1887
Volume 41 Number 8
  • E-ISSN: 1365-2478

Abstract

A

Depth migration consists of two different steps: wavefield extrapolation and imaging. The wave propagation is firmly founded on a mathematical frame‐work, and is simulated by solving different types of wave equations, dependent on the physical model under investigation. In contrast, the imaging part of migration is usually based on ‘principles’, rather than on a physical model with an associated mathematical expression. The imaging is usually performed using the U/D concept of Claerbout (1971), which states that reflectors exist at points in the subsurface where the first arrival of the downgoing wave is time‐coincident with the upgoing wave.

Inversion can, as with migration, be divided into the two steps of wavefield extrapolation and imaging. In contrast to the imaging principle in migration, imaging in inversion follows from the mathematical formulation of the problem. The image with respect to the bulk modulus (or velocity) perturbations is proportional to the correlation between the time derivatives of a forward‐propagated field and a backward‐propagated residual field (Lailly 1984; Tarantola 1984).

We assume a physical model in which the wave propagation is governed by the 2D acoustic wave equation. The wave equation is solved numerically using an efficient finite‐difference scheme, making simulations in realistically sized models feasible. The two imaging concepts of migration and inversion are tested and compared in depth imaging from a synthetic offset vertical seismic profile section. In order to test the velocity sensitivity of the algorithms, two erroneous input velocity models are tested. We find that the algorithm founded on inverse theory is less sensitive to velocity errors than depth migration using the more U/D imaging principle.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.1993.tb00896.x
2006-04-27
2024-03-28
Loading full text...

Full text loading...

References

  1. Berkhout, A.J.1985. Seismic Migration: Imaging of Acoustic Energy by Wavefield Extrapolation. A. Theoretical aspects. Elsevier Science Publishing Co.
    [Google Scholar]
  2. Berkhout, A.J.1986. Seismic inversion in terms of pre‐stack migration and multiple elimination. Proceedings of the IEEE74, 415–427.
    [Google Scholar]
  3. Beylkin, G. and Burridge, R.1990. Linearised inverse scattering problems in acoustics and elasticity. Wave Motion12, 15–52.
    [Google Scholar]
  4. Chang, W.F. and Mc Mechan, G.A.1986. Reverse‐time migration of offset vertical seismic profiling data using the excitation‐time imaging condition. Geophysics51, 67–84.
    [Google Scholar]
  5. Claerbout, J.F.1971. Toward a unified theory of reflector mapping. Geophysics36, 467–481.
    [Google Scholar]
  6. Dai, T. and Kuo, J.‐T.1986. Real data results of Kirchhoff elastic wave migration. Geophysics51, 1006–1011.
    [Google Scholar]
  7. Dillon, P.B.1988. Vertical seismic profile migration using the Kirchhoff integral. Geophysics53, 786–799.
    [Google Scholar]
  8. Dillon, P.B.1990. A comparison between Kirchhoff and GRT migration on VSP data. Geophysical Prospecting38, 757–777.
    [Google Scholar]
  9. Dillon, P.B., Ahmed, H. and Roberts, T.1988. Migration of mixed‐mode VSP wavefields. Geophysical Prospecting36, 825–846.
    [Google Scholar]
  10. Holberg, O.1987. Computational aspects of the choice of operator and sampling interval for numerical differentiation in large‐scale simulation of wave phenomena. Geophysical Prospecting35, 629–655.
    [Google Scholar]
  11. Hu, L. and Mc Mechan, G.A.1986. Migration of VSP data by ray equation extrapolation in 2D variable velocity media. Geophysical Prospecting34, 704–734.
    [Google Scholar]
  12. Keho, T.H.1984. Kirchhoff migration for vertical seismic profiles. 54th SEG meeting, Atlanta. Expanded Abstracts, 694–696.
  13. Kohler, K. and Koenig, M.1986. Reconstruction of reflecting structures from vertical seismic profiles with a moving source. Geophysics51, 1923–1938.
    [Google Scholar]
  14. Lailly, P.1984. The seismic inverse problem as a sequence of before stack migrations. In: Inverse Problems of Acoustic and Elastic Waves. F.Santosa , Y. H.Pao , W. W.Symes , C.Holland (eds), 206–220. Society of Industrial and Applied Mechanics.
    [Google Scholar]
  15. Miller, D., Oristaglio, M. and Beylkin, G.1987. A new slant on seismic imaging: migration and internal geometry. Geophysics52, 943–964.
    [Google Scholar]
  16. Morse, P.M. and Feshbach, H.1953. Methods of Theoretical Physics. McGraw‐Hill Book Co.
    [Google Scholar]
  17. Seeman, B. and Horowicz, L.1983. Vertical seismic profiling. Separation of upgoing and downgoing acoustic waves in a stratified medium. Geophysics48, 555–568.
    [Google Scholar]
  18. Suprajitno, M. and Greenhalgh, S.A.1985. Separation of upgoing and downgoing waves in vertical seismic profiling by contour‐slice filtering. Geophysics50, 950–962.
    [Google Scholar]
  19. Tarantola, A.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49, 1259–1266.
    [Google Scholar]
  20. Treitel, S., Shanks, J.L. and Frasier, C.W.1967. Some aspects of fan filtering. Geophysics32, 789–800.
    [Google Scholar]
  21. Wapenaar, C.P.A., Peels, G.L., Budejicky, V. and Berkhout, A.J.1989. Inverse extrapolation of primary seismic waves. Geophysics54, 853–863.
    [Google Scholar]
  22. Whitmore, N.D. and Lines, L.R.1986. Vertical seismic profiling depth migration of a salt dome flank. Geophysics51, 1087–1109.
    [Google Scholar]
  23. Wiggins, J.W.1984. Kirchhoff integral extrapolation and migration of nonplanar data. Geophysics49, 239–1248.
    [Google Scholar]
  24. Wiggins, J.W. and Levander, A.R.1984. Migration of multiple offset synthetic vertical seismic profile data in complex structures. In: Advances in Geophysical Data Processing1, M.Simaan (ed.), 269–289. JAI Press, London .
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.1993.tb00896.x
Loading
  • Article Type: Research Article

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error