Second‐order interpolation of traveltimes

Vanelle, C.; Gajewski, Dirk

doi:10.1046/j.1365-2478.2002.00285.x

Cited by 29 publications

(33 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It can, however, be shown (VANELLE and GAJEWSKI, 2002), that a hyperbolic approximation Vol. 159, 2002 Amplitude Migration Weights from Travel Times of travel times is superior to the parabolic expansion (C.1).…”

Section: Appendix C Travel Times and Second-order Derivative Matricesmentioning

confidence: 99%

“…This is, however, not necessary since these derivatives can be extracted from traveltime data, that is required for the construction of the diffraction travel-time surface for the stack in any event. Using these derivatives also leads to an effective and highly accurate algorithm for interpolating travel times from the coarse input grid onto the fine migration grid (VANELLE and GAJEWSKI, 2002). The geometrical spreading can also be written in terms of second-order derivatives of travel times (see Appendix B).…”

Section: Schleichermentioning

confidence: 99%

“…These travel times were resampled from the original 10 m fine grid required by FDES for sufficient accuracy and stored on a coarse grid of 50 m in either direction. Diffraction travel times were interpolated from this coarse grid onto a fine migration grid of 5 m in z direction using the hyperbolic approximation as described in Appendix C (for a more detailed description, see VANELLE and GAJEWSKI, 2002). The migration weights were also computed from the coarse grid travel times using the coefficients determined from the hyperbolic approximation.…”

Section: Applicationsmentioning

confidence: 99%

“…The definition of small depends on the velocity model under consideration. For a simple model, the sensitivity of the interpolation with regard to the coarse grid to fine grid ratio was investigated in VANELLE and GAJEWSKI (2002). For a multi-valued travel-time field the Taylor expansion is valid if the different branches of the travel-time curve are treated separately.…”

Section: Appendix C Travel Times and Second-order Derivative Matricesmentioning

confidence: 99%

See 3 more Smart Citations

True Amplitude Migration Weights from Travel Times

Vanelle

Gajewski

2002

Pure and Applied Geophysics

View full text Add to dashboard Cite

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.

show abstract

Section: Appendix C Travel Times and Second-order Derivative Matricesmentioning

confidence: 99%

Section: Schleichermentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Section: Appendix C Travel Times and Second-order Derivative Matricesmentioning

confidence: 99%

See 2 more Smart Citations

True Amplitude Migration Weights from Travel Times

Vanelle

Gajewski

2002

Pure and Applied Geophysics

View full text Add to dashboard Cite

show abstract

“…I demonstrate the traveltime interpolation with examples ranging from velocity models with analytic solutions to a 3-D extension of the highly complex Marmousi model. Parts of this chapter were published in Vanelle and Gajewski (2002a).…”

Section: Introductionmentioning

confidence: 99%

Traveltime-based true-amplitude migration

Vanelle

Spinner

Hertweck³

et al. 2006

GEOPHYSICS

Self Cite

View full text Add to dashboard Cite

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

show abstract

True Amplitude Migration Weights from Travel Times

Vanelle

Gajewski

2002

Seismic Waves in Laterally Inhomogeneous Media

View full text Add to dashboard Cite

Second‐order interpolation of traveltimes

Cited by 29 publications

References 12 publications

True Amplitude Migration Weights from Travel Times

True Amplitude Migration Weights from Travel Times

Traveltime-based true-amplitude migration

True Amplitude Migration Weights from Travel Times

Contact Info

Product

Resources

About