An Automatic Geophysical Inversion Procedure Using a Genetic Algorithm

  • F. Mansanné
  • M. Schoenauer
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 80)


One of the most interesting challenges of the last twenty years in geophysics is the determination of the structure of the underground from data from geophysical prospection. The goal of the inverse problem in seismic reflection is to identify the velocity distribution in the underground from recorded reflection profiles of acoustic waves. This identification problem can be turned into an optimization problem whose the objective function is quite irregular. Indeed, it is highly nonlinear, exhibits several local minima and can be globally discontinuous. An efficient way to find a global optimum (or a good local optimum) for such a problem is to use stochastic algorithms like Genetic Algorithms. The work presented in this paper relies on the use of an hybrid GA, based on a variable-length piecewise-constant representation built on Voronoi diagrams. The choice of a reliable fitness function is also a crucial step for the success of the inversion method. The classic least square error (LSE) can be successfully used for the inversion of simple models in reasonable computing times. However, when dealing with more complex models that are greedier in terms of computing time, the LSE criterion alone is not sufficient, and had to be coupled with the Semblance, a more geophysical criterion, introduced by Taner and Koehler (1969), in which the adaptability of a model is derived from the flatness of imaged events in the migrated cube. Numerical results on 2D simulated data illustrate the effectiveness of the proposed approach, and enlighten some weaknesses of each criterion (LSE or Semblance) considered alone.


