The limits of ray theory when measuring shear wave splitting in the lowermost mantle with ScS waves

Observations of shear wave splitting provide unambiguous evidence of the presence of anisotropy in the Earth's lowermost mantle, a region known as D-aEuro3. Much recent work has attempted to use these observations to place constraints on strain above the core-mantle boundary (CMB), as this may help map flow throughout the mantle. Previously, this interpretation has relied on the assumption that waves can be modelled as infinite-frequency rays, or that the Earth is radially symmetric. Due to computational constraints it has not been possible to test these approximations until now. We use fully 3-D, generally anisotropic simulations of ScS waves at the frequencies of the observations to show that ray methods are sometimes inadequate to interpret the signals seen. We test simple, uniform models, and for a D-aEuro3 layer as thin as 50 km, significant splitting may be produced, and we find that recovered fast orientations usually reflect the imposed fast orientation above the CMB. Ray theory in these cases provides useful results, though there are occasional, notable differences between forward methods. Isotropic models do not generate apparent splitting. We also test more complex models, including ones based on our current understanding of mineral plasticity and elasticity in D-aEuro3. The results show that variations of anisotropy over even several hundred kilometres cause the ray-theoretical and finite-frequency calculations to differ greatly. Importantly, models with extreme mineral alignment in D-aEuro3 yield splitting times not dissimilar to observations (delta t a parts per thousand 3 s), suggesting that anisotropy in the lowermost mantle is probably much stronger than previously thought-potentially similar to 10 per cent shear wave anisotropy or more. We show that if the base of the mantle is as complicated as we believe, future studies of lowermost mantle anisotropy will have to incorporate finite-frequency effects to fully interpret observations of shear wave splitting.