The thermochemical structure of lithospheric and asthenospheric mantle exert primary controls on surface topography and volcanic activity. Volcanic rock compositions and mantle seismic velocities provide indirect observations of this structure. Here, we compile and analyze a global database of the distribution and composition of Neogene-Quaternary intraplate volcanic rocks. By integrating this database with seismic tomographic models, we show that intraplate volcanism is concentrated in regions characterized by slow upper mantle shear-wave velocities and by thin lithosphere (i.e. <100 km). We observe a negative correlation between shear-wave velocities at depths of 125–175 km and melt fractions inferred from volcanic rock compositions. Furthermore, mantle temperature and lithospheric thickness estimates obtained by geochemical modeling broadly agree with values determined from tomographic models that have been converted into temperature. Intraplate volcanism often occurs in regions where uplifted (but undeformed) marine sedimentary rocks are exposed. Regional elevation of these rocks can be generated by a combination of hotter asthenosphere and lithospheric thinning. Therefore, the distribution and composition of intraplate volcanic rocks through geologic time will help to probe past mantle conditions and surface processes.

Here, the authors compile a global geochemical database of Neogene-Quaternary intraplate volcanism. By comparing the distribution and composition of these rocks with tomographic models they show that intraplate volcanism can be used to constrain upper-mantle structure at the time of eruption.

Mantle convection drives plate tectonics, redistributes heat, cycles chemical species, and generates dynamic topography at the Earth’s surface. Constraining spatio-temporal changes in the thermochemical structure of the mantle will help to refine our understanding of these interlinked phenomena. This significant challenge requires careful integration of diverse observations. Two well-established methodologies for probing the thermochemical state of the mantle are igneous geochemistry and seismic tomography. It is particularly useful to analyze the relationship between igneous geochemistry and upper mantle structure away from complications associated with active plate boundaries in order to understand the interaction between mantle composition, temperature and melting through geologic time.

An important difficulty is that composition of partial melts within the mantle and shear-wave velocity of mantle rocks are both sensitive to the combined effects of temperature and chemical composition. The uppermost mantle is subdivided into a mechanically strong lithosphere and a weak underlying asthenosphere that is ~100–200 km thick. For a given mantle source composition, the depth and degree of melting are principally controlled by a combination of asthenospheric temperature and lithospheric thickness^{1}. The extent of melting increases with increasing potential temperature, _{p}, and decreasing pressure so that elevated asthenospheric temperature and/or thinner lithosphere produce greater volumes of melt. Given suitable assumptions, the location, volume and composition of volcanic rocks can be used to analyze the thermal structure of the uppermost mantle^{2–4}. Nevertheless, it is important to bear in mind that the distribution and composition of volcanic rocks are also significantly influenced by mantle composition, by the geometry of mantle flow, and by the interaction between melts and surrounding rocks as they ascend to the surface^{5–11}.

Global seismic tomographic models demonstrate that shear-wave velocity anomalies, Δ_{s}, occur throughout the upper mantle. Although it is agreed that shear waves propagate slower through warm mantle and faster through cold mantle, it is also clear that _{s} varies in a non-linear fashion with pressure and temperature^{12,13}. Furthermore, shear-wave speed is also sensitive to mantle composition and to the presence of interstitial melt^{14,15}. By analyzing the distribution and composition of volcanic rocks in conjunction with shear-wave velocity anomalies, it is possible to determine temperature variations within the upper mantle. A related approach has been successfully used along mid-oceanic ridges where lithospheric thickness can be assumed to be negligible^{16,17}.

Here, we investigate a more general problem by analyzing intraplate regions, where both asthenospheric temperature and lithospheric thickness vary. Our principal aim is to quantity the relationship between the composition of volcanic rocks and mantle seismic velocities with a view to constraining the size, extent and surface expression of putative thermal anomalies. We are less concerned with the more difficult problem of how these anomalies are generated in the first place. First, we examine correlations between the distribution and composition of Neogene-Quaternary intraplate volcanism, Δ_{s}, and lithospheric thickness. Secondly, we estimate potential temperature and lithospheric thickness using a combination of geochemical and seismologic techniques. Finally, we scrutinize the link between intraplate volcanism and the distribution of emergent marine sedimentary deposits, which are a tangible manifestation of dynamic topographic uplift. Although our primary focus is on relatively youthful volcanic rocks, we are hopeful that our quantitative framework will provide helpful tools for interrogating the Phanerozoic record of these processes.

