Numerical simulation of seismic wave propagation in media with viscoelastic intrusions


  • D.M. Vishnevsky Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
  • V.N. Lisitsa Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
  • G.V. Reshetova The Institute of Computational Mathematics and Mathematical Geophysics of SB RAS (ICM&MG SB RAS)


elasticity, seismic attenuation, finite-difference schemes, domain decomposition, parallel algorithms


Seismic attenuation is a widespread property of the Earth’s interior due to low consolidation and fluid saturation of the rocks. However, viscoelastic formations typically take as few as 10 to 20% of the model. Thus, the use of computationally intensive algorithms, oriented on viscoelasticity, in the entire computational domains makes the simulations inefficient. In this paper an original algorithm based on the coupling of the elastic and viscoelastic statements is presented. The computationally intensive approach is used only in subdomains embedding the viscoelastic formations, whereas the ideal elastic equations are solved elsewhere. As a result, the speed-up of the hybrid algorithm is 1.7 compared to a purely viscoelastic implementation.

Author Biographies

D.M. Vishnevsky

V.N. Lisitsa

G.V. Reshetova


  1. Белоносов М.А., Костов К., Решетова Г.В., Соловьёв С.А., Чеверда В.А. Организация параллельных вычислений для моделирования сейсмических волн с использованием аддитивного метода Шварца // Вычислительные методы и программирование. 2012. 13. 525-535.
  2. Костин В.И., Лисица В.В., Решетова Г.В., Чеверда В.А. Конечно-разностный метод численного моделирования распространения сейсмических волн в трехмерно-неоднородных разномасштабных средах // Вычислительные методы и программирование. 2011. 12. 321-329.
  3. Лисица В. Нерасщепленный идеально согласованный слой для системы уравнений динамической теории упругости // Сиб. журн. вычисл. матем. 2007. 10. 285-297.
  4. Asvadurov S., Knizhnerman L., Pabon J. Finite-difference modeling of viscoelastic materials with quality factors of arbitrary magnitude // Geophysics. 2005. 69. 817-824.
  5. Blanch J.O., Robertson A., Symes W.W. Modeling of a constant Q: methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique // Geophysics. 1995. 60. 176-184.
  6. Bohlen T. Parallel 3D viscoelastic finite difference seismic modeling // Computers and Geosciences. 2002. 28. 887-899.
  7. Brossier R., Operto S., Virieux J. Seismic imaging of complex onshore structures by 2D elastic frequency-domain fullwaveform inversion // Geophysics. 2009. 74. WCC63-WCC76.
  8. Carcione J.M. Seismic modeling in viscoelastic media // Geophysics. 1993. 58. 110-120.
  9. Carcione J.M., Cavallini F. A rheological model for inelastic anisotropic media with applications to seismic wave propagation // Geophys. J. Int. 1994. 119. 338-348.
  10. Carcione J.M., Gei D. Theory and numerical simulation of fluid-pressure diffusion in anisotropic porous media // Geophysics. 2009. 74. N31-N39.
  11. Carcione J.M., Kosloff D., Kosloff R. Wave propagation simulation in a linear viscoacoustic medium // Geophys. J. Roy. Astr. Soc. 1988. 93. 393-407.
  12. Carcione J.M., Kosloff D., Kosloff R. Wave propagation simulation in a linear viscoelastic medium // Geophysical J. 1988. 95. 597-611.
  13. Carcione J.M., Morency C., Santos J.E. Computational poroelasticity - a review // Geophysics. 2010. 75. 75A229-75A243.
  14. Christensen R.M. Theory of viscoelasticity. An introduction. New York: Academic Press, 1971.
  15. Dong Z., McMechan G.A. 3D viscoelastic anisotropic modeling of data from a multicomponent, multiazimuth seismic experiment in northeast Texas // Geophysics. 1995. 60. 1128-1138.
