1887
Volume 58 Number 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media.

We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces.

Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.2010.00879.x
2010-05-04
2024-03-28
Loading full text...

Full text loading...

References

  1. AminzadehF., BracJ. and KunzT.1997. 3‐D Salt and Overthrust Models . SEG.
    [Google Scholar]
  2. ChoiY., MinD.‐J. and ShinC.2008. Two‐dimensional waveform inversion of multi‐component data in acoustic‐elastic coupled media. Geophysics56, 863–881.
    [Google Scholar]
  3. EwingW.M., JardetzkyW.S. and PressF.1957. Elastic Waves in Layered Media . McGraw‐Hill.
    [Google Scholar]
  4. GauthierO., VirieuxJ. and TarantolaA.1986. Two‐dimensional nonlinear inversion of seismic waveforms: Numerical results. Geophysics51, 1387–1403.
    [Google Scholar]
  5. HaT., ChungW. and ShinC.2009. Waveform inversion using a back‐propagation algorithm and a Huber function norm. Geophysics74, R15–R24.
    [Google Scholar]
  6. HouseL., LarsenS. and BednarJ.B.2000. 3‐D elastic numerical modeling of a complex salt structure. 70th SEG meeting, Calgary , Canada , Expanded Abstracts, 2201–2204.
  7. KolbP., CollinoF. and LaillyP.1986. Pre‐stack inversion of a 1‐D medium. Proceedings of the IEEE74, 498–508.
    [Google Scholar]
  8. KomatitschD., BarnesC. and TrompJ.2000. Wave propagation near a fluid‐solid interface: A spectral‐element approach. Geophysics65, 623–631.
    [Google Scholar]
  9. KomatitschD., TsuboiS. and TrompJ.2005. The spectral‐element method in seismology. Geophysical Monography Series157, 205–227.
    [Google Scholar]
  10. LaillyP.1983. The seismic inverse problem as a sequence of before stack migrations. In: Conference on Inverse Scattering: Theory and Application (eds J.B.Bednar , R.Redner , E.Robinson and A.Weglein ), pp. 206–220. Society for Industrial and Applied Mathematics, Philadelphia .
    [Google Scholar]
  11. LeeH.‐Y., LimS.‐C., MinD.‐J., KwonB.‐D. and ParkM.2009. 2D time‐domain acoustic‐elastic coupled modelling: A cell‐based finite‐difference method. Geosciences Journal13, 407–414.
    [Google Scholar]
  12. MoraP.1987. Nonlinear two‐dimensional elastic inversion of multioffset seismic data. Geophysics52, 1211–1228.
    [Google Scholar]
  13. PrattR.G., ShinC. and HicksG.J.1998. Gauss‐Newton and full Newton method in frequency domain seismic waveform inversion. Geophysical Journal International133, 341–362.
    [Google Scholar]
  14. PyunS., ShinC. and BednarJ.B.2007. Comparison of waveform inversion, part 2: Amplitude approach. Geophysical Prospecting55, 477–485.
    [Google Scholar]
  15. ShinC. and ChaY.H.2008. Waveform inversion in the Laplace domain. Geophysical Journal International173, 922–931.
    [Google Scholar]
  16. ShinC. and HaW.2008. A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains. Geophysics73, VE119–VE133.
    [Google Scholar]
  17. ShinC. and MinD.‐J.2006. Waveform inversion using a logarithmic wavefield. Geophysics71, R31–R42.
    [Google Scholar]
  18. ShinC., PyunS. and BednarJ.B.2007. Comparison of waveform inversion, part 1: Conventional wavefield vs logarithmic wavefield. Geophysical Prospecting55, 449–464.
    [Google Scholar]
  19. ShinC., YoonK., MarfurtK.J., ParkK., YangD., LimH.Y. et al . 2001. Efficient calculation of a partial‐derivative wavefield using reciprocity for seismic imaging and inversion. Geophysics66, 1856–1863.
    [Google Scholar]
  20. TarantolaA.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49, 1259–1266.
    [Google Scholar]
  21. ZhangJ.2004. Wave propagation across fluid‐solid interfaces: A grid method approach: Geophysical Journal International159, 240–252.
    [Google Scholar]
  22. ZienkiewiczO.C., TaylorR.L. and ZhuJ.Z.2005. The Finite Element Method: Its Basis and Fundamentals . Butterworth‐Heinemann.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.2010.00879.x
Loading
/content/journals/10.1111/j.1365-2478.2010.00879.x
Loading

Data & Media loading...

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