We have compiled a global database that consists of >20, 000 geochemical analyses of Neogene-Quaternary intraplate volcanic rocks (Database 1; Fig. ^{18}. Global surface-wave tomographic models have a horizontal resolution of 200–600 km, which means that these restrictions ensure co-location of intraplate volcanic rocks and pertinent observations of sub-surface structure^{19–22}. The majority of analyses are of mafic samples that are located far from active plate boundaries, although we have included analyses from locations adjacent to several extensional provinces and subduction zones that exhibit intraplate-like compositions (e.g., western North America, Anatolia, East African Rift). We have carried out a literature review to identify and remove samples pertaining to subduction zone processes (see

_{s}, taken from SL2013sv tomographic model at depth of 150 ± 25 km^{21}. Red/white/blue contours = positive/zero/negative values of Δ_{s} plotted at intervals of 0.1 km s^{−1}; yellow circles = loci of intraplate magmatic samples <10 Ma and located <400 km from locus of eruption based upon present-day plate speeds (see ^{27}. Black contours = thickness values at intervals of 50 km. Encircled numbers highlight loci where gently dipping Late Cretaceous-Cenozoic marine strata crop out at elevation: 1 = western North America; 2 = southernmost South America; 3 = eastern Australia; and 4 = north Africa^{55}.

If the distribution of volcanic rocks is compared with the pattern of upper mantle shear-wave velocities, it is clear that intraplate volcanism is concentrated within regions where negative shear-wave velocity anomalies occur at depths of 150 ± 25 km. Figure ^{21}). This global vertical shear-wave velocity model exploits body and surface waves that include both fundamental and higher modes with periods of 11–450 s. It is important to emphasize that similar results have been obtained for a range of other tomographic models (Supplementary Fig. _{s} correlates with geochemical indicators of melt fraction within intraplate settings^{23–25}. Intraplate volcanism is almost completely absent in regions where Δ_{s} is positive. There is a similarly compelling spatial relationship between the distribution of intraplate volcanic rocks and lithospheric thickness (Fig. _{s} and ^{26}. Here, we utilize the revised and modified _{s}-to-^{27}, which is based upon an empirical anelastic parameterization (see “Methods”^{13}). Lithospheric thickness is estimated by tracking the depth to the 1175 °C isothermal surface^{27}. This isothermal surface is chosen since it provides a good fit to the peak change in the orientation of azimuthal anisotropy, which is characteristic of the transition between rigid lithosphere and convecting asthenosphere within oceanic regions^{28,29}. In the continental realm, it is clear that intraplate volcanic rocks are concentrated within regions where the lithosphere is <100 km thick.

These visual associations can be quantified by formally examining relationships between, Σ_{I}, the cumulative areal distribution of binned intraplate volcanic samples, Δ_{s}, and lithospheric thickness (see “Methods”). Eighty-nine percent of Σ_{I} occurs in regions underlain by negative values of Δ_{s} whose areal distribution only constitutes 61% of global area (Fig. _{I} occurs in regions underlain by continental lithosphere <100 km thick whose areal distribution constitutes 62% of global area (Fig. ^{30}). The probability that co-location of intraplate samples, negative values of Δ_{s}, and anomalously thin continental lithosphere arises from chance is <1 in 10^{100}.

_{s} from SL2013sv tomographic model at depths of 150 ± 25 km where globe is subdivided into 1° bins weighted according to _{s}; red line = cumulative areal distribution of binned intraplate volcanic samples; black/red numbered dashed lines = percentages of global surface and of intraplate volcanism with Δ_{s} < 0 km s^{−1}; ^{−107} (“Methods”). ^{−154}. _{s} at depths of 150 ± 25 km from SL2013sv tomographic model. Circles and error bars = average value ± _{s}, plotted as function of depth for four different tomographic models. Solid/dash-dot/dashed/dotted lines = SL2013sv/CAM2016Vsv/SEMUCB-WM1/S40RTS tomographic models^{19,21,22,34}; _{s}, plotted as function of depth as before.

The ratio of La and Sm concentrations in mafic igneous rocks is often used to track mantle melting^{31–33}. Since La is less compatible within the mantle source compared with Sm, the La/Sm content of a melt decreases as melt fraction increases. The relationship between La/Sm and Δ_{s} is a useful way to explore the role that sub-plate thermal anomalies play in generating intraplate volcanism. In order to assess this relationship, we sub-divide our global database of La/Sm and Δ_{s} measurements into 1° bins and determine the Pearson product-moment correlation coefficient, _{s} at 150 ± 25 km depth to represent asthenospheric mantle. Mineral loss or accumulation can significantly alter the composition of a lava sample away from that of the original mantle melt. Removal or addition of mineral cargo will decrease or increase MgO concentration of the melt, respectively. Thus, MgO content is considered to be a useful indicator of either process. Here, we have excised all samples that have MgO contents <9 wt% and >14.5 wt% from Database 1 to ensure that we only retain samples that are close to the composition of primitive mantle melts. For this filtered version of Database 1, only bins with >5 samples that have been analyzed for La and Sm concentrations are exploited in order to mitigate the influence of local compositional heterogeneity.

