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.