The numerical-analytical method of solving the problem of seismic and acoustic-gravity wave propagation for the inhomogeneous model Earth–Atmosphere

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.