The Propagation of Love waves in a layer over a half-space is theoretically studied for cases where the upper or lower boundary of the layer can be represented by a hyporbola.
Curvilinear coordinates are used. Approximate solutions of various modes exist. Among the component harmonic waves of a mode, the representative one for each given position can be specified. This explains the position dependancy of phase velocity. The condition of transmission and refiection of Love waves for this model and the case in which one-half of the hyperbola is replaced by a straight line are discussed.