The Effect of Rayleigh-Love Coupling in an Anisotropic Medium

It is well known that for a weakly anisotropic medium, at angular frequency ω and propagation azimuth ψ Rayleigh and Love wave phase speeds are given approximately by V(ω,ψ) = A₀ + A2c cos 2 ψ + A₂ₛ sin 2 ψ + A4c cos 4 ψ + A₄ₛ sin 4 ψ. Previous theories of the propagation of surface waves in anisotropic media based on non-degenerate perturbation theory predict that the dominant components are expected to be 2ψ for Rayleigh waves and 4ψ for Love waves. This paper is motivated by recent observations of previously unexpected anisotropy: the 2ψ component for Love waves and 4ψ for Rayleigh waves. To illuminate this phenomenon, we present a quasi-degenerate theory of Rayleigh-Love coupling based on the application of Hamilton's Principle to Rayleigh and Love waves propagating in a weakly anisotropic medium. We show that the unexpected components are actually expected in the presence of strong Rayleigh-Love coupling and recent observations of Rayleigh and Love wave 2ψ and 4ψ anisotropy can be fit successfully with physically plausible models of a depth-dependent tilted transversely isotropic (TTI) medium. In addition, the ellipticity parameter ηX, introduced here, is better constrained and we present evidence that the mantle should be modeled as a tilted orthorhombic medium rather than a TTI medium. We also provide information about the polarization of the quasi-Love waves, coupling between fundamental mode Love and overtone Rayleigh waves in both continental and oceanic settings, and practical suggestions for observers. For comparison, we present a theory of SV-SH coupling for horizontally propagating body waves, with particular emphasis on results for a TTI medium.