There is a positive correlation between La/Sm ratios and Δ_{s} values for the SL2013sv tomographic model at a depth of 150 ± 25 km (_{s} at a depth of 150 ± 25 km, which are indicative of higher temperatures at this depth. The value of this correlation does not significantly change if different methods of binning and filtering are employed, if locations adjacent to mid-oceanic ridges are excluded, or if regions where plate subduction has recently occurred are excised (Supplementary Figs. _{s} are shown as a function of depth for the SL2013sv, CAM2016Vsv, SEMUCB-WM1 and S40RTS global tomographic models^{19,21,22,34}. In each case, the value of _{s} are expected to decrease as mantle temperature increases, these observations suggest that intraplate volcanism is sensitive to temperature variations within the uppermost mantle.

Notwithstanding this correlation, melt chemistry and upper mantle shear-wave velocity can also be influenced by changes in lithospheric thickness, by the composition of the mantle source region, and by depth of the base of the melt column, which is controlled by a combination of mantle temperature and composition^{11,14,32,35}. Although we define the lithosphere-asthenosphere boundary to be the 1175 °C isothermal surface, the base of the actual thermal boundary layer probably extends to greater depths. Global surface-wave tomographic models have a vertical resolution of 25–50 km^{19,21,22,34}. Variations in thickness of the thermal boundary layer coupled with seismic resolution may, therefore, influence values of Δ_{s} estimated within the asthenospheric mantle. Consequently, any correlation between La/Sm and Δ_{s} could also be influenced by lithospheric thickness variations. At depths where Δ_{s} values are affected by lithospheric thickness, a positive correlation between La/Sm and Δ_{s} is expected. In Fig. _{s} are shown for the suite of tomographic models as a function of depth. Beneath intraplate volcanic provinces, lithospheric thickness correlates significantly with Δ_{s} at depths ≤100 km. At depths ≥150 km, this correlation rapidly becomes insignificant (i.e., where _{s} (i.e., _{s} and La/Sm at these depths are principally controlled by temperature variations within the asthenospheric mantle.

Composition of the mantle source region affects the values of both La/Sm and Δ_{s} since melting occurs to a lesser degree within a depleted source region, depleted mantle has lower initial La/Sm values than fertile mantle, and shear waves propagate faster through depleted mantle than through fertile mantle^{14,36}. To determine how the thermochemical structure of the mantle controls melt composition, we carried out principal component analysis on a suite of eight incompatible element concentrations taken from our filtered and binned version of Database 1 (see “Methods”). We then calculated correlations for each of these principal components with respect to geochemical and geophysical indicators of mantle temperature and depletion. The first principal component, _{1}, accounts for 79 ± 1% of the variance within our filtered and binned version of Database 1. The weightings of _{1} are ~0.4 for all elements with the exception of Yb (Fig. _{1} suggests that _{1} is primarily sensitive to melt fraction variation.

_{1}, for first principal component, _{1}. Database 1 is screened and binned as described in caption of Fig. _{1} for each element with range of weighting for 99 binning configurations. In this case, band is narrower than width of line. Proportion of variance described by _{1} is given in bottom left-hand corner. _{2}. _{3}. _{1}, generated using synthetic model that was run 99 times for appropriate range of _{p}, lithospheric thickness, and mantle composition. Colored line/shaded band = average value/range of _{1} for each element. _{2}. _{3}.

As melt fraction increases, incompatible elemental concentrations, and thus _{1}, will decrease within the melt. Alternatively, since these elemental concentrations can vary as a function of source depletion, _{1} may instead be primarily sensitive to mantle composition. To investigate these contrasting hypotheses, we generate correlations for _{1} with respect to La/Sm, Δ_{s} and ^{6,36}. If variations in _{1}, La/Sm, Δ_{s} and _{1} to positively correlate with La/Sm, but to negatively correlate with Δ_{s} and _{1} positively correlates with both La/Sm and Δ_{s}, and it negatively correlates with _{s} variations were primarily dependent upon mantle composition then the most depleted mantle would be associated with the fastest shear-wave speeds (i.e., _{s} would positively correlate). Since the opposite relationship is observed, it is less likely that the correlation between La/Sm and Δ_{s} is controlled by source compositional variations. Instead, we conclude that _{1} is sensitive to melt fraction variations. This result is anticipated since temperature changes are known to have a greater effect upon _{s} than mantle composition^{12,14}. We infer that upper mantle temperature variations are a dominant control on the positive relationship between melt fraction (i.e., _{1} and La/Sm values) and Δ_{s}. Note that, while fractional crystallization can have a modest influence on the value of La/Sm, _{1} does not correlate with MgO concentrations and the observed range of La/Sm values is too great to be controlled by fractional crystallization alone (Supplementary Fig.

