Skip to main content
SpringerLink
Log in

Laplace–Fourier-Domain Waveform Inversion for Fluid–Solid Media

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

Full waveform inversion algorithms are widely used in the construction of subsurface velocity models. In the following study, we propose a Laplace–Fourier-domain waveform inversion algorithm that uses both Laplace-domain and Fourier-domain wavefields to achieve the reconstruction of subsurface velocity models. Although research on the Laplace–Fourier-domain waveform inversion has been published recently that study is limited to fluid media. Because the geophysical targets of marine seismic exploration are usually located within solid media, waveform inversion that is approximated to acoustic media is limited to the treatment of properly identified submarine geophysical features. In this study, we propose a full waveform inversion algorithm for isotropic fluid–solid media with irregular submarine topography comparable to a real marine environment. From the fluid–solid system, we obtained P and S wave velocity models from the pressure data alone. We also suggested strategies for choosing complex frequency bands constructed of frequencies and Laplace coefficients to improve the resolution of the restored velocity structures. For verification, we applied our Laplace–Fourier-domain waveform inversion for fluid–solid media to synthetic data that were reconstructed for fluid–solid media. Through this inversion test, we successfully restored reasonable velocity structures. Furthermore, we successfully extended our algorithm to a field data set.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Bae, H.S., Shin, C., Cha, Y.H., Choi, Y. and Min, D.-J. (2010), 2D acoustic-elastic coupled waveform inversion in the Laplace domain, Geophys. Prospect. 58, 997–1010.

    Google Scholar 

  • Brenders, A.J. and Pratt, R.G. (2007), Full waveform tomography for lithospheric imaging: results from a blind test in a realistic crustal model, Geophys. J. Int. 168, 133–151.

    Google Scholar 

  • Brossier R., Operto S. and Virieux J. (2009), Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion, Geophys. 74, WCC105–WCC118.

  • Bunks C., Saleck F.M., Zaleski S. and Chavent G. (1995), Multiscale seismic waveform inversion, Geophys. 60, 1457–1473.

  • Chung, W., Shin, C. and Pyun. S. (2010), 2D Elastic waveform inversion in the Laplace domain, Bull. Seismol. Soc. Am. 100, 3239–3249.

    Google Scholar 

  • Choi, Y., Min. D-.J. and Shin C. (2008), Frequency-domain elastic full waveform inversion using the New pseudo-Hessian matrix: Experience of elastic Marmousi-2 synthetic data, Bull. Seismol Soc Am. 98, 2402–2415.

  • Cohen, G.C. (2002), High-order numerical methods for transient wave equations, Scientific computation ISSN, 1434–8322.

  • Gauthier, O., Virieus, J. and Tarantola, A. (1986), Two-dimensional nonlinear inversion of seismic waveforms: Numerical results, Geophys. 51, 1387–1403.

  • Geller R.J. and Hara T. (1993), Two efficient algorithms for iterative linearized inversion of seismic waveform data, Geophys. J. Int. 115, 699–710.

    Google Scholar 

  • Ha, T., Chung, W. and Shin, C. (2009), Waveform inversion using a back-propagation algorithm and a Huber function, Geophys. 74, R15–R24.

    Google Scholar 

  • Ha, W., Pyun, S.,Yoo, J. and Shin, C. (2010), Acoustic full waveform inversion of synthetic land data and marine data in the Laplace domain, Geophys. Prospect. 58, 1033–1047.

  • Kim, J. and Kim, S. (1999), A multifrontal solver combined with graph paratitioners, AIAA Journl. 38, 964–970.

    Google Scholar 

  • Kim, M., Choi, Y., Cha, Y.H. and Shin, C. (2009), 2-D Frequency domain waveform inversion of Coupled Acoustic-elastic media with an irregular interface, Pure appl. geophys. 166, 1967–1985.

  • Kolb, P., Collino, F. and Lailly, P. (1986), Pre-stack inversion of a 1-D medium, Proceedings of the IEEE 74, 498–508.

  • Komatitsch, D., Barnes, C. and Tromp, J. (2000), Wave propagation near a fluid-solid interface: A spectral-element approach, Geophys. 65, 623–631.

  • Lailly, P. (1983), The seismic inverse problems as a sequence of before stack migrations, (ed. Bednar, J.B., Redner, R., Robinson, E. and Weglein, A.B.), Conference on Inverse Scattering: Theory and applications, Society for Industrial and Applied Mathematics.

  • Lee H.-Y., Lim S.-C., Min D.-J., Kwon B.-D. and Park M. (2009), 2D time-domain acoustic-elastic coupled modelling: A cell-based finite-difference method, Geosciences Journal 13, 407–414.

    Google Scholar 

  • Mora, P. (1987), Nonlinear two-dimensional elastic inversion of multioffset seismic data, Geophys. 52, 1211–1228.

    Google Scholar 

  • Operto S., Ravaut C., Improta L., Virieux J., Herrero A. and DellAversana P. (2004), Quantitative imaging of complex structures from dense wide-aperture seismic data by multiscale traveltime and waveform inversions: a case study, Geophys. Prospect. 52, 625–651.

