The intervening 520 km discontinuity ( 520) is commonly associated with the wadsleyite to ringwoodite transition (Shearer, 1990(Shearer, , 1996;;Sinogeikin et al., 2003). It has a subtler seismic contrast, is more sporadically detected and, unlike the 410 and 660, it is not incorporated in widely used 1D reference Earth models such as PREM and AK135 (Dziewonski & Anderson, 1981;Kennett et al., 1995;Sinogeikin et al., 2003;W. Wang & Wu, 2022). Additionally, some observations suggest that the 520 may split into two separate discontinuities which has been interpreted to reflect the combination of the wadsleyite to ringwoodite phase transition and exsolution of Ca-perovskite in areas of basalt enrichment (Deuss & Woodhouse, 2001;Saikia et al., 2008;Tian et al., 2020). Thus, the 520 remains a relatively uncertain structure despite its importance as a marker of the abundance of olivine polymorphs and potential enrichment of basalt in the mantle transition zone due to the long-term flux of subducting slabs, whose basaltic crust may separate from the depleted mantle lithosphere (Anderson & Bass, 1986;Ballmer et al., 2015;van Keken et al., 1996).

Relatively infrequent detection of the 520, compared to 410 and 660, may be largely attributed to challenges in resolution. Its subtler contrast (<2% from Zhou et al., 2022) and potentially wider depth interval (20-22 km from Tsujino et al., 2019) weaken the 520's ability to generate distinct seismic phases and make its visibility more frequency-dependent than that of the 410. The low amplitude of seismic phases sensitive to the 520 often results in large uncertainties when estimating its properties and may lead to null detections under sparse sampling (Lawrence & Shearer, 2006). Therefore, a carefully designed method targeting the 520 in a well-instrumented area is needed.

Here, 520s detection and characterization are advanced using a Markov chain Monte Carlo (MCMC) method to fit seismic receiver function data from more than 2,000 broadband seismometers across the United States (Figure 1), simultaneously in six frequency bands. Their footprint covers a variety of tectonic settings extending from an active and long-lived subduction zone in the west across the cratonic interior to a passive eastern margin that has not experienced subduction since the Mesozoic (Seton et al., 2012). Inversions using parameterizations with and without the 520 enable statistical evaluation of its spatially varying significance and seismic properties.

We extracted three-component (P-SV-SH) P-to-S receiver functions from broadband waveform data in the contiguous U.S. using a multi-channel deconvolution method (Mercier et al., 2006). We then filtered the SV component data in six different frequency bands, namely 2-15, 3-15, 4-15, 5-30, 6-30, and 7-30 s. The time-domain receiver functions were converted to depth-domain via raytracing the P-to-S phase in an existing 3D tomographic model (Schmandt & Lin, 2014). We grouped the receiver functions in 300 km radius caps based on their piercing points at 500 km depth and stacked them in depth-domain (Figures S1 and S2 in Supporting Information S1).

Each 300 km radius cap contains >1,000 traces. Grouping the data at 500 km depth, rather than by seismometer location, increases the coherence of the P-to-S conversions and strengthens the detection power for the 520.

The observational uncertainties of the stacked receiver functions were estimated using the standard deviation of preferred parameters from bootstrap resampling with 200 iterations.

Our parameterizations of the input shear wave velocity structure at transition zone depths are shown in Figure 1c.

We fixed the absolute S wave velocity at 300 and 750 km depths in each cap using values from an existing body wave tomography model (Schmandt & Lin, 2014). We then used four parameters: (a) top of transition depth, (b) base of transition depth and absolute Vs at the (c) beginning and (d) end of each linear transition-to define a discontinuity as an enhanced linear gradient. Consequently, the models have 12 parameters when including three discontinuities and eight parameters when only including the 410 and the 660. The second parameterization forms a subset of the first and therefore allows using an F-test to indicate a confidence of 520 detections.

Following Bissig et al. (2021), we adopted a MCMC inversion method to estimate the model parameters. We used a reflectivity code to calculate synthetic receiver functions (Levin & Park, 1997) and matched the slowness distribution of the observed data during the stack process (Munch et al., 2018). The path integrated attenuation effects were corrected using the structure from PREM (Dziewonski & Anderson, 1981; Text S1 in Supporting Information S1). We used the Residual Sum of Square (RSS) to indicate the goodness of waveform fitting. The RSS is defined as:

where obs and syn represent the observed and synthetic waveforms respectively. The σ is the observational uncertainty from bootstrap resampling with 200 iterations. Index i and j are for sample points and frequency bands, respectively. The likelihood function is:

where N stands for the total number of points when calculating the RSS. Our prior distributions of model parameters are uniform functions spanning a plausible range of mantle transition zone seismic properties (Table S1 in Supporting Information S1) and samples were drawn with the Metropolis-Hastings algorithm. The standard deviation of the depth Gaussian function is 1.5 km while that for absolute Vs is 0.015 km/s. Such steps offer 30%-50% acceptance rate during the inversion. For each region, we ran 100,000 iterations (four chains with 25,000 iterations per chain). A burn-in period takes approximately 1,000 iterations (Movie S1). We used the high-performance clusters at the Center for Advanced Research Computing at the University of New Mexico (∼25,000 CPU hours). We averaged model parameters from the best 200 iterations to define the final models and treated their standard deviations as inversion errors (Text S2 in Supporting Information S1; see Figure S3 in Supporting Information S1 for examples of posterior distributions). Movie S1 gives an animated example.

We tested the algorithm by inverting synthetic receiver functions from a pyrolite composition with a potential temperature of 1600 K (F. Wang et al., 2018;Xu et al., 2008) (Figure 2). The input model contains three olivine polymorph phase transitions: the olivine to wadsleyite transition near 410 km, the wadsleyite to ringwoodite transition near 540 km, and the decomposition of ringwoodite near 660 km (Figure 2a). Additionally, the gradual and nonlinear transition from majorite garnet to bridgmanite also contributes to the velocity gradient at depths greater than ∼640 km (Figure 2a). The overlap of multiple phase transitions complicates the structure of the 660 discontinuity and may invalidate our parameterization of one linear gradient. However, this simplification should not interfere with evaluating the significance of the 520.

The inverted model parameters were converted to discontinuity depths and Vs contrast for comparison with mineral physics data (Figure S4 in Supporting Information S1). We calculated the discontinuity depths by averaging the depths at the top and bottom of a linear gradient. We calculated the Vs contrast by extrapolating the velocity gradients above and below the discontinuity to the expected depth and reported a fractional velocity jump at the middle depth (Figure S4 in Supporting Information S1).

The inversion fits the major characteristics of the synthetic receiver functions (Figure 2b). The recovered depths and Vs contrasts for the 410 and the 520 agree with the two corresponding phase transitions (Figures 2c and 2d), indicating that the linear parameterization works for simple structures. However, while the inverted 660 depth is similar to the value from the ringwoodite transition, the Vs contrast is much larger and clearly incorporates contributions from the majorite transition (Figures 2a and 2d). Such a result suggests that a more sophisticated model parameterization is needed to associate seismic properties of the 660 with specific phase transitions. Here, we focus on the 520 and 410 because each is associated with phase transition of olivine polymorphs, which can be effectively modeled with our simple parameterization.

We used an F-test to evaluate the confidence levels of 520 detections. Our null hypothesis is that adding a 520 discontinuity does not significantly improve the goodness of fit to the observations. Assuming the random noise follows a normal distribution, an F-test requires

to reject the null hypothesis at a confidence level of 1 -𝛼. The p1 and p2 are the number of model parameters, which are 12 and 8 respectively. The ndf stands for the number of degrees of freedom, which was estimated to be 46 (Walsh et al., 2013;Figure S5 and Text S3 in Supporting Information S1). The finv is the inverse of cumulative F-distribution function, with inputs of the probability, numerator degrees of freedom, and denominator degrees of freedom. At 95% confidence, the F-test requires an RSS ratio greater than 1.31 to reject the null hypothesis (Figure S5b in Supporting Information S1).

A widespread 520 is supported by the statistical confidence map and waveform examples (Figure 3; see Figure S6 in Supporting Information S1 for a version without interpolation). About 84% (54 out of the 64 caps) of the area surpasses 95% confidence in requiring a 520 to better fit the observations. The results are consistent with an olivine-rich mantle where the wadsleyite to ringwoodite phase transition is nearly ubiquitous. The null detections are limited to a narrow north-south band near where the tomographically inferred subducting Juan de Fuca slab reaches transition zone depths (Schmandt & Lin, 2014; Figure S2 in Supporting Information S1). While a low olivine fraction could explain its apparent absence, destructive stacking of the 520s signal arising from misrepresented 3D velocity anomalies or large amplitude phase transition topography may also contribute.

Previously reported splitting of the 520 discontinuity (Deuss & Woodhouse, 2001;Tian et al., 2020), that is, a 560 km discontinuity (560), is not a significant feature in our results (Figure 3; Figure S7 in Supporting Information S1). The exsolution of Ca-perovskite is hypothesized to create the 560 and therefore its visibility may reflect concentrations of subducted oceanic crust near the bottom of transition zone (Saikia et al., 2008). The absence of deeper detections at ∼560 km indicates that the shallower wadsleyite-ringwoodite transition is more important to fitting P-to-S conversions across the study area. Consequently, it appears that basaltic crust is not sufficiently concentrated in the mid-transition zone to make Ca-perovskite exsolution the dominant phase transition. Given the long history of subduction beneath the western margin of North America, the new results favor entrainment of slab crust to greater depths, either highly localized near the bottom of the transition zone or extending into the lower mantle.

Discontinuity depths further support that the wadsleyite-ringwoodite transition is the dominant cause of the 520 (Figure 4b; see Figure S8 in Supporting Information S1 for a version without interpolation). The 520 depths from the positive detections (95% confidence) have a mean of 506 km with a standard deviation of 10 km. Despite that the depths are generally shallower than the 520 km implied by its name, they agree well with modern mineral physics predictions of 500-514 km for the wadsleyite to ringwoodite transition within 50 K of a normal mantle adiabat (Tsujino et al., 2019;Zhou et al., 2022; Figure 5b). Moreover, a mean depth slightly shallower than 520 km is consistent with previous seismic detections at both global and regional scales (∼515 km from Julià & Nyblade, 2013; ∼510 km from Tian et al., 2020).

