Direct Search Simulated Annealing for Nonlinear Global Optimization of Rayleigh Waves

  • Xiaochun Lv
  • Hanming Gu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7390)


Nonlinear global optimization of Rayleigh wave dispersion curves not only undergoes computational difficulties associated with being easily entrapped in local minima for most local-search methods but also suffers from the high computational cost for most global optimization methods due to its multimodality and its high nonlinearity. In order to effectively overcome the above described difficulties, we proposed a new Rayleigh wave dispersion curve inversion scheme based on Direct Search Simulated annealing (DSSA), an efficient and robust algorithm which hybridized direct search methods, as local search methods, and simulated annealing, as a meta-heuristic method. The performance of the proposed procedure is tested on a four-layer synthetic earth model and a real-world example. Results from both synthetic and real field data demonstrate that DSSA applied to nonlinear inversion of Rayleigh waves should be considered good not only in terms of computation time but also in terms of accuracy due to its global and fast convergence in the final stage of exploration.


Nonlinear Global Optimization Simulated annealing Genetic algorithms Artificial neural network Rayleigh waves 


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  1. 1.
    Park, C.B., Miller, R.D., Xia, J.: Multichannel Analysis of Surface Waves. Geophysics 64, 800–808 (1999)CrossRefGoogle Scholar
  2. 2.
    Xia, J., Miller, R.D., Park, C.B.: Estimation of Near-surface Shear-wave Velocity by Inversion of Rayleigh Wave. Geophysics 64(3), 691–700 (1999)CrossRefGoogle Scholar
  3. 3.
    Xu, Y., Xia, J., Miller, R.D.: Quantitative Estimation of Minimum Offset for Multichannel Surface-wave Survey with Actively Exciting Source. Journal of Applied Geophysics 59, 117–125 (2006)CrossRefGoogle Scholar
  4. 4.
    Luo, Y., Xia, J., Miller, R.D., Xu, Y., Liu, J., Liu, Q.: Rayleigh-wave Dispersive Energy Imaging Using A High-resolution Linear Radon Transform. Pure and Applied Geophysics 165, 903–922 (2008)CrossRefGoogle Scholar
  5. 5.
    Song, X., Gu, H., Liu, J., Zhang, X.: Estimation of Shallow Subsurface Shear-wave Velocity by Inverting Fundamental and Higher-mode Rayleigh Waves. Soil Dynamics and Earthquake Engineering 27(7), 599–607 (2007)CrossRefGoogle Scholar
  6. 6.
    Song, X., Gu, H.: Utilization of Multimode Surface Wave Dispersion for Characterizing Roadbed Structure. Journal of Applied Geophysics 63(2), 59–67 (2007)CrossRefGoogle Scholar
  7. 7.
    Yamanaka, H., Ishida, H.: Application of Genetic Algorithm to An Inversion of Surface Eave Dispersion Data. Bulletin of the Seismological Society of America 86, 436–444 (1996)MathSciNetGoogle Scholar
  8. 8.
    Beaty, K.S., Schmitt, D.R., Sacchi, M.: Simulated Annealing Inversion of Multimode Surface Wave Dispersion Curves for Geological Structure. Geophysical Journal International 151, 622–631 (2002)CrossRefGoogle Scholar
  9. 9.
    Ryden, N., Park, C.B.: Fast Simulated Annealing Inversion of Surface Waves on Pavement Using Phase-velocity Spectra. Geophysics 71(4), R49–R58 (2006)Google Scholar
  10. 10.
    Shirazi, H., Abdallah, I., Nazarian, S.: Developing Artificial Neural Network Models to Automate Spectral Analysis of Surface Wave Method in Pavements. Journal of Computing in Civil Engineering 21(12), 722–729 (2009)Google Scholar
  11. 11.
    Tillmann, A.: An Unsupervised Wavelet Transform Method for Simultaneous Inversion of Multimode Surface Waves. Journal of Environmental & Engineering Geophysics 10(3), 287–294 (2005)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Dal Moro, G., Pipan, M.: Joint Inversion of Surface Wave Dispersion Curves and Reflection Travel Times via Multi-objective Evolutionary Algorithms. Journal of Applied Geophysics 61(1), 56–81 (2007)CrossRefGoogle Scholar
  13. 13.
    Maraschini, M., Foti, S.: A Monte Carlo Multimodal Inversion of Surface Waves. Geophysical Journal International 182(3), 1557–1566 (2010)CrossRefGoogle Scholar
  14. 14.
    Buchen, P.W., Ben-Hador, R.: Free-mode Surface-wave Computations. Geophysical Journal International 124, 869–887 (1996)CrossRefGoogle Scholar
  15. 15.
    Chunduru, R.K., Sen, M.K., Stoffa, P.L.: Hybrid Optimization Methods for Geophysical Inversion. Geophysics 62(4), 1196–1207 (1998)Google Scholar
  16. 16.
    Sen, M.K., Stoffa, P.L.: Nonlinear One-dimensional Seismic Waveform Inversion Using Simulated Annealing. Geophysics 56(10), 1624–1638 (1991)CrossRefGoogle Scholar
  17. 17.
    Hedar, A., Fukushima, M.: Hybrid Simulated Annealing And Direct Search Method For Nonlinear Unconstrained Global Optimization. Optimization Methods and Software 17(5), 891–912 (2002)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xiaochun Lv
    • 1
  • Hanming Gu
    • 1
  1. 1.Institute of Geophysics and GeomaticsChina University of GeosciencesWuhanChina

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