Melt fraction, and therefore both La/Sm and _{1}, vary as a function of both asthenospheric temperature and lithospheric thickness. We can disentangle the relative contributions of these quantities by using the second principal component, _{2}, which accounts for 14% of the variance and is dominated by variations in Yb. Compatibility of Yb within the mantle increases at depths greater than 60–80 km where garnet becomes stable at the expense of spinel^{32,37}. Since Yb is far more compatible in garnet-bearing mantle relative to spinel-bearing mantle, Yb concentrations within a melt are more sensitive to the depth at which melting occurs than to changes in melt fraction. Therefore, we can use _{2} as a proxy for comparing the respective contributions of melting within the spinel and garnet stability fields. The contribution of melting within the garnet stability field relative to the spinel field is greater beneath thicker lithosphere or in regions where elevated asthenospheric temperature acts to deepen the onset of melting. Consequently, _{2} can act as a proxy for lithospheric thickness, provided that asthenospheric _{p} remains constant. Alternatively, _{2} can act as a proxy for asthenospheric _{p}, provided that lithospheric thickness is fixed. Δ_{s} at depths of 150 ± 25 km is sensitive to asthenospheric _{p} variations, but insensitive to lithospheric thickness (Fig. _{2} and Δ_{s} at 150 ± 25 km depths (_{s} at depths of 150 ± 25 km (Fig. ^{11,38}). These studies were primarily concerned with major element measurements, which we do not consider here. Such opposing views are reconcilable since lithospheric thickness may have a more significant impact upon major element composition than _{p} if melts stall and thermally re-equilibrate at or near the base of the lithosphere^{25}.

The third principal component, _{3}, accounts for 7 ± 1% of the variance and is primarily sensitive to variations in Ba, Nb, and K. Subduction zone melting is commonly enriched in Ba and K but depleted in Nb. Partial melting of metasomatized lithospheric mantle can exhibit anomalously high, or anomalously low, normalized concentrations of K and Ba relative to Nb^{39,40}. The low variance of _{3} suggests that there are minor contributions either from prior subduction zone magmatism, from melting of metasomatized lithospheric mantle, or from both. _{3} has low variance and does not correlate either with La/Sm or with Δ_{s} at depths of 150 ± 25 km (Supplementary Fig.

These results are corroborated by analysis of synthetic principal components that are calculated for a suite of geochemical models. One-hundred and fifty synthetic trace element distributions were calculated by randomly varying values of _{p}, lithospheric thicknesses, and mantle compositions within fixed limits (i.e., 1250–1450 °C, 35–75 km, and primitive/depleted mantle, respectively; see “Methods”). This procedure is repeated 99 times. The first synthetic principal component, _{1}, is similar to _{1} both in terms of elemental weightings and variance (Fig. _{1} strongly correlates with _{p} and does not significantly correlate either with lithospheric thickness or with mantle depletion (_{1} and _{1} are primarily sensitive to changes in _{p}. _{2} accounts for 8 ± 4% of the variance and, like _{2}, it is dominated by variations in Yb (Fig. _{2} correlates with lithospheric thickness but does not correlate either with _{p} or with mantle depletion (_{2} and lithospheric thickness may indicate that _{2} is also primarily sensitive to lithospheric thickness variations. _{3} has a similar distribution of weightings as _{3} but not as strong weighting for Ba, K, and Nb. As expected, _{3} does not consistently correlate with _{p}, lithospheric thickness or depletion. These observations add strength to the idea that _{3} represents lithospheric contamination, which is not accounted for by this synthetic model. Note that conclusions based on these synthetic models depend upon the assumption that asthenospheric _{p}, lithospheric thickness, and mantle depletion are uncorrelated with respect to each other on Earth.

The global distribution of intraplate magmatism together with a positive correlation between La/Sm and Δ_{s} at a depth of 150 ± 25 km suggest that intraplate magmatism is principally associated with elevated asthenospheric temperatures beneath thin lithosphere. This inference can be quantitatively investigated by analyzing relationships between the chemical composition of volcanic rocks, shear-wave velocity anomalies and asthenospheric potential temperature, _{p}. An important goal is to compare geochemical and geophysical estimates of _{p}.

First, the chemical composition of intraplate volcanic rocks is used to constrain the depth and degree of mantle melting. Here, we exploit a geochemical inverse modeling strategy, which minimizes the misfit between observed and calculated concentrations of rare earth elements (REE) by systematically varying melt fraction as a function of depth (“Methods”^{2,41}). In this polybaric model, REE concentrations are calculated by integrating instantaneous melt compositions along isentropic melting paths. These melting paths are determined by a combination of potential temperature of the mantle source region, _{p}, and lithospheric thickness, _{p} and a chosen melting parameterization. Here, we exploit the hydrous lherzolitic melting model described by Katz et al.^{35}. Note that some model parameters have been updated to honor experimental constraints that have subsequently been obtained (“Methods”^{42}). This melting model requires a _{p} value of 1312 °C in order to generate the average crustal thickness at a mid-oceanic ridge (i.e., 6.9 km^{29}). We assume that this value represents the potential temperature of ambient asthenospheric mantle. For each volcanic province, we systematically vary _{p} and _{p} and _{p} and _{p} and _{p} and

Figure _{p} and _{p} and _{p} = 1366 ± 15 °C and ^{24}). The misfit function shows that there is minimal trade-off between _{p} and _{p} = 1367 ± 28 °C and ^{43}). The misfit function shows that there is a negative trade-off between _{p} and

_{p}, and of lithospheric thickness, _{p} and ^{42} corrected for appropriate water content and labeled by values of potential temperature; pair vertical dotted lines at 63 and 72 km = limits of spinel-garnet transition zone^{37,43}. _{p} and

Inverse modeling has been carried out for intraplate volcanic analyses from our filtered and binned version of Database 1 (Supplementary Fig. _{p} and _{p} with values determined at 150 ± 25 km depths for the SL2013sv model (“Methods”^{21,27}). Note that the geochemical inverse model and the _{s}-_{p} = 1333 °C, would be required to generate the average oceanic crustal thickness for the _{s}-^{27,29}. Globally, we observe a positive correlation of _{p}, which is the temperature anomaly with respect to ambient asthenospheric mantle (Fig.

