Green's Tensor Function for Lamb's Problem. The General Anisotropic Case

The complete solution of Lamb's three-dimensional problem of determining the elastic disturbance resulting from a point force in a half-space is addressed. The derived expression for the half-space Green's function is valid for a general anisotropic medium and is given in a two-dimensional space-time spectral representation, which is well suited for numerical evaluation. It is expressed with respect to the displacement and traction vectors involved as well as the full-space Green's dyadic (or displacement tensor) and triadic (or stress tensor) functions.