Geodesic
The numerical-analytical method of solving the problem of seismic and acoustic-gravity wave propagation for the inhomogeneous model Earth–Atmosphere
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 1, pp. 37-46 
B. G. Mikhailenko; G. V. Reshetova. The numerical-analytical method of solving the problem of seismic and acoustic-gravity wave propagation for the inhomogeneous model Earth–Atmosphere. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 1, pp. 37-46. http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a3/
@article{SJVM_2006_9_1_a3,
     author = {B. G. Mikhailenko and G. V. Reshetova},
     title = {The numerical-analytical method of solving the problem of seismic and acoustic-gravity wave propagation for the inhomogeneous model {Earth{\textendash}Atmosphere}},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {37--46},
     year = {2006},
     volume = {9},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a3/}
}
TY  - JOUR
AU  - B. G. Mikhailenko
AU  - G. V. Reshetova
TI  - The numerical-analytical method of solving the problem of seismic and acoustic-gravity wave propagation for the inhomogeneous model Earth–Atmosphere
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2006
SP  - 37
EP  - 46
VL  - 9
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a3/
LA  - ru
ID  - SJVM_2006_9_1_a3
ER  - 
%0 Journal Article
%A B. G. Mikhailenko
%A G. V. Reshetova
%T The numerical-analytical method of solving the problem of seismic and acoustic-gravity wave propagation for the inhomogeneous model Earth–Atmosphere
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2006
%P 37-46
%V 9
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a3/
%G ru
%F SJVM_2006_9_1_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper considers a numerical-analytical method of solving the problem of seismic and acoustic-gravity wave propagation for the inhomogeneous model “Earth-Atmosphere”. The seismic wave propagation is described by a system of the first order dynamic equations of elasticity theory; the propagation of acoustic-gravity waves in the atmosphere is described by the linearized Navier–Stokes equations. The algorithm proposed is based on a combination of the integral Laguerre transform with respect to time, finite integral Bessel transform along the radial coordinate with a finite difference method along the vertical coordinate. The paper presents some examples of calculation of seismic and acoustic-gravity waves for the inhomogeneous model Earth–Atmosphere for various locations of a source.

[1] Francis S. H., “Global propagation of atmospheric gravity waves. A review”, J. Atmosph. and Terrestrial Physics, 37 (1975), 1011–1054 | DOI

[2] Gossard E. E., Hooke W. H., Waves in the Atmosphere, Developments in Atmospheric Sci., 2, Elsevier Sci. Publ. Comp., 1975

[3] Alekseev A. S., Glinskii B. M., Dryakhlov S. I. i dr., “Effekt akustoseismicheskoi induktsii pri vibroseismicheskom zondirovanii”, DAN, 346:5 (1996), 664–667

[4] Artru J. et al., “Ionospheric detection of gravity waves induced by tsunamis”, Geophys. J. Int., 160 (2005), 840–848 | DOI

[5] Linkov E. M., Petrova A. N., Osipov K. S., “Seismogravitatsionnye pulsatsii Zemli i vozmuscheniya atmosfery, kak vozmozhnye predvestniki silnykh zemletryasenii”, DAN, 313:5 (1990), 1095–1098

[6] Gasilova L. A., Petukhov Yu. V., “K teorii poverkhnostnykh voln, rasprostranyayuschikhsya vdol raznykh granits razdela v atmosfere”, Izvestiya AN. Fizika atmosfery i okeana, 35:1 (1999), 14–23 | MR

[7] Razin A. V., “Rasprostranenie sferichnogo akusticheskogo delta-impulsa vdol granitsy gaz – tverdoe telo”, Izvestiya AN. Fizika Zemli, 1993, no. 2, 73–77

[8] Konyukh G. V., Mikhailenko B. G., “Application of the Laguerre integral transform for solving dynamic seismic problems”, Bull. of the Novosibirsk Computing Center. Series: Mathematical Modeling in Geophysics, 1998, no. 4, 79–91 | MR | Zbl

[9] Mikhailenko B. G., “Spectral Laguerre method for the approximation solution of time-dependent problems”, Appl. Math. Lett., 12 (1999), 105–110 | DOI | MR | Zbl

[10] Mikhailenko B. G., Mikhailov A. A., Reshetova G. V., “Numerical Modeling of transient seismic fields in viscoelastic media based on the Laguerre spectral method”, Pure Appl. Geophys., 160 (2003), 1207–1224 | DOI

[11] Virieux J., “P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method”, Geophysics, 51 (1986), 889–901 | DOI

[12] Berenger J. P., “A perfectly matched layer for the absorption of electromagnetic waves”, J. Comput. Phys., 114 (1994), 185–200 | DOI | MR | Zbl

[13] Collino F., Tsogka C., “Application of PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media”, Geophysics, 66:1 (2001), 294–307 | DOI

[14] Mikhailenko B. G., Reshetova G. V., “The perfectly matched layers technique in 3D seismic modeling”, Proc. Intern. Symp. on Math. Modeling of Dynamic Processes in Atmosphere, Ocean and Solid Earth, Novosibirsk, 2004, 91–97