Stochastic numerical study on the propagation characteristics of P-Wave in heterogeneous ground

지반의 비균질성이 탄성파 전파 특성에 미치는 영향에 대한 추계론적 수치해석 연구

  • Song, Ki-Il (Department of Civil Engineering, Inha University)
  • Received : 2012.11.19
  • Accepted : 2013.01.07
  • Published : 2013.01.31


Various elastic wave-based site investigation methods have been used to characterize subsurface ground because the dynamic properties can be correlated with various geotechnical parameters. Although the inherent spatial variability of the geotechnical parameters affects the P-wave propagation characteristics, ground heterogeneity has not been considered as an influential factor. Thus, the effect of heterogeneous ground on the travel-time shift and wavefront characteristics of elastic waves through stochastic numerical analyses is investigated in this study. The effects of the relative correlation lengths and relative propagation distances on the travel-time shift of P-waves considering various intensities of ground heterogeneity were investigated. Heterogeneous ground fields of stiffness (e.g., the coefficient of variation = 10 ~ 40%) were repeatedly realized in numerical finite difference grids using the turning band method. Monte Carlo simulations were undertaken to simulate P-wave propagation in heterogeneous ground using a finite difference method-based numerical approach. The results show that the disturbance of the wavefront becomes more significant with stronger heterogeneity and induces travel-time delays. The relative correlation lengths and propagation distances are systematically related to the travel-time shift.


