Volume 4, Issue 6 e2023AV001014
Research Article
Open Access

Strong Physical Contrasts Across Two Mid-Lithosphere Discontinuities Beneath the Northwestern United States: Evidence for Cratonic Mantle Metasomatism

Tianze Liu

Corresponding Author

Tianze Liu

Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, UC San Diego, La Jolla, CA, USA

Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Falmouth, MA, USA

Correspondence to:

T. Liu,

[email protected]

Contribution: Conceptualization, Methodology, Software, Validation, Formal analysis, ​Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization

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Emily J. Chin

Emily J. Chin

Geosciences Research Division, Scripps Institution of Oceanography, UC San Diego, La Jolla, CA, USA

Contribution: Validation, ​Investigation, Writing - review & editing, Visualization, Supervision

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Peter Shearer

Peter Shearer

Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, UC San Diego, La Jolla, CA, USA

Contribution: Conceptualization, Methodology, Validation, ​Investigation, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition

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First published: 11 December 2023

Peer Review: The peer review history for this article is available as a PDF in the Supporting Information.

Abstract

Mid-lithosphere discontinuities are seismic interfaces likely located within the lithospheric mantle of stable cratons, which typically represent velocities decreasing with depth. The origins of these interfaces are poorly understood due to the difficulties in both characterizing them seismically and reconciling the observations with thermal-chemical models of cratons. Metasomatism of the cratonic lithosphere has been reported by numerous geochemical and petrological studies worldwide, yet its seismic signature remains elusive. Here, we identify two distinct mid-lithosphere discontinuities at ∼87 and ∼117 km depth beneath the eastern Wyoming craton and the southwestern Superior craton by analyzing seismic data recorded by two longstanding stations. Our waveform modeling shows that the shallow and deep interfaces represent isotropic velocity drops of 2%–8% and 4%–9%, respectively, depending on the contributions from changes in radial anisotropy and density. By building a thermal-chemical model including the regional xenolith thermobarometry constraints and the experimental phase-equilibrium data of mantle metasomatism, we show that the shallow interface probably represents the metasomatic front, below which hydrous minerals such as amphibole and phlogopite are present, whereas the deep interface may be caused by the onset of carbonated partial melting. The hydrous minerals and melts are products of mantle metasomatism, with CO2-H2O-rich siliceous melt as a probable metasomatic reagent. Our results suggest that mantle metasomatism is probably an important cause of mid-lithosphere discontinuities worldwide, especially near craton boundaries, where the mantle lithosphere may be intensely metasomatized by fluids and melts released by subducting slabs.

Key Points

  • Two mid-lithosphere discontinuities at ∼87 and ∼117 km depth exist beneath the eastern Wyoming craton and southwestern Superior craton

  • The shallow and deep interfaces represent isotropic velocity drops of 2%–8% and 4%–9%, respectively

  • The shallow and deep interfaces may represent the metasomatic front and the onset of carbonated partial melting, respectively

Plain Language Summary

Based on xenolith and seismic-tomography evidence, the mantle lithospheres of stable cratons were commonly believed to be contiguous bodies with low temperatures and low content of volatile and incompatible elements, which are critical for the longevity of cratons. Nonetheless, in recent decades, many studies using converted and reflected seismic waves detected interfaces typically representing significant seismic-velocity reductions with depth within the mantle lithosphere of many cratons globally (“mid-lithosphere discontinuities” or MLDs). The sizes of the velocity reductions at the MLDs usually require the presence of significant volumes of hydrous minerals or even volatile-rich partial melts, which challenges the canonical compositional model of cratonic mantle lithospheres. The volatile-bearing phases causing MLDs likely originate from mantle metasomatism, a process widely documented yet poorly understood due to limited xenolith evidence. Here, we conduct a detailed case study of the MLDs beneath the northwestern United States and find that the two MLDs beneath the study area can be explained with a metasomatic front and the onset of carbonated partial melting, which are likely products of melt-assisted mantle metasomatism. Our results suggest mantle metasomatism as a likely origin of MLDs and the possibility of using seismic techniques to better characterize mantle metasomatism beneath cratons.

1 Introduction

Cratons are long-lived continental blocks having experienced little internal deformation since their formation in the Precambrian. The longevity of cratons has been attributed to their mantle lithosphere having: (a) a high viscosity due to low temperatures and low water content, which resists convective removal, and (b) neutral buoyancy due to chemical depletion, which inhibits subduction (Sleep, 2005). The low temperatures of cratonic mantle lithospheres have been inferred as high-velocity, low-attenuation bodies by numerous seismic tomography studies (e.g., Dalton et al., 2008; Panning & Romanowicz, 2006; Schaeffer & Lebedev, 2013), and the chemically depleted nature of cratonic mantle lithospheres is revealed by global mantle xenolith data (Lee et al., 2011). These results have established high seismic velocities and high degrees of chemical depletion as two hallmarks of the lithospheric mantle beneath cratons.

However, a growing body of evidence across different disciplines is challenging the canonical view that cratonic mantle lithospheres are contiguous bodies with high seismic velocities and high degrees of chemical depletion: Seismological studies employing different types of scattered-wave methods consistently detect discontinuities within the mantle lithospheres beneath cratons, usually defined as the depth extent of the high-velocity anomaly in seismic tomography models, across different continents (e.g., Abt et al., 2010; Ford et al., 20102016; S. M. Hansen et al., 2015; Krueger et al., 2021; T. Liu & Shearer, 2021; Miller & Eaton, 2010; Savage & Silver, 2008; Sodoudi et al., 2013; Tharimena et al., 2017; Wirth & Long, 2014), although a recent study doubted the existence of such interfaces beneath the contiguous U.S. (Kind et al., 2020). These intra-lithosphere interfaces are commonly termed mid-lithosphere discontinuities (MLDs) and are found to predominantly represent velocity reductions with depths up to 12% (Wölbern et al., 2012), which suggests that cratonic mantle lithospheres contain fine-scale structures beyond the resolution of typical tomography images. On the other hand, metasomatism of cratonic mantle lithospheres caused by hydrous fluids or siliceous melts has been documented globally based primarily on mantle xenolith data (e.g., Bell et al., 2005; Carlson et al., 2004; Downes et al., 2004; Ionov et al., 2006; Pearson et al., 1995; Simon et al., 2007), suggesting that mantle metasomatism is likely pervasive beneath cratons and thus has a profound effect on the internal structures of their mantle lithospheres.

Mantle metasomatism can reduce the seismic velocities of cratonic mantle lithosphere by precipitating low-velocity hydrous and carbonate minerals (e.g., amphiboles, phlogopite, and magnesite) and thus has been proposed as a possible cause of MLDs by some seismological studies (e.g., Krueger et al., 2021; Rader et al., 2015; Selway et al., 2015; Wölbern et al., 2012). Specifically, the global survey of Krueger et al. (2021) showed a correlation between MLD detection and thermotetonic ages of cratons, providing evidence for a metasomatism origin of MLDs. A recent series of experimental investigations further established the stability pressure-temperature fields of amphiboles, phlogopite, magnesite, and carbonated melt in cratonic mantle lithospheres fluxed by various metasomatic reagents (e.g., CO2-H2O-rich melts and CO2-rich aqueous fluids; Saha & Dasgupta, 2019; Saha et al., 20182021). Nonetheless, seismic observations have shown that MLDs are spatially highly variable in both depth and amplitude beneath the contiguous U.S. (T. Liu & Shearer, 2021) and around the globe (Krueger et al., 2021), suggesting that MLDs in different regions likely have distinct origins closely associated with regional tectonic evolution. Therefore, the connection between the origins of MLDs and mantle metasomatism can only be confidently established through case-by-case studies incorporating local geophysical and petrological observations and mineral-physical constraints, an outstanding research gap waiting to be filled.

In addition to causing MLDs, mantle metasomatism likely plays a key role in the evolution of cratons. The introduction of fluids and metasomatic minerals can significantly weaken cratonic mantle lithospheres and thus facilitate their removal by mantle convection, plumes, and slab subduction, which could lead to the destruction of cratons (Lee et al., 2011). The metasomatic density reduction in a certain depth range of the cratonic mantle lithosphere could cause density inversions (high-density materials over low-density materials), which could also destabilize cratonic lithospheres and thus promote their convective removal, similar to the effects of ecologitized lower crusts (Hacker et al., 2015). Understanding the global prevalence of these processes requires constraints on the spatial extent of mantle metasomatism, which are traditionally difficult to acquire due to the scarcity and uneven distribution of mantle-xenolith samples. Therefore, using seismically observed MLDs as proxies for mantle metasomatism can improve understanding of the role played by mantle metasomatism in the life cycles of continents. Achieving this goal also requires a better understanding of the connection between MLDs and mantle metasomatism.

Here, we conduct a detailed case study of the northwestern U.S. cratons to establish the connection between MLDs and mantle metasomatism. We first image two distinct MLDs beneath two longstanding stations located in the eastern Wyoming craton and southwestern Superior craton using teleseismic SH reverberations. We then associate the two MLDs with different metasomatic phases using a regional thermal-chemical model that incorporates xenolith thermobarometry constraints and experimental phase-equilibrium data and discuss the implications of our findings on the study of MLDs and craton evolution.

2 Seismic Characterizations of the MLDs

2.1 Data and Methods

We use seismic waveform data recorded by two longstanding stations RSSD and ECSD located in the eastern Wyoming craton and southwestern Superior craton, respectively (near the western and eastern borders of the state of South Dakota; Figures 1a and 1b). We choose the two stations for four reasons: (a) They are permanent stations with high data quality and long recording times (>15 years), providing large numbers of earthquake records to form stable waveform stacks. (b) They are located on two different Archean cratons (Figures 1a and 1b) and thus enable us to resolve potential lateral variations in lithospheric structure within the North American craton. (c) Eilon et al. (2018) presented one-dimensional (1D) velocity profiles down to 300 km depth for the two stations (hereafter “EFD18”) estimated using a joint inversion of P-receiver functions (PRFs), S-receiver functions (SRFs), and Rayleigh-wave dispersion data. These models provide us with reference velocity models to map the waveform stacks from the time domain to the depth domain and also offer the opportunity to directly compare our MLD images with those from previous studies. (d) The waveform stacks of the two stations from two narrow back-azimuth windows nearly 90° apart (southwest and northwest) show consistent features in the time windows corresponding to the lithosphere mantle (Figures 2c and 2d), suggesting little contribution from azimuthal anisotropy and lateral heterogeneity. These observations allow us to model the observed waveforms using 1D velocity models with vertical transverse isotropy (VTI), the simplest form of seismic anisotropy (see Section 10 for details).