    Google Scholar 

  • Plessix, R.-E. (2009), Three-dimensional frequency-domain full-waveform inversion with an iterative solver, Geophys. 74, WCC149–WC157.

  • Plessix, R.-E., Baeten, G., de Maag, J.W., Klaassen, M., Zhang, R. and Tao, Z. (2010), Application of acoustic full waveform inversion to a low-frequency large-offset land data set, 80th SEG Annual Meeting, Expended Abstracts, Denver, USA, 930–934.

  • Pratt, R. G. (1990), Frequency domain elastic wave modelling by finite differences: A tool for cross-hole seismic imaging, Geophys. 55, 626–632.

  • Pratt, R.G., Shin, C. and Hicks, G.J. (1998), Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion, Geophys. J. Int. 133, 341–362.

    Google Scholar 

  • Pratt, R. G., and Worthington, M. H. (1990), Acoustic wave equation inverse theory applied to multi-source cross-hole tomography Part I: Acoustic wave-equation method, Geophys. Prospect. 38. 287–310.

    Google Scholar 

  • Pyun S., Son W. and Shin C. (2011), 3D acoustic waveform inversion in the Laplace domain using an iterative solver, Geophys. Prospect. 59, 386–399.

    Google Scholar 

  • Sears T.J., Singh S.C. and Barton P.J. (2008), Elastic full waveform inversion of multi-component OBC seismic data, Geophys. Prospect. 56, 843–862.

    Google Scholar 

  • Shin, C. and Min, D.-J. (2006), Waveform inversion using a logarithmic wavefield, Geophys. 71, R31–R42.

  • Shin, C. and Cha, Y.H. (2008), Waveform inversion in the Laplace domain, Geophys. J. Int. 173, 922–931.

    Google Scholar 

  • Shin, C. and Ha, W. (2008), A comparison between behavior of missfit functions for waveform inversion in the frequency and Laplace domains, Geophys. 73, VE119–VE133.

  • Shin, C., Jang, and Min, D.J. (2001), Improved amplitude preservation for prestack depth migration by inverse scattering theory, Geophys. Prospect. 49, 592–606.

  • Shin, C. and Cha, Y.H. (2009), Waveform inversion in the Laplace-Fourier domain, Geophys. J. Int. 177, 1067–1079.

    Google Scholar 

  • Shin, C., Koo, N.-H., Cha, Y.H. and Park, K.P. (2010), Sequentially ordered single-frequency 2-D acoustic waveform inversion in the Laplace-Fourier-domain, Geophys. J. Int. 181, 935–950.

    Google Scholar 

  • Shipp R.M. and Singh S.C. (2002), Two-dimensional full wavefield inversion of wide-aperture marine seismic streamer data, Geophys. J. Int.151, 325–344.

    Google Scholar 

  • Sirgue, L., Barkved, O.I., van Gestel, J.P., Askim, O.J. and Kommedal, J.H. (2009), 3D Waveform Inversion on Valhall Wide-azimuth OBC, 71st EAGE Conference and Exhibition.

  • Sirgue, L. and Pratt, G. (2004), Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies, Geophys. 69, 231–248.

  • Stoughton, D., Stefani, J. and Michell, S. (2001), 2D elastic model for wavefield investigations of subsalt objectives, deep water Gulf of Mexic, 71st SEG meeting, Expanded Abstracts, San Antonio, Texas, USA, 1269–1272.

  • Tarantola, A. (1984), Inversion of seismic reflection data in the acoustic approximation, Geophys. 49, 1259–1266.

    Google Scholar 

  • Zhang J. (2004), Wave propagation across fluid-solid interfaces: A grid method approach, Geophys. J. Int. 159, 240–252.

    Google Scholar 

  • Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z. (2005), The finite element method: its basis and fundamentals, Butterworth-Heinemann.

  • Vigh, D., Starr, W., Kapoor, J. and Li, H. (2010), 3D full waveform inversion on a Gulf of MexicoWAZ data set, the 80th SEG Annual Meeting, Expanded Abstracts, Denver, USA, 957–961.

Download references

Acknowledgments

The authors would like to thank TOTAL for their financial support of the Laplace-domain waveform inversion project. We are grateful to GX Technology for providing the field data sets. This work was supported by a scholarship from the Korea Ocean Research & Development Institute (F63110446B).

Author information

Authors and Affiliations

  1. Department of Energy Systems Engineering, Seoul National University, Seoul, 151-742, Korea

    Seung-Goo Kang & Changsoo Shin

  2. Agency for Defense Development, Jinhae, P.O. Box 18, Changwon, 645-600, Korea

    Ho Seuk Bae

Authors
  1. Seung-Goo Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ho Seuk Bae
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Changsoo Shin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ho Seuk Bae.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kang, SG., Bae, H.S. & Shin, C. Laplace–Fourier-Domain Waveform Inversion for Fluid–Solid Media. Pure Appl. Geophys. 169, 2165–2179 (2012). https://doi.org/10.1007/s00024-012-0467-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-012-0467-7

Keywords

Search

Navigation