Abstract
Rayleigh's principle is combined with Backus' harmonic tensor decomposition to investigate the effect of a small anisotropy on the propagation of Love and Rayleigh surface waves in an arbitrarily stratified half-space. A slight elastic anisotropy gives rise to an azimuthal dependence of the phase velocities of both Love and Rayleigh waves of the form c(ω, θ) = A1(ω) + A2(ω) cos 2θ + A3(ω) sin 2θ + A4(ω) cos 4θ + A5(ω) sin 4θ where ω is the angular frequency and θ is the azimuth of the wave-number vector. This azimuthal dependence of the Love and Rayleigh wave phase velocities produces, in turn, a similar azimuthal dependence of the Love and Rayleigh wave group velocities. In view of the accumulating evidence from seismic refraction surveys of upper mantle anisotropy under oceans, the theory may be applicable to Love and Rayleigh wave propagation along oceanic paths.
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