ARTICLE

Pre-stack inversion of angle gathers using a hybrid evolutionary algorithm

PUNEET SARASWAT1 MRINAL K. SEN2,3
Show Less
1 Department of Applied Geophysics, Indian School of Mines, Dhanbad, Jharkhand, India 826004.,
2 Institute of Geophysics, University of Texas at Austin, 10100 Burnet Road, Building 19, Austin, TX 78758, U.S.A.,
3 CSIR - National Geophysical Research Institute, Uppal Road, Hyderabad, India 500006.,
JSE 2012, 21(2), 177–200;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

Saraswat, P. and Sen, M.K., 2012. Pre-stack inversion of angle gathers using a hybrid evolutionary algorithm. Journal of Seismic Exploration, 21: 177-200. Inversion of pre-and post-stack seismic data for acoustic and shear impedances is a highly non-linear and ill-posed problem. A deterministic inversion of band-limited seismic data produces smooth models that are devoid of high frequency variations observed in well logs. The objective of this paper is two-fold, i.e., to develop an efficient scheme to explore and exploit the model space, and to efficiently sample broadband models statistically. We demonstrate that the use of starting models from fractal based a priori pdfs helps us to derive elastic models of very high resolution. We also introduce a new hybrid inversion algorithm that takes advantage of both deterministic and stochastic methodologies. A deterministic inversion based on conjugate gradient (CG) method produces smooth models while a stand-alone stochastic method based on differential evolution (DE) produces high-resolution models of nearly the same accuracy. A hybrid algorithm that uses CG solution as a starting model converges much faster than a standalone DE to very good solutions. We demonstrate our results with application to a field seismic dataset. The hybrid algorithm can also be used to sample the most significant parts of the model space rapidly resulting in estimates of uncertainty.