Supported by : Inha University


  1. Song, K.I., Cho, G.C. (2006), "Effect of spatial distribution of geotechnical parameters on tunnel deformation", Journal of Korean Tunnelling and Underground Space Association, Vol. 8, No. 3, pp. 249-257.
  2. Song, K.I., Cho, G.C., Lee, S.W. (2011), "Effects of spatially variable weathered rock properties on tunnel behavior", Probabilistic Engineering Mechanics, Vol. 26, No. 3, pp. 413-426.
  3. Baig, A.M., Dahlen, F.A., Hung, S.H. (2003), "Traveltimes of waves in three-dimensional random media", Geophys. J. Int., Vol. 153, pp. 467-482.
  4. Dahlen, F.A., Hung, S.H, Nolet, G. (2000), "Frẻchet kernels for finite frequency traveltimes-I. Theory", Geophys. J. Int., Vol. 141, pp. 157-174.
  5. Fehler, M., Sato, H., Huang, L.J. (2000), "Envelope broadening of outgoing waves in 2D random media: a comparison between the Markov approximation and numerical simulations", Bull. Seismol. Soc. Am., Vol. 90, No. 4, pp. 914-928.
  6. Hador, R.B., Buchen, P.W. (1999), "Love and rayleigh waves in non-uniform media", Geophys. J. Int., Vol. 137, pp. 521-534.
  7. Horike, M., Takeuchi, Y. (2000), "Possibility of spatial variation of high-frequency seismic motions due to random-velocity fluctuation of sediments", Bull. Seismol. Soc. Am., Vol. 90, No. 1, pp. 48-65.
  8. Hung, S.H., Dahlen, F.A., Nolet, G. (2000), "Frechet kernels for finite frequency traveltimes-II. examples", Geophys. J. Int., Vol. 141, pp. 175-203.
  9. Iooss, B. (1998), "Seismic reflection traveltimes in two-dimensional statistically anisotropic random media", Geophys. J. Int., Vol. 135, No. 3, pp. 999-1010.
  10. Itasca Consulting Group Inc. (2002), FLAC - Fast Lagrangian Analysis of Continua User's Guide, Itasca Consulting Group, Inc., Minneapolis, MN.
  11. Jones, A.L., Kramer, S.L., Arduino, P. (2002), "Estimation of uncertainty in geotechnical properties for performance-based earthquake engineering", PEER report 2002/16. p. 114.
  12. Kim, J., Song, K.I., Cho, G.C., Lee, S.W. (2008), "Evaluation of the time-dependent characteristics of grouted particulate", Modern Physics Letters B, Vol. 22, No. 11, pp. 899-904.
  13. Lantuejoul, C. (1994), "Non conditional simulation of stationary isotropic multigaussian random functions", In: Armstrong, M., Dowd, P.A. (Eds.), Geostatistical Simulations, Kluwer Academic, Dordrecht, pp. 147-177.
  14. Lee, I.M., Choi, S.S., Kim, S.T., Kim, C.K., Jun. J.S. (2002), "3D analysis of fracture zones ahead of tunnel face using seismic reflection", Journal of Korean Tunnelling and Underground Space Association, Vol. 4, No. 4, pp. 301-317.
  15. Li, X., Hudson, J.A. (1996), "Multiple scattering of elastic waves from a continuous and heterogeneous region", Geophys. J. Int., Vol. 126, pp. 845-862.
  16. Lysmer, J., Kuhlemeyer, R.L. (1969), "Finite Dynamic Model for Infinite Media", Journal of the Engineering Mechanics Division, ASCE, Vol. 95, pp. 859-877.
  17. Marion, D., Mukerji, T., Mavko, G. (1994), "Scale effects on velocity dispersion: from ray to effective medium theories in stratified media", Geophysics, Vol. 59, pp. 1613-1619.
  18. Matheron, G. (1973), "The intrinsic random functions and their applications", Advances in Applied Probability, Vol. 5, pp. 439-468.
  19. Mavko, G., Mukerji, T., Dvorkin, J. (1998), The rock physics handbook, Cambridge University Press. p. 511.
  20. Metropolis, N., Ulam, S. (1949), "The monte carlo method", Journal of the American Statistical Association, Vol. 44, No. 247, pp. 335-341.
  21. Mukerji, T., Mavko, G., Mujica, D., Lucet, N. (1995), "Scale-dependent seismic velocity in heterogeneous media", Geophysics, Vol. 60, No. 4, pp. 1222-1233.
  22. Nigam, N.C. (1983), Introduction to Random Vibrations, MIT Press, Cambridge, MA. p. 360.
  23. Nour, A., Slimani, A., Laouami, N., Afra, H. (2003), "Finite element model for the probabilistic seismic response of heterogeneous soil profile", Soil Dyn Earthquake Engng, Vol. 23, No. 5, pp. 331-348.
  24. Ostoja-Starzewski, M., (1989), "Wavefront propagation in discrete random media via stochastic Huygens' minor principle", Journal of the Franklin Institute, Vol. 326, No. 2, pp. 281-293.
  25. R Development Core Team (2004), R: a language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, (
  26. Rahman, M.S., Yeh, C.H. (1999), "Variability of seismic response of soils using stochastic finite element method", Soil Dyn Earthquake Engng, Vol. 18, pp. 229-245.
  27. Robertsson, J.O.A, Blanch, J.O., Symes, W.W. (1994), "Viscoelastic finite-difference modeling", Geophysics, Vol. 59, No. 9, pp. 1444-1456.
  28. Sahimi, M., Allaei, S.M.V. (2008), "Numerical simulation of wave propagation, Part II: parallel computing", Computing in Science & Engineering, Vol. 10, No. 4, pp. 76-83.
  29. Santamarina, J.C., Fratta, D. (2005), Discrete Signals and Inverse Problems, England: John Wiley & Sons Ltd. p. 350.
  30. Schlather, M. (2001), "Simulation and analysis of random fields", R News, Vol. 1, No. 2, pp. 18-20.
  31. Shapiro, N.M., Campillo, M., Singh, S.K., Pacheco, J. (1998), "Channel seismic waves in the accretionary prism of the middle america trench", Geophys. Res. Lett., Vol. 25, pp. 101-104.
  32. Tripathi, J.N., Ram, A. (1997), "Elastic-wave scattering in a random medium characterized by the von karman correlation function and smallscale inhomogeneities in the lithosphere", Geophys. J. Int., Vol. 131, No. 3, pp. 682-698.
  33. Villiappan, S., Murti, V. (1984), Finite Element Constraints in the Analysis of Wave Propagation Problem, UNICV Report No. R-218, The University of New South Wales, School of Civil Engineering. p. 48.
  34. Yang, H.H., Hung, S.H. (2005), "Validation of ray and wave theoretical travel-times in heterogeneous random media", Geophys. J. Int., Vol. 32, L20302.
  35. Yi, M.J., Kim, J.H., Chung, S.H. (2003), "Enhancing the resolving power of least-squares inversion with active constraint balancing", Geophysics, Vol. 68, No. 3, pp. 931-941.
  36. You, K.H. (2011), "Analysis on the effect of strength improvement and water barrier by tunnel grouting reinforcement", Journal of Korean Tunnelling and Underground Space Association, Vol. 13, No. 4, pp. 291-304.
  37. Zendgui, D., Berrah, M.K., Kausel, E. (1999), "Stochastic deamplification of spatially varying seismic motions", Soil Dyn Earthquake Engng, Vol. 18, No. 6, pp. 409-421.
  38. Zerva, A., Zervas, V. (2002), "Spatial variation of seismic ground motions: an overview", Applied Mechanical Review, Vol. 55, No. 3, pp. 271-297.
  39. Zerwer, A., Cascante, G., Hutchinson, J. (2002), "Parameter Estimation in Finite Element Simulations of Rayleigh Waves", J. Geotech. Geoenviron. Eng., Vol. 128, No. 3, pp. 250-261.
  40. Zhao, L., Jordan, T.H., Chapman, C.H. (2000), "Three-dimensional Frẻchet differential kernels for seismic delay times", Geophys. J. Int., Vol. 141, pp. 558-576.

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