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

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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. 
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     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--Atmosphere}},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a3/}
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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/