_{p} determined by geochemical inverse modeling and that determined by calibration of SL2013sv tomographic model where ambient mantle temperatures are assumed to be 1312 °C and 1333 °C, respectively. Open circles with vertical and horizontal error bars = calculated values of temperature for global distribution of intraplate volcanism ± 1.5× minimum misfit; black line 1:1 relationship; _{p} at depths of 150 ± 25 km calculated from SL2013sv tomographic model. Red/white/blue contours = positive/zero/negative values of Δ_{p} at intervals of 50 °C; colored circles = geochemical values of Δ_{p}; yellow line between ^{58,59}. _{s} at depths of 150 ± 25 km along transect calculated from SL2013sv tomographic model; open circles = observed values of La/Sm averaged into 1° bins that lie within <200 km of transect; red circles = bins with > 5 values of La/Sm. _{p} at depths of 150 ± 25 km calculated from SL2013sv tomographic model where color scale is shown at right-hand side of panel _{p} calculated for screened and binned version of Database 1 ± 1.5× minimum misfit. Dashed black line at Δ_{p} = 0 is for visual guidance.

We acknowledge that limitations of both geochemical and tomographic methodologies could give rise to Δ_{p} discrepancies (e.g., refs. ^{14,26,43,44}). Global tomographic models are considerably damped and smoothed. Ray path coverage of the upper mantle is variable, spatial resolution is limited to ~200–600 km, and lateral smearing of fast velocities can sometimes occur adjacent to thick cratonic lithosphere. These spatial resolution issues could account for the small number of intraplate volcanic regions that fall on regions with positive values of Δ_{s} at depths of 150 ± 25 km. Calibration of the _{s}–^{26}. The presence of melt within the mantle may reduce _{s} as a result of poroelastic effects that are not accounted for within this parameterization^{15}. However, the amount of melt retained within the mantle is probably very small (i.e., ~0.1%), especially at a depth of 150 km, which in most regions is beneath the peridotite solidus^{35,45}. Since the reduction of _{s} caused by poroelastic effects should scale as a function of melt fraction, these effects can be considered to be negligible^{46}. The parameterization does not account for compositional variations, which means that temperature estimates for continental regions, especially depleted cratonic cores, may involve additional uncertainties. In continental regions with thin lithosphere (i.e., ≲75 km), additional uncertainties can arise as a result of inaccuracies in the parameterization of crustal structure. These inaccuracies can cause “bleeding” of slow crustal velocities into the uppermost mantle that are interpreted as hotter temperatures, which yield underestimates of lithospheric thickness^{26}. Nevertheless, temperature profiles calculated using this tomographic approach provide acceptable fits to continental geothermal profiles derived from xenolith thermobarometric observations for locations with a range of lithospheric thicknesses (50–200 km^{27}). The observed negative correlation between _{s} at depths of 150 ± 25 km also indicates that, in regions of thin lithosphere, shear-wave velocities are controlled by thermal anomalies rather than by compositional variations associated with depletion and enrichment (Supplementary Fig. ^{47}.

Geochemical inverse modeling of intraplate volcanic rocks necessarily depends upon a simplified treatment of mantle source composition, upon the depth of the spinel-garnet phase transition, upon experimentally determined partition coefficients, and upon details of the melting model^{2}. Changes in values of input parameters inevitably affect absolute values of _{p} and _{p} and ^{43}. Furthermore, the inverse model assumes a uniform lherzolitic source and does not consider harzburgitic and pyroxenitic lithologies. For example, the presence of harzburgite and pyroxenite within the mantle can lead to over- and underestimates of _{p}, respectively, if a purely peridotitic model is implemented^{48}. These sources of uncertainty could be responsible for low temperature values recorded in some provinces and for the minor, but systematic, offset between geochemical and tomographic temperature estimates (Fig. _{s} (_{s}, lithospheric thickness changes represent an important secondary geochemical signal. Since our geochemical potential temperatures are calculated by accounting for lithospheric thickness changes, the decrease in correlation coefficient that we observe may result from removal of this secondary signal. Despite the inherent uncertainties associated with both modeling approaches, the positive correlation between these independent estimates affirms the underpinning assumptions and highlights the potential rewards of combining temperatures estimated from geochemical analyses of intraplate volcanic rocks with temperatures calculated by calibrating tomographic models.

