”

Section: Discussionmentioning

confidence: 99%

“…Current research focuses on four main issues: wavefield extrapolation (Stork, 2013;Zhang and Yao, 2013), alternative imaging conditions (Valenciano and Biondi, 2003;Zhang and Sun, 2008;Liu et al, 2011), amplitude preservation (Zhang et al, 2007a;Zhang and Sun, 2008), and how to efficiently generate common image gathers (CIGs) (Xu et al, 2011). We will consider each of these issues in turn.…”

Section: Reverse-time Migrationmentioning

confidence: 99%

Least-Squares Reverse-Time Migration

Yao

Jakubowicz

2012

SEG Technical Program Expanded Abstracts 2012

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Conventional migration methods, including reverse-time migration (RTM) have two weaknesses: first, they use the adjoint of forward-modelling operators, and second, they usually apply a crosscorrelation imaging condition to extract images from reconstructed wavefields. Adjoint operators, which are an approximation to inverse operators, can only correctly calculate traveltimes (phase), but not amplitudes. To preserve the true amplitudes of migration images, it is necessary to apply the inverse of the forward-modelling operator. Similarly, crosscorrelation imaging conditions also only correct traveltimes (phase) but do not preserve amplitudes. Besides, the examples show crosscorrelation imaging conditions produce strong sidelobes. Least-squares migration (LSM) uses both inverse operators and deconvolution imaging conditions. As a result, LSM resolves both problems in conventional migration methods and produces images with fewer artefacts, higher resolution and more accurate amplitudes. At the same time, RTM can accurately handle all dips, frequencies and any type of velocity variation. Combining RTM and LSM produces least-squares reverse-time migration (LSRTM), which in turn has all the advantages of RTM and LSM.In this thesis, we implement two types of LSRTM: matrix-based LSRTM (MLSRTM) and non-linear LSRTM (NLLSRTM). MLSRTM is a matrix formulation of LSRTM and is more stable than conventional LSRTM; it can be implemented with linear inversion algorithms but needs a large amount of computer memory. NLLSRTM, by contrast, directly expresses migration as an optimisation which minimises the ‫ܮ‬ 2 norm of the residual between the predicted and observed data. NLLSRTM can be implemented using non-linear gradient inversion algorithms, such as non-linear steepest descent and non-linear conjugated-gradient solvers.We demonstrate that both MLSRTM and NLLSRTM can achieve better images with fewer artefacts, higher resolution and more accurate amplitudes than RTM using three synthetic examples. The power of LSRTM is also further illustrated using a field dataset. Finally, a simple synthetic test demonstrates that the objective function used in LSRTM is sensitive to errors in the migration velocity.As a result, it may be possible to use NLLSRTM to both refine the migrated image and estimate the migration velocity.

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“…In a very different approach, Stork (2013) proposed to apply inverted time varying filtering to the input seismic traces before back-propagation in RTM to reduce the time dispersion error. He demonstrated the effectiveness of the method by showing numerical examples, but without going into analytical details.…”

Section: Introductionmentioning

confidence: 99%

Solutions to numerical dispersion error of time FD in RTM

Dai¹,

Liu²,

2014

SEG Technical Program Expanded Abstracts 2014

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Finite difference (FD) methods used in reverse time migration (RTM) often have imbalanced accuracies in approximating time and space derivatives. Coarse spacing combined with low order FD in the time domain induces numerical dispersion error, which results in phase rotation and depth errors in RTM images. We describe two different methods to resolve the time numerical dispersion issue: 1) a wave propagation algorithm called Explicit Time Evolution (ETE), which employs optimized stencils and coefficients to cost-effectively achieve improved accuracy, and 2) a time varying phase shift (TVPS) method applied to the input seismic traces before RTM to compensate for the dispersion from time FD.

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Eliminating Nearly All Dispersion Error from FD Modeling and RTM with Minimal Cost Increase

Cited by 52 publications

References 0 publications

Finite-difference time dispersion transforms for wave propagation

Finite-difference time dispersion transforms for wave propagation

Least-Squares Reverse-Time Migration

Solutions to numerical dispersion error of time FD in RTM

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