Details are in the caption following the image

Summary of the station and xenolith locations, key geological boundaries, and our seismic observations. (a) Locations of RSSD and ECSD and boundaries of Archean (dark pink) and Proterozoic (light pink) terrains of North America. The Midcontinent Rift is shown in purple. Red box: boundary of the close-in map in (b). (b) Close-in map showing the location of the stations and Homestead (H) and Williams (W) mantle xenoliths. The terrain boundaries in (a, b) are simplified from Whitmeyer and Karlstrom (2007). (c) Depth-domain SH-reverberation stacks produced using all available events for RSSD (left) and ECSD (right). Blue and red denote impedance increases and decreases with depth, respectively. Gray curve: Vs models from EF18.

Details are in the caption following the image

Summary of the method and the event locations, waveform stacks, and reflection-point distribution of different back-azimuth windows. (a) Schematic of the difference between using shallow and deep events for SH-reverberation studies. Solid and dashed curves: ray paths of the deep and shallow events, respectively. (b) Distribution of the events used for our analysis. Blue, green, and white circles: events of the southwest-Pacific group, northwest-Pacific group, and others, respectively. (c, d): time-domain waveform stacks (left) and event back-azimuth distributions (right) for RSSD and ECSD, respectively. The vertical scale of the window containing the Moho and MLD reverberations is increased by 10 times to better show the weak signals. Thick and thin wiggles: the stacks and corresponding uncertainties, respectively. Blue, green, and black wiggles: stacks for the southwest-Pacific group, northwest-Pacific group, and all events, respectively. (e) and (f): Locations of the SH-reverberation reflection points (blue, green, and white circles) at 100 km depth for RSSD and ECSD, respectively. The reflection points of the three event groups are colored accordingly.

We use the teleseismic SH-reverberation method to image the structures above 175 km depth beneath RSSD and ECSD (Shearer & Buehler, 2019; T. Liu & Shearer, 2021). Specifically, we use only events deeper than 175 km to eliminate the ambiguity between source-side and receiver-side scattering (Figure 2a) following T. Liu and Shearer (2021). We filter the SH-component waveforms to below 0.1 Hz, align the traces to their S arrival times, and remove traces with low signal-noise ratios, prolonged source wavelets, and abnormally strong coda energy (see T. Liu and Shearer (2021) for details about the data-processing workflow). Because ScS arrives in the same time window as the reverberation phases for lithospheric discontinuities in the epicentral distance range 65–85° (Figure 4a in T. Liu and Shearer (2021)), we further remove the events in this distance range to minimize the interference of ScS. At the expense of reducing the number of available events, this procedure is likely more effective in reducing ScS contamination and avoids possible processing artifacts compared to muting ScS energy using predicted travel times as applied in T. Liu and Shearer (2021). We then map the traces from the time domain to the depth domain using EFD18 and stack them linearly to form the depth-domain stacks in Figure 1c. We hereafter term arrivals representing impedance increasing with depth “positive” and color them blue, and arrivals representing impedance decreasing with depth “negative” and color them red (Figure 1c). Because we directly stack the traces without applying source normalization as in receiver-function techniques, the reference pulses of our stacks have sidelobes that vary with the traces included in the stacks (Figures 1c2c, and 2d). Nonetheless, the reference pulses can be estimated from the observed waveforms and used to generate synthetic waveforms for waveform modeling (Section 9).

2.2 Observations

2.2.1 Overview

The depth-domain stacks of both stations show a positive peak at ∼50 km depth, although the peak of RSSD is very weak and barely distinguishable from the trailing sidelobe of the reference pulse (Figure 1c). The depths of these peaks agree very well with the Moho depths in EFD18 (gray curves in Figure 1c) and thus likely represent the Moho beneath the two stations.

Below the Moho at RSSD, we observe a strong and broad negative arrival at 50–100 km consisting of two peaks at ∼60 km and ∼85 km depth (Figure 1c). Considering the width of the trailing sidelobe of the reference pulse, the shallow negative peak may largely consist of the Moho sidelobe, but the deep negative peak is unlikely to be affected by the sidelobe and thus likely represents a negative interface at ∼85 km depth (Figure 1c). Below this interface, we observe another distinct yet weak negative arrival at ∼115 km depth, which likely represents a deeper negative interface (Figure 1c). At greater depths, we observe a positive arrival followed by a negative arrival. We refrain from interpreting these arrivals because event hypocenter errors and the finite widths of ScS and sS arrivals may cause their energy to leak into the bottom part of the image. At ECSD, we observe a negative peak at ∼85 km, which is too far away from the Moho to be its sidelobe and thus likely represents a negative interface (Figure 1c). Immediately below this interface, we observe a positive peak, which could partly be due to the sidelobe of the negative phase above it. At greater depths, we observe a strong negative arrival at ∼120 km and a weaker one at ∼150 km (Figure 1c). Following the argument for RSSD, we interpret the former as a negative interface at ∼120 km while leaving the interpretation of the latter open. We will hereafter refer to the two negative interfaces with definitive interpretations beneath the two stations as “MLD1” and “MLD2,” respectively, because they likely reside within the lithosphere as defined by the high-velocity region extending to ∼200 km depth beneath the North America cratons (e.g., Schaeffer & Lebedev, 2013).

2.2.2 Comparison With Previous Studies

Although our Moho depths at both stations agree well with those from EFD18, our mantle structures appear to be significantly different. At RSSD, our results show at least two distinct negative interfaces at ∼85 km and ∼115 km depth, whereas EFD18 shows a broad negative velocity gradient zone between the Moho and ∼100 km depth, with the strongest gradient immediately below the Moho (Figure 1c). This broad negative velocity gradient zone is underlain by an equally broad velocity recovery zone extending to ∼150 km depth. Lateral heterogeneity might contribute to the disagreement between our results and EFD18 given that our events are primarily from the northwest and southwest (Figure 2), whereas the SRF events used for constructing EFD18 are from the southeast (Eilon et al., 2018). Intriguingly, the depths of our two MLDs beneath RSSD appear to agree with the two MLDs identified on the SRF stacks of Krueger et al. (2021), although the two SRF MLDs are detected on the stacks of two different back-azimuth groups (Figure 6b in Krueger et al. (2021); the back-azimuth group RSSD1 in Krueger et al. (2021) overlaps with our northwest-Pacific group.) Our results are more consistent between different back-azimuth groups compared to Krueger et al. (2021), probably because the reflection-point-station distances of SH reverberations are smaller (generally <50 km at 100 km depth; Figures 2e and 2f) compared to the conversion-point-station distances of SRFs (∼140 km at 100 km depth), which could cause the SRFs from different back azimuths to sample different structures. This reason was also used by Krueger et al. (2021) to explain the discrepancy between their results for the two back-azimuth groups. The discrepancy between EFD18 and the results of Krueger et al. (2021) is difficult to understand because the constraints on mantle discontinuities in both studies come from SRFs. A possible reason for this disagreement is that the S-to-P phases were processed differently in the two studies (see Eilon et al. (2018) and Krueger et al. (2021) for details), which highlights the importance of nuances in S-to-P data processing (see Section 20). In summary, at RSSD the general agreement on the depths of MLD1 and MLD2 between our results and those from Krueger et al. (2021) indicates that the two interfaces are real features instead of imaging artifacts.

At ECSD, we find two MLDs at ∼85 km and ∼120 km depth, whereas EFD18 showed two low-velocity layers bounded by broad velocity gradients with the maximum negative velocity gradients immediately below the Moho and at ∼120 km depth, respectively (Figure 1c). Our MLD2 thus may correspond to the deeper negative velocity gradient zone in EFD18, whereas our MLD1 does not seem to agree with EFD18 in the same depth range (Figure 1c). Krueger et al. (2021) did not identify any robust MLDs beneath ECSD, though their stack in Figure 6c appears to show a weak and broad negative peak at 125–145 km depth, which was not identified probably because the amplitude of the peak is below their prescribed uncertainty range. This peak may correspond to our MLD2 due to their similar depths. The disagreement between our results and the two SRF studies could also partially result from lateral heterogeneity because our events are mostly from the northwest and southwest, whereas those used by Eilon et al. (2018) and Krueger et al. (2021) are from the southeast.

We also compare our results with the PRF images at the two stations from Ford et al. (2016). The Moho depths estimated by Ford et al. (2016) at RSSD and ECSD are ∼53 km and ∼50 km respectively, consistent with our results (Figure 1c). Below the Moho, Ford et al. (2016) found two interfaces with significant negative azimuth-invariant components at ∼86 km and ∼139 km depths beneath RSSD and one such interface at ∼135 km depth beneath ECSD. The two interfaces beneath RSSD may correspond to our MLD1 and MLD2, and the interface beneath ECSD may correspond to our MLD2, though the depths of the deeper MLDs from Ford et al. (2016) are less consistent with the depths of our MLD2s possibly due to complexities in the velocity models used for converting time to depth. Ford et al. (2016) also resolved multiple interfaces below the Moho with significant azimuthal variation beneath the two stations, which appear to disagree with the azimuth-invariant feature of our waveform stacks (Figures 2b–2d).

Using the SS-precursor technique, Tharimena et al. (2017) imaged the LAB beneath the North America continental interior at a depth of 170–180 km and found no MLDs beneath North America, which appear to contradict our results (Figure 2 in Tharimena et al. (2017)). This discrepancy likely results from the use of waveform stacks from all SS records that bounced within the study area, which represents the 1D average lithosphere structure of the whole continent. The Tharimena et al. (2017) waveform stack thus may have failed to capture the MLDs beneath North America, which were shown to be spatially heterogeneous structures at least beneath the contiguous US (T. Liu & Shearer, 2021).

2.2.3 Evaluation of Azimuthal Variation

Since we use only events deeper than 175 km, the back azimuths of the events are limited to three narrow back-azimuth corridors containing three major subduction zones with deep slab penetration: South America, southwest Pacific, and northwest Pacific (Figures 2b–2d). Fortunately, the three back-azimuth windows are approximately 90° apart (Figures 2b–2d), allowing us to evaluate the degree of azimuthal variation of our observed MLD signals despite the poor back-azimuth coverage of our events. We choose to compare the waveform stacks of the southwest-Pacific (240–270°) and northwest-Pacific (300–330°) events because the two corridors contain the most events (Figures 2b–2d).

At RSSD, the sidelobes of the reference pulses are significantly different between the waveform stacks of the two event groups likely due to the different events included in the stacks (Figure 2c). The signals at 20–35 s, which include the Moho arrival and its sidelobe, also appear inconsistent between the two groups. This discrepancy may be due to lateral heterogeneity in Moho structures beneath the station (Figure 2c). Nonetheless, the waveforms at 35–60 s, which contain the arrivals of MLD1 and MLD2, are generally consistent between the two groups, although the northwest-Pacific stack shows more high-frequency variation and greater uncertainties likely due to its significantly lower stacking fold compared to the southwest-Pacific stack (Figure 2c). This contrast in azimuthal consistency between the Moho and MLD arrivals provides further evidence that the MLD signals are unlikely caused by Moho sidelobes. At 60–75 s, the discrepancy between the two stacks increases again, which could be due to anisotropy, lateral heterogeneity, or leakage of ScS and sS energy. We will not further discuss these features in this paper.