In order to highlight the consistency between geochemical and tomographic estimates of mantle potential temperature and lithospheric thickness, we present a hemispherical transect that summarizes regional variations of La/Sm, Δ_{s} at a depth of 150 ± 25 km, Δ_{p} at a depth of 150 ± 25 km, and _{s} are associated with the Icelandic plume (Fig. _{s} values increase again, although there is some scatter. As expected, there are concomitant increases and decreases in geochemical and tomographic estimates of Δ_{p} (Fig. ^{49}. Note that in regions where the lithosphere is >125 km thick, a correlation between tomographically derived estimates of lithospheric thickness and the values of Δ_{p} at a depth of 150 ± 25 km is expected since these values of _{p} reside within the lithospheric mantle (e.g., North Sea, Tanzania).

Our global analysis of volcanic provinces and shear-wave velocity anomalies suggests that a combination of asthenospheric temperature anomalies and lithospheric thickness variations helps to determine the spatial distribution of intraplate magmatism. This inference is manifest by a range of geochemical and geophysical observations. First, the bulk of Neogene-Quaternary intraplate volcanism coincides with slow shear-wave velocity anomalies and thin lithosphere. Secondly, there is a positive correlation between La/Sm values of intraplate volcanic rocks and the average magnitude of these shear-wave velocity anomalies within an asthenospheric channel centered on 150 ± 25 km. Thirdly, potential temperatures and lithospheric thicknesses calculated by geochemical inverse modeling of REE concentrations generally match those values obtained from a _{s}-^{17}. Note that, in addition to the influence of temperature anomalies, these correlations could be partly modified by mantle compositional variation or by crystal fractionation beneath mid-oceanic ridges^{50,51}.

Intraplate volcanism is spatially associated with thin lithosphere and its melt composition can be used to estimate asthenospheric temperature. Both thinning of undepleted lithospheric mantle and elevated asthenospheric temperature are significant means for generating regional uplift on horizontal length scales of order 10^{3} km and on timescales of order 10 Ma. Therefore, our results have direct implications for the spatial and temporal evolution of dynamic topography, which is generated and maintained by mantle convective processes^{52,53}. We define dynamic topography to embrace long-wavelength topography generated by mantle flow, isostatic responses to thermochemical processes within the convecting mantle, as well as regional changes in thickness of the lithospheric mantle^{54,55}. If we assume an equilibrated lithospheric thickness of _{0} = 120–150 km at mean sea level, the amount of regional uplift is given by_{1} is the present-day lithospheric thickness, ^{−5}^{ ∘}C^{−1} is thermal expansivity, Δ_{1} = 1390 °C is ambient asthenospheric temperature (i.e., the temperature at 150 km depth provided _{p} = 1330 °C, mantle rock density = 3300 kg m^{−3}, and specific heat capacity = 1187 J kg^{−1 }K^{−1} (refs. ^{42,56,57}). If lithospheric thickness is reduced to, say, _{1} = 60 km, if Δ^{ ∘}C, and if ^{−1}. Thus, a significant corollary of our proposed mechanism for generation of intraplate volcanism is rapid large-scale uplift. This prediction is easily tested by examining the relationship between topographic elevation and emergent (but undeformed) marine sedimentary rocks that crop out in regions where intraplate volcanism predominates, where asthenospheric temperatures are anomalously high, and where continental lithosphere is anomalously thin. Dramatic examples include western North America, southernmost South America, eastern Australia, and North Africa where marine deposits of negligible dip indicate that hundreds of meters of wholesale rapid uplift occurred during Cenozoic times (Fig. ^{55}). In western Arabia and in eastern Anatolia, Cenozoic marine rocks occur at Jabal Umm Himar and within the Sivas Basin at present-day elevations of 1.2 and 1.5 km, respectively (Fig. ^{[ 58,59}). Regional uplift of these undeformed marine deposits can be achieved by a combination of emplacement of an asthenospheric temperature anomaly and lithospheric mantle thinning^{60,61}.

Dynamic topography undoubtedly makes a profound contribution to relative sea-level changes, ancient oceanic circulation, fluvial drainage patterns, and sedimentary deposition^{62–67}. Here, we have shown that intraplate magmatism, positive asthenospheric temperature anomalies and thinned lithosphere are closely related during Neogene-Quaternary times. Removal or thinning of lithospheric mantle produces regional uplift but subsidence will eventually occur as the lithosphere conductively cools and re-thickens^{68,69}. These processes generate vertical motions of the order of hundreds of meters at the Earth’s surface that are superimposed on motions generated by mantle convection. There is considerable debate about the way in which mantle flow contributes to dynamic topography, and about the relative contributions of the upper and lower mantle^{70}. By combining the distribution and composition of intraplate volcanism with calibrated tomographic models, we have shown that asthenospheric temperature variation and lithospheric thickness changes can make a significant contribution to dynamic topography. Since intraplate magmatism occurs throughout the stratigraphic record, we suggest that a combined analysis of igneous rocks and stratigraphy could help to elucidate the history of mantle convective and dynamic topographic phenomena throughout the Phanerozoic Era.

