The elastodynamic Green's tensor for a half-space with an embedded anisotropic layer

The two-dimensional elastodynamic Green's tensor is found in the form of a generalized ray expansion, for an isotropic half-space in which is embedded an anisotropic layer. Particular attention is paid to the displacement of the free surface when the source transmits waves through the layer. The first motion approximation, in which individual terms are replaced by their asymptotic forms close to their arrival times, is shown to provide a fair representation without the massive computation that the full solution requires. An example which lacks symmetry shows that the layer can transmit significant SH waves from a source of P-SV type; this phenomenon is relevant to studies of the earth's upper mantle.