THREE-DIMENSIONAL ORTHOGONALITY RELATIONS FOR EIGENWAVES AND THEIR IMPLEMENTATION FOR THE DYNAMIC PROBLEMS OF LAYERED SLABS
The orthogonality relations for 3D waves in layered transversely isotropic slabs are derived in the explicit form. Their physical meaning is discussed. Some generalizations for the cases of infinite media or for the case of fluid loaded slabs are considered. The boundary value problems with a discrete spectrum are analyzed; a modal formulation of the transparent boundary conditions is suggested for the lateral surface of a virtual cylinder including all sources, scatterers, etc. The applications of the presented formalism to the problem of wave propagation and diffraction in elastic solids are discussed.