Efficient 2.5-D true‐amplitude migration

Dellinger, Joe; Gray, Samuel H.; Murphy, Gary E.; Etgen, John

doi:10.1190/1.1444790

Cited by 27 publications

(15 citation statements)

References 11 publications

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“…For this same reason, we have also spent considerably more algorithm development time devising computationally efficient approximations of the Kirchhoff migration operator G T j than we have of the Kirchhoff modeling operator G j (see, e.g., Gray, 1997, andHanitzsch et al, 1994). We therefore start with a description of G T j as implemented in our 2.5-D true-amplitude prestack Kirchhoff depth-migration algorithm (Gray and May, 1994;Dellinger et al, 2000), and define G j as the transpose of G T j . One distinct advantage of the eikonal-equation-based Kirchhoff versus the computationally more expensive waveequation-based migration schemes is that we are able to account for 3-D spreading measured by 2-D seismic lines by means of asymptotic ray theory (Bleistein, 1987).…”

Section: Appendix a The Kirchhoff Migration Operator And Its Transposementioning

confidence: 98%

“…In this paper, we will instead begin with our workhorse production common-offset Kirchhoff-migration operator, G T , developed by Gray (Gray and May, 1994;Dellinger et al, 2000) based on earlier work by Bleistein (1987) and described in Appendix A:…”

Section: Kirchhoff Modelingmentioning

confidence: 99%

“…Following Bleistein (1987) and Dellinger et al (2000), we then express Kirchhoff migration as the following cascade of operations:…”

Section: Appendix a The Kirchhoff Migration Operator And Its Transposementioning

confidence: 99%

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Kirchhoff modeling, inversion for reflectivity, and subsurface illumination

Duquet

Marfurt²,

Dellinger³

2000

GEOPHYSICS

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167

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Because of its computational efficiency, prestack Kirchhoff depth migration is currently one of the most popular algorithms used in 2-D and 3-D subsurface depth imaging. Nevertheless, Kirchhoff algorithms in their typical implementation produce less than ideal results in complex terranes where multipathing from the surface to a given image point may occur, and beneath fast carbonates, salt, or volcanics through which raytheoretical energy cannot penetrate to illuminate underlying slower-velocity sediments. To evaluate the likely effectiveness of a proposed seismic-acquisition program, we could perform a forward-modeling study, but this can be expensive. We show how Kirchhoff modeling can be defined as the mathematical transpose of Kirchhoff migration. The resulting Kirchhoff modeling algorithm has the same low computational cost as Kirchhoff migration and, unlike expensive full acoustic or elastic waveequation methods, only models the events that Kirchhoff migration can image.Kirchhoff modeling is also a necessary element of constrained least-squares Kirchhoff migration. We show how including a simple a priori constraint during the inversion (that adjacent common-offset images should be similar) can greatly improve the resulting image by partially compensating for irregularities in surface sampling (including missing data), as well as for irregularities in ray coverage due to strong lateral variations in velocity and our failure to account for multipathing. By allowing unstacked common-offset gathers to become interpretable, the additional cost of constrained leastsquares migration may be justifiable for velocity analysis and amplitude-variation-with-offset studies.One useful by-product of least-squares migration is an image of the subsurface illumination for each offset. If the data are sufficiently well sampled (so that including the constraint term is not necessary), the illumination can instead be calculated directly and used to balance the result of conventional migration, obtaining most of the advantages of least-squares migration for only about twice the cost of conventional migration.

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Section: Appendix a The Kirchhoff Migration Operator And Its Transposementioning

confidence: 98%

Section: Kirchhoff Modelingmentioning

confidence: 99%

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Kirchhoff modeling, inversion for reflectivity, and subsurface illumination

Duquet

Marfurt²,

Dellinger³

2000

GEOPHYSICS

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167

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“…This paper is an outgrowth of an earlier paper by the first author (Bleistein 1999), with active involvement at the reviewing stage by the second author. The thesis of that earlier paper and this one is that Hagedoorn's (1954)‘string construction technique’ or, equivalently, ‘ruler and compass technique’ really anticipated the methods that we now call Kirchhoff migration (Schneider 1978) and Kirchhoff inversion (Bleistein 1987a, 1987b; Docherty 1991; Hanitzsch 1995, 1997; Gray 1997; Dellinger et al 2000). That is, a mathematical description of the string construction is equivalent to the Kirchhoff migration processes in the following sense.…”

Section: Introductionmentioning

confidence: 99%

From the Hagedoorn imaging technique to Kirchhoff migration and inversion

Bleistein

Gray²

2001

Geophysical Prospecting

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The seminal 1954 paper by J.G. Hagedoorn introduced a heuristic for seismic reflector imaging. That heuristic was a construction technique – a ‘string construction’ or ‘ruler and compass’ method – for finding reflectors as an envelope of equal traveltime curves defined by events on a seismic trace. Later, Kirchhoff migration was developed. This method is based on an integral representation of the solution of the wave equation. For decades Kirchhoff migration has been one of the most popular methods for imaging seismic data. Parallel with the development of Kirchhoff wave‐equation migration has been that of Kirchhoff inversion, which has as its objectives both structural imaging and the recovery of angle‐dependent reflection coefficients. The relationship between Kirchhoff migration/inversion and Hagedoorn's constructive technique has only recently been explored. This paper addresses this relationship, presenting the mathematical structure that the Kirchhoff approach adds to Hagedoorn's constructive method and showing the relationship between the two.

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“…Several methods for traveltime interpolation have also been proposed, e.g., parabolic and hyperbolic approximations (Ursin, 1982;Gjøystdal et al, 1984;Schleicher et al, 1993b) or Fourier (sinc) interpolation (Brokešová, 1996) to name only a few. Since the standard method to compute the weight functions is to perform dynamic ray tracing for each point under consideration, much effort has gone into finding simplified, more economic expressions for them, as shown by, e.g., Dellinger et al (2000) or Zhang et al (2000). Hanitzsch et al (2001) introduce an interesting method that applies the weight after the stacking.…”

Section: Introductionmentioning

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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Efficient 2.5-D true‐amplitude migration

Cited by 27 publications

References 11 publications

Kirchhoff modeling, inversion for reflectivity, and subsurface illumination

Kirchhoff modeling, inversion for reflectivity, and subsurface illumination

From the Hagedoorn imaging technique to Kirchhoff migration and inversion

Traveltime based true‐amplitude migration

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