For this study, we primarily exploited the SL2013sv tomographic model^{21}. This global upper mantle model uses body and surface waves that include both fundamental and higher modes with periods of 11–450 s. A total of ~750,000 seismograms were analyzed by ref. ^{21} and misfits were calculated by comparing observed and calculated waveforms (≤18th overtone). Significantly, the SL2013sv model inverts for crustal structure during the optimization process whereas other global models mostly, but not always, use a defined a priori crustal architecture. The SL2013sv model has a vertical resolution of 25–50 km and chequerboard tests demonstrate that features with diameters of ~600 km can be clearly resolved at lithospheric depths. In areas of greater ray-path coverage (e.g., North America, Europe) finer scale features should be resolvable. Here, this model is shown relative to AK-135 reference model recomputed for a reference period of 50s and slightly modified following a preliminary optimization^{71}. This reference model also incorporates laterally varying crustal structure that is initially based upon CRUST2.0 and is continually updated during optimization^{21,49}. Descriptions of the CAM2016Vsv, SEMUCB-WM1 and S40RTS tomographic models are provided in ^{19,22,34}.

We exploit a _{s}-to-^{27} to the SL2013sv tomographic model^{21}. This scheme was originally developed by ref. ^{26} and it has been updated to exploit an empirical formula, which describes _{s} as a function of pressure and temperature^{13}. Several of the parameters used in this empirical formula were experimentally constrained^{13}. However, seven material constants are required to be independently calibrated for each different tomographic model. These constants are: _{r}, _{a}, _{a} and

All seven empirically determined parameters are permitted to vary within physically plausible limits (e.g., refs. ^{13,26,72}). The resultant _{s}(_{1}–_{4}). For oceanic lithosphere, _{s} varies as a function of depth and plate age^{12}. Oceanic plate profiles parallel to plate spreading (i.e., flowlines) taken from the SL2013sv tomographic model are averaged and _{s} as a function of depth and plate age is determined. These stacked tomographic profiles are compared to values of _{s} estimated by applying the _{s}-to-^{29}. _{1} is then calculated by computing the rms misfit between observed and calculated _{s} profiles at depths of 75 and 100 km^{27}. Oceanic plate cooling models can only be used to minimize the difference between observed and calculated values of _{s} at depths ≤125 km^{29}. Therefore, a second misfit function, _{2}, is constructed at depths beneath the upper-thermal boundary layer (i.e., from >225 to 400 km). _{s} values as a function of depth for the SL2013sv tomographic model are averaged across oceanic regions and compared with values of _{s} estimated from a 1333 °C isentrope calculated for peridotite using material constants from ref. ^{42}. Both the oceanic plate cooling model and the temperature profile for convecting mantle are assumed to have a _{p} of 1333 °C^{27,29,42}. Mantle with a _{p} value of 1333 °C is considered to be at ambient temperatures within the final model. These empirically derived parameters are used to provide a prediction of shear-wave attenuation, ^{−1} (ref. ^{73}). The calculated value of ^{−1} can be compared to an estimate of seismic attenuation at depths >150 km beneath old oceanic floor (>100 Ma^{74}). The misfit between observed and predicted ^{−1}, _{3}, is calculated for these locations. Finally, the misfit between an assumed value of shear viscosity, _{4}, is calculated. The combined misfit, _{s}, is quantified by summing weighted versions of these four rms misfit functions, _{1}–_{4}, where

_{1}–_{4} are weighting coefficients with values of 10, 1, 2 and 2, respectively^{27}. See refs. ^{27} and^{47} for a detailed explanation of this _{s}-to-

A two-sample Kolmogorov–Smirnov test is used to calculate how likely it is that two cumulative distribution functions, CDFs, are drawn from the same reference distribution^{30}. The probability,

Database 1 is used to define locations of recent intraplate volcanism. Here, Database 1 is filtered to remove samples that are >10 Ma and samples that are >400 km from their predicted site of eruption. Note that we do not filter for MgO content. For ease of analysis, we have subdivided the Earth’s surface into 1° × 1° bins where _{i} and _{i}, by _{i} is the latitude of the bin such that_{s} is <1 in 10^{100}. The probability that bins containing intraplate volcanic samples are randomly distributed such that they lie above thin (<100 km thick) lithosphere is <1 in 10^{150}.

The quality of correlation between two datasets, for example between La/Sm and Δ_{s}, can be determined using the Pearson product-moment correlation coefficient,

The symbols _{i} and _{i} denote the _{0}, and the slope, _{1}, which define the linear best-fit to observed values are calculated using

To determine the statistical significance of these correlations, we can use either the population correlation coefficient or a look-up table of

Before principal component analysis is carried out, Database 1 is filtered so that only samples with 9 < MgO wt% <14.5, which are <10 Ma, which are <400 km from their predicted site of eruption, and which contain all eight incompatible trace elements, are included. These measurements are binned in the way described in the main text and any bins that have ≤5 samples are removed. Each bin is then normalized to average composition for each element within the filtered and binned version of Database 1. Principal component analysis is carried out using the statsmodels.multivariate.pca routine from the Python software package where the following settings are selected: number of calculated components = 3; standardize = “True”; and method = “NIPALS”.