At ECSD, despite the differences in reference-pulse sidelobes, the stacks of the two back-azimuth groups show consistent Moho, MLD1, and MLD2 arrivals (Figure 2d), indicating a weaker degree of lateral heterogeneity compared to RSSD. In addition, the negative arrival at ∼65 s, which corresponds to the arrival at ∼150 km depth in the depth-domain stack, also appears to be consistent between the two back-azimuth groups, suggesting that it may also represent a negative interface without azimuthal variation (Figures 1c and 2d). Nonetheless, we choose not to interpret this feature due to possible contamination from ScS and sS. In summary, our azimuthal analysis indicates that MLD1 and MLD2 beneath the two stations can be modeled as azimuth-invariant negative interfaces. Therefore, we will hereafter only use the observed waveform stack computed using all events to compare with synthetic waveforms. We also caution that our results cannot eliminate the possibility of the presence of azimuthal anisotropy in the mantle beneath the two stations because (a) our events only have limited back-azimuth coverage (Figures 2c and 2d), and (b) some azimuthally anisotropic models may not show as strong manifestations for SH-reverberation observations as for other observations (e.g., PRF; Ford et al., 2010).

2.3 Waveform Modeling

2.3.1 Source Wavelets and Initial Models

To further constrain the size of velocity drops required to explain the MLDs beneath RSSD and ECSD, we compute synthetic waveforms using 1D isotropic and anisotropic velocity models and compare them with the observed waveforms. The synthetic waveforms are computed in two steps. First, we compute Green's functions using the reflectivity method (Kennett, 2009). Second, we estimate the source wavelet from the observed waveform and convolve it with the Green's function to produce the synthetic waveform. To estimate the source wavelet, we assume that the observed signal before a certain time (t0) consists solely of the source wavelet and that the source wavelet after t0 tapers to zero exponentially with a characteristic time tc (gray dotted curves in Figures 3b and 4b). Because the Moho phase arrives close to the reference pulse (Figures 2c and 2d), the choices of t0 and tc significantly affect the Moho phase on the synthetic waveforms. We thus estimate t0 and tc by fitting the synthetic Moho phases to the observed ones.

Details are in the caption following the image

Waveform-fitting for RSSD using 1D isotropic models. (a1, a2): Vs models. Light gray: reference models from EFD18. Dark gray: EFD18 models with smoothed Moho velocity gradients and homogenized mantle velocities. Yellow dotted and solid: best-fit models for the MLD1 window without and with enforcing a zero NVG thickness, respectively. Orange dotted and solid: best-fit models for the MLD2 window without and with enforcing a zero NVG thickness, respectively. Red dotted and solid: best-fit models for the combined window without and with enforcing a zero NVG thickness, respectively. (b) Observed and synthetic waveforms. Black thick and thin: observed waveform and uncertainty. Gray dotted: estimated source wavelet. Other colored waveforms: synthetic waveforms computed using the models with the same colors and styles in (a1, a2). Yellow and orange dotted vertical lines: time windows for computing the misfits for MLD1 and MLD2, respectively. (c1, c2): Misfit reductions as functions of percentage Vs drops and NVG thicknesses for MLD1 and MLD2, respectively. Yellow cross and arrow: best-fit parameter combinations for MLD1 without and with enforcing a zero NVG thickness, respectively. Orange cross and arrow: best-fit parameter combinations for MLD2 without and with enforcing a zero NVG thickness, respectively. Red crosses and arrows: parameter combinations for MLD1 and MLD2 for the combined window without and with enforcing a zero NVG thickness, respectively.

Details are in the caption following the image

Same as Figure 3, but for ECSD.

We first tried using EFD18 to compute the synthetic waveforms and found that the synthetics significantly overpredict the amplitudes of the Moho phase for both stations regardless of the t0 and tc choices, although the arrival times are relatively well captured (light gray solid curves in Figures 3b and 4b). We thus reduce the amplitude of the Moho phase while keeping its arrival time unchanged by replacing the sharp Moho in EFD18 with a linear velocity gradient zone spanning a depth range containing the Moho. We manually adjust the depth range of the Moho gradient zone, t0, and tc until a reasonable fit to the observed Moho phase is achieved. We then replace the mantle part of the model with a homogeneous half space having a velocity equal to the velocity immediately below the Moho (dark gray curves in Figures 3a1, 3a2, 4a1, and 4a2). We will use this model with a homogeneous mantle velocity as the initial model for building models with negative velocity gradient zones (NVGs) in the mantle. The companion source wavelet (dotted gray curves in Figures 3b and 4b) will be used to compute the synthetic waveforms for all models. Our initial models produce significantly weaker Moho phases than the EFD18 models for both stations, which are more consistent with our observed Moho phases (solid dark gray, light gray, and black curves in Figures 3b and 4b).

The more gradual Moho suggested by our SH-reverberation observations compared with EFD18 may be due to two reasons. First, the Moho in EFD18 is constrained using PRFs, whose Moho P-to-S conversion points are closer to the stations than the Moho reflection points of our SH-reverberation observations, causing PRFs to be less sensitive to lateral variations in Moho depth and sharpness, which likely has a smoothing effect on our Moho phases. This interpretation is supported by the apparent lateral variation in Moho structure shown by the stacks of events from two back-azimuth groups at RSSD (Figure 2c). Second, PRF conversion amplitudes are mostly sensitive to velocity contrasts across interfaces, whereas SH-reverberation amplitudes are sensitive to both contrasts in Vs and density. Therefore, a reduced density contrast across the Moho could weaken the SH Moho reflection without significantly affecting the P-to-S conversion. Such a reduced density contrast could be caused by ecologitization of the lower crust (Hacker et al., 2015).

2.3.2 Trade-Offs Between Model Parameters

In a stratified VTI medium, changes in anisotropy alone (no isotropic Vs drop) could cause negative SH reflections. Hereafter, we will define a medium with the velocity of horizontally traveling and horizontally polarized S waves (VSH) greater than that of horizontally traveling and vertically polarized S waves (VSV) as a medium with positive radial anisotropy. This parametrization of anisotropy is also commonly used in surface-wave studies (e.g., Panning & Romanowicz, 2006). An increase in radial anisotropy is thus defined as an increase in VSH − VSV. Here, we choose to characterize the amount of radial anisotropy using anisotropy amplitude a defined as the difference between VSH and VSV normalized by their mean (hereafter “average Vs V ¯ s ${\bar{V}}_{s}$ ):
a = V S H V S V V ¯ s = 2 V S H V S V V S H + V S V \begin{align*}\hfill a& =\frac{{V}_{SH}\,-\,{V}_{SV}}{{\bar{V}}_{s}}\hfill \\ \hfill & =\frac{2\left({V}_{SH}\,-\,{V}_{SV}\right)}{\left({V}_{SH}\,+\,{V}_{SV}\right)}\hfill \end{align*}
This definition was used by some studies analyzing anisotropic signatures of P-receiver functions (e.g., Schulte-Pelkum & Mahan, 2014). Another way of characterizing radial anisotropy is using the “radially anisotropic parameter” ξ defined as:
ξ = V S H 2 V S V 2 $\xi =\frac{{V}_{SH}^{2}}{{V}_{SV}^{2}}$
This definition is commonly used in surface-wave tomography studies (e.g., Panning & Romanowicz, 2006). It can be shown that:
ξ 1 + 2 a $\xi \approx 1+2a$
In Section 10, we will convert our estimated anisotropy amplitude as functions of depth to ξ to facilitate the comparison with previous tomography results. In VTI mediums, in addition to a or ξ, another parameter is needed to characterize the shape of the phase velocity surfaces. Here, we choose to use Kawakatsu's fifth parameter ηκ, which measures the deviation of the phase-velocity surfaces from an ellipse (Kawakatsu, 2016a). We will assume ηκ = 1, which indicates perfectly elliptical phase-velocity surfaces, for all our anisotropic models.

Our synthetic tests show that an increase in radial anisotropy with depth can also generate negative SH reflections similar to a decrease in isotropic Vs with depth (Figure 5a). Specifically, in the case of a zero gradient-zone thickness, a 7.5% increase in radial anisotropy generates almost the same reflection phase as a 5.0% decrease in isotropic Vs (solid red and purple curves in Figure 5a). This behavior can be conceptually understood using the phase-velocity and polarization surfaces (Figure 5b). In a VTI medium, the SH waves remain decoupled from the P and SV waves as in the case of isotropy, and the velocity of SH waves is reduced for near-vertically traveling waves (pumpkin-shaped velocity surface; Figure 5b). Because in SH reverberations, the incident angles of the downgoing waves are usually small (∼20° at the Moho), an increase in radial anisotropy with depth is equivalent to a decrease in isotropic Vs with depth and thus can also generate negative SH reflections. Therefore, a trade-off exists between the changes in isotropic Vs and radial anisotropy estimated from observed SH-reverberation waveforms, which needs to be considered in the waveform modeling (Section 10).

Details are in the caption following the image

Trade-offs between different factors in determining SH-reflection amplitude. (a) Synthetic SH-reverberation waveforms computed using various layer-over-half space models. Red: models with a 5% isotropic Vs drop in the half space. Purple: models with a 7.5% positive radial anisotropy (VSH > VSV) in the half space. Solid, dashed, and dotted: models with gradient-zone thicknesses of 0, 8, and 15 km. (b) Phase-velocity surfaces for the P, fast S (S1), and slow S (S2) waves in the medium with a 7.5% radial anisotropy. Gray bars: projections of S1 and S2 polarization directions onto the horizontal plane. Gray cross: zenith. (c) Same as (a) but for models with isotropic Vs drops and density drops. Red: same as red waveforms in (a). Brown: models with a 5% density drop in the half space.

In addition, density reductions across the MLDs may also contribute to the observed signals because SH-reflection amplitudes are controlled by contrasts in impedance, the product of Vs and density. Similar to the case with an increase in anisotropic amplitude, we compute synthetic waveforms using models with a 5% isotropic Vs drop or density drop over 0, 8, and 15 km depth and compare them (Figure 5c). The results show that the SH-reflection amplitude generated by the density drop is slightly higher than the one generated by the Vs drop given the same gradient-zone thickness and that the amplitude decreases with increasing gradient-zone thickness for both density and Vs drops (Figure 5c). We note that the degree of density drop assumed here may be unrealistic because a lithosphere with a high-density layer overlying a low-density one (density inversion) is gravitationally unstable and could lead to the convective removal of the dense layer (Jull & Kelemen, 2001). We will further discuss the trade-offs between Vs and density reductions across MLDs in Section 11 and the dynamic viability of models with density inversions in Section 22.

