Comparison of weights in prestack amplitude‐preserving Kirchhoff depth migration

Hanitzsch, C.

doi:10.1190/1.1444282

Cited by 60 publications

(19 citation statements)

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“…Three different theoretical approaches (BLEISTEIN, 1987;KEHO and BEYDOUN, 1988;SCHLEICHER et al, 1993) have led to formulations of the weight functions. As DOCHERTY (1991) and HANITZSCH (1997) have shown, these results are closely related.…”

Section: Introductionsupporting

confidence: 55%

“…Although SCHLEICHER et al (1993) state that the modulus of the weight function can also be determined from travel times, HANITZSCH (1997) points out that computing travel-time derivatives along dipping surfaces is expensive and numerically unstable. In this paper we propose an alternative strategy for determining travel-time derivatives that does not suffer from the instability of numerical differentiation.…”

Section: Introductionmentioning

confidence: 99%

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True Amplitude Migration Weights from Travel Times

Vanelle

Gajewski

2002

Pure and Applied Geophysics

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3-D amplitude preserving prestack migration of the Kirchhoff type is a task of high computational effort. A substantial part of this effort is spent on the calculation of proper weight functions for the diffraction stack. We propose a new strategy to compute the migration weights directly from coarse gridded travel-time data which are in any event needed for the summation along diffraction time surfaces. The technique employs second-order travel-time derivatives that contain all necessary information on the weight functions. Their determination alone from travel times significantly reduces the requirements in computational time and particularly storage, since it is done on the fly. Application of the method shows good accordance between numerical and analytical results for the simple types of models considered in this study.

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Section: Introductionsupporting

confidence: 55%

Section: Introductionmentioning

confidence: 99%

True Amplitude Migration Weights from Travel Times

Vanelle

Gajewski

2002

Pure and Applied Geophysics

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“…They propose a weight function that can be derived using paraxial ray theory for arbitrary configuration. A comparison of the three methods can be found in Hanitzsch (1997).…”

Section: Chapter 6 Amplitude Preserving Migrationmentioning

confidence: 99%

Traveltime based true‐amplitude migration

Vanelle

Gajewski

2000

SEG Technical Program Expanded Abstracts 2000

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Amplitude-preserving migration based on a weighted diffraction stack is a task of high computational costs. Three factors determine the major contributions to the computational effort: The diffraction time surface must be computed for each image point as well as proper weight functions. Finally, the summation is carried out over the whole aperture of the experiment. I propose a new strategy for amplitude-preserving migration that is entirely based on traveltimes, thus called traveltime-based true-amplitude migration. Its foundation is a hyperbolic traveltime expansion. High accuracy is achieved because second-order spatial derivatives are included in order to acknowledge the curvature of the wavefront. The algorithm permits the determination of the interpolation coefficients from traveltime tables sampled on a coarse grid, thus reducing the requirements in data storage. The method also provides a tool for the interpolation between sources. Application to various velocity models confirms that savings up to a factor of 10 5 are possible in data storage with no significant loss in accuracy. Also, the interpolation is 5-6 times faster than the calculation of traveltime tables using a fast finite differences eikonal solver. Since it is possible to express true-amplitude weight functions in terms of second-order traveltime derivatives a traveltime-based relationship for the weights can be established. As a consequence, the weight functions can be directly computed from the interpolation coefficients. This reduces the need in computational time, and particularly storage, because the weights are computed on-the-fly. Application of the weight functions shows good agreement between numerical and analytical results for the simple type of models considered in this work. For complex models the good accuracy of the geometrical spreading, which can be computed using the same interpolation coefficients as for the weight functions, was also demonstrated. This indicates that the migration technique will also perform well for complex models. A further significant reduction of the computational effort involved in the migration can be achieved if the summation is carried out only over those traces that really contribute to the stack, i.e. by limiting the migration aperture. Moreover, the optimum migration aperture can also be determined from the traveltime coefficients. Examples show that limited aperture migration reduces the requirements in computational time by 80% in 2-D, and by more than 90% in 3-D media. At the same time, the image quality is enhanced by suppressing migration noise. Since the foundation of the method, the hyperbolic traveltime expansion, is not limited to isotropic models the technique has a high potential to be extended to anisotropic media.iii iv

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“…A so-called "true-amplitude" formulation of common-shot Kirchhoff migration proposed by Keho and Beydoun (1988) and Hanitzsch (1997) is…”

Section: Kirchhoff Migrationmentioning

confidence: 99%

Least-squares Reverse-time Migration

Yao¹,

Jakubowicz²

2012

Proceedings

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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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Comparison of weights in prestack amplitude‐preserving Kirchhoff depth migration

Cited by 60 publications

References 0 publications

True Amplitude Migration Weights from Travel Times

True Amplitude Migration Weights from Travel Times

Traveltime based true‐amplitude migration

Least-squares Reverse-time Migration

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