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).