The nature and origin of the two large low-velocity provinces (LLVPs) in the lowest part of the mantle remain controversial. These structures have been interpreted as a purely thermal feature, accumulation of subducted oceanic lithosphere or a primordial zone of iron enrichment. Information regarding the density of the LLVPs would help to constrain a possible explanation.

In this work, we perform a density inversion for the entire mantle, by constraining the geometry of potential density anomalies using tomographic vote maps. Vote maps describe the geometry of potential density anomalies according to their agreement with multiple seismic tomographies, hence not depending on a single representation. We use linear inversion and determine the regularization parameters using cross-validation. Two different input fields are used to study the sensitivity of the mantle density results to the treatment of the lithosphere. We find the best data fit is achieved if we assume that the lithosphere is in isostatic balance.

The estimated densities obtained for the LLVPs are systematically positive density anomalies for the LLVPs in the lower 800–1000 km of the mantle, which would indicate a chemical component for the origin of the LLVPs. Both iron-enrichment and a mid-oceanic ridge basalt (MORB) contribution are in accordance with our data, but the required superadiabatic temperature anomalies for MORB would be close to 1000 K.

Seismology has systematically revealed more and more of the heterogeneity in the mantle. Interpretations of seismic images often aim at determining the density of features, because buoyancy is the driver of mantle dynamics. For instance, much research has focused on tracing sinking slabs in order to understand how subduction works (e.g.

The two LLVPs are antipodal regions of decreased seismic velocity that extend from the core–mantle boundary about 400–800 km into the mantle and cover about 25 % of the surface of the core–mantle boundary

The debate regarding the LLVPs is often centred on their density, because density allows one to distinguish between a purely thermal and a thermo-chemical origin. However, direct determinations of density using seismological and geodetic methods have led to contradictory results, indicating either positive

Combining seismology and gravity to investigate the mantle is a well-established approach that typically includes dynamical modelling of mantle convection

While viscosity inversions can successfully explain the geoid with variance reductions of 80 % or more

Furthermore, the modelled geoid associated with a certain density distribution is partly based on the dynamic topography caused by this density distribution. Thus, viscosity inversion should also reproduce surface topography, since it is an important part of the total gravity effect. However, before the dynamic predictions can be compared to real topography, the isostatic part of topography must be removed using crustal models. While the agreement between predicted and non-isostatic topography has been increasing

The justification for directly inverting for density instead of going through viscosity is that the gravity field is only affected indirectly by the viscosity distribution, through viscosity's influence on the deformation of the boundaries (surface and core–mantle boundary)

In this contribution, we explore an alternative approach for fitting the gravity field using mantle density structure. Instead of density–velocity conversion, we use tomographic vote maps

We use satellite gravity data from the global gravity field model GOCO05S

As a first step we calculate an ice-corrected Bouguer anomaly based on the topography of ETOPO1

Since we are interested in the mantle density structure, the second step is to account for the gravity effect of the crust and/or lithosphere. Two inherently different approaches exist to achieve this. The first option is to assume some form of isostatic compensation and use this to account for the crust and/or lithosphere. Alternatively, the gravity effect of crustal models, such as Crust1.0

In light of this discrepancy, we explore two approaches. In the first approach, we assume that continental topography is compensated by crustal thickness variations, whereas ocean floor depth is compensated by variations in the mantle lithosphere density (the same isostatic model as in

Input data for the inversions.

In the second approach, we use our recent crustal model based on kriging

The isostatic residual is very similar to the free-air anomaly (Fig.

Additional constraints are required to overcome the inherent non-uniqueness of a density inversion. We use information from whole mantle seismic tomographies in the form of vote maps

Vote maps at 2700 km depth.

