1887
Volume 46, Issue 2
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

[

The norm and its variants, such as the hybrid / norm and the Huber norm, that are used to solve amplitude variation with offset (AVO) inversion optimisation problems, are mostly known to give a more robust solution than the classical least-squares ( norm) method by reducing the influence of outliers significantly, although never ignoring it. To deal with data having many outliers, biweight norm using iteratively reweighted least-squares (IRLS) as robust inversion method can improve robustness by ignoring outliers in computing the misfit measure. However, biweight norm uses a higher-order descending weighting on the measured data, which results in poor performance when dealing with the well measured data. Hampel’s three-part redescending M-estimate function as robust measure could be considered as a three-part combination of the norm and norm with excluding outliers, which could perform better. This paper describes an iterative reweighted least M-estimate (IRLM) algorithm as a robust AVO inversion. The synthetic and field seismic data tests show that the IRLM algorithm gives far more robust model estimates than the conventional Huber norm and biweight norm.

,

In this paper, an IRLM algorithm which uses Hampel’s three-part redescending M-estimate function as the misfit measure is proposed for robust AVO inversion. By combining the advantages of the Huber norm and biweight norm, the proposed IRLM algorithm performs better in the complex noise environment.

]
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2015-06-01
2026-01-24

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References

  1. Agnew D. C. 1989 Robust pilot spectrum estimation for the quality control of digital seismic data: Bulletin of the Seismological Society of America 79 180 188
    [Google Scholar]
  2. Aki, K., and Richards, P. G., 1980, Quantitative seismology: theory and methods: W. H. Freeman.
  3. Arora N. Biegler L. T. 2001 Redescending estimators for data reconciliation and parameter estimation: Computers & Chemical Engineering 25 1585 1599 10.1016/S0098‑1354(01)00721‑9
    https://doi.org/10.1016/S0098-1354(01)00721-9 [Google Scholar]
  4. Beaton A. E. Tukey J. W. 1974 The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data: Technometrics 16 147 185 10.1080/00401706.1974.10489171
    https://doi.org/10.1080/00401706.1974.10489171 [Google Scholar]
  5. Bube K. P. Langan R. T. 1997 Hybrid l1/l2 minimization with applications to tomography: Geophysics 62 1183 1195 10.1190/1.1444219
    https://doi.org/10.1190/1.1444219 [Google Scholar]
  6. Buland A. Kolbjørnsen O. Hauge R. Skjæveland Ø. Duffaut K. 2008 Bayesian lithology and fluid prediction from seismic prestack data: Geophysics 73 C13 C21 10.1190/1.2842150
    https://doi.org/10.1190/1.2842150 [Google Scholar]
  7. Fa R. Tsimenidis C. C. Sharif B. S. 2004 Robust MMSE receiver employing Hampel-type nonlinear preprocessing for DS-CDMA communication in impulsive noise: Electronics Letters 40 489 491 10.1049/el:20040323
    https://doi.org/10.1049/el:20040323 [Google Scholar]
  8. Guitton A. Symes W. 2003 Robust inversion of seismic data using the Huber norm: Geophysics 68 1310 1319 10.1190/1.1598124
    https://doi.org/10.1190/1.1598124 [Google Scholar]
  9. Gunning J. Glinsky M. E. 2004 Delivery: an open-source model-based Bayesian seismic inversion program: Computers & Geosciences 30 619 636 10.1016/j.cageo.2003.10.013
    https://doi.org/10.1016/j.cageo.2003.10.013 [Google Scholar]
  10. Gunning J. Glinsky M. E. 2006 Wavelet extractor: a Bayesian well-tie and wavelet extraction program: Computers & Geosciences 32 681 695 10.1016/j.cageo.2005.10.001
    https://doi.org/10.1016/j.cageo.2005.10.001 [Google Scholar]
  11. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. A., 1986, Robust statistics: the approach based on influence functions: Wiley.
  12. Huber, P. J., 1981, Robust statistics: Wiley.
  13. Ji J. 2012 Robust inversion using biweight norm and its application to seismic inversion: Exploration Geophysics 43 70 76
    [Google Scholar]
  14. Li, Y., Zhang, Y., and Claerbout, J., 2010, Geophysical applications of a novel and robust l 1 solver: SEG Technical Program Expanded Abstracts, 29, 3519–3523.
  15. Liu Y. Liu C. Wang D. A. 2009 1D time-varying median filter for seismic random, spike-like noise elimination: Geophysics 74 V17 V24 10.1190/1.3043446
    https://doi.org/10.1190/1.3043446 [Google Scholar]
  16. Pyun S. Son W. Shin C. 2009 Frequency-domain waveform inversion using an l 1-norm objective function: Exploration Geophysics 40 227 232 10.1071/EG08103
    https://doi.org/10.1071/EG08103 [Google Scholar]
  17. Rousseeuw, P. J., and Leroy, A. M., 1987, Robust regression and outlier detection: Wiley.
  18. Scales J. A. 1987 Tomographic inversion via the conjugate gradient method: Geophysics 52 179 185 10.1190/1.1442293
    https://doi.org/10.1190/1.1442293 [Google Scholar]
  19. Scales J. A. Gersztenkorn A. 1988 Robust methods in inverse theory: Inverse Problems 4 1071 1091 10.1088/0266‑5611/4/4/010
    https://doi.org/10.1088/0266-5611/4/4/010 [Google Scholar]
  20. Tarantola, A., 1987, Inverse problem theory: Elsevier.
  21. Taylor H. L. Banks S. C. McCoy J. F. 1979 Deconvolution with the l 1 norm: Geophysics 44 39 52 10.1190/1.1440921
    https://doi.org/10.1190/1.1440921 [Google Scholar]
  22. Weng, J., and Leung, S., 1997, Adaptive nonlinear RLS algorithm for robust filtering in impulse noise: Proceedings of the 1997 IEEE International Symposium on Circuits and Systems (ISCAS’97), 4, 2337–2340.
  23. Zhang R. Castagna J. 2011 Seismic sparse-layer reflectivity inversion using basis pursuit decomposition: Geophysics 76 R147 R158 10.1190/geo2011‑0103.1
    https://doi.org/10.1190/geo2011-0103.1 [Google Scholar]
  24. Zhang R. Sen M. Srinivasan S. 2013 A prestack basis pursuit seismic inversion: Geophysics 78 R1 R11 10.1190/geo2011‑0502.1
    https://doi.org/10.1190/geo2011-0502.1 [Google Scholar]
  25. Zhu, R., 2009, Active control of impulsive noise: University of Minnesota.
  26. Zou, Y., Chan, S. C., and Ng, T. S., 1999, A robust M-estimate adaptive filter for impulse noise suppression: Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing, 4, 1765–1768.
/content/journals/10.1071/EG13038
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Iterative reweighted least M-estimate AVO inversion
Exploration Geophysics 46, 159 (2015); https://doi.org/10.1071/EG13038
/content/journals/10.1071/EG13038
/content/journals/10.1071/EG13038
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  • Article Type: Research Article
Keyword(s): AVO; Hampel’s three-part redescending M-estimate function; IRLM algorithm; outliers; robust

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