This paper considers numerical-analytical methods of solving the problem of propagation of seismic and acoustic-gravity waves for the inhomogeneous model “Earth – Atmosphere”. The seismic wave propagation is described by a system of the first order dynamic equations of the elasticity theory; the propagation of acoustic-gravity waves in the atmosphere are 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.

The research was done under financial support of RFBR grant 04-05-64177.