2.3.3 Isotropic Models

We first consider the simplest case where the observed MLD arrivals are caused only by isotropic Vs drops. To obtain the best-fitting models, we insert MLDs with various properties into our reference models, compute the synthetic waveforms, and compare them with the observations. Specifically, we assume that the mantle part of the model contains two MLDs represented by linear negative velocity gradients (NVGs) and a linear positive velocity gradient (PVG) between the two MLDs, with each velocity gradient parameterized by three parameters: depth, percentage velocity increase/decrease, and thickness. We then use a three-step grid-search method to find the best-fitting model. First, we assume that the model contains only MLD1 and search for its parameters that minimize the root-mean-square misfit (hereafter “misfit” for simplicity) in a 10 s window centered at the arrival time of the MLD1 arrival (40 s for both stations; yellow dashed lines in Figures 3b and 4b). The resulting best-fit models, waveforms, and parameter combinations are shown in yellow in Figures 3 and 4. Second, we assume that the model contains only MLD2 and search for parameters minimizing the misfit in a 10 s window centered at the arrival time of the MLD2 arrival (52.5 and 55 s for RSSD and ECSD, respectively; orange dashed lines in Figures 3b and 4b). The results are shown in orange in Figures 3 and 4. Third, we assume that the model contains both MLD1 and MLD2 with a PVG between them and fix the depth of MLD1 and thicknesses of MLD1 and MLD2 at the best-fit values found in the previous steps while searching for the parameters of the PVG that minimize the misfit in the time window enclosing both the windows for MLD1 and MLD2 defined in the previous steps (35–57.5 s and 35–60 s for RSSD and ECSD, respectively). Due to the finite widths of our reference pulses (Figures 3b and 4b), the amplitude of an MLD arrival may be affected by the addition of another one close in time. We thus search for the best-fit velocity drops at MLD1 and MLD2 again in a reduced range (±5%) around their previous best-fit values to obtain the final velocity-drop estimates for the two MLDs. The results of this final step are shown in red in Figures 3 and 4.

To explore the well-known trade-off between the velocity contrast across a gradient zone and its thickness in modeling scattered-phase amplitudes (e.g., Mancinelli et al., 2017), we plot the misfit as a function of Vs drop and gradient-zone thickness at Step One (MLD1) and Two (MLD2) for both stations, which shows strong trade-offs between the two parameters in all cases, with an increasing thickness requiring a greater velocity drop (Figures 3c1, 3c2, 4c1, and 4c2). We thus present two sets of parameter estimates for the two MLDs, one with no constraint on the gradient-zone thickness and the other with a zero gradient-zone thickness (first-order discontinuity). The results estimated without constraints on gradient-zone thickness are shown as dotted models and waveforms and crosses in Figures 3 and 4, whereas models with a zero gradient-zone thickness are shown as solid models and waveforms and arrows. Given the positive trade-off between the gradient-zone thickness and Vs drop, the Vs-drop estimate in the case of a first-order discontinuity can be regarded as the lower bound of the size of Vs drop required to explain our observations (Figures 3c1, 3c2, 4c1, and 4c2). We further define the uncertainty of our Vs-drop estimates as the range where the misfits are within 0.01 from the best estimate in the case of a first-order discontinuity (error bars in Figures 3c1, 3c2, 4c1, and 4c2). We choose 0.01 as the misfit threshold because it is the approximate uncertainty level of our waveform stacks (thick and thin black waveforms in Figures 3b and 4b). We acknowledge that we likely underestimate the true Vs-drop uncertainties with our uncertainty definition because it does not account for the trade-off between the gradient-zone thickness and Vs drop; we instead characterize the latter with our two sets of estimates with and without constraints on the gradient-zone thickness.

For RSSD, when the MLD thicknesses are allowed to vary, Step One gives an MLD1 centered at 86 km with a Vs drop of 15% and a thickness of 22 km (dotted yellow models in Figure 3a1 and yellow cross in Figure 3c1, which is covered by the red cross), and Step Two gives an MLD2 centered at 116 km with a Vs drop of 8% and a thickness of 0 km (dotted orange models in Figure 3a1, which is covered by the solid one, and orange cross in Figure 3c2). In Step Three, the PVG is estimated to have no velocity increase and a thickness of 14 km, yielding a final depth of 111 km for MLD2 (dotted red model in Figure 3a2). Step Three also increases the Vs drop at MLD2 to 11% (red cross in Figure 3c2) likely because the trailing sidelobe of the MLD1 arrival (dotted yellow waveform in Figure 3b) requires a greater amount of Vs drop at MLD2 to explain its amplitude. In contrast, when the MLD thicknesses are fixed at 0 km, Step One gives the same depth but a significantly smaller Vs drop of 8% for MLD1 (solid yellow model in Figure 3a1 and yellow arrow in Figure 3c1, which is covered by the red arrow), and Step Two gives the same depth and Vs drop for MLD2 (solid orange model in Figure 3a1 and orange arrow in Figure 3c2). Step Three does not change the Vs drops at the two interfaces (red arrows in Figures 3c1 and 3c2) and yields a zero Vs increase for the PVG and a final depth of 112 km for MLD2 (solid red model in Figure 3a2). For MLD1, the thick gradient zone with a greater Vs drop produces a slightly smaller misfit compared to the sharp gradient zone with a smaller Vs drop (Figure 3c1) likely because the former generates a broader arrival on the synthetic waveform, which is more consistent with the observation than the latter, although the difference between the two synthetic waveforms is largely within the uncertainty range of the observations (solid and dotted red waveforms in Figure 3b). This preference for a thicker gradient zone likely also causes the high uncertainty (±5%) for the Vs drop at MLD1 (Figure 3c1). In contrast, the best-fit gradient-zone thickness for MLD2 is zero even without explicit constraints likely due to the impulsive shape of the arrival (Figure 3b), which probably also causes the small Vs-drop uncertainty (±2%). In summary, at RSSD, MLD1 is possibly a thick gradient zone with a Vs drop greater than 8%, whereas MLD2 is likely a sharp discontinuity with a Vs drop of ∼8%.

For ECSD, when the MLD thicknesses are not fixed a priori, MLD1 is estimated to be at 88 km with a Vs drop of 5% and zero thickness, and MLD2 is constrained to be centered at 122.5 km with a Vs drop of 12% occurring over 17 km (Figures 4a2, 4c1, and 4c2). The PVG between the two MLDs is estimated to have a small Vs increase of 1% (dashed red model in Figure 4a2). When the MLD thicknesses are fixed at zero, the Vs drop at MLD1 is slightly reduced to 4%, whereas the Vs drop at MLD2 is significantly reduced to 9% with its depth slightly reduced to 122 km (Figures 4a2, 4c1, and 4c2). For MLD1, the misfits given by the parameter combinations in our searching range are generally greater than the other cases (Figure 4c1) likely because a positive peak at ∼35 s preceding the MLD1 arrival is not well fitted (Figure 4b). We speculate that this positive peak may be due to a positive velocity gradient between the Moho and MLD1, which is not included in our models. For simplicity, we will not attempt to fit this feature in this paper. The high misfit likely also causes the relatively large Vs-drop uncertainty (±4%) for MLD1 (Figure 4c1). For MLD2, the thick gradient zone with a greater Vs drop yields a slightly smaller misfit than the sharp discontinuity with a smaller Vs drop (Figure 4c2), although the difference between the two synthetic waveforms is hardly visible (solid and dotted red waveforms in Figure 4b). The uncertainty of the Vs drop at MLD2 is estimated to be ±3% (orange error bar in Figure 4c2). In summary, at ECSD, MLD1 is likely a sharp interface with a Vs drop of ∼4%, whereas MLD2 may also be relatively sharp with a minimum Vs drop of ∼9%.

Although we find the best-fitting Vs increases across the PVGs beneath the two stations to be below 1%, a greater amount of velocity increase across the PVG may only slightly degrade the waveform fit while significantly increasing the absolute Vs below MLD1. This adjustment could render our models more consistent with previous surface-wave studies, which generally showed high absolute Vs (>4.5 km s−1) in the depth range 120–150 km (e.g., Porter et al., 2016; Shen & Ritzwoller, 2016; Yuan et al., 2014). Adding a velocity recovery zone beneath MLD2 could also increase the average Vs at 120–150 km depth without significantly degrading the waveform fit. We thus perform tests by adding the above two types of velocity recovery zones to our best-fit models with zero MLD thicknesses (Figures S1 and S2 in Supporting Information S1). The results show that even allowing the velocity to completely recover in the depth range between the two MLDs and between MLD2 and 150 km depth only causes small changes to the synthetic waveforms, which are of the same order of magnitude as the uncertainties of our observed waveform stack (Figures S1 and S2 in Supporting Information S1). Therefore, significant velocity recoveries may be present between the two MLDs and below MLD2, and our waveform-fitting procedure may have underestimated the absolute Vs in the depth range containing the MLDs. Nonetheless, given that SH reverberations are only sensitive to sharp vertical changes in medium properties, we will only focus on constraining the medium-property contrasts across the MLDs in this paper. Fully retrieving the medium-property models beneath the two stations likely requires combining scattered-phase and surface-wave observations (Eilon et al., 2018), which will be the subject of future studies (Section 24).

2.3.4 Anisotropic Models

As mentioned in Section 8, both a reduction in isotropic Vs and an increase in radial anisotropy amplitude a can cause negative arrivals (Figure 5). We thus quantify the trade-off between the two factors by fitting the observed waveforms using various 1D VTI models (Figure 6). The synthetic waveforms are computed using the open-source software Aniplane.jl (T. Liu, 2023), which derives the displacement-stress matrix for each layer following Crampin (1981) and generates the synthetic waveforms using the reflectivity method (Kennett, 2009). We parameterize the models in the same way as in the isotropic case except that the thicknesses of both MLDs are fixed at zero, which gives the minimum isotropic Vs drops and increases in a required to produce the MLD arrivals. We assume that the model above MLD1 is isotropic and that the relative isotropic Vs reduction and the increase in a across the MLDs are linearly related by a factor c. For example, when c = 2.0, an MLD with a 5% isotropic Vs drop will have a 10% increase in a. Similarly, an interface with a 5% isotropic Vs increase will have a 10% decrease in a. This model is based on the assumption that physical mechanisms causing isotropic Vs drops also cause increases in radial anisotropy. One such mechanism is horizontal veins and sills rich in volatile-bearing phases (L. N. Hansen et al., 2021). We then search for the best-fit model parameters (Vs drop and depth of MLD1, Vs increase and thickness of the PVG, and Vs drop of MLD2) around the best-fit parameters estimated for the isotropic case. Specifically, we consider two cases with c = 1.0 and 2.0 to explore the trade-off between the isotropic and anisotropic contributions to the MLD signals (Figure 6).

