Comparing ray-theoretical and finite-frequency teleseismic traveltimes: implications for constraining the ratio of S-wave to P-wave velocity variations in the lower mantle

A number of seismological studies have indicated that the ratio R of S-wave and P-wave velocity perturbations increases to 3–4 in the lower mantle with the highest values in the large low-velocity provinces (LLVPs) beneath Africa and the central Pacific. Traveltime constraints on R are based primarily on ray-theoretical modelling of delay times of P waves (ΔT_P) and S waves (ΔT_S), even for measurements derived from long-period waveforms and core-diffracted waves for which ray theory (RT) is deemed inaccurate. Along with a published set of traveltime delays, we compare predicted values of ΔT_P, ΔT_S, and the ΔT_S/ΔT_P ratio for RT and finite-frequency (FF) theory to determine the resolvability of R in the lower mantle. We determine the FF predictions of ΔT_P and ΔT_S using cross-correlation methods applied to spectral-element method waveforms, analogous to the analysis of recorded waveforms, and by integration using FF sensitivity kernels. Our calculations indicate that RT and FF predict a similar variation of the ΔT_S/ΔT_P ratio when R increases linearly with depth in the mantle. However, variations of R in relatively thin layers (< 400 km) are poorly resolved using long-period data (T > 20 s). This is because FF predicts that ΔT_P and ΔT_S vary smoothly with epicentral distance even when vertical P-wave and S-wave gradients change abruptly. Our waveform simulations also show that the estimate of R for the Pacific LLVP is strongly affected by velocity structure shallower in the mantle. If R increases with depth in the mantle, which appears to be a robust inference, the acceleration of P waves in the lithosphere beneath eastern North America and the high-velocity Farallon anomaly negates the P-wave deceleration in the LLVP. This results in a ΔT_P of about 0, whereas ΔT_S is positive. Consequently, the recorded high ΔT_S/ΔT_P for events in the southwest Pacific and stations in North America may be misinterpreted as an anomalously high R for the Pacific LLVP.