The first step is to discretize the inversion problem by extracting regions of potential density anomalies from the vote map individually for each depth. Our underlying assumption is that density anomalies only occur in horizontally connected regions where at least

Our inversion is a two-step approach. First, we forward calculate for each potential density anomaly region its characteristic gravity response. Second, the characteristic gravity responses of all of the potential density anomalies are placed into a matrix

The gravity effect of each potential density anomaly is estimated by approximating it as a collection of point masses. Each point mass represents a volume

The gravity kernel

Next, the gravity response of all of the potential density anomalies are placed into a matrix

The unknown density values of the potential density anomalies are placed in a vector

The optimal

In

By design, the training misfit is minimal when

Apart from constraining the regularization parameters, this procedure also gives a bootstrap estimate

The surface and CMB deformations implied by the density model recovered by inversion are important to judge the quality of the results. The surface topography predicted by the density model should roughly agree with the residual topography, because topography is strongly sensitive to density. The magnitude of the CMB deformation is required to assess how much it affects the gravity field fitting.

We determine the deformation of the upper and lower domain boundary caused by density structure as a postprocessing step after inversion. We use both an isostatic and a simple dynamic formulation to determine this deformation.

Let

We convert the density difference associated with undulating topography into a surface density

Isostatic surface topography is calculated in the same way using the upper 300 km of the domain and a density contrast of 2670 kg m

To determine the dynamic surface and CMB topography we use the propagator matrix approach of

The resulting kernels show that for the assumed viscosity structure, the influence of density anomalies below 500 km on topography is limited, even at very long wavelengths (Fig.

Topography and CMB kernels calculated using the propagator matrix approach

A grid search of

Results of the inversion using the isostatic residual.

The inversion is able to reasonably reproduce the main features of the isostatic residual gravity field (Fig.

In the spectral domain, the predicted gravity field is able to reproduce the long-wavelength part up to spherical harmonic (SH) degree 10 (Fig.

The inverted density anomalies show no clear correlation with sign of the velocity anomaly (Sect.

Density anomaly slices through selected depths of the inversion results using the isostatic residual.

The upper 100 km of the inversion results contain very little density variations (Fig.

At greater depths, subducted slabs would be expected in the density structure. This is overall reflected in our density inversion results, but not all slabs are resolved as positive density anomalies over their complete depth range. For example, the Andean slabs can be seen at a depth of 900 km as an anomaly of

The LLVPs have systematically a positive density anomaly of up to

The preferred regularization parameters derived by the cross-validation
procedure are similar to those for the isostatic residual,

Results of the inversion using the crustal residual.

Overall the inverted density variations are much larger for the crustal residual than for the isostatic residual (Fig.

Density anomaly slices through selected depths of the inversion results using the crustal residual.

At depths of 600 and 900 km, some subduction-related density anomalies can be seen, but overall correlation is poor. Only in the lowest mantle a more consistent picture emerges, in particular the LLVPs are resolved as positive density anomalies (

While the main features observed are the LLVPs, it is important to also scrutinize the results for the remaining mantle. A long-wavelength error in the upper-mantle density structures leads to an incorrect estimate of the density of the LLVPs. In the upper mantle above the transition zone (410–670 km depth) much of the seismic image can be linked to tectonic features: thick and cold lithospheric roots underlie the cratonic cores of the continents and can extend up to 300 km deep

The cratonic lithospheric mantle density is the result of a complex interaction between temperature, composition and mineralogy

The density of the oceanic mantle is expected to increase with age, following the cooling trend, which also explains seafloor subsidence. The inversion with crustal residual shows some decreased density associated with mid-oceanic ridges, but vote maps are unsuited to resolve the continuous gradient associated with the cooling of the plate. When using the isostatic residual, ocean floor subsidence and the cooling trend has already been accounted for during the isostatic correction and is thus not resolved by the inversion.

Subducted slabs are denser than surrounding mantle immediately after subduction. As the plate sinks, heat diffuses into the plate from the surrounding mantle, so that the plate slowly loses its negative buoyancy. How quickly a subducted plate thermally equilibrates depends on how effectively heat is transported to the slab by convection and conduction. Since some slabs seem to stagnate on mantle discontinuities, it is conceivable for a slab to loose all or most of its negative buoyancy. We compared our results with the slab depth contours from Slab 1.0

Out of the 12 slabs contained in Slab1.0, only five are detected as positive velocity anomalies based on the vote maps (Fig.