Details are in the caption following the image

Waveform-fitting using radially anisotropic models for (a) RSSD and (b) ECSD. Left panels: Vs models. Red, light purple, and dark purple solid: best-fit V ¯ s ${\bar{V}}_{s}$ for the isotropic model and the anisotropic models with the scaling between V ¯ s ${\bar{V}}_{s}$ drop and percentage increase in a c = 1.0 and 2.0, respectively. Light purple and dark purple dashed: VSH (high) and VSV (low) for the anisotropic models with c = 1.0 and 2.0, respectively. Middle panels: ξ models. Light purple and dark purple: models corresponding to those in the same color in the left panel. Black dashed: SEMum-NA14 (Yuan et al., 2014). Black dotted: CSEM_North_America (Krischer et al., 2018). Gray dashed: GLAD-M25 (Lei et al., 2020). Gray dotted: SAVANI_US (Porritt et al., 2021). Right panels: observed and synthetic waveforms. Red, light purple, and dark purple: synthetic waveforms computed using the models in the same colors. The rest of the objects are the same as those in Figures 3 and 4.

The results show that the best-fit anisotropic models produce waveforms closely resembling those generated by the best-fit isotropic models while requiring significantly smaller isotropic Vs reductions (light and dark purple in Figure 6). For RSSD, c = 1.0 yields isotropic Vs reductions of 5% for MLD1 and 6% for MLD2 (light purple models in the left panel of Figure 6a), whereas c = 2.0 gives Vs reductions of 4% for both interfaces (dark purple models in the left panel of Figure 6a). In the case of c = 1.0, ξ increases from 1.00 (isotropic) to ∼1.10 at MLD1 and ∼1.25 at MLD2 (light purple models in the middle panel of Figure 6a), whereas when c = 2.0, ξ increases to ∼1.20 at MLD1 and ∼1.40 at MLD2 (dark purple models in the middle panel of Figure 6a). For ECSD, c = 1.0 yields a model with isotropic Vs decreasing by 3% and 6% at MLD1 and MLD2, respectively (light purple models in the left panel of Figure 6b). The PVG in the best-fit model has an isotropic Vs increase of 1%, which corresponds to a decrease in radial anisotropy by 1% (light purple models in Figure 6b). Correspondingly, ξ increases to ∼1.05 at MLD1, slightly decreases in the PVG, and increases to ∼1.15 at MLD2 (light purple models in the middle panel of Figure 6b). In the case of c = 2.0, the best-fit model has Vs reductions of 2% and 4% at MLD1 and MLD2, with ξ increasing to ∼1.10 and ∼1.30, respectively at the two interfaces (dark purple models in Figure 6b). An interesting observation is that all best-fit anisotropic models show similar VSV values (dashed models with lower values in the left panels of Figure 6) to those of the best-fit isotropic models (red models in the left panels of Figure 6) regardless of their anisotropy amplitudes. A likely explanation for this phenomenon is that in our VTI models, near-vertically traveling SH waves sample the portion of the SH phase-velocity surface close to its minimum (the zenith), where the velocities of SH and SV waves are equal (the SH and SV phase-velocity surfaces are tangent to each other at the zenith; Figure 5b). This property of VTI mediums, combined with the fact that the SV velocity is constant across all directions (Figure 5b), causes VSV, the velocity of horizontally traveling SV waves in each layer, to be close to the corresponding phase velocities of the near-vertically traveling SH waves, which controls the SH reflection coefficients at the layer boundaries.

Since ξ is a parameter that has been reported by many surface-wave tomography studies that account for radial anisotropy, we compare our ξ profiles with the profiles extracted for the two stations from four well-known recent tomographic models: SEMum-NA14 (hereafter SEMum for simplicity; dashed black model in the middle panels of Figure 6; Yuan et al., 2014), CSEM_North_America (hereafter CSEM for simplicity; dotted black model in the middle panels of Figure 6; Krischer et al., 2018), GLAD-M25 (hereafter GLAD for simplicity; dashed gray model in the middle panels of Figure 6; Lei et al., 2020), and SAVANI_US (hereafter SAVANI for simplicity; dotted gray model in the middle panels of Figure 6; Porritt et al., 2021). The comparison shows that except for the depth range above MLD1 in the case with c = 1.0, our ξ is significantly greater than those given by all four models, which largely show ξ < 1.10 (middle panels of Figure 6). Three possible factors may have contributed to this discrepancy: First, we may have overestimated the increases in anisotropy amplitude and thus ξ across the MLDs, which would imply greater isotropic Vs reductions at the MLDs than in the cases with c = 1.0 and 2.0 (Figure 6). Second, our method may not have yielded the correct absolute anisotropy amplitude because SH reflection amplitudes are only sensitive to anisotropy contrasts across interfaces, whereas the surface-wave models may have underestimated the degree of anisotropy variation with depth due to the broad depth-sensitive kernels of surface-wave dispersion measurements. In this case, our ξ profiles should have similar mean values and variation trends as the surface-wave ξ profiles. Among the four surface-wave models, SEMum and GLAD show ξ increasing with depth in 50–150 km depth, whereas CSEM and SAVANI show ξ decreasing with depth (middle panels of Figure 6). Our results can thus become compatible with SEMum and GLAD if we reduce the mean values of our ξ profiles to the mean values of the surface-wave ξ profiles, which should have little effect on the synthetic waveforms. Third, other model assumptions may have caused the surface-wave models to underestimate the absolute ξ or its variation with depth in the mantle lithosphere. For example, Figure 1 of Kawakatsu (2016b) demonstrated that the phase velocity of fundamental-mode Rayleigh waves at 30 s is not only sensitive to VSV in the upper mantle but also ηκ in the crust and upper mantle as well as the velocity of horizontally propagating P waves in the crust. Different previous surface-wave studies likely made different assumptions about these parameters, which could have contributed to the diversity of their resulting ξ profiles (middle panels of Figure 6).

2.3.5 Models With Density Reductions

We explore the trade-off between isotropic Vs and density drops at the MLDs in a similar way as we did for changes in radial anisotropy. Specifically, we assume that density drops are linearly related to Vs drops by a factor c and search for the best-fit models assuming c = 0.5 and 1.0, which is based on the assumption that physical mechanisms causing Vs drops (e.g., volatile-bearing phases) also cause density drops (Figure 7; Chheda et al., 2014; Saha et al., 2018). The results show that when c = 0.5, the best-fit Vs drops across MLD1 and MLD2 beneath RSSD are reduced to 5% and 6% (2.5% and 3% density drops), respectively (light brown models in Figure 7a). For ECSD, the Vs drops across MLD1 and MLD2 are 3% and 6% (1.5% and 3% density drops), respectively (light brown models in Figure 7b). In the case of c = 1.0, the Vs reductions across MLD1 and MLD2 are both 4% (4% density drops) for RSSD (dark brown models in Figure 7a) and 2% and 4% (2% and 4% density drops), respectively, for ECSD (Vs and density also increase by 1% in the PVG in this case; dark brown models in Figure 7b). Similar to the previous cases with changes in radial anisotropy, the best-fit waveforms generated using the models with density changes are almost identical to the corresponding best-fit waveforms with only isotropic Vs changes (right panels of Figure 7). These results demonstrate that the presence of density drops across the MLDs can significantly reduce the size of Vs drops required to explain the amplitude of the observed signals and that the relative contributions from Vs and density reductions are difficult to determine without additional constraints.

Details are in the caption following the image

Same as Figure 6 but showing models with density reductions at the MLDs for (a) RSSD and (b) ECSD. Left panels: Vs models. Red, light brown, and dark brown: best-fit Vs models without density variations and with the scaling between Vs and density drop c = 0.5 and 1.0, respectively. Middle panels: density models. Red, light brown, and dark brown: models corresponding to those in the same color in the left panel. Right panels: observed and synthetic waveforms. Red, light brown, and dark brown: synthetic waveforms computed using the models in the same colors. The rest of the objects are the same as those in Figures 3 and 4.

2.3.6 Summary of Models With Anisotropy and Density Variations

Assuming that our observed MLD signals are caused only by isotropic Vs drops, the minimum amount of isotropic Vs reductions required to produce the signals (assuming a zero gradient-zone thickness) is 4%–9% (Figures 3 and 4), which is significantly greater than the 1%–4% estimated by Krueger et al. (2021) for global cratons using SRFs. Specifically, at RSSD, where Krueger et al. (2021) found similar depths for the two MLDs as we observe here, their study estimated ∼4% isotropic Vs drops across both MLDs in contrast to our estimates of ∼8% (Figure 3). One way to reconcile our results with previous SRF results is assuming that the drops in isotropic Vs are accompanied by increases in radial anisotropy and density reductions, which can significantly reduce the amount of isotropic-Vs reductions required to explain our observed signals (Figures 6 and 7). Specifically, scaling factors c = 2.0 for the radial-anisotropy case and c = 1.0 for the density-reduction case can both approximately halve the amount of isotropic-Vs reduction in the preferred models for RSSD (Figures 6a and 7a), rendering the results generally consistent with those from Krueger et al. (2021). The amount of radial-anisotropy increase and density decrease required to achieve similar degrees of isotropic Vs reductions across MLDs will be further reduced if both parameters are allowed to vary.

Despite the ability of the models with radial-anisotropy and density variations to reconcile our results with previous SRF ones, they also present their own challenges: Our preferred radially anisotropic models show significantly greater variation in ξ with depth than previous tomography models (Figure 6), and density inversions could destabilize the lithosphere (see Section 22 for detailed discussions). Addressing these issues requires a better understanding of how radial anisotropy and density vary with depth in the lithosphere, which cannot be achieved with the SH-reverberation technique alone because the reflection phases are only sensitive to gradients in medium properties and a trade-off exists between different model parameters in explaining the phase amplitudes (Figures 6 and 7). An obvious solution is to combine multiple types of observations, for example, SH reverberations, SRFs, and surface waves. We will discuss the sensitivities, advantages, and disadvantages of common methods for studying MLDs in detail in Section 24.

