LETTERSPUBLISHED ONLINE: 19 JANUARY 2014 | DOI: 10.1038/NGEO2063

Mapping the mass distribution of Earth’s mantleusing satellite-derived gravity gradientsIsabelle Panet1*, Gwendoline Pajot-Métivier1, Marianne Greff-Lefftz2, Laurent Métivier1,Michel Diament2 and Mioara Mandea3

The dynamics of Earth’s mantle are not well known1.Deciphering mantle flow patterns requires an understand-ing of the global distribution of mantle density2,3. Seismictomography has been used to derive mantle density dis-tributions, but converting seismic velocities into densitiesis not straightforward4,5. Here we show that data fromthe GOCE (Gravity field and steady-state Ocean CirculationExplorer) mission6 can be used to probe our planet’s deepmass structure. We construct global anomaly maps of theEarth’s gravitational gradients at satellite altitude and use asensitivity analysis to show that these gravitational gradientsimage the geometry of mantle mass down to mid-mantledepths. Our maps highlight north–south-elongated gravitygradient anomalies over Asia and America that follow a beltof ancient subduction boundaries, as well as gravity gradientanomalies over the central Pacific Ocean and south of Africathat coincide with the locations of deep mantle plumes. Weinterpret these anomalies as sinking tectonic plates andconvective instabilities between 1,000 and 2,500 km depth,consistent with seismic tomography results. Along the formerTethyan Margin, our data also identify an east–west-orientedmass anomaly likely in the upper mantle. We suggest that bycombining gravity gradients with seismic and geodynamic data,an integrated dynamic model for Earth can be achieved.

Understanding our planet’s evolution requires elucidation ofits internal structure and composition, as well as the mechanismof its heat loss. Over the past decades, tremendous advanceshave been gained from seismological, geochemical and geologicaldata interpretation, mineral physics experiments and numericalmodelling. Yet, unravelling the deep Earth’s dynamics and itsinterplay with surface tectonics is still hampered by the lackof information on the global density distribution, responsiblefor the buoyancy forces driving the mantle flows and the platemotions, and on the viscosity, which controls the convectiveflows1–3. The seismic tomography provides an image of theglobal three-dimensional internal structure through maps of fastand slow seismic anomalies, which delineate deep convectiveinstabilities and, at relatively smaller scales, plates sinking into themantle7,8. However, converting seismic velocities into densities isnot straightforward, as both depend on temperature and chemicalcomposition and are strongly affected by phase changes—thesethree factors influencing each other4. Also, seismic velocities cangreatly vary with direction through non-density contrast-inducedmechanisms, such as anisotropic crystal alignment by flow ornon-hydrostatic stresses5. Hence, we need further information tointerpret the seismic signal in terms of density variations versus

1Institut National de l’Information Géographique et Forestière, Laboratoire LAREG, Université Paris Diderot, GRGS, Bat. Lamarck A, Case 7071, 35 rueHélène Brion, 75205 Paris Cedex 13, France, 2Université Paris Diderot, Sorbonne Paris-Cité, Institut de Physique du Globe de Paris, UMR 7154 CNRS,F-75013 Paris, France, 3Centre National d’Etudes Spatiales, 2, place Maurice Quentin, 75039 Paris, France. *e-mail: isabelle.panet@ign.fr

other physical processes. Global data to describe the densitydistribution at depth are thus essential to get a full picture of ourplanet’s dynamics2,9,10.

With the European Space Agency’s Gravity field and steady-stateOcean Circulation Explorer (GOCE) satellite6, a new class ofobservations has emerged to probe the Earth’s interior structure:satellite gravity gradients. Originally imagined by Cavendish in thelate 18th century to accurately determine the Earth’s density fromthe gravity differences between close points, this early measure-ment concept experienced a recent growth to image the Earth’ssubsurface. Because they sense tiny variations of the gravity vectorin different directions, gravity gradients are much more sensitiveto the spatial structure and directional properties of the attract-ing masses than classical observations on gravitational intensity11.Tracking distance changes due to gravitational attraction differ-ences between two co-orbiting satellites12, the GRACE missionopened the way towards realizing this concept by satellites, afterthe first gravity observations from space made by CHAMP. Thefull gravitational gradient tensor has been measured from spacefor the first time by the GOCE mission. With its three pairs ofultra-sensitive accelerometers perceiving gravitational accelerationslightly differently onboard the satellite, the GOCE space gradiome-ter indeed measures, on a 255-km altitude orbit, the second-orderderivatives of the gravitational potential in all directions13 (seeSupplementary Information).

Reaching their optimal accuracy at scales smaller than 750 km,the gradiometric measurements are combined with a GOCE-orbitbased model, dominating at scales larger than ∼1,000–1,200 km.From these data along the orbit, expressed in a north–west-upframe by the GOCE High-level Processing Facility14, we builtglobal anomaly maps of the Earth’s gravitational gradients atsatellite altitude with respect to an Earth model obtained fromthe hydrostatic equilibrium of a rotating preliminary referenceEarth model (PREM)-layered15 spheroid (see SupplementaryInformation). The obtained anomalies reflect irregularities inthe mass distribution and interface deflections with respect tothe reference model (Fig. 1a). Because they are calculated atthe GOCE altitude, