1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 49, Issue 5
  5. Article
Volume 49 Number 5
  • E-ISSN: 1365-2478

Abstract

A prestack reverse time‐migration image is not properly scaled with increasing depth. The main reason for the image being unscaled is the geometric spreading of the wavefield arising during the back‐propagation of the measured data and the generation of the forward‐modelled wavefields. This unscaled image can be enhanced by multiplying the inverse of the approximate Hessian appearing in the Gauss–Newton optimization technique. However, since the approximate Hessian is usually too expensive to compute for the general geological model, it can be used only for the simple background velocity model.We show that the pseudo‐Hessian matrix can be used as a substitute for the approximate Hessian to enhance the faint images appearing at a later time in the 2D prestack reverse time‐migration sections. We can construct the pseudo‐Hessian matrix using the forward‐modelled wavefields (which are used as virtual sources in the reverse time migration), by exploiting the uncorrelated structure of the forward‐modelled wavefields and the impulse response function for the estimated diagonal of the approximate Hessian. Although it is also impossible to calculate directly the inverse of the pseudo‐Hessian, when using the reciprocal of the pseudo‐Hessian we can easily obtain the inverse of the pseudo‐Hessian. As examples supporting our assertion, we present the results obtained by applying our method to 2D synthetic and real data collected on the Korean continental shelf.

Loading

Article metrics loading...

/content/journals/10.1046/j.1365-2478.2001.00279.x
2008-07-07
2024-04-24

  • From This Site

    /content/journals/10.1046/j.1365-2478.2001.00279.x
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. BaysalE.1982. Modelling and migration by the Fourier transform method. PhD thesis, University of Houston.
  2. ChangW.F. & McMechanG.A.1986. Reverse‐time migration of offset vertical seismic profiling data using the excitation‐time imaging condition. Geophysics48, 1514–1524.
    [Google Scholar]
  3. ChaventG. & JacewitzC.A.1995. Determination of background velocities by multiple migration fitting. Geophysics60, 476–490.
    [Google Scholar]
  4. DennisJ.1977. Nonlinear least squares and equations. In: The State of the Art of Numerical Analysis (ed. D. Jacobs ). Academic Press, Inc.
  5. HagedoornJ.G.1954. A process of seismic reflection interpretation. Geophysical Prospecting2, 85–127.
    [Google Scholar]
  6. HemonC.1978. Equation d'onde et models. Geophysical Prospecting26, 790–821.
    [Google Scholar]
  7. KolbP., CollinoF., LaillyP.1986. Prestack inversion of a 1D medium. Proceedings of the IEEE74, 498–508.
    [Google Scholar]
  8. LaillyP.1983. The seismic inverse problem as a sequence of before stack migration. In: Conference on Inverse Scattering: Theory and Application (eds J.B.Bednar , R.Rednar , E.Robinson and A.Welgein ). SIAM.
  9. LoewenthalD. & MuftiI.R.1983. Reversed time migration in spatial frequency domain. Geophysics48, 627–635.
    [Google Scholar]
  10. MarfurtK.J.1984. Accuracy of finite‐difference and finite‐element modelling of the scalar and elastic wave equation. Geophysics49, 533–549.
    [Google Scholar]
  11. MarfurtK.J. & ShinC.S.1989. The future of iterative modelling of geophysical exploration. In: Supercomputers in Seismic Exploration (ed. E.Eisner). Seismic Exploration 21, 203–228.
  12. McMechanG.A.1983. Migration by extrapolation of time‐dependent boundary values. Geophysical Prospecting31, 413–420.
    [Google Scholar]
  13. MoraP.1987. Nonlinear two‐dimensional elastic inversion of multioffset seismic data. Geophysics52, 1211–1228.
    [Google Scholar]
  14. PrattR.G.1999. Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model. Geophysics64, 888–901.
    [Google Scholar]
  15. PrattR.G., ShinC., HicksG.J.1998. Gauss‐Newton and full Newton methods in frequency‐space seismic waveform inversion. Geophysical Journal International133, 341–362.
    [Google Scholar]
  16. ShinC.1988. Nonlinear elastic wave inversion by blocky parameterization. PhD thesis, Tulsa University.
  17. ShinC. & ChungS.1999. Understanding CMP stacking hyperbola in terms of partial derivative wavefield. Geophysics64, 1774–1782.
    [Google Scholar]
  18. TarantolaA.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49, 1259–1266.
    [Google Scholar]
  19. WhitmoreN.D.1983. Iterative depth migration by backward time propagation. 53rd SEG meeting, Las Vegas, USA, Expanded Abstracts, Session: S101.
  20. WhitmoreN.D. & LinesL.R.1986. Vertical seismic profiling depth migration of a salt dome flank. Geophysics51, 1087–1109.
    [Google Scholar]
  21. ZhuJ. & LinesL.R.1997. Implicit interpolation in reverse‐time migration. Geophysics62, 906–917.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1046/j.1365-2478.2001.00279.x
Loading
Improved amplitude preservation for prestack depth migration by inverse scattering theory
Geophysical Prospecting 49, 592 (2001); https://doi.org/10.1046/j.1365-2478.2001.00279.x
/content/journals/10.1046/j.1365-2478.2001.00279.x
/content/journals/10.1046/j.1365-2478.2001.00279.x
Loading

Data & Media 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