1. Introduction
Recordings of long-period (T > 10 s) shear waves are useful
data to map seismic discontinuities and velocity gradients in the mantle
transition zone (MTZ) (e.g., Shearer, 1990). The mineral-phase
transitions near depths of 410 and 660 km produce the highest amplitude
shear-wave reflections from the mantle after the ScS wave arrival (e.g.,
Shearer & Buehler, 2019), before the SS arrival (e.g., Flanagan &
Shearer, 1998), and between multiple ScS reflections (e.g., Revenaugh &
Jordan, 1991) in stacks of transverse-component seismograms. We call
these boundaries the “410-km discontinuity” and “660-km
discontinuity” in this paper and define the MTZ as the layer of the
mantle between the 410-km and 660-km discontinuities. The depths of the
410-km and the 660-km discontinuities and the thickness of the MTZ
constrain the temperature and composition of the mantle (e.g., Bina &
Hellfrich, 1994; Xu et al. 2008) and heat and mass transfer between the
upper and lower mantle.
Most seismological studies of hundreds to thousands of waveforms are
based on 1-D seismic reference profiles and ray theory to facilitate the
analysis and computations. However, long-period shear waves are
sensitive to seismic inhomogeneities in the mantle beyond the geometric
ray so ray-theoretical calculations of traveltimes and waveform shifts
may be inaccurate (e.g., Tromp et al. 2005). Modeling inaccuracies have
been discussed thoroughly for the SS wave and its precursors (e.g.,
Neele et al. 1997; Zhao & Chevrot, 2003; Bai et al. 2012; Guo & Zhou,
2020; Koroni & Trampert, 2016, 2021), but they exist for all
long-period seismic wave reflections and conversions in the MTZ,
including the multiple ScS reverberations (e.g., Haugland et al. 2020)
and receiver functions (e.g., Deng & Zhou, 2015).
The receiver-side shear-wave reverberation in the upper mantle is the
phase of interest in this paper. It has been introduced by Shearer &
Buehler (2019), a study we abbreviate as SB19 from hereon, as a new wave
type for probing the upper mantle and the MTZ. Using USArray waveforms
and a common-reflection-point (CRP) imaging method, SB19 estimated the
depths of the 410-km and 660-km discontinuities to be 40–50 km deeper
beneath the western US than beneath the central and eastern US. This is
an important study outcome as it implies that the seismic contrast in
the upper mantle beneath the tectonically active western US and
tectonically stable central and eastern US extends into the MTZ.
SB19 used ray theory and the 1-D iasp91 velocity model to relate
traveltimes to reflector depths. They acknowledged that 3-D seismic
velocity heterogeneity may have a significant effect on the amplitude,
coherence, and depths of the 410-km and the 660-km discontinuities in
the CRP images. In this paper, we follow up on their recommendation to
investigate how 3-D velocity structure changes the interpretation of CRP
imaging results and to test the hypothesis that the 410-km and 660-km
discontinuities beneath the US are unperturbed. In Section 2, we confirm
that the 410-km and 660-km discontinuities are 40–50 km deeper beneath
the western US than the central-eastern US if the traveltime analysis is
based on a 1-D reference structure. In Section 3, we explore how
strongly 3-D shear-velocity inhomogeneities, as constrained by
shear-wave velocity tomography, perturb reverberation traveltimes and
how ray-theoretical traveltime corrections change the CRP images. In
Section 4, we use spectral-element method seismograms to evaluate the
accuracy of ray theory in predicting the reverberation traveltimes and
whether undulations on the 410-km and 660-km discontinuities are
resolvable by long-period shear wave reflections (section 4). In section
5, we discuss our key findings.