Genetic Algorithm Voronoi Diagram Voronoi Cell Salt Dome Less Square Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    K. Al-Yaha. Velocity analysis by iterative profile migration; PHD thesis Standford University, 1987.Google Scholar
  2. 2.
    T. N. Bishop, K. P. Bube, R. T. Culter, R. T. Langan, P. L. Love, J. R. Resnick, R. T. Shuey & S. Spinder. Tomographic determination of velocity and depth in laterally varying media; Geophysics, 50, p:903–923, 1985.CrossRefGoogle Scholar
  3. 3.
    F. Boschetti. Application of genetic algorithms to the inversion of geological data; PhD thesis, University of Western Australia, 1995.Google Scholar
  4. 4.
    F. Boschetti, M. C. Dentith, &, R. D. List. Inversion of seismic refraction data using genetic algorithm; Geophysics, 61, N°6, p:1715–1727, 1996.CrossRefGoogle Scholar
  5. 5.
    J. Brac. Simulation de la propagation des ondes acoustiques 2D et 3D et élastiques 2D; I. F. P report N°44220, December 1997.Google Scholar
  6. 6.
    K. Broto. Accès à l’information cinématique pour la détermination du modèle de vitesse par tomographic de réflexion 3D; Ph Thesis University of Pau, 1999.Google Scholar
  7. 7.
    V. Cervený, I. A. Molotkov & I. Psencik. Ray Theory in Seismology; Charles University Press, Praha, 1997.Google Scholar
  8. 8.
    E. Chauris & M. Noble. Testing The behavior of differential semblance for velocity estimation; Meeting SEG, 1998.Google Scholar
  9. 9.
    SKL. Chiu & RN. Stewart. Tomographic determination of 3-dimentional seismic velocity structure using well logs, vertical seismic profiles, and surface seismic data; Geophysics, 52, p:1085–1098, 1987.CrossRefGoogle Scholar
  10. 10.
    J. F. Claerbout. Coarse grid calculations of wave in inhomogeneous media with application to delineation of complicated seismic structure; Geophysics, 35(3), p:407–418, 1970.CrossRefGoogle Scholar
  11. 11.
    J. F. Claerbout. Fundamentals of Geophysical Data Processing; McGraw-Hill Book Co, 1976.Google Scholar
  12. 12.
    P. Docherty, R. Silva, S. Singh, Z. M. Song & M. Wood. Migration velocity analysis using a genetic algorithm; Geophysical Prospecting, 45, p:865–878, 1997.CrossRefGoogle Scholar
  13. 13.
    V. Farra & R. Madariaga. Non-linear reflection tomography; Geophys. J, 95, p:135–147, 1988.CrossRefGoogle Scholar
  14. 14.
    J. K. Hao & R. Dorne. Tabu search for graph coloring, T-coloring and set T-coloring; Presented at the 2nd Intl Conf on Metaheuristics, Sophia-Antipollis, France, July, 1997.Google Scholar
  15. 15.
    J. P. d’Issernio & M. Lassagne. Identification d’inclusions élastiques par Aglorithmes Génétiques; stage de DEA de l’Ecole Poly technique, 1998.Google Scholar
  16. 16.
    S. Jin & R. Madariaga. Background velocity inversion with a genetic algorithm; Geophysical Research letter, 20, p:93–96, 1996.CrossRefGoogle Scholar
  17. 17.
    S. Jin &, R. Madariaga. Nonlinear velocity inversion by a two-step Monte Carlo method; Geophysics, 59, p:577–590, 1994.CrossRefGoogle Scholar
  18. 18.
    P. Lailly & D. Sinoquet. Smooth velocity models in reflection tomography for imaging complex geological structures; Geophys, J. Int, 124, p:349–362, 1996.CrossRefGoogle Scholar
  19. 19.
    L. R. Lines & S. Treitel. Tutorial: a review of least-squares inversion and its application to geophysical problems] Geophys. Prospect, 32, p:159–186, 1994.Google Scholar
  20. 20.
    F. Mansanné. Annual report of I. F. P; N°54072, May 2000.Google Scholar
  21. 21.
    F. Mansanné, A. Ehinger, F. Carrère & M. Schoenauer. Evolutionary Algorithms as Fitness Function Debuggers; Accepted and presented in the Eleventh International symposium on methodologies for intelligent systems, Versaw Poland, June 1999.Google Scholar
  22. 22.
    F. Mansanné. Amélioration de la vitesse de convergence d’un AG par l’utilisation d’une méthode locale; Accepted and Presented in EA99, Dunkerque, 1999.Google Scholar
  23. 23.
    F. Mansanné. Analyse d’algorithmes d’évolution artificielle appliqués au domaine pétrolier: inversion sismique et approximation de fonctions; thèse de Doctorat de l’Universite de Pau, Decembre 2000.Google Scholar
  24. 24.
    P. Merz & B. Freidleben. A genetic local approach to the quadratic assignment problem; in Proc of the 7th Conf on Genetic Algorithms (ICGA),Th Back, Ed. , San Fransisco, CA, p:465–472, Morgan Kaufmann, 1997.Google Scholar
  25. 25.
    Z. Michalewicz, D. Dasgupta, R. G Le Riche & M. Schoenauer. Evolutionary Algorithms for Constrained Engineering Problems; Computers & Industrial Engineering Journal, vol 30(2), April 1996.Google Scholar
  26. 26.
    V. Schnecke. Hybrid Genetic Algorithms for Solving Constrained Packing and Placement Problems; Ph. D thesis, Department of Mathematics/Computer Science, University of Osnabriick, Germany, 1996.Google Scholar
  27. 27.
    H. P. Schwefel. Numerical optimization of computer models; John Wiley & Sons, New York, 1981.Google Scholar
  28. 28.
    M. Schoenauer, L. Kallel, & F. Jouve. Mechanical inclusions identification by evolutionary computation; Europeen Journal of Finite Elements, 5(5–6), p:619–648, 1996.Google Scholar
  29. 29.
    M. Schoenauer, A. Ehinger & B. Braunschweig. Non parametric identification of geological models; In Proceedings of 5th IEEE International Conference On Evolutionary Computation, IEEE press, 1998.Google Scholar
  30. 30.
    M.Schoenauer & Spyros Xanthakis. Constrained GA optimization; In proceedings of the 5th International Conference on Genetic Algorithm, Urbana Champaign, 1993.Google Scholar
  31. 31.
    M. K Sen & P. L. Stoffa. Rapid sampling of the model space using genetic algorithms: examples from seismic waveform inversion; Geophysical Journal International 108, p:281–292, 1992.Google Scholar
  32. 32.
    D. E. Goldberg. Genetic algorithms in search, optimization and machine learning; Reading, MA: Addison Wesley, 1989.Google Scholar
  33. 33.
    P. L Stoffa & M. K Sen. Nonlinear multiparameter optimization using genetic algorithms: inversion of plane-wave seismograms; Geophysics, 56, 1991.Google Scholar
  34. 34.
    W. W. Symes & J. Carrazone. Velocity inversion by Differential Semblance optimization; Geophysics 56, p:154–163, 1991.CrossRefGoogle Scholar
  35. 35.
    M. Taner & F. Koehler. Velocity spectra-digital computer derivation and applications of velocity functions; Geophysics 34, p:859–881, 1969.CrossRefGoogle Scholar
  36. 36.
    C. L. Varela, P. L. Stoffa & M. Sen. Migration misfit and reflection tomography: criteria for prestack migration velocity estimation in laterally varying media; 64th SEG meeting, Los Angeles, USA, Expanded Abstract, p: 1347–1350, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • F. Mansanné
    • 1
  • M. Schoenauer
    • 2
  1. 1.Laboratoire de Mathématiques, ERS 2055Université de PauPauFRANCE
  2. 2.CMAP, UMR CNRS 7641Ecole PolytechniquePalaiseauFRANCE

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