Mathematical modeling of seismic and acousto-gravitational waves in a heterogeneous earth–atmosphere model

A numerical–analytical solution to problems of seismic and acoustic-gravitational wave propagation is applied to a heterogeneous Earth–Atmosphere model. The seismic wave propagation in an elastic half-space is described by a system of first order dynamic equations of the elasticity theory. The propagation of acoustic-gravitational waves in the atmosphere is described by the linearized Navier–Stokes equations. The algorithm proposed is based on the integral Laguerre transform with respect to time, the finite integral Bessel transform along the radial coordinate with a finite difference solution of the reduced problem along the vertical coordinate. The algorithm is numerically tested for the heterogeneous Earth–Atmosphere model for different source locations.