Eigenwaves of a transversely isotropic layer interfaced to an isotropic half-plane

The waveguide structure formed by a transversely isotropic layer interfaced to an isotropic half-plane is considered. The general solution of equations describing the elastic wave propagation in a transversely isotropic medium is obtained. The spectrum of the waveguide structure is determined. The semi-inner product is defined on the space of the eigenwaves. It is shown that the waves corresponding to the discrete spectrum form the system of orthogonal functions with respect to the semi-inner product.