Keywords
global optimization
pre-stack
inversion
differential evolution
References
  1. Aki, K. and Richards, P.G., 1980. Quantitative Seismology: Theory and methods. W.H. Freeman
  2. & Co., San Francisco.
  3. Chundru, R.K., Sen, M.K. and Stoffa, P.L., 1997. Hybrid optimization methods for geophysical
  4. inversion. Geophysics, 62: 1196-1207.
  5. Caccia, D.C., Percival, D., Cannon, M.J., Raymond, G. and Bassingthwaighte, J.B., 1997.
  6. Analyzing exact fractal time series: Evaluating dispersional analysis and rescaled range
  7. methods. Physica A, 246: 609-632.
  8. Chamoli, A., Bansal, A.R. and Dimri, V.P., 2007. Wavelet and rescaled range approach for the
  9. Hurst coefficient for short and long time series. Comput. Geosci., 33: 83-93.
  10. Contreras, A., Torres-Verdin, C. and Fasnacht, T., 2006. AVA simultaneous inversion of partially
  11. stacked seismic amplitude data for the spatial delineation of lithology and fluid units of
  12. deepwater hydrocarbon reservoirs in the central Gulf of Mexico. Geophysics, 71: E41-E48.
  13. Dimri, V.P., 2005. Fractals in geophysics and seismology: An introduction. In: Dimri, V.P. (Ed.),
  14. Fractal Behaviour of the Earth System. Springer Verlag, Berlin: 1-18.
  15. Dimri, V.P., 2011. Fractal Models in Seismic Exploration. Handbook of Geophysical
  16. Exploration-Seismic Exploration. Elsevier Science Publishers, Amsterdam.
  17. Emanual, A.S., Alameda, G.D., Behrens, R.A. and Hewett, T.A., 1987. Reservoir performance
  18. prediction methods based on fractal geostatistics. 62nd Ann. Techn. SPE Conf.: 16971.
  19. Fatti, J.L., Smith, G.C., Vail, P.J., Strauss, P.J. and Levitt, P.R., 1994. Detection of gas in
  20. sandstone reservoirs using AVO analysis: A 3-D seismic case history using the Geostack
  21. technique. Geophysics, 59: 1362-1376.
  22. Francis, A.M., 1997. Acoustic impedance inversion pitfalls and some fuzzy analysis. The Leading
  23. Edge, 16: 275-278.
  24. Ghazali, A.R., Verschuur, D.J. and Gisolf, A., 2010. Multi-dimensional non-linear full waveform
  25. inversion of gas cloud reflection data using a genetic algorithm and a blended acquisition
  26. approach. Expanded Abstr., 80th Ann. Internat. SEG Mtg., Denver: 29, 935.
  27. Goodway, W., Chen, T. and Downton, J., 1997. Improved AVO fluid detection and lithclogy
  28. discrimination using Lamé petrophysical parameters; 'Lambda-Rho', 'Mu-Rho', &
  29. 'Lambda/Mu fluid stack', from P- and S-inversions. CSEG Mtg. Techn. Abstr., 148-151;
  30. Extended Abstr., 59th EAGE Conf., Geneva: 6-51.
  31. Hardy, H.H., 1992. The fractal character of photos of slabbed cores. Mathemat. Geol., 24: 73-97.
  32. Hewett, T.A., 1986. Fractal distribution of reservoir heterogeneity and their influence on fluid
  33. transport. 61st Ann. Techn. SPE Conf.: 15386.
  34. Jervis, M., Sen, M.K. and Stoffa, P.L., 1993a. 2D migration velocity estimation using a genetic
  35. algorithm. Geophys. Res. Lett., 20: 1495-1498.
  36. Jin, S. and Madariaga, R., 1993. Background velocity inversion with a genetic algorithm. Geophys.
  37. Res. Lett., 20: 93-96.
  38. Kennett, B.L.N., 1983. Seismic wave propagation in stratified media. Cambridge University Press,
  39. Cambridge.
  40. Koutsoyiannis, D., 2002. Internal report,
  41. http://www. itia.ntua. gr/getfile/511/2/2002HSJHurstSuppl.pdf
  42. Ma, X.-Q., 2002. Simultaneous inversion of prestack seismic data for rock properties using
  43. simulated annealing. Geophysics, 67: 1877-1885. ,
  44. Mallick, S., 1999. Some practical aspects of prestack waveform inversion using a genetic algorithm:
  45. an example from the east Texas Woodbine gas sand. Geophysics, 64: 326-336.
  46. Mandelbrot, B.B., 1965. A fast fractional Gaussian noise generator. Water Resourc. Res., 7:
  47. 543-553.
  48. Mishra, S.K., 2006. Global optimization by differential evolution and particle swarm methods:
  49. evaluation on some benchmark functions. Social Sci. Res. Netw.
  50. Sambridge, M.S. and Drijkoningen, G.G., 1992. Genetic algorithms in seismic waveform inversion.
  51. Geophys. J. Internat., 109: 323-342.
  52. 200 SARASWAT & SEN
  53. Sambridge, M.S. and Gallagher, K., 1993. Earthquake hypocenter location using genetic algorithms.
  54. Bull. Seismol. Soc. Am., 83: 1467-1491.
  55. Scales, J.A., 1987. Tomographic inversion via the conjugate gradient method. Geophysics, 52: 179.
  56. Saupe, D., 1988. Algorithms for random fractals. In: The Science of Fractal Images, Chapter 2.
  57. Springer-Verlag, Berlin.
  58. Sen, M.K. and Stoffa, P.L., 1991. Nonlinear one-dimensional seismic waveform inversion using
  59. simulated annealing. Geophysics, 56: 1624-1638.
  60. Sen, M.K. and Stoffa, P.L., 1992. Seismic waveform inversion using global optimization. J. Seismic
  61. Explor., 1: 9-27.
  62. Sen, M.K. and Stoffa, P.L., 1995. Global Optimization Methods in Geophysical Inversion. Elsevier
  63. Science Publishers, Amsterdam.
  64. Sen, M.K., 2006. Seismic Inversion. SPE, Tulsa.
  65. Smith, G.C. and Gidlow, P.M., 1987. Weighted stacking for rock property estimation and detection
  66. of gas. Geophys. Prosp., 35: 993-1014.
  67. Srivastava, R.P. and Sen, M.K., 2009. Stochastic inversion of post-stack seismic data using fractal
  68. prior. J. Geophys. Engin., 6: 412-425.
  69. Srivastava, R.P. and Sen, M.K., 2010. Stochastic inversion of pre-stack seismic data using fractal
  70. based starting models. Geophysics, 75: 47-59.
  71. Storn, R. and Price, K., 1997. Differential evolution - a simple and efficient heuristic for global
  72. optimization over continuous spaces. J. Global Optimiz., 11: 341-359.
  73. ter Braak, C.J.F., 2006. A Markov Chain Monte Carlo version of the genetic algorithm Differential
  74. Evolution: easy Bayesian computing for real parameter spaces. Statist. Comput., 16:
  75. 239-249.
  76. Turcotte, D.L., 1997. Fractals and Chaos in Geology and Geophysics. Cambridge University Press,
  77. Cambridge.
  78. Varela, O.J., Torres-Verdin, C. and Sen, M.K., 2006. Enforcing smoothness and assessing
  79. uncertainty in nonlinear one-dimensional pre-stack seismic inversion. Geophys. Prosp., 54:
  80. 239-259.
  81. Wang, Y., 1999. Simultaneous inversion for model geometry and elastic parameters. Geophysics,
  82. 64: 182-190.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing