5. Discussion and conclusions
The receiver-side S wave reverberation, denoted as Ssds, is a useful data type to map the shear velocity structure in the upper mantle, including undulations of the 410-km and 660-km discontinuities of mineral phase transitions. Ssds complements SS precursor and P-to-S wave conversion (i.e., receiver function) imaging of the mantle because of its unique wave path geometry. In agreement with the analysis by SB19, we observe in record sections of waveform stacks that the Ss410s-S and Ss660s traveltime differences vary by up to 10 s across stations from the USArray. If the traveltime differences are attributed entirely to undulations on the 410-km and 660-km discontinuities, it implies that the 410-km and 660-km discontinuities are 40–50 km deeper beneath the western US than the central and eastern US. In turn, this would mean that the contrast between the tectonically active western US and the stable central and eastern US persists as a temperature or compositional contrast in the mantle transition zone and that there is a link between uppermost mantle and mantle transition zone dynamics.
However, the correlation between the resolved depth of the 410-km discontinuity (and the 660-km discontinuity) and tomographic maps of the shear-velocity structure in the upper mantle is high. This indicates that velocity heterogeneity in the uppermost mantle contributes significantly to the Ss410s-S and Ss660s-S traveltimes and the spatial variations of the depth of the 410-km discontinuity inferred from CRP imaging. Ray-theoretical corrections of traveltimes for velocity heterogeneity by shifting segments of the waveforms containing Ss410s and Ss660s prior to CRP stacking reduce the variation in the depth of the 410-km discontinuity by a factor of two.
For at least two reasons we find ray-theoretical corrections imprecise. First, seismic tomography has uncertainties. Global models S40RTS, SEMUCB-WM1, and TX2015 agree on the east–west contrast but disagree on the magnitude of the traveltime perturbations (see Figure 4). Each model underestimates the S-wave traveltime delay at USArray stations (see Figure 5) which is consistent with the fact that tomographic models underestimate the magnitude of traveltime and waveform perturbations. Hence, the effect on the estimated depths of the 410-km and 660-km discontinuities depends on the chosen tomographic model. SB19 notes that the traveltime corrections may introduce incoherence in the CRP images and use that as a factor in determining the value of traveltime corrections.
Second, our experiments with spectral-element method synthetics demonstrate that ray-theoretical predictions of the Ss410s-S and Ss660s traveltime differences are inaccurate. CRP images derived from waveforms computed for a mantle with 3-D velocity heterogeneity and horizontal phase boundaries show the expected deepening of the 410-km and 660-km discontinuities below the western US and shallowing beneath the central and eastern US where the shear velocities are relatively low and high, respectively. After applying traveltime corrections for the 3-D wave speed structure, the 410 and 660 remain undulating boundaries. In fact, the 410-km and the 660-km discontinuities in the corrected CRP image are deeper beneath the central-eastern US than beneath the western US, opposite to the uncorrected CRP image. This indicates that ray theory overpredicts the Ssds-S difference time by about a factor of two. This is the case for S40RTS, SEMUCB-WM1, and TX2015 and presumably also finer-scale regional tomographic models when finite-frequency effects are stronger. The inaccuracy of ray-theoretical predictions of the traveltime perturbations of long-period waves has been studied previously. For example, Neele et al. (1997) and Zhao & Chevrot (2003) have pointed out that for the broad SS sensitivity kernels at the reflection points on the surface or the mantle discontinuities. Bai et al. (2012) and Koroni & Trampert (2016) illustrate how the finite wave effects affect CRP images built from SS precursors similarly to the study here.
Finally, we note that the resolution of the depths of the 410-km and 660-km discontinuities depends on spatial scales of the undulations. Our experiments with spectral element method synthetics indicate that the Ssds-S traveltime difference is sensitive to 5° × 5° and 8° × 8° sinusoidal variations of the depths of the 410-km and 660-km discontinuities albeit that the height of the undulations is underestimated. Spatial variations of the 410-km and 660-km discontinuities on a 2° × 2° scale are not resolvable because such variations are smaller than the width of the Fresnel zone of Ssds at a period of 10 s.
Although it is beyond the scope of this work, it is better to simultaneously estimate the topography of the 410-km and 660-km discontinuities and shear velocity heterogeneity in the mantle of multiple data sets (e.g., Gu et al. 2003, Moulik and Ekström, 2014) using finite-frequency kernels that relate waveform perturbations to velocity heterogeneity and phase boundary topography (e.g., Guo & Zhou, 2020) or, preferably, using an adjoint tomography approach (Koroni & Trampert, 2021). Based on our experiments, the evidence for large-scale variations of the depth of the 410-km discontinuity beneath the USArray is weak. As is well established, estimates of the thickness of the MTZ are not affected strongly by shear velocity heterogeneity. We find the thickness of the MTZ to vary by about 10 km, which is consistent with the receiver-function study of USArray data by Gao & Liu (2014) and much smaller than global variations of the MTZ observed in SS precursors studies (e.g., Flanagan & Shearer, 1998; Chambers et al. 2005).