The normal mode solution for Love waves from a shear fault in a stratified layer over the half-space is investigated with special attention to the azimuthal behavior of amplitude compared with the radiation pattern of SH waves. It is found that Love waves are denoted by the sum of two terms associated with a particular set of rays of physical significance. For the torsional oscillation of a homogeneous elastic sphere due to the shear fault, a similar relation is recognized between higher radial modes and rays. The mode-ray relations obtained in the above two cases coincide with the ones derived in other literature from quite different considerations that interpret the normal modes by interference phenomena.
The radiation patterns of SH waves and of normal modes are found to be related through the apparent equivalent take-off angle lh, which is defined so that the radiation pattern of square amplitude for a normal mode may be equal to the pattern of the sum of the square amplitudes for SH waves emitted in the two directions specified by the take-off angles lh and π-lh. Provided that the apparent equivalent take-off angles are known beforehand as a function of the eigen-frequency and the focal depth, it is easy to obtain the azimuthal dependence of amplitude of the normal modes excited by a shear fault of arbitrary dip and slip, because the azimuthal behavior is the same as the radiation pattern of SH waves associated with the apparent equivalent take-off angles. Numerical experiments are shown for the fundamental torsional oscillation of a Gutenberg-Bullen A' spherical earth excited by a pure dip slip and a pure strike slip fault at depth 5.35km.