Numerical modeling of acoustic-gravity waves propagation in a~heterogeneous ``Earth--Atmosphere'' model with a~wind in the atmosphere

B. G. Mikhailenko ; A. A. Mikhailov

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 2, pp. 149-162.

Résumé

A numerical-analytical solution for seismic and acoustic-gravitational 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 the elasticity theory. Propagation of acoustic-gravitational waves in the atmosphere is described by the linearized Navier–Stokes equations with the a wind. The proposed algorithm is based on the integral Laguerre transform with respect to time, the finite integral Fourier transform along the spatial coordinate with the finite difference solution of the reduced problem.

Bibliographie

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

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

[3] Razin A. V., “Rasprostranenie sferichnogo akusticheskogo delta-impulsa vdol granitsy gaz–tvërdoe telo”, Izv. RAN. Fizika Zemli, 1993, no. 2, 73–77

[4] Mikhailenko B. G., Reshetova G. V., “Matematicheskoe modelirovanie rasprostraneniya seismicheskikh i akustogravitatsionnykh voln dlya neodnorodnoi modeli Zemlya–Atmosfera”, Geologiya i geofizika, 47:5 (2006), 547–556

[5] Mikhailenko B. G., “Spectral Laguerre method for the approximate solution of time dependent problems”, Applied Mathematics Letters, 12 (1999), 105–110 | DOI | MR | Zbl

[6] Konyukh G. V., Mikhailenko B. G., Mikhailov A. A., “Application of the integral Laguerre transforms for forward seismic modeling”, J. of Computational Acoustics, 9:4 (2001), 1523–1541 | DOI | MR

[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 and Applied Geophysics, 160 (2003), 1207–1224 | DOI

[8] Mikhailenko B. G., Mikhailov A. A., Reshetova G. V., “Numerical viscoelastic modeling by the spectral Laguerre method”, Geophysical Prospecting, 51 (2003), 37–48 | DOI

[9] Imomnazarov Kh. Kh., Mikhailov A. A., “Ispolzovanie spektralnogo metoda Lagerra dlya resheniya lineinoi dvumernoi dinamicheskoi zadachi dlya poristykh sred”, Sib. zhurn. industrialnoi matematiki, 11:3(35) (2008), 86–95 | MR | Zbl

[10] Mikhailov A. A., “Modelirovanie seismicheskikh polei dlya 2.5D neodnorodnykh vyazkouprugikh sred”, Tr. Mezhdunar. konf. “Matematicheskie metody v geofizike”, Chast 1, Novosibirsk, 2003, 146–152

[11] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1974 | MR

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

[13] Sd Y., Van der Vorst H. A., “Iterative solution of linear systems in the 20th century”, J. of Computational and Applied Mathematics, 123 (2000), 1–33 | DOI | MR | Zbl

[14] Sonneveld P., “CGS, a fast Lanczos-type solver for nonsymmetric linear system”, SIAM J. of Scientific and Statistical Computing, 10 (1989), 36–52 | DOI | MR | Zbl

[15] Mikhailenko B. G., Mikhailov A. A., “Chislennoe reshenie 2.5D dinamicheskoi zadachi seismiki s ispolzovaniem algoritmov rasparallelivaniya”, Parallelnye vychislitelnye tekhnologii, (PaVT'2012), Tr. Mezhdunar. nauchn. konf. (Novosibirsk, 26–30 marta 2012 g.), Izdatelskii tsentr YuUrGU, Chelyabinsk, 2012, 612–620