Modeling the Wind Influence on Acoustic-Gravity Propagation Waves in a Heterogeneous Earth-Atmosphere Model

  • B. Mikhailenko
  • A. A. Mikhailov
  • G. V. ReshetovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9045)


A numerical-analytical algorithm for modeling of seismic and acoustic-gravity waves propagation is applied to a heterogeneous “Earth-Atmosphere" model. Seismic wave propagation in an elastic half-space is described by a system of first-order dynamic equations of elasticity theory. The propagation of acoustic-gravity waves in the atmosphere is described by the linearized Navier-Stokes equations with the wind. The algorithm is based on the integral Laguerre transform with respect to time, the finite integral Fourier transform with respect to a spatial coordinate combined with a finite difference method for the reduced problem.


Seismic waves Acoustic-gravity waves Navier-stokes equations Laguerre transform Finite difference method 



This work was supported by the Russian Foundation for Basic Research (project 14-05-00867).


  1. 1.
    Alekseev, A.S., Glinsky, B.M., Dryakhlov, S.I., et al.: The effect of acoustic-seismic induction in vibroseismic sounding. Dokl. RAN. 346(5), 664–667 (1996)Google Scholar
  2. 2.
    Gasilova, L.A., Petukhov, Y.V.: On the theory of surface wave propagation along different interfaces in the atmosphere. Izv. RAN. Fizika atmosfery i okeana 35(1), 14–23 (1999)MathSciNetGoogle Scholar
  3. 3.
    Razin, A.V.: Propagation of a spherical acoustic delta wavelet along the gas-solid interface. Izv. RAN. Fizika zemli. 2, 73–77 (1993)Google Scholar
  4. 4.
    Mikhailenko, B.G., Reshetova, G.V.: Mathematical simulation of propagation of seismic and acoustic-gravitational waves for an inhomogeneous Earth-Atmosphere model. Geologiya i geofizika 47(5), 547–556 (2006)Google Scholar
  5. 5.
    Mikhailenko, B.G.: Spectral Laguerre method for the approximate solution of time dependent problems. Appl. Math. Lett. 12, 105–110 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Konyukh, G.V., Mikhailenko, B.G., Mikhailov, A.A.: Application of the integral Laguerre transforms for forward seismic modeling. J. Comput. Acoust. 9(4), 1523–1541 (2001)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Mikhailenko, B.G., Mikhailov, A.A., Reshetova, G.V.: Numerical modeling of transient seismic fields in viscoelastic media based on the Laguerre spectral method. J. Pure Appl. Geophys. 160, 1207–1224 (2003)CrossRefGoogle Scholar
  8. 8.
    Mikhailenko, B.G., Mikhailov, A.A., Reshetova, G.V.: Numerical viscoelastic modeling by the spectral Laguerre method. Geophys. Prospect. 51, 37–48 (2003)CrossRefGoogle Scholar
  9. 9.
    Imomnazarov, K.K., Mikhailov, A.A.: Use of the spectral Laguerre method to solve a linear 2D dynamic problem for porous media. Sib. Zh. Industr. matem. 11(2), 86–95 (2008)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Mikhailov, A.A.: Simulation of seismic fields for 2.5D inhomogeneous viscoelastic media. Proc. of the Intern. Conference “Mathematical Methods in Geophysics". Novosibirsk. Part 1, 146–152 (2003)Google Scholar
  11. 11.
    Suetin, P.K.: Classical orthogonal polynomials, p. 327. Nauka, Moscow (1999)Google Scholar
  12. 12.
    Virieux, J.: P-, SV- wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 51, 889–901 (1986)CrossRefGoogle Scholar
  13. 13.
    Saad, Y., Van der Vorst, H.A.: Iterative solution of linear systems in the 20\(^{th}\) century. J. Comput. Appl. Math. 123, 1–33 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Sonneveld, P.: CGS, a fast Lanczos-type solver for nonsymmetric linear system. SIAM J. Sci. Stat. Comput. 10, 36–52 (1989)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • B. Mikhailenko
    • 1
  • A. A. Mikhailov
    • 1
  • G. V. Reshetova
    • 1
    Email author
  1. 1.The Institute of Computational Mathematics and Mathematical GeophysicsNovosibirskRussia

Personalised recommendations