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