Comparison with Slab1.0

The reason might be that the tomography models are too heterogeneous in quality and resolution to resolve these relatively narrow features. Of course, vote maps are not the only way to extract features from seismic tomographies, and an alternative would be to use the “best” seismic tomography model available instead of a collection of models. But there are no clear criteria to decide which tomography result is the best, except that newer results are probably based on more and better data. Furthermore, there is some evidence that the differences between tomographic models partly reflect different regularization parameters, rather than different resolved features

Still, out of the five detected slabs, four have positive density contrasts (

Based on these results, we think that our density inversion gives acceptable results overall for most of the mantle. The binary classification scheme we use to extract regions from the vote maps leads to a very rough representation in the upper 300 km, which likely contributes to the poor data fit obtained using the crustal residual. In addition, we assume a constant density contrast over the vertical resolution of 100 km. Thus, the volume of relatively thin structures like slabs might be smeared out over a too large depth range.

We compare the recovered density values with velocity values from the SMEAN2 tomography, an update of SMEAN

Next, we calculated the distribution of the

In the case of the isostatic residual, the median conversion factor changes significantly with depth (Fig.

Distribution of density-anomaly-to-velocity-anomaly ratios as a function of depth. The blue line is the distribution for fast velocity anomalies, and the red line is for slow velocity anomalies. The yellow line gives the median of the ratio distribution. Note that the median sometimes appears to lie outside the distribution, which is due to heavy tails that are not visible on this scale. Furthermore, the histograms for slow and fast anomalies are scaled to have the same maximum height for easier visual comparison.

The velocity–density scaling relations we calculated could have the following causes. The small scaling values in the upper 300 km is due to the fact that we use the isostatic residual. The increased scaling factors in the transition zone depths could be related to undulations in the phase transitions depths, because the higher-pressure phases have both higher density and velocity. Thus, any undulation of the phase transition would strongly affect both density and velocity. The negative velocity-anomaly-to-density-anomaly ratios we calculated below 1200 km depth zone can only be explained by compositional variations. In Appendix A we calculate sensitivities of density and velocity to temperature, iron content and MORB (mid-oceanic ridge basalt) fraction changes. We find that the sensitivities to iron content and MORB fraction are fairly constant below the transition zone, whereas the temperature sensitivity slowly decreases with depth. Thus, the velocity and density values below the transition zone could be more indicative of compositional variations than above the transition zone.

The joint geodynamic–tomographic model Gypsum

However, the negative conversion factors might also be affected by unmodelled dynamic effects. Depending on the viscosity model, the geoid kernel can become negative at the longest wavelengths in the lower mantle

In the case of the crustal residual, the increased overall density variation leads to higher velocity anomaly to density anomaly scaling values (Fig.

We calculated the contribution of the mantle to surface topography. This allows one to assess the quality of our results, because the predicted mantle topography contribution should be zero for the isostatic residual and equal to the residual topography in the crustal residual case.

In the isostatic case, the upper mantle contributes less than 250 m to surface topography (Fig.

Isostatic contributions to boundary deformations from inverted density model. To facilitate comparison with the dynamic topography in Fig.

These results are also confirmed by the dynamic topography calculation. With the two-layer viscosity model that we chose, the topography kernels are essentially zero except for the upper 300 km of the mantle. Hence, the predicted dynamic topography is very similar to the isostatic topography. Even at degree 2, where one would expect the strongest signal from dynamic topography, according to the kernels, there is hardly any topographic contribution, because the high-density LLVPs (the dominating degree 2 structure) are overlaid by negative density anomalies. The existence of a low-density layer on top of the LLVPs was also observed in a mantle convection simulation

The inversion results with the crustal residual reproduce the main feature of the residual topography of our crustal model to first order. The isostatic topography contribution of the upper 300 km is considerable (up to 1.5 km). In the North American and Siberian craton, the isostatic topography is mainly negative due to the strong influence of thick, dense lithosphere, but in other areas (e.g. South Africa) the topographic contribution is negative. In the oceans, the expected signal from ocean floor spreading can only be seen in the Pacific. This is because the vote maps only reflect the oceanic cooling trends in a very crude way, such that only the broad ridges in the Pacific can be captured using this technique.

Still, there is qualitative agreement between the residual topography of the crustal model we used and the topography contribution from the upper mantle. The remaining misfit is due to an imperfect crustal model and the poor representation of the lithospheric mantle in the vote maps. In a recent model

We did not explicitly include the gravity effect of CMB deformation in our inversion. To estimate the impact of CMB topography, we use the results based on the isostatic residual gravity. If the lower 800 km of the mantle is isostatically balanced on the CMB and assuming a density contrast of 4500 kg m

These results also hold if dynamic topography is calculated using a two-layer viscosity model at least at the wavelengths where the gravity signal of the CMB would be visible (compare Figs.

Dynamic contributions to boundary deformations from inverted density model and a two-layer viscosity model. The results are filtered to spherical harmonic degree 30.

Comparing our results with published CMB topography estimates based on seismological methods

The results obtained with isostatic and crustal residual disagree substantially. The correlation coefficient calculated for individual depth slices is typically less than 0.5 and even negative for some depths. The highest correlations are found in the depth ranges of 2500–2800 and 1500–2000 km and are mainly due to the influence of the LLVPs. In addition, the magnitude of the density anomalies is on average 4 times larger based on the crustal residual, which agrees with the relative magnitude of the input gravity fields.

Based on the fit to the data, the isostatic residual is preferred, because it achieves both higher absolute and relative data fit. However, the isostatic Moho depths disagree with the seismological determinations. Furthermore, the crustal residual lacks a correction for the oceanic cooling trend, which clearly contributes to the crustal residual. Thus, the better data fit preference for the isostatic residual is not as straightforward.

In any case, the isostatic and crustal residuals are extreme examples of how the crust and upper mantle can be accounted for in a gravity inversion. Our results clearly demonstrate that these different approaches lead to an enormous spread in terms of the recovered densities in the mantle. At the same time, signals from the deep Earth in terms of gravity or topography might affect modelling of the upper Earth. Commonly, high-pass filtering is used to remove the signal of the deep Earth

Broadly speaking, the LLVPs could originate from any combination of increased temperature and compositional variation. After their first discovery, the LLVP were initially considered as a purely thermal feature: two “superplumes” that rise from the core–mantle boundary

In contrast to this isochemical view, some authors have proposed that the LLVPs are chemically distinct from the normal (pyrolitic) mantle. The chemical distinctiveness of the LLVP can either be accumulated over time or be a primitive reservoir that separated early in Earth's history

Our inversion results indicate a positive density anomaly for the LLVPs both using isostatic and crustal residual. This would rule out a purely thermal origin of the LLVPs, since such a scenario would lead to negative density anomalies.

In order to test different scenarios using our inversion results, we make use of the petrological database of

We assume a negative S-wave velocity deviation of 2 % for the LLVPs, since most mantle tomographies display roughly this amount of slowness. Our inversion results would place the density anomaly of the LLVP between 0.1 % (isostatic residual) and 0.3 % (crustal residual), but due to possible isostatic compensation at the CMB, (Sect.

A temperature increase of 670 K leads to the required velocity reduction; however it would also entail a density change of

Adding a MORB fraction leads to higher required temperatures, because MORB is slightly faster than pyrolitic mantle at the depths of the LLVPs, according to our petrophysical calculations. Our lowest density estimate (

Based on our results it is difficult to express preference for MORB or iron enrichment. Since MORB is introduced to the mantle by subduction, plate reconstructions place some constraints on the amount of MORB produced.

In this paper we have presented how the gravity field and tomographic vote maps can be combined to estimate the density distribution inside the mantle. We have shown that the method is able to reasonably recover expected features in the mantle without requiring any information about the viscosity structure. Still, our recovered density structure leads to qualitative agreement between isostatic and residual topography. Furthermore, our results indicate that the LLVPs are slightly denser and hence chemically distinct.

In our first-order analysis, the nonlinear dependencies of velocity and density, the impact of melt, heterogeneity inside the LLVPs, and the possible presence of post-perovskite is neglected. However, our results can be reconciled with our present knowledge about rock properties at these extreme conditions.

One important difference compared to previous methods is that in our method density is free to vary independent of seismic velocity. While this gives the necessary freedom to the density inversion, it ignores the strong evidence for the important role of temperature. In the future, more precise petrophysical data could help to put constraints on the relative importance of temperature and composition. This would also help to reconcile our results with previous viscosity inversions.

Furthermore, our results show that the lithospheric mantle is critical to resolve disagreements between bottom-up and top-down methods. In fact, depending on how the lithosphere is treated, the inverted density anomalies can change by a factor of 4. Thus, a combined approach is necessary, where the uncertainties in seismic determinations of the lithosphere are considered in conjunction with signals resulting from deeper density anomalies.

Our inversion breaks down the mantle volume into discrete volumes with a constant density anomaly. This reduces the number of unknowns compared to a continuous inversion and means that less regularization is required. However, using vote maps to extract features from a collection of seismic tomographies is the most basic way to do this, and a more refined method (e.g.

Instead of relying on seismic tomographies or derived quantities like vote maps, it might be beneficial to stay closer to seismic data. The canonical choice would be seismic travel times and normal modes (as in

We derived a simple 1-D adiabatic model of Earth's mantle, based on a petrological database

The main relations – density

We begin this integration at a depth of 80 km, with a pressure of 2.5 GPa and

Instead, we relied on Rayleigh wave dispersion curves to choose the temperature at the top of the model. Using Mineos

The resulting temperature curve for the preferred model is nearly linear but shows a distinct kink below the 660 km discontinuity, due to the different properties of perovskite and a slower temperature increase at greater depths due to the decrease in thermal expansivity

We then applied first-order perturbations in terms of temperature, iron content and mid-oceanic ridge basalt (MORB) fraction to the adiabatic model. The vertical resolution of our density models is 100 km, so we applied the perturbation over the same depth range. To determine the sensitivity to temperature variations, we simply used our existing lookup table from PerpleX, while for compositional variations we determined new phase equilibria and corresponding rock properties with FeO content increased by 1 %. For the MORB we proceeded somewhat differently, because the MORB is likely not in phase equilibrium with the surrounding mantle rocks, due to the long timescale of chemical diffusion

Results of the adiabatic model.

First-order perturbation curves for deviations from a adiabatic, hydrostatic model with pyrolitic composition. The red and blue background shading indicates negative and positive changes of the respective quantity.

All input data of the study are freely available. Gravity data can be downloaded from International Centre for Global Earth Models (ICGEM); vote maps are available from

All software required to repeat the calculations presented here is available on GitHub (

The supplement related to this article is available online at:

JE developed the initial idea of the project; WS developed the code and ran the calculations. BS benchmarked the topography kernel calculations. WS prepared the article with contributions from JE and BS.

The authors declare that they have no conflict of interest.

The authors thank John Brodholt for his comments on an earlier version of this manuscript. We also thank the two anonymous reviewers for their constructive criticism that helped improve our article.

This work was carried out as part of the European Space Agency's Support to Science Element “3D Earth – A dynamic living planet”. Bernhard Steinberger received partial support from the Centre of Excellence project 223272 through the Research Council of Norway.

This paper was edited by Taras Gerya and reviewed by two anonymous referees.