The propagation of waves due to the presence of an SH point source in the interior of a piecewise continuously stratified half-space is studied. The physical parameters governing the wave propagation, i.e. the rigidity and the density, are assumed to be arbitrary piecewise continuous functions of depth with constant finite limiting values as depth goes to infinity. The analysis is based on spectral theory of boundary value problems associated with ordinary linear second order differential equations. It is found for the time harmonic case that the final field representations are given in the form of a finite residue series, plus a branch line integral, the first representing the normal mode contribution to the field. The field expression appears to have a symmetrical form with respect to field point depth and source depth, involving solutions connected with free wave propagation. This enables one to draw immediately conclusions regarding the influence of the source depth and the frequency on the spectral excitation of the normal modes if numerical knowledge of free Love waves is assumed to be known.