Rayleigh-Love Wave Coupling in an Azimuthally Anisotropic Medium

Abstract

We present the generalized representation of the equations of motion for an elastic solid in a concise vector form with arbitrary orthogonal curvilinear coordinates and no assumption on symmetry of elastic moduli. For the particular case of the Cartesian coordinates, this representation leads to the generalized y-method for eigenvalues of surface wave dispersion in an anisotropic plane-stratified medium. The generalized y-method is the integration method to find eigenvalues of surface wave dispersion by iterating numerical depth-integration of first-order ordinary differential equations that are derived from the generalized representation of the equations of motion and Hookean law. Based on the generalized y-method, we present some numerical results for dispersion curves and azimuthal variations of surface wave velocities to fully display Rayleigh-Love wave coupling in Kawasaki's (1986) azimuthally anisotropic model for the upper mantle beneath the Pacific ocean.
When Rayleigh-Love wave coupling takes place in a particular period range between a pair of nearby modes, surface waves display the following distinct singularities: (1) a difference of phase velocities of the pair of the modes is smaller than about 0.5 km/s, (2) a pair of dispersion curves of group velocities cross each other, (3) polarizations of particle motion directions are twisted along the pair of dispersion curves from Rayleigh- to Love-types and from Love- to Rayleigh-types. These sigularities are dependent on the relative depth- and azimuthal-distribution of the upper mantle anisotropy. When Rayleigh-Love wave coupling does not take place, the first-order perturbation theory works well.