Method of projectors and the construction of Green's function of the wave equation

In the present article problems related to the propagation of waves in elastic anisotropic media with arbitrary types of symmetry are considered. Such problems are important for solid-body physics and for geophysics. An expansion of Green`s function of the wave equation of the theory of elasticity is presented in the form of additive terms corresponding to the contributions of each of the three waves propagating in a solid body with designated anisotropic characteristics. An appropriate representation for the roots of the characteristic equation specifying the rate of wave propagation is presented. To illustrate the computation technique examples of certain types of media are considered. A representation is obtained for the static Green`s function that does not require knowledge of the exact roots of the characteristic equation (assuming there is no degeneracy present).