3 Inferring the Origins of MLDs

3.1 Possible Origins of MLDs

Previous studies have proposed many different physical mechanisms for MLDs, which can be broadly divided into four categories: (a) changes in composition, which includes the appearance of hydrous minerals (e.g., Fu et al., 2022; Krueger et al., 2021; Rader et al., 2015; Selway et al., 2015), and the decrease in depletion level (magnesium number Mg#; e.g., Yuan & Romanowicz, 2010), (b) the onset of partial melt (e.g., Thybo, 2006), (c) the onset of elastically accommodated grain-boundary sliding, which can be due to increasing temperature or water content (e.g., Karato et al., 2015), and (d) changes in seismic anisotropy, which is usually attributed to the lattice-preferred orientation (LPO) of olivine in unaltered peridotite (e.g., Ford et al., 2016; Yang et al., 2023; Yuan & Romanowicz, 2010). We prefer changes in composition and the presence of partial melts as the causes of our observed MLDs because they can generate significant azimuthal-invariant velocity drops in the mantle lithosphere (e.g., Chantel et al., 2016; Saha & Dasgupta, 2019; Saha et al., 2018). We will focus on models with compositional changes and partial melts in the coming sections and discuss other possible origins of MLDs in Section 23.

3.2 Mantle Metasomatism and MLDs

One of the most commonly invoked physical mechanisms for MLDs is the presence of significant volumes of volatile-bearing phases (e.g., amphiboles and micas) with low velocities and possibly also low densities in the cratonic mantle lithosphere (e.g., Aulbach et al., 2017; Krueger et al., 2021; Selway et al., 2015), which are generated through metasomatic reactions between depleted peridotite and volatile-rich metasomatic reagents likely of slab origins. A series of recent experiments systematically explored the stability of metasomatic minerals and partial melts in the cratonic mantle lithosphere fluxed with different metasomatic reagents and the size of the resulting velocity drops (Saha & Dasgupta, 2019; Saha et al., 20182021). Among different scenarios discussed by these studies, the reaction between depleted peridotite and CO2-H2O-rich siliceous melts causes the greatest amount of Vs drop (up to 6%) due to the precipitation of hydrous minerals (Saha et al., 2018), which is similar to our estimated Vs reductions across the MLDs beneath the two stations (2%–9%; Figures 3, 4, 6, and 7). In addition, the presence of trace amounts of carbonate melt at temperatures above the magnesite stability field could further reduce the bulk Vs (Saha et al., 2018). Moreover, Both RSSD and ECSD are located close to the boundaries of Archean cratons (Figures 1a and 1b), where volatile-rich melts from ancient subducting slabs likely percolated through and reacted with the original depleted cratonic mantle lithosphere. Specifically, RSSD is located on the Black Hills of South Dakota, where alkalic and carbonatitic magmas were intruded during the Cenozoic (Duke, 2009). These relatively recent magmatic activities likely strongly altered the mantle lithosphere beneath RSSD, causing the overall stronger MLDs beneath it than ECSD (Figures 3, 4, 6, and 7). We thus test if this melt-assisted metasomatism model could explain our MLD observations.

Figure 8 shows the final equilibrium pressures and temperatures of xenoliths from the Eocene Homestead and Williams diatremes (Figure 1b). We assume that these xenoliths are representative of the Wyoming craton, but may be less representative of the mantle lithosphere beneath the southwestern Superior province. Nonetheless, due to the great area of the Superior province and the scarcity of mantle xenoliths, the two sites are likely still among the sites closest to ECSD. For comparison, xenoliths from stable cratons (Slave, Kaapvaal, and Siberia; See Figure Caption for references) are also shown. Steady-state geotherms are calculated using the methods outlined in Rudnick et al. (1998) (see Table S1 in Supporting Information S1 for all input parameters). These geotherms assume a surface heat flow of 45 mW m−2, which is representative of local heat flow measurements (Blackwell et al., 2011) as well as global Archean cratons (Artemieva, 2009), and crustal heat productions ranging from 0.4 to 0.7 μW m−3. Both the Homestead and Williams xenoliths plot at higher temperatures compared to the stable craton data, suggesting an elevated present-day geotherm beneath the Wyoming craton generally consistent with a crustal heat production of ∼0.5 μW m−3 (Note that all P-T data in Figure 8 utilize the thermobarometer from Brey and Köhler (1990) to minimize inherent artifacts of different thermobarometers when their results are compared (cf. Chin et al. (2012)).) Besides, the Wyoming-craton xenoliths are largely from shallower depths than the ones from other stable cratons, indicating possible lithospheric thinning, metasomatism, and hydration thought to be associated with the Laramide Orogeny (Carlson et al., 2004; Currie & Beaumont, 2011). Chin et al. (2021) also showed that pyroxene water contents of the Homestead and Williams xenoliths are elevated compared to other cratonic peridotites. Specifically, the Homestead and Williams xenoliths approach or overlap the hydration state of peridotite samples from beneath the Colorado Plateau (Chin et al., 2021), a craton-like lithosphere that was directly in the path of the Laramide flat slab and is thought to have been significantly re-hydrated by it (Li et al., 2008). We note that the temperature beneath the Wyoming craton likely reached the maximum during the time of lithosphere modification (e.g., Laramide) and then gradually decreased to today's value, which is relevant to the interpretation of our MLD observations.

Details are in the caption following the image

Temperature versus depth plot showing modeled geotherms, xenolith data, phase boundaries, and inferred MLD and LAB depths. Geotherms are computed assuming a surface heatflow of 45 mWm−2, crustal heat-production rates of 0.4–0.7 μW m−3, a mantle heat-production rate of 0.03 μW m−3 (Rudnick et al., 1998), and a crustal thickness of 50 km (this study). The mantle adiabat is from Katsura (2022). Xenolith P-T data are from the following studies: Slave craton (Aulbach et al., 2007; Kopylova & Caro, 2004), Kaapvaal craton (Gibson et al., 2008; Ionov et al., 2010), Wyoming Craton (Homestead, MacDougal Springs, Squaw Creek, Williams; Hearn Jr, 2004; Chin et al., 2012). Dry and wet (water-saturated) solidi are from Katz et al. (2003).

Fluxing of the Wyoming-craton lithosphere by CO2-H2O-rich siliceous melts, presumably of Laramide flat slab origin, may have resulted in substantial deposition of hydrous minerals (phlogopite, amphiboles) and carbonate minerals (magnesite) and even left behind “frozen” carbonated melt at certain depth ranges of the mantle lithosphere. Indeed, phlogopite is present in the Homestead xenoliths (Hearn Jr, 2004), although it is absent in the Williams xenoliths. The Homestead xenoliths were also found to contain more hydrous pyroxenes compared to the Williams xenoliths (Chin et al., 2021). To determine the stability depth ranges of these phases beneath the Wyoming craton and their relations with our observed MLDs, we compare the xenolith P-T data, reference geotherms, and experimental P-T conditions of hydrous phases in depleted peridotite fluxed by variable amounts of CO2-H2O-rich siliceous melts reported in Saha et al. (2018). The comparison shows that amphibole is stable in the range shallower than ∼110 km given the possible geotherms (Figure 8), suggesting that MLD1 beneath the two stations might be caused by the presence of amphibole in 90–110 km, whereas MLD2 is unlikely to be associated with amphibole. In contrast, phlogopite is shown to be stable down to at least 130 km and thus could contribute to reducing the seismic velocities below MLD1. At greater depths, the solidus, which coincides with the stability boundary between magnesite and carbonated melt (Saha et al., 2018), intersects the geotherms at 110–120 km depth (Figure 8), suggesting that the minimum stable depth of carbonated melt can be as shallow as 110 km, which coincides with the depth range of MLD2 beneath the two stations (Figure 8). In addition, the decomposition of amphibole at ∼110 km depth could also cause hydrous melting around the depth. Given the strong effect of small amounts of partial melts on Vs (Chantel et al., 2016), the onset of carbonated and hydrous melt could be the main cause of MLD2 beneath the two stations.

3.3 “Melt-Percolation Barrier” Model

Based on our seismic observations and thermal-chemical model, we propose a “Melt-percolation barrier” model to explain the MLDs beneath the two stations (Figure 9). During a metasomatism event (e.g., the Laramide orogeny), CO2-H2O-rich siliceous melts, which are possibly released by a subducting slab beneath the cratonic lithosphere, percolated upward through the lithospheric mantle and started reacting with the peridotite to form phlogopite once they reached its stability field (Figure 9). The reaction consumed the melts and may also have hindered their further ascent by creating networks of phlogopite-rich veins and sills, which have been observed in mantle xenoliths from the Wyoming craton (e.g., Carlson et al., 2004; Hearn Jr, 2004). A predominantly horizontal extension of the veins and sills can cause an increase in radial anisotropy and thus contribute to our observed MLD signals (Section 10; L. N. Hansen et al., 2021). We note that the anisotropic signatures on our long-period seismic observations can only be generated by a sufficiently thick layer (at least a few kilometers) containing large numbers of horizontally oriented veins and sills. Field observations of such structures are extremely rare since they require the exposure of large sections of mantle rock. Tommasi et al. (2017) reported strong shape- and crystal-preferred orientation of hydrous minerals in the Finero peridotites in the southern Alps, which could serve as an approximation for the structure that we propose. If sufficient melts are injected into the mantle lithosphere, the melts will migrate further upward into the amphibole-stable zone (<110 km), and the formation of amphiboles will further consume the melts and impede their upward migration (Figure 9). The result of this process is a melt-depletion front (equivalent to a metasomatic front) slightly above the lower boundary of the amphibole stability zone, which defines MLD1 below the two stations (Figure 9). Although carbonated melts might have been stable at shallower depths due to a hotter geotherm during the metasomatism event, they are likely only stable below 110–120 km depth beneath the two stations today, which, together with possible hydrous melt caused by the decomposition of amphibole, defines MLD2 (Figure 9).

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Schematics for the “melt-percolation barrier” model for the origin of MLDs.

The “Melt-percolation barrier model” explains two of our key seismic observations. First, the model predicts similar MLD1 and MLD2 depths given similar geotherms, which is consistent with the similar MLD depths observed for the two stations (Figures 1, 3, and 4). The model can also explain the slightly deeper (∼10 km) MLD2 beneath ECSD than RSSD (Figures 1, 3, and 4), which could be due to the colder geotherm beneath the southwestern Superior province causing a greater melt-onset depth. A remaining question is what controls the layer thickness between MLD1, that is, the metasomatic front, and the lower boundary of the amphibole stability field, which appears to be ∼20 km beneath both stations despite the differences in temperature and melt supply between the two regions (Figure 8). We speculate that the thickness is determined by the rates of metasomatic reaction and melt diffusion, although a quantitative assessment requires numerical simulations of the behaviors of reactive melts in the mantle lithosphere using realistic parameters, which is beyond the scope of this paper. Second, the metasomatic minerals generated by the melt-peridotite reactions are less dense and may cause radial anisotropy by forming horizontally oriented veins and sills, which will reduce the amount of isotropic Vs drops required to explain our observed MLD signals (Figures 6 and 7) and thus render our results more consistent with previous results obtained using other methods (e.g., Krueger et al., 2021). The stronger MLD1 beneath RSSD can also be explained by a more abundant melt supply below the Wyoming craton during the Laramide period as evidenced by the widespread alkalic and carbonititic magmatism in the area (Duke, 2009), which likely deposited a greater volume of metasomatic minerals below MLD1 beneath RSSD and thus caused stronger isotropic Vs, density, and anisotropy contrasts (Figures 6 and 7).

3.4 Metasomatic Reagents: Melts Versus Aqueous Fluids

In addition to CO2-H2O-rich siliceous melts, aqueous fluids rich in CO2 could also cause metasomatism of the mantle lithosphere (Saha & Dasgupta, 2019). Whereas the introduction of melts enriches the depleted peridotite with both volatiles and incompatible elements (e.g., Na and K), the infiltration of aqueous fluids only increases the volatile contents in the system (Table 1 in Saha & Dasgupta, 2019). This key difference causes distinct resulting phase assemblages for the two reagents, with melts generally favoring the deposition of metasomatic minerals (e.g., amphiboles and phlogopite) and fluids favoring the formation of melts (Saha & Dasgupta, 2019). We have chosen to use the phase equilibrium data from Saha et al. (2018) measured for melt-assisted metasomatism primarily because the resulting solid assemblage produces greater Vs drops (up to ∼6%) due to its greater hydrous-phase content compared to the Vs drops produced by fluid-assisted metasomatism reported in Saha and Dasgupta (2019) (below 3%). Nonetheless, the Vs drops reported in both studies are estimated without including the effects of melts despite clear evidence for the presence of up to 6% of melts in many of their resulting phase assemblages (Table 2 in Saha & Dasgupta, 2019). Given the strong influence of melts on bulk Vs (Chantel et al., 2016) and the fact that fluid-assisted metasomatism stabilizes greater amounts of melt at lower temperatures (Saha & Dasgupta, 2019), the Vs reductions caused by fluid-assisted metasomatism could be comparable or even greater than the melt-assisted case if the Vs-reducing effects of melts are accounted for.

In the case of fluid-assisted metasomatism (i.e., no enrichment of incompatible elements), the stability fields of the hydrous phases are greatly reduced due to the low alkaline-water ratio (Saha & Dasgupta, 2019; Saha et al., 2021). Specifically, phlogopite decomposes and generates hydrous partial melts at ∼1000°C and ∼3.5 GPa (Figure 4 in Saha and Dasgupta (2019)), a P-T condition generally consistent with the geotherm of the Wyoming craton at the depth of our MLD2 (Figure 8). MLD2 could thus originate from partial melting caused by the decomposition of phlogopite in the case of fluid-assisted metasomatism. Another important hydrous mineral, amphibole, was shown to be unstable in the P-T range tested in Saha and Dasgupta (2019) (2–4 GPa and 850–1150°C). Nonetheless, because the stability of hydrous minerals is highly sensitive to the alkaline-water ratio (Saha & Dasgupta, 2019; Saha et al., 2021), there likely exists a mixture of incompatible elements and water that causes amphibole and phlogopite to decompose at the P-T conditions of our MLD1 and MLD2, respectively. In this case, MLD1 is caused by the initiation of partial melt due to the decomposition of amphibole, and MLD2 by a significant increase in the melt content due to the decomposition of phlogopite (Figure S3 in Supporting Information S1). The mantle lithosphere above MLD1 contains small volumes of the two hydrous phases, which are insufficient to generate significant velocity drops (Figure S3 in Supporting Information S1).

The scenario with fluids as the metasomatic reagents discussed above requires smaller volumes of hydrous minerals compared to the case with melts as the reagents and thus may be more consistent with mantle-xenolith evidence. Nonetheless, given the sparse and potentially biased sampling of mantle xenoliths, a relatively thin (∼20 km; Figure 8) and laterally intermittent layer with significant volumes of hydrous minerals could remain largely unsampled by xenoliths (Section 21). Because both the presence of hydrous minerals and partial melts could explain the seismic signature of MLD1 beneath the two stations, our observations are insufficient to determine its origin. On the other hand, electric-conductivity structure constrained using magnetotellurics could potentially distinguish between the two models because melts are much more potent in increasing the conductivity of the medium compared to hydrous minerals. Although we cannot uniquely determine the metasomatic reagents responsible for the two MLDs, we have shown that mantle metasomatism can generate two MLDs at the observed depths. The significant azimuthal-invariant velocity drops at the two MLDs also suggest mantle metasomatism as their most probable origin.

4 Discussions

4.1 Do MLDs Exist Beneath the Central US?

Among different seismic imaging techniques, the SRF technique is most widely used for imaging MLDs because the S-to-P conversions at mantle interfaces arrive before direct S and thus are free from the interference of crustal multiple-reflection phases. Using the SRF technique, a series of papers have identified one or multiple MLDs beneath a significant portion of the central US (e.g., Abt et al., 2010; Hopper & Fischer, 20152018). Nonetheless, a recent study processed the S-to-P phases using a direct stacking approach and found no evidence for MLDs beneath the central US (Kind et al., 2020). The authors thus claimed that the MLDs beneath the central US found by previous SRF studies are Moho sidelobes generated by the deconvolution procedure (Kind et al., 2020). This controversy highlights the challenges in characterizing MLDs seismically and thus calls for independent seismic observations to address this issue. Here, using the SH-reverberation method, we present strong evidence for the presence of MLDs beneath two stations separated by ∼600 km in the central US. Moreover, the depths of the two MLDs beneath RSSD agree well with the ones found by Krueger et al. (2021) using the SRF technique. These findings support the presence of MLDs beneath at least parts of the central US. We also note that the discrepancy between different studies using S-to-P phases to study MLDs is not limited to that between Kind et al. (2020) and previous SRF studies; another example is the disagreement between EFD18, which suggested an MLD at ∼70 km depth beneath RSSD and Krueger et al. (2021), which showed two MLDs at ∼85 km and ∼110 km depths beneath the station. These discrepancies suggest that nuances in the processing of S-to-P phases may have major impacts on the results.

4.2 Are Cratonic Mantle Lithospheres Compositionally Heterogeneous?

The metasomatic origin of MLDs requires enrichment of the depleted cratonic mantle lithosphere by volatile and incompatible elements, which apparently contradicts mantle-xenolith evidence suggesting a cratonic lithosphere highly depleted in the two components (e.g., Lee et al., 2011). For example, Saha et al. (2021) argued that based on xenolith evidence, the average cratonic peridotite is too depleted in incompatible elements to stabilize enough hydrous minerals to explain the full spectrum of Vs drops observed for MLDs. To reconcile the metasomatic origin of MLDs with geochemical evidence, we propose that the cratonic mantle lithosphere is probably highly heterogeneous in composition, with some domains significantly refertilized by volatile and incompatible elements through metasomatism (Figure 10) and the rest remaining largely intact (Figure 10). The enriched domains may be mostly located near the craton boundaries, where fluids and melts released by past subducting slabs could have metasomatized the mantle lithosphere and generated strong MLDs (Figure 10). This model is consistent with stronger MLDs observed near craton boundaries compared to craton interiors globally (Krueger et al., 2021). Because the enriched domains are likely spatially intermittent, they are probably less well-sampled by mantle xenoliths, which are also sparsely distributed. Furthermore, some unknown mechanisms may cause kimberlite eruptions, the primary host for mantle xenoliths in cratons, to preferentially entrain mantle rocks that are not metasomatized. A tentative model is that kimberlite eruptions, the main host of cratonic mantle xenoliths, may happen in different domains from mantle metasomatism because the two processes have dramatically different time scales: kimberlite usually erupt very rapidly, whereas mantle metasomatism requires extended periods of contact between depleted peridotite and metasomatic reagents to allow for complete reactions. Given the scarcity of mantle-xenolith samples, methods capable of better characterizing the true spatial extents of mantle metasomatism are required to test the hypothesis of compositional heterogeneity beneath cratons. Our results suggest that the detection of MLDs may be a reliable indicator for the presence of mantle metasomatism beneath the station, which provides a promising method to explore compositional heterogeneity beneath cratons.

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Schematics illustrating the likely diverse origins of the MLDs in different parts of a craton. Note that the different processes in the top panel likely happened during different periods of the craton's life span.

4.3 Implications on Craton Stability

Although cratons have generally remained stable since their formations in the Precambrian, the reactivation and even destruction of cratons during the Phanerozoic have also been extensively documented (e.g., the destruction of the eastern North China craton; Zhu & Xu, 2019, and references therein.). MLDs caused by volatile-bearing phases and melts may facilitate the modification of the cratonic lithosphere in two ways. First, the presence of significant volumes of hydrous minerals and trace amounts of melts can rheologically weaken the mantle lithosphere and thus facilitate its modification by mantle convection (L. Liu et al., 2018; Bedle et al., 2021; Wang et al., 2023). We note that a recent petrological study found that whereas volatile-rich melts significantly weaken the upper mantle, the presence of hydrous minerals up to 25 vol.% does not (Tommasi et al., 2017). These results suggest that trace amounts of melts within the cratonic mantle lithosphere may play a critical role in promoting its destruction. Second, the presence of significant volumes of hydrous minerals in a depth range in the mantle lithosphere can reduce its density compared to the materials above it, causing gravitational instability. This scenario is similar to the case where an eclogitized lower crust is denser than the underlying mantle and thus could cause its delamination (Jull & Kelemen, 2001). The combined effects of metasomatism-induced strength reduction and density inversion may have facilitated the partial removal of the mantle lithosphere beneath the Wyoming craton as suggested by some studies (e.g., Dave & Li, 2016; Humphreys et al., 2015). In contrast, the Superior province appeared to have stayed stable despite the possible presence of density inversion in its mantle lithosphere, probably because its mantle lithosphere is cooler and thus stronger, which inhibits the delamination process (Jull & Kelemen, 2001). Nonetheless, if the Superior province is reheated by a plume in the future, the density inversion could destabilize the mantle lithosphere and trigger its destruction. In summary, mantle metasomatism may have caused the destruction of some cratons in the past and prepared others for the same fate in the future.

4.4 Other Origins of MLDs

Our metasomatism model for the MLDs beneath the two stations can be regarded as a combination of changes in composition (hydrous phases), melt content (carbonated melt), and anisotropy (sub-horizontal veins and sills rich in hydrous phases), although the origin of the anisotropy in our model is not olivine LPO as suggested by most previous studies. In addition to these three factors, onsets of EAGBS may also contribute to our observed MLD signals because the hydration of the lower lithosphere (Chin & Palin, 2022) by metasomatism could have enabled EAGBS (Figure 10), causing a few percent of velocity drop and thus reducing the amount of hydrous phases and melts required to explain our observed MLD signals (Karato et al., 2015; Saha et al., 2021). Nonetheless, a recent experimental study rejected EAGBS as a possible cause of sharp velocity drops in the upper mantle (Cline II et al., 2018), highlighting the controversy over this mechanism.

Abrupt changes in olivine LPO with depth, which are likely associated with deformations during craton formation, could also generate seismically detectable MLDs (Figure 10). The evidence for this physical mechanism is scarce because observing its hallmark, an azimuthal variation in scattered-phase amplitude and polarity (e.g., Figure 3 in Ford et al., 2016), requires reasonably good back-azimuth coverage of the events, which is difficult to achieve for both SRF and SH-reverberation techniques, the two most commonly used methods for studying MLDs (See Section 24). So far, only a few PRF studies have reported contrasts in azimuthal anisotropy across MLDs (e.g., Ford et al., 2016; Wirth & Long, 2014), which are probably due to sharp changes in olivine LPO with depth. Nonetheless, the significant variation of azimuthal anisotropy with depth beneath cratons reported by previous tomography studies (e.g., Yuan & Romanowicz, 2010) suggests that changes in olivine LPO may play a more important role in causing MLDs than currently understood.

Some previous studies attempted to find a universal physical model for the MLDs observed globally (e.g., EAGBS proposed by Karato et al., 2015), yet recent seismological investigations are painting an increasingly complicated picture of MLDs, suggesting likely diverse origins of MLDs in different regions. For example, the continental-scale study of T. Liu and Shearer (2021) found highly variable MLD depths and amplitudes beneath the central US, with some regions underlain by multiple MLDs, and the global-scale study of Krueger et al. (2021) detected MLDs only beneath ∼50% of the long-running stations and found that the MLD amplitudes generally decrease from craton edges to interiors. These findings suggest that MLDs beneath different areas probably have distinct properties (e.g., depth, amplitude, and azimuthal variation) and thus different origins. This complexity is ultimately caused by the long and complicated histories of cratons (Figure 10). Therefore, finding a universal physical model for MLDs may be unrealistic. Instead, future studies should focus on uncovering the origins of MLDs on a case-by-case basis, which requires more detailed investigations and synthesis of knowledge across different disciplines.

4.5 Methods for Studying MLDs and Future Directions

So far, most of the observational constraints of MLDs come from SRFs. In addition to the well-known sensitivity of the S-to-P amplitude in SRFs to isotropic Vs changes, the amplitude is also affected by changes in radial anisotropy (e.g., extended Figure 6 in Hua et al., 2023), with the dependence involving both anisotropy amplitude and Kawakatsu's fifth parameter (ηκ; Kawakatsu, 2018). Despite the broad application of the SRF technique to studying MLDs, it also has three well-known limitations: First, the depth resolution is limited due to the low frequency range of teleseismic S waves and the small temporal separations between the S-to-P phases generated at different interfaces (Figure 1e in T. Liu & Shearer, 2021). Second, the S-to-P conversion points are usually far from the recording station and thus may cause events from different back azimuths to sample different structures (e.g., RSSD1 and RSSD2 in Figure 6b of Krueger et al., 2021), which could degrade the result if the events from different back azimuths are averaged. Moreover, the shape of the SRF scattering kernel also limits its use in imaging interfaces with strong lateral changes (Hua et al., 2020). Third, to avoid interference from other global phases, SRF studies typically only use events within a relatively narrow distance range (e.g., 65–80° in Krueger et al., 2021), which limits the number of available events.

Compared to the SRF method, the SH-reverberation technique has better depth resolution (Figure 1c in T. Liu & Shearer, 2021) and is less affected by lateral heterogeneity (Section 4), rendering it a powerful tool for imaging MLDs and other lithospheric discontinuities. As shown in Section 8, the SH-reverberation amplitude is sensitive to changes in isotropic Vs, radial anisotropy, and density, and the relative contributions from the three factors cannot be determined without independent constraints (Figures 6 and 7). Similar to the SRF method, the SH-reverberation method also has limitations in event availability: Deep events are often used to avoid the ambiguity between source- and receiver-side scatterers (Figure 2a), and the events in 65–85° are sometimes excluded to avoid interference from ScS.

Given the complementary sensitivities of different scattered-phase imaging methods, an obvious future direction is combining different types of observations to better constrain the physical property changes across the MLDs. Specifically, integrating SRF and SH-reverberation observations may hold the potential to independently constrain the changes in isotropic Vs, radial anisotropy, and density across MLDs beneath long-running stations where both methods provide high-quality observations (e.g., RSSD and ECSD). Nonetheless, we caution that combining different types of observations at a single station requires the assumption that the structure beneath the station can be approximated with a 1D model, which may not be valid in some cases as evidenced by the discrepancy between the SRF stacks for two different back-azimuth windows at RSSD (Krueger et al., 2021). In addition to scattered-phase observations, surface-wave observations can also be incorporated to better constrain the absolute velocities in the mantle lithosphere (Eilon et al., 2018). Specifically, we note that the current tomography models of the contiguous US seem to disagree on the trend of radial-anisotropy variation in the lithosphere (Figure 6), that is if the maximum of radial-anisotropy is located in the crust or the mantle lithosphere. This issue is worth further investigation given the potential for radial-anisotropy contrasts to cause MLDs (Figures 5a and 6).

Magnetotellurics (MT) can also provide valuable information on the origins of MLDs due to its sensitivity to volatile content (Selway, 2014). Specifically, electrical-resistivity models may be used to distinguish between MLD models with hydrous minerals and melts as the cause for velocity reductions because the latter is likely significantly more conductive than the former (Section 18). Bedrosian and Frost (2023) presented a 3D electrical-resistivity model of the Wyoming craton and the surrounding region and argued that the lithosphere mantle below the Wyoming craton is largely unaffected by metasomatism as evidenced by the mantle high-resistivity body extending down to ∼200 km. Nonetheless, their results showed that the mantle resistivity above ∼175 km depth beneath two locations in the core of the Wyoming craton is significantly lower than that beneath the Superior province in the same depth range (Figure 7a in Bedrosian and Frost (2023)). In addition, the mantle resistivity in this depth range beneath the two Wyoming locations is also lower than the one predicted for dry olivine, an end-member composition for an intact cratonic mantle lithosphere (Figure 7a in Bedrosian and Frost (2023)). These two pieces of evidence suggest that even the mantle lithosphere beneath the core of the Wyoming craton is unusually conductive compared to that of an intact craton, probably due to fluids or melts introduced through metasomatism. Compared to the core of the Wyoming craton, the regions near its boundary were shown to be underlain by mantle lithospheres with even lower resistivity (Bedrosian & Frost, 2023), evidence for stronger effects from metasomatism. Given that our station RSSD is located near the eastern boundary of the Wyoming craton (Figures 1a and 1b), a metasomatic origin of the MLDs beneath the station is generally consistent with the results of Bedrosian and Frost (2023). Distinguishing between melts and volatile-bearing phases as the cause of our observed velocity drops requires a quantitative analysis of the resistivity model, which is beyond the scope of this paper. Globally, cratonic mantle lithospheres are often imaged as high-resistivity bodies, suggesting high degrees of volatile extraction and low temperatures (e.g., Evans et al., 2011). Nonetheless, prominent low-resistivity anomalies within cratonic mantle lithospheres have also been reported, with the Central Slave Mantle Conductor as a well-known example (Jones et al., 20012003). The top of this structure coincides well with a strong negative seismic interface and thus has been interpreted as a metasomatic horizon, below which the velocity and resistivity are reduced by the presence of hydrous minerals and graphite, respectively (Chen et al., 2009). Given the complementary sensitivity of seismic and electromagnetic methods, joint seismic-MT analyses like Chen et al. (2009) may be the key to unveiling the mysteries surrounding MLDs.

Lastly, the current understanding of MLDs is severely restricted by data availability because both the SRF and SH-reverberation methods require data from long-running stations, which are much scarcer in cratons than in tectonically active regions (e.g., west coast of the US; Figure 5g in T. Liu & Shearer, 2021). This lack of station coverage is especially acute given the growing body of evidence suggesting that the internal structures of cratons may be as complicated as tectonically active regions (Krueger et al., 2021; T. Liu & Shearer, 2021). Although increasing the number of permanent seismic stations in cratons may not be feasible in the short term due to a lack of resources, keeping the current global and regional seismic networks (e.g., Global Seismographic Network), which provide crucial station coverage for many cratons globally, operative is critical for continuing accumulating the seismic data required for better understanding the structure and evolution of cratons.

5 Conclusions

We detect two distinct MLDs at ∼87 (MLD1) and ∼117 (MLD2) km depth beneath the eastern Wyoming craton and the southwestern Superior craton with 2%–9% isotropic Vs drops, depending on the contributions from contrasts in density and radial anisotropy. MLD1 and MLD2 are probably caused by the appearance of significant volumes of hydrous minerals and the onset of carbonated partial melting, respectively. The hydrous minerals and melts are likely products of melt-assisted metasomatism of the mantle lithosphere. Our results suggest that metasomatism is probably the cause for the strong MLDs observed globally near craton boundaries, where the mantle lithosphere could have been intensely metasomatized by fluids and melts released by past subducting slabs. The apparent contradiction between the metasomatism origin of MLDs and mantle-xenolith evidence suggests significant compositional heterogeneity in cratonic mantle lithospheres.

Acknowledgments

We thank Vera Schulte-Pelkum for her advice on seismic anisotropy. We thank Zach Eilon for sharing the velocity model EFD18. We thank Hongzhan Fei for insightful discussions about hydrous minerals and their stability fields. We thank Karen Fischer and two anonymous reviewers, whose critical comments helped us greatly improve this paper. T.L. was supported by the National Science Foundation (NSF) Grant EAR-2123529. The facilities of EarthScope Consortium were used for access to waveforms, related metadata, and/or derived products used in this study. These services are funded through the Seismological Facility for the Advancement of Geoscience (SAGE) Award of the NSF under Cooperative Support Agreement EAR-1851048.

    Conflict of Interest

    The authors declare no conflicts of interest relevant to this study.

    Data Availability Statement

    The seismic waveform data are publicly available through the Seismological Facility for the Advancement of Geoscience (SAGE) data management center https://ds.iris.edu/mda/ by the network code “IU” (RSSD) and “US” (ECSD). The heat-flow data are publicly available through the National Geothermal Data System (NGDS) http://geothermal.smu.edu/gtda/. The open-source software Aniplane.jl and the data products of this paper are publicly available on Zenodo (T. Liu, 2023; T. Liu et al., 2023). Some of the figures are created using the Generic Mapping Tools (GMT; Wessel et al., 2019).