www.sciencemag.org/content/344/6179/80/suppl/DC1

Supplementary Materials for

Geophysical and Geochemical Evidence for Deep Temperature Variations Beneath Mid-Ocean Ridges Colleen A. Dalton,* Charles H. Langmuir, Allison Gale

*Corresponding author. E-mail: colleen_dalton@brown.edu

Published 4 April 2014, Science 344, 80 (2014)

DOI: 10.1126/science.1249466

This PDF file includes:

Materials and Methods Supplementary Text Figs. S1 to S29 Table S1 References (31–38)

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Materials and Methods Methods

The majority of MORB samples in our major-element data set have experienced cooling in the shallow crust that has modified their compositions from that of their parental melts. To draw inferences about the mantle from MORB compositions, it is necessary to correct for the effects of low-pressure crystallization. Two different approaches were used to correct for this fractional crystallization. The first involved correcting all major-element data to their composition at MgO=8 wt.% (“8-values”). The second involved correcting all major-element data back to compositions in equilibrium with forsterite-90 (Fo90) mantle olivine (“90-values”). Details of the two methods follow.

1. Correcting to MgO=8 wt.% The variations in each oxide are treated as a function of MgO, and each datum with

MgO=5.5-8.5 wt. % is corrected by shifting its value along a line of constant slope (“liquid line of descent”) to the point where MgO=8 wt.%. For the majority of ridge segments, the constant slope is either the slope of the best-fitting line determined from orthogonal regression of the original data or the canonical value obtained from experimentally determined liquid lines of descent. For samples with MgO>8.5 wt.%, the values are first corrected to MgO=8.5 wt.% using experimentally determined slopes for olivine crystallization and then corrected to MgO=8 wt.% as described above. In the final step, the mean and standard deviation of the fractionation-corrected major-element compositions (8-values) are determined for each ridge segment from the individual values corrected to MgO=8 wt.%.

2. Correcting to Fo90 mantle olivine Every sample with MgO<8.5 wt.% is first shifted along a line of constant slope to its

value at MgO=8.5 wt.%, similar to the correction process described above. MgO=8.5 wt.% is chosen because the liquid lines of descent defined by our data at most ridge segments exhibit a slope change at MgO=8.5 wt.%, corresponding to the appearance of plagioclase in the crystallizing assemblage. Olivine is then added in 0.1% increments to these compositions until they are in equilibrium with Fo90. Samples with MgO>8.5 wt.% MgO (i.e., samples for which plagioclase crystallization has not yet begun) only require the incremental olivine addition in order to be in equilibrium with Fo90. Once all individual sample compositions are corrected to equilibrium with Fo90 olivine, those samples are averaged to estimate a 90-value for each ridge segment

Note that the fractionation correction is only performed on MORB samples from ridge segments that contain data from at least three unique locations, resulting in fractionation-corrected values for 246 ridge segments. Fig. S3 shows that the values obtained using the two methods are highly correlated and thus the results and conclusions of this study do not depend on which correction method we use for the comparisons. We choose to focus on the 90-values in this study because they are more easily compared to pooled-melt compositions calculated by petrological melting models.

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Supplementary Text S1 Comparison of seismic models to ridge depths and geochemistry

In this section, we describe how the seismic model is compared to axial ridge-depth values and geochemical observations. These three data sets differ in both their spatial coverage and their resolution. The global VS model S40RTS (1) is defined everywhere in the mantle but has finite resolution due to both the wavelength of seismic waves and the parameterization of the seismic model. Mean ridge depths have been calculated for each of the 771 segments in our newly created mid-ocean-ridge catalog, but these segments are highly variable in length (between 6.6 and 375.8 km; median value = 66.7 km). Fractionation-corrected major-element chemistry, which has been calculated for 246 of the 771 segments, is distributed unevenly across the globe. For a comparison to be meaningful, these differences must be reconciled.

