A Unified Treatment of SKS Splitting and Surface-Wave Anisotropy for Media with Arbitrary Elastic Symmetry

Xiongwei Liu, Michael H Ritzwoller

SKS splitting and azimuthal anisotropy of surface-wave phase speed are two of the primary observational constraints on crustal and upper-mantle anisotropy, yet anisotropy models derived from surface waves commonly underpredict the magnitude of observed SKS splitting. We present a unified treatment of the two observables for weakly anisotropic media with arbitrary elastic symmetry. We derive a new first-order asymptotic theory relating anisotropy to SKS splitting intensity, validate it against numerical simulations, and compare it directly with quasi-degenerate surface-wave theory that includes Rayleigh--Love coupling. Including Rayleigh--Love coupling in the surface-wave theory used to interpret azimuthal anisotropy changes the inferred elastic tensor in ways that can strongly affect predicted SKS splitting. We demonstrate these effects using surface-wave and SKS observations and anisotropy models from Alaska. First, accounting for Rayleigh--Love coupling produces substantially larger $G_{c,s}$, increasing splitting intensity even for vertically incident SKS waves. Second, at the small non-zero incidence angles characteristic of SKS propagation, the parameters $K_{c,s}$, $M_{c,s}$, and $D_{c,s}$, which are important for Rayleigh--Love coupling in surface-wave theory, also contribute directly to SKS splitting, with $M_{c,s}$ particularly important. We show that at five example points in Alaska, a surface-wave anisotropy model derived using theory that includes Rayleigh--Love coupling reproduces the observed SKS splitting intensities. A reference model constructed without accounting for coupling systematically underpredicts them. Both models reproduce the fast-axis orientations reasonably well. We conclude that neglecting Rayleigh--Love coupling in surface-wave inversions can lead to substantial underestimation of the anisotropy relevant to SKS splitting, particularly where Rayleigh--Love coupling is strong, which may help explain the apparent need for anisotropy below the depth range sampled by surface waves.