To construct a synthetic dataset, elemental concentrations are calculated using the INVMEL model for a range of _{p} values, lithospheric thicknesses, and mantle compositions. Random distributions of _{p}, lithospheric thickness and _{p}, lithospheric thickness and _{p}, lithospheric thickness and

The INVMEL-v12 geochemical model is used to calculate rare earth element (REE) concentrations generated by mantle melting for different values of _{p} and lithospheric thickness^{41}. Concentration of each REE within an instantaneous melt, _{l}, and concentration within the residue, _{s}, are related to each other by two equations, which must be simultaneously solved. These equations are^{75}. _{l} and _{s} at each depth, the expressions in Eq. (8) are numerically integrated using a fourth-order Runga-Kutta scheme from the base of the melting interval, where _{l} by

The mean composition of all of the melt extracted from the melting interval 0–^{35} updated using revised parameter values from ref. ^{42}. _{p}, lithospheric thickness, _{cpx}. ^{76}. _{cpx} = 0.17 is fixed for all models.

Composition of the mantle source region used in this modeling procedure varies as a function of the average value of ^{77}). Note that varying REE element concentrations within the source region as a function of ^{42} and assuming an _{p} = 1312 ± 28 °C is required to generate 6.9 ± 2.2 km of oceanic crust at a mid-oceanic ridge, assuming a triangular melt geometry^{29}. We thus assume that 1312 °C is the ambient value of _{p}. Within the mantle, the aluminous phase present varies as a function of depth between plagioclase, spinel and garnet. The mineral proportions used within each stability field are given in Supplementary Table ^{2,37}.

The bulk distribution coefficient of the melting assemblage, _{n}, where _{1}. _{1} is assumed to be located where _{n} = 0, between _{1}. The proportion of olivine to orthopyroxene remains fixed and the concentration of these minerals within the source region is varied so that

To calculate the bulk distribution coefficient for a given element within the solid assemblage, _{i}, must be parameterized. Values of _{i} for each REE in olivine, orthopyroxene and spinel are listed in Supplementary Table _{i} entering into site _{A} is Avogadro’s number, ^{78}. The constants required to calculate _{i} for REEs in clinopyroxene, plagioclase and garnet as a function of pressure, temperature and chemistry are listed in Supplementary Tables _{mol}, Cr_{2}O_{4mol}, Al_{2}O_{3mol}, FeO_{mol}, MgO_{mol}, CaO_{mol} are the fraction by weight of each oxide within garnet divided by their respective molecular weights (Supplementary Table ^{79}). Partitioning of REEs into clinopyroxene depends upon the proportions of Ca and Al within the clinopyroxene phase, ^{78}. These proportions are calculated using_{i}, _{mol}, _{i} and _{i} are the proportions of oxide

Before comparing calculated REE concentrations, _{ol}, to ensure that the melt is in equilibrium with olivine of 90% forsterite content, is calculated. The equations of ref. ^{4} are used, assuming Fe^{3+}/∑Fe = 0.15^{43}. The average _{ol} value for all samples within a given volcanic province is used and no REEs are assumed to be present within the cumulate olivine. Corrected observed REE concentrations,

To identify that model that best fits the corrected REE concentrations, _{p} and _{p} is varied between 1250–1550 °C and _{p} and _{p} and _{c} is the standard deviation of _{p} and _{p} and _{p} and

P.W.B. acknowledges support by Shell Research. We are grateful to K. Czarnota, I. Frame, L. Kennan, M.J. Hoggard, M. Klöcking, D. Lyness, F. M^{c}Nab, C.P.B. O’Malley, F. Richards, G. Roberts, O. Shorttle, and K. Warners for their help. D. McKenzie generously provided software for the INVMEL forward model. Y. Niu provided an insightful review. Figures were prepared using Generic Mapping Tools software. Database 1 was compiled with the aid of the GEOROC database (

All authors jointly contributed to the conceptualization and design of this research project. P.W.B. collated the geochemical database, performed the geochemical modeling, carried out the statistical analysis, and drafted the figures. P.W.B. and N.J.W. wrote the paper with assistance and advice from J.M. and S.N.S.

All geochemical data analyzed during this study are included in this published article and are included and appropriately referenced within Supplementary Data File _{s}-to-^{19–22,27,80}).

The INVMEL software package is available on request from D. McKenzie. All other codes used can be provided by the authors upon request.

The authors declare no competing interests.

_{2}O

^{2+}on garnet–melt trace element partitioning: experiments in FCMAS and quantification of crystal-chemical controls in natural systems

Supplementary Information

Peer Review File

Description of Additional Supplementary Files

Supplementary Data 1

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