To facilitate our comparisons, we define a system of 242 nodes at which to compare the data sets. These nodes are evenly spaced at intervals of 220 km along the six longest ridge systems: Mid-Atlantic Ridge (MAR), Southwest Indian Ridge (SWIR), Central Indian Ridge (CIR), Southeast Indian Ridge (SEIR), Pacific-Antarctic Ridge (PAR), and East Pacific Rise (EPR) (fig. S1D). They are located away from continents and subducting slabs, where lateral smoothing in the seismic model might bias VS values. Values of VS can then obtained directly at each of these nodes, since S40RTS is defined everywhere in the mantle. However, the finite resolution of the seismic model results in an inherent smoothing or averaging of the Earth’s true seismic properties such that the value of the seismic model at a particular (x,y) location is influenced not only by the Earth’s seismic properties at that location but also by the seismic properties at locations within a lateral radius R. Since S40RTS is defined using spherical harmonics to degree and order 40, we use R=5o (550 km) in the horizontal direction to calculate “smoothed” values of ridge depth and geochemistry at each node.

1. Comparison of VS and ridge depth: We calculate a “smoothed” ridge depth value

DRj for the jth node from the mean (“raw”) segment depths using

!

DR j

=

Zi X i /dij( )i=1

N

"

Xi / dij( )i=1

N

",

where Zi is the mean ridge depth of the ith segment, Xi is the length of the ith segment, and dij is the distance from the jth node to the midpoint of the ith segment. The sum is over the N ridge segments with dij<5o. This averaging scheme therefore gives more weight to longer ridge segments that are located closer to the jth node. Fig. S4A provides a comparison of the relationship between ridge depth and VS at 300 km using the “smoothed” DRj values at the 242 nodes. The effect of this smoothing can be assessed by comparing VS and ridge depth using the 584 “raw” Zi values from the six longest ridge systems and VS values sampled at the (x,y) location corresponding to the midpoints of the 584 individual ridge segments (fig. S4B). Fig. S5 provides the correlation coefficient as a function of depth in the mantle for each of these two scenarios, which demonstrates that

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the global correlations between ridge depth and VS can be seen in both the “smoothed” and “raw” ridge depths.

2. Comparison of VS and geochemistry: There are 246 segments for which

geochemistry is available. Excluding back-arc spreading centers because of their proximity to subducting slabs, which might bias VS, reduces this to 225 segments. When only the six longest ridge systems are included, this value is further reduced to 182 segments. Of the 242 nodes, there are 113 for which at least one ridge segment with geochemistry is located within the specified radius of 5o. We calculate average geochemistry at each of these 113 nodes using a weighted-average of the geochemistry for nearby segments, similar to the calculation of DRj described above, resulting in “smoothed” values of geochemistry at those 113 nodes. Fig. S6B shows the relationship between Na8.0 and VS at 200 km using the “smoothed” geochemistry values at 113 nodes. The same relationship is shown using the 225 “raw” segment geochemistry values and the corresponding values of VS in fig. S6A. Fig. S7 summarizes the correlation coefficient as a function of depth between Na8.0, Fe8.0, Ca8.0/Al8.0, and VS calculated using both the “smoothed” and the “raw” segment geochemistry. These comparisons demonstrate that the global correlations between geochemistry and VS can be seen in both the “smoothed” and the “raw” MORB compositions.

S2 Spreading-rate dependence of VS Fig. S9A summarizes the correlation between spreading rate and shear velocity in

three different global seismic models: S40RTS, S362ANI (31), and SEMum (32). In all three cases, spreading rate is anti-correlated with VS in the shallow mantle. This anti-correlation is strongest near 75-100 km and becomes weak in the depth range 100-200 km. The values used for the calculation of correlation coefficient for S40RTS at 75-km depth are shown in fig. S9B for reference. We interpret the strong anti-correlation at shallow depths to be an artifact of the smoothing that is inherent to the seismic models due to the model parameterization and the wavelength of seismic waves. If a seismic model averages true Earth seismic properties within a horizontal radius R about a given location, then for locations along the mid-ocean ridge the averaging will include older seafloor at slower-spreading ridges than at faster-spreading ridges. Older seafloor is underlain by colder temperatures in the uppermost mantle than younger seafloor, and colder temperatures result in higher shear velocity. Thus, averaging seismic properties within radius R will incorporate higher shear velocities at slow-spreading ridges and lower shear velocities at fast-spreading ridges, in agreement with the observations. We focus our analysis on mantle depths > 150 km to minimize bias from this artificial spreading-rate dependence.

S3 Choice of global seismic model Fig. S5 summarizes the correlation, as a function of depth in the mantle, between

ridge depth and shear velocity for two different global seismic models: S40RTS and SEMum (32). Comparisons performed with both models indicate that a strong correlation exists and that it extends to greater depths (>300 km) than previously recognized. When

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S40RTS is used, the correlation extends to >500 km; when SEMum is used, the correlation extends to 350 km. Very similar results are obtained for the comparison between Na8.0 and VS. A clear relationship between the two variables exists to depths > 200 km, although the peak of the correlation occurs at slightly shallower depths for SEMum (fig. S12).

S4 Calculation of ridge depth: effect of temperature and composition In this section, we describe how axial ridge depth is calculated as a function of

mantle temperature and mantle composition. Ridge depth is controlled by the thickness and density of the crust and the density of the mantle column, which varies with temperature, pressure, and composition (9).

1. Temperature variations: To derive the sensitivity of axial ridge depth to mantle

temperature variations, we first calculate depth profiles of temperature and melt fraction using the melting function of (33) for adiabatically upwelling mantle with potential temperatures in the range 1100-1650°C. We then use the MELTS software program (20, 37) to calculate the thickness of the crust and the composition of the pooled melts for adiabatically upwelling mantle (DMM; 34) with potential temperatures in the range 1100-1650oC. Our results are not changed if we instead calculate crustal thickness using the expression provided by (9). We determine crustal density by applying Perple_X (21) to the pooled melt compositions.

The calculation of mantle density takes into account temperature, pressure, and the effect of melt removal on peridotite composition (including plagioclase, spinel, and garnet stability). We use the DMM composition of (34) as representative of the fertile upper mantle, which does not experience melting beneath the ridge. We determine the density of DMM mantle as a function of temperature and pressure using Perple_X. We parameterize density in the residual mantle, which has experienced melt removal beneath the ridge, as a function of temperature, pressure, and melt-fraction removed by applying Perple_X to the laboratory melting experiments of (35) and (36). Then, for each temperature and melt-fraction profile calculated using (33), it is straightforward to calculate a corresponding profile of mantle density.

We follow the approach of (9) and treat each ridge segment as an isostatically balanced column containing four layers: water, crust, residual mantle, and fertile mantle (fig. S13). The total pressure P at the base of each column is calculated as P=∫ρ(h)*g*dh, where ρ(h) indicates density as a function of depth h in the column and g is gravitational acceleration. Pressure at the base of all columns is assumed to be equal at some compensation depth. The temperature anomaly (i.e., potential temperature) associated with each ridge segment is assumed to extend to the compensation depth. Our preferred calculations use a compensation depth of 400 km, since the observations exhibit strong correlations to depths > 400 km, indicating that mantle temperature variations must persist to those depths if temperature variations are responsible for the observations. Our preferred calculations also assume that water depth = 0 m at potential temperature = 1550oC. All calculations show shallower ridges at higher mantle potential temperature, reflecting the combined effects of less-dense warmer mantle and thicker oceanic crust due to more melting. Assuming a larger (smaller) compensation depth results in a larger

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(smaller) range of ridge depths for a given temperature range, as the temperature-controlled density differences in the mantle represent a higher fraction of the total column. Choosing a different temperature for water depth = 0 will shift the absolute temperature values up or down, but the trends would be largely unchanged relative to each other.

2. Compositional variations: To evaluate the sensitivity of ridge depth to mantle

chemical variations, the crustal thickness and density that result from melting five hypothetical mantle compositions at potential temperatures of 1350oC and 1450oC are calculated using MELTS and Perple_X. The five mantle compositions are obtained by linearly mixing DMM with the log-normal ALL MORB composition of (19), as summarized in Table S1. We have also performed these calculations using the residual peridotite compositions from the melting experiments of (35) and (36). Those calculations are not shown here but yield the same results and conclusions.

Density along the 1350oC and 1450oC adiabats is determined for each of the five mantle compositions using Perple_X. The total pressure at the base of each column is determined as for the temperature variations described above. Each composition is assumed to extend from the Moho to the isostatic compensation depth (fig. S14). Although enriched mantle compositions (low Mg#) experience more melting and therefore generate thicker oceanic crust than depleted compositions at the same temperature, the isostatic balance calculation predicts increasing ridge depth with increasing mantle fertility owing to the greater density of enriched mantle (fig. S15). Thus a positive relationship between crustal thickness and axial ridge depth is expected for variations in mantle composition, whereas an inverse relationship between crustal thickness and ridge depth is expected for variations in mantle temperature. Our preferred calculations use a compensation depth of 400 km, since the observations exhibit strong correlations to depths > 400 km, indicating that mantle chemical variations must persist to those depths if mantle chemical variations are responsible for the observations. Water depth = 0 m is chosen so that the water depth for the DMM composition at 1350oC and 1450oC agrees with the variable-temperature water depth calculated for this composition at these temperatures (i.e., fig. S13).

S5 Calculation of VS: effect of temperature and composition To predict VS as a function of temperature, we use (3), which is a parameterization

of laboratory experiments that describe the temperature dependence, frequency dependence, and grain-size dependence of shear modulus and attenuation. Importantly, the model of (3) incorporates the effects of anelasticity, which is temperature-dependent, and allows extrapolation in temperature, pressure, and grain size. We use grain size = 2 cm and activation volume = 10-5 m3/mol.

To predict VS as a function of composition, we calculate elastic shear velocities for the five hypothetical compositions (Table S1) at constant temperature using Perple_X and the thermodynamic database of (28). This approach neglects the effect of anelasticity on wave speed. However, since the calculations are performed at a uniform temperature, it is expected that anelasticity will affect all VS values at a given depth by the same amount and will not alter the composition-dependent trends. Fig. S22 shows that the

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sensitivity of VS to composition depends on temperature, with stronger sensitivity at lower temperatures, consistent with results of earlier studies (4).

S6 Petrological modeling The effect of mantle temperature and composition on the geochemistry of the pooled

melt was calculated using two approaches. First, the equations provided by (10) were used to predict concentrations of FeO, MgO, and Na2O in the melt for adiabatic melting of the mantle. The calculations were carried out for fractional mantle melting with 150 ppm water content. Second, the pMELTS thermodynamic model (38) was used, which provides predictions of CaO and Al2O3 (plus many other major and trace elements) in addition to FeO, MgO, and Na2O. The pMELTS calculations were carried out for near-fractional melting (0.5% residual porosity) of dry, adiabatically-upwelling mantle. We consider two end-member scenarios: (i) variable mantle potential temperature (1250-1600oC) for the DMM composition of (34); and (ii) constant mantle potential temperature (1350oC and 1450oC) for variable mantle compositions. Here we present results calculated for five hypothetical mantle compositions obtained by linearly mixing DMM with the ALL MORB log-normal mean composition of (19), as summarized in Table S1.

Figs. S16-S21 provide a comparison of the observed and predicted chemistry, axial ridge depths, and shear velocity. The robust result of the calculations is the slope on the various diagrams. Translation of the various curves can occur through modest changes in the Na2O or Mg/(Mg+Fe) content of the mantle source. For example, a 10% change in Na2O in the source would result in a 10% translation of the curves in Na2O MORB concentration. These figures highlight two important points. First, the global trends in all observations are fit better by variations in mantle temperature at constant composition than by variations in mantle composition at constant temperature (where we have prescribed compositional variations by adding and removing basalt from normal mantle). Second, a global temperature range of 200-250oC is consistent with all observations considered here. These figures also highlight the critical information that seismology contributes to the debate about temperature versus composition beneath mid-ocean ridges. The expected relationships between Na90 and axial ridge depth, Ca90/Al90 and axial ridge depth, and Na90 and Ca90/Al90 due to temperature variations are qualitatively similar to the expected relationships due to compositional variations, making it difficult to discriminate between the two hypotheses using only those observations. The Fe90 contents are a more decisive discriminant, but variations in Fe90 have been subject to debate in the petrological community (e.g., 12). The strong temperature sensitivity of shear velocity provides robust support for the important role for temperature.

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Fig. S1 Variations along the mid-ocean-ridge system. (A) Mean axial ridge depth for 771 ridge segments. (B) MORB Na2O contents adjusted to be in equilibrium with Fo90 olivine for 246 ridge segments. Triangles: 34 locations used by (16). (C) Shear-wave speed at 300-km depth from (1) at the midpoint of 771 ridge segments. Black squares: 49 hotspots from (30). (D) Locations of 242 evenly-spaced nodes.

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Fig. S2 (A) Raw mean ridge depth and Na90 for 225 segments. Error bars show +/- one standard deviation. (B) Comparison of Na90 and Fe90 for 225 segments. Color-coded by Ca90/Al90 ratio.

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Fig. S3 Comparison of MORB compositions corrected for low-pressure fractionation with two different approaches. Shown for 225 ridge segments. (A) Na90=Na2O composition adjusted to be in equilibrium with Fo90 olivine. Na8=Na2O composition adjusted to MgO=8 wt.%. Correlation coefficient is 0.98. (B) As in (A) but for FeO. Correlation coefficient is 0.97.

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Fig. S4 Comparison of DR and VS at 300-km depth. (A) Points correspond to smoothed DR values at 242 grid nodes along the MAR (green), SWIR, CIR, and SEIR (red), and EPR and PAR (blue). (B) Points correspond to unsmoothed DR values at 584 locations.

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Fig. S5 Correlation coefficient between axial ridge depth (DR) and mantle shear velocity (VS). Results are shown for the 242 smoothed DR values and 584 raw (unsmoothed) DR values, as described in the text. (A) The global seismic model is S40RTS (1). (B) The global seismic model is SEMum (32).

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Fig. S6 Comparison of Na8.0 and VS at 200-km depth. Color-coded by Fe8.0. (A) Unsmoothed Na8.0 values for 225 ridge segments. (B) Smoothed Na8.0 values at 113 grid nodes.

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Fig. S7 Correlation coefficient between VS in the mantle and MORB chemistry. (A) Correlation between VS and Na8.0. Results are shown for 225 unsmoothed compositions along all ridges excluding back-arc spreading centers, 182 unsmoothed compositions along the six longest ridge systems, and 113 smoothed compositions at 113 grid nodes. (B) As in (A) but here the comparison is between VS and Fe8.0 and VS and Ca8.0/Al8.0 for 225 unsmoothed compositions and 113 smoothed compositions.

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Fig. S8 (A) Comparison of DR and Na8.0 at 225 ridge segments, color-coded by distance from nearest hotspot. (B) Comparison of DR and VS at 300-km depth at 242 grid nodes.

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Fig. S9 (A) Correlation coefficient between VS and spreading rate calculated using three global seismic models: S40RTS, SEMum (32), and S362ANI (31). (B) Comparison of spreading rate and VS at 75-km depth from S40RTS. Values from six ridge systems are labeled.

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Fig. S10 (a) Comparison of shear velocity at 110-km depth and Na8.0 at the 34 global locations considered by (16). The seismic-velocity model used here is RG5.5 (38), which is the same model used in the analysis of (16). (b) As in (a), but here the seismic model is S40RTS (1) at 100-km depth. The correlation apparent in (a) vanishes when a modern seismic model is used. (c) As in (b), but here the seismic model is S40RTS at 325 km, providing evidence of a strong correlation at depths > 200 km. (d-f) As in (a)-(c) but the comparison is with Fe8.0. Points are color-coded by ocean basin. Black: Atlantic Ocean. Red: Pacific Ocean. Green: Red Sea. Blue: Indian Ocean.

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Fig. S11 As in fig. S10 but for the comparison of (17), which was focused on the Mid-Atlantic Ridge. Ref. (17) used the seismic model RG5.5 (38). The points are color-coded by latitude along the ridge.

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Fig. S12 Correlation coefficient between Na8.0 and mantle shear velocity (VS). Results are shown for 225 unsmoothed compositions along all ridges excluding back-arc spreading centers, 182 unsmoothed compositions along the six longest ridge systems, and 113 smoothed compositions at 113 grid nodes. (A) The global seismic model is S40RTS. (B) The global seismic model is SEMum (32).

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Fig. S13 (Left) Sensitivity to temperature variations: depth profiles of temperature and melt fraction for four TP values. Schematic isostatically balanced columns are shown for TP=1300oC and 1500oC. (Right) Sensitivity of water-depth calculation, as a function of mantle potential temperature, to the assumed compensation depth (200 km, 300 km, 400 km). Predictions are shown for two different calculations of residual mantle density. For “W”, the experimental melting data of (35) are used as input to Perple_X. For “BS”, the melting experiments of (36) are instead used.

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Fig. S14 Sensitivity to compositional variations: depth profiles of Mg# and melt fraction for four hypothetical mantle compositions at TP=1350oC. Example isostatic columns are shown for Mg#=89 and 92.

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Fig. S15

Sensitivity of water-depth calculation, as a function of Mg#, to the assumed compensation depth (200 km, 300 km, 400 km). Calculation assumes potential temperature = 1350oC. Water-depth for DMM composition is prescribed to be 3.9 km in order to achieve agreement the variable-temperature calculations performed on DMM (i.e., fig. S13).

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Fig. S16 (A) Grey symbols show observed relationship between ridge depth and Na90. Circles show predicted values for variable temperature (1250o-1550oC) at constant composition. Na90 is calculated using the approach of (10) and ridge depth is calculated using the isostatic approach described in supplementary text S4. Triangles and diamonds show predicted values for variable composition at potential temperature = 1350o and 1450oC, respectively. They are labeled according to the Mg# of the source composition used for the melting calculations. (B) As in (A) but for Fe90.

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Fig. S17 As in fig. S16 but here the comparison is between Na90 and Fe90, which are calculated using the approach of (10).

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Fig. S18 As in fig. S16 but here Na90 and Fe90 are calculated using MELTS (20, 37).

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Fig. S19 Comparison of observed and predicted relationships between Na90 and Fe90 and Na90 and Ca90/Al90. Geochemical predictions are performed using MELTS.

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Fig. S20 Comparison of observed and predicted relationships between ridge depth and Ca90/Al90 and Fe90 and Ca90/Al90. Geochemical predictions are performed using MELTS.

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Fig. S21 Comparison of observed and predicted relationships between Na90 and VS at 300-km depth. Na90 is predicted using MELTS. VS as a function of temperature is predicted using (3), and VS as a function of composition is predicted using (21).

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Fig. S22 VS as a function of Mg#, plotted relative to the VS value for the most fertile composition. Predictions are made using Perple_X (21) at 800oC and 1200oC at pressures of 3 GPa and 9 GPa. The five most depleted mantle compositions used for the predictions are obtained from the 3 GPa melting experiments of (35). The four most enriched mantle compositions are obtained by linear mixing between the starting composition of (35) and 5%, 10%, 15%, and 20% MORB.

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Fig. S23 Correlation coefficient between VS and 242 smoothed DR values (green) and between VS and 225 unsmoothed Na90 values (blue). 95% confidence limits on both curves are plotted with green and blue dashed lines. These limits were calculated using the Fisher transformation with z=1.96.

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Fig. S24 Northern Mid-Atlantic Ridge. Map view of (A) VS at 300-km depth (1); (B) Na8.0; (C) mean axial ridge depth (unsmoothed). Diamonds show hotspots locations from (30) plus St. Paul/Amsterdam.

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Fig. S25 As in fig. S24 but for the southern Mid-Atlantic Ridge.

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Fig. S26 As in fig. S24 but for the Southwest Indian Ridge.

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Fig. S27 As in fig. S24 but for the Southeast Indian Ridge.

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Fig. S28 As in fig. S24 but for the Pacific-Antarctic Ridge.

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Fig. S29 As in fig. S24 but for East-Pacific Rise.

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Table S1. Summary of five hypothetical compositions obtained by linearly mixing DMM (34) with the ALL MORB log-normal mean of (19). SiO2* Al2O3 FeO MgO CaO Na2O Mg# DMM -10% NMORB 43.96 2.75 7.95 42.07 2.26 0.004 90.4 DMM -5% NMORB 44.32 3.40 8.07 40.28 2.73 0.15 89.9 DMM 44.71 3.98 8.18 38.73 3.17 0.28 89.4 DMM +10% NMORB 45.17 4.89 8.33 36.13 3.85 0.49 88.5 DMM +15% NMORB 45.37 5.25 8.40 35.15 4.11 0.57 88.2 *In wt. %. Concentrations of MnO, Cr2O3, TiO2, and NiO are not listed.

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