  16. Drossaert F.H., Giannopoulos A. A nonsplit complex frequency-shifted pml based on recursive integration for fdtd modeling of elastic waves // Geophysics. 2007. 72. T9-T17.
  17. Duveneck E., Bakker P.M. Stable P-wave modeling for reverse-time migration in tilted TI media // Geophysics. 2011. 76. S65-S75.
  18. Engquist B., Majda A. Absorbing boundary conditions for the numerical simulation of waves // Math. Comp. 1977. 31. 629-651.
  19. Hagstrom T., Lau S. Radiation boundary conditions for Maxwell’s equations: a review of accurate time-domain formulations // J. Comput. Math. 2007. 25. 305-336.
  20. Hestholm S., Ruud B. 3D free-boundary conditions for coordinate-transform finite-difference seismic modelling // Geophysical Prospecting. 2002. 50. 463-474.
  21. Knopoff L. Q // Reviews of Geophysics. 1964. 2. 625-660.
  22. Komatitsch D., Martin R. An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation // Geophysics. 2007. 72. SM155-SM167.
  23. Kostin V., Lisitsa V., Reshetova G., Tcheverda V. Simulation of seismic waves propagation in multiscale media: impact of cavernous/fractured reservoirs // Lecture Notes in Computer Science. Vol. 7133. Heidelberg: Springer, 2012. 54-64.
  24. Kruger O.S., Saenger E.H., Oates S.J., Shapiro S.A. A numerical study on reflection coefficients of fractured media // Geophysics. 2007. 72. D61-D67.
  25. Kwok F. Optimized additive Schwarz with harmonic extension as a discretization of the continuous parallel Schwarz method // SIAM J. on Numerical Analysis. 2011. 49. 1289-1316.
  26. Levander A.R. Fourth-order finite-difference P-SV seismograms // Geophysics. 1988. 53. 1425-1436.
  27. Lisitsa V., Reshetova G., Tcheverda V. Finite-difference algorithm with local time-space grid refinement for simulation of waves // Computational Geosciences. 2012. 16. 39-54.
  28. Lisitsa V., Vishnevskiy D. Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity // Geophysical Prospecting. 2010. 58. 619-635.
  29. Liu Y., Sen M.K. Acoustic VTI modeling with a time-space domain dispersion-relation-based finite-difference scheme // Geophysics. 2010. 75. A11-A17.
  30. Magoules F., Putanowicz R. Optimal convergence of non-overlapping Schawarz methods for the Helmholtz equation // J. of Computational Acoustics. 2005. 13. 525-545.
  31. Moczo P., Bystricky E., Kristek J., Carcione J.M., Bouchon M. Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures // Bull. of the Seismological Society of America. 1997. 87. 1305-1323.
  32. Saenger E.H., Gold N., Shapiro S.A. Modeling the propagation of the elastic waves using a modified finite-difference grid // Wave Motion. 2000. 31. 77-92.
  33. Suh S.Y., Yeh A., Wang B., Cai J., Yoon K., Li Z. Cluster programming for reverse time migration // The Leading Edge. 2010. 29. 94-97.
  34. Vavrycuk V. Velocity, attenuation, and quality factor in anisotropic viscoelastic media: a perturbation approach // Geophysics. 2008. 73. D63-D73.
  35. Virieux J. P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method // Geophysics. 1986. 51. 889-901.
  36. Virieux J., Operto S., Ben-Hadj-Ali H., Brossier R., Etienne V., Sourbier F., Giraud L., Haidar A. Seismic wave modeling for seismic imaging // The Leading Edge. 2009. 28. 538-544.
  37. White R.E. The accuracy of estimating Q from seismic data // Geophysics. 1992. 57. 1508-1511.
  38. Zhang D., Lamoureux M., Margrave G., Cherkaev E. Rational approximation for estimation of quality q factor and phase velocity in linear, viscoelastic, isotropic media // Computational Geosciences. 2011. 15. 117-133.



How to Cite

Вишневский Д., Лисица В., Решетова Г. Numerical Simulation of Seismic Wave Propagation in Media With Viscoelastic Intrusions // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2013. 14. 155-165



Section 1. Numerical methods and applications

Most read articles by the same author(s)

1 2 > >>