The elastodynamic Green's tensor in an anisotropic half-space

We study the effect of the free surface on waves from buried sources in an elastic half-space with azimuthal isotropy. The exact Green's tensor is obtained in the form of a Hankel transform over the horizontal wavenumber. The integrals are then evaluated at the far-field by means of the stationary phase approximation. An alternative representation of the Green's tensor is offered in the form of a hybrid multipole expansion valid also in the near-field.