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.Attempts at revealing the mode-ray relation have been made by many authors. BRUNE (1964) proposed an excellent idea of connecting rays and normal modes of a spherical earth and applied the method successfully for obtaining torsional higher mode dispersion curves from body wave phases. BEN-MENAHEM (1964) also revealed the mode-ray duality from the analytical considerations.The contribution of theoretical seismograms to the study of this problem is significant and valuable results have
Ray theory is applied successfully to derive asymptotic frequency equations of the radial oscillations of a homogeneous elastic sphere and a sphere with one concentric surface of discontinuity in it , and of the spheroidal oscillation of a homogeneous sphere. The method is similar to the one used for getting frequency equations for plane stratified media , and is based on the idea that for steady vibration of a sphere to be possible some interference condition has to be satisfied by body waves traveling in it . It is shown that these equations are identical to those obtained by the normal mode theory.It is found that the solotone effect has an immediate connection with multiple reflections of body waves at the discontinuity in the medium . Decoupling of P-and S-waves at high frequencies is well illustrated for the spheroidal modes in terms of the distribution of eigenfrequencies and the radial dependence of eigenfunctions.
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