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

Xiongwei Liu, Michael H Ritzwoller

Observations of SKS splitting and surface-wave azimuthal anisotropy are two of the primary geophysical constraints on crust and upper-mantle anisotropy, yet the two methods often yield apparently inconsistent inferences about the strength and vertical extent of anisotropy. Here we show that neglecting anisotropy parameters associated with Rayleigh-Love coupling is an important and largely overlooked contributor to this discrepancy. We present a unified treatment of SKS splitting and surface-wave anisotropy. Specifically, we derive a new asymptotic expression for SKS splitting in weakly anisotropic media with arbitrary symmetry, validate it against numerical simulations, and compare it directly with quasi-degenerate surface-wave anisotropy theory. We demonstrate that the same anisotropy parameters associated with Rayleigh-Love coupling also enter SKS splitting predictions, linking the two observables within a common formalism. Because these parameters influence both observables, neglecting Rayleigh-Love coupling in surface-wave inversions can bias estimates of mantle anisotropy and lead to under-prediction of SKS splitting. Example observations from Alaska show that surface-wave inversions that account for Rayleigh-Love coupling produce stronger inferred mantle anisotropy and substantially reduce the depth extent required to explain SKS splitting, thereby helping to resolve an apparent inconsistency between surface-wave and SKS observations.