The proximity of the shallower olivine-wadsleyite transition at the 410 is a useful reference for more detailed evaluations of the 520 (Figure 4). The depths of the 520 and 410 show a strong positive correlation coefficient of 0.68 (Figure 5a). Temperature and hydration levels are the major influences on the depths of the two-phase transitions (Inoue et al., 2010). Since both transitions have positive Clapeyron slopes (4.0 MPa/K for olivine-wadsleyite from Katsura et al. [2004]; 6.91 MPa/K for wadsleyite-ringwoodite from Suzuki et al. [2000]; 4.11 MPa/K for wadsleyite-ringwoodite from Inoue et al., 2006), similar thermal variations near the two discontinuities would predict positively correlated topography consistent with our results. In contrast, varying hydration levels would predict anti-correlated topography because increasing water content elevates the 410 and depresses the 520 (Inoue et al., 2010). Our estimated ratio between the 520 and the 410 depths ranges from 0.9 to 1.5 at 95% confidence, with a best fit value of 1.2 (Figure 5a; Text S4 in Supporting Information S1). The observationsal results generally agree with mineral physics predictions using a ratio of the two Clapeyron slopes (Inoue et al., 2006;Katsura et al., 2004;Suzuki et al., 2000; Figure 5a), indicating a dominant role for thermal anomalies in altering 410 and 520 topography. For Clapeyron slope estimates of 4.11-6.91 MPa/K (Inoue et al., 2006;Suzuki et al., 2000), the observed 45 km variation of 520 depths corresponds to a lateral temperature range of 230-390 K (Text S5 in Supporting Information S1). A similar range of ∼250 K is predicted by 410 topography using a Clapeyron slope of 4.0 MPa/K (Katsura et al., 2004). Both the 410 and 520 topography maps suggest cooler temperatures beneath the cratonic interior of the United States (e.g., Schmandt & Lin, 2014; Figure S2 in Supporting Information S1). Given the evidence that the 520 represents the wadsleyite-ringwoodite transition, the abundance of olivine polymorphs should primarily control the magnitude of its Vs contrast, with more minor effects due to hydration levels (Zhou et al., 2022; Figure 5c). Under dry conditions, a pure olivine transition zone could give a 520 discontinuity with a Vs contrast of 3.30% (Zhou et al., 2022). Increasing hydration of wadsleyite will reduce the Vs constrast (e.g., W. Wang & Wu, 2022;Zhou et al., 2022). The observed 520 Vs contrasts from all caps have a mean of 1.9% with a standard deviation of 0.9%. Horizontal variability in Vs contrasts generally shows higher values beneath the central United States and lower values near the eastern and western margins (Figures 4c and 4d).

The results could reflect lateral variations in the abundance of olivine polymorphs, with a more olivine-enriched transition zone beneath the continental interior (see Text S5 in Supporting Information S1 for additional discussion). However, many factors including uncertainty of heterogeneous 3D velocity and attenuation may influence variations among individual sub-array estimates of the 520 Vs contrast, so we focus on estimating mean olivine abundance. The standard error of the mean 520 contrast is 0.1% so a one-sigma interval on the mean contrast is 1.8%-2.0%. Assuming a water partitioning ratio of 2:1 between wadsleyite and ringwoodite and an Fe# of 7.6 in wadsleyite (Ishii et al., 2018;Zhang & Bass, 2016;Zhou et al., 2022), the mean Vs contrast range is consistent with an olivine abundance of 54%-61% under dry conditions (Figure 5c). Incorporating 1.0 wt% water into wadsleyite increases the estimates to 58%-66%.

The range of olivine abundance (54%-61% under dry condition and 58%-66% with 1.0 wt% hydrous level) estimated from the mean Vs contrast at 520 is similar to the 56% abundance in the pyrolite model (Frost, 2008;Green & Falloon, 1998). Scarcity of evidence for basalt enrichment in the study area, which would favor a more prominent 560 and a less prominent 520 than we found (Saikia et al., 2008), is consistent with an olivine-rich composition like pyrolite. The widespread presence of a single 520 consistent with a normal mantle geotherm and near-pyrolite olivine abundance suggests that while the seismic signals from the 520 are subtler than those of the 410 and 660, the wadsleyite-ringwoodite transition can be a valuable marker of mantle physical state where adequate seismic resolution exists. Here, the properties of the 520 indicate that the relevance of the olivine-rich pyrolite model of the upper mantle extends to mid-transition zone depths.

reviewer for evaluating the manuscript and helpful suggestions. IRIS Data Services provide the seismic data in this study and are funded through the Seismological Facilities for the Advancement of Geoscience Award of the NSF under Cooperative Support Agreement EAR-1851048. The UNM Center for Advanced Research Computing, supported in part by the NSF, provided the computing resources. This research was supported by NSF EAR-1554908 and EAR-1664471.