Rayleigh-Love coupling is a diagnostic tool for detecting anisotropic lateral structure in the upper mantle. The inference of mantle anisotropy, however, is complicated by the 21 independent parameters to be constrained in the fourth-order elastic tensor. We simplify the elastic tensor to possess hexagonal symmetry about an arbitrary axis, a reasonable first-order model for deformed peridotite. The elastic tensor in this case is determined by the orientation of the symmetry axis and five linear coefficients that can be related to the Backus/Crampin equations for the azimuthal dependence of head wave velocity in marine refraction. Three anisotropic parameters B, C, and E govern the P wave cos 2&xgr;, cos 4&xgr;, and SV wave cos 2&xgr; terms, respectively, where &xgr; is the angle from the symmetry axis.

We estimate coupling interaction between pairs of seismic free oscillations using zonally symmetric lateral structure models with angular wavenumber s. Zonally symmetric models afford computational simplicity and emphasize forward scattering interaction. For mode pairs with angular degrees l, l', coupling interaction tends to peak near s-‖l-l'‖ and s=l+l'. For mode pairs with f≲20 mHz from distinct dispersion branches, particularly fundamental spheroidal and toroidal modes, the sensitivity to smooth isotropic lateral structure is very weak relative to anisotropic lateral structure. Sensitivity to the P wave cos 2&xgr; coefficient B tends to peak near the crust-mantle interface, suggesting poor potential for depth resolution. Sensitivity to C and E for fundamental and first overtone modes, however, often peaks at 100- to 250-km depth and is often maximal for symmetry axes oriented between the vertical and horizontal. The parameter C≲0.01 is small and weakly constrained in most estimates from seismic data and mineralogical studies. The parameter E=0.01-0.03 in most estimates, and shear wave splitting studies argue for significant shear anisotropy in the uppermost mantle. Therefore it appears that S wave anisotropy is the likely tool for constraining global-scale mantle deformation in the deep lithosphere and asthenosphere with coupled-mode surface wave anomalies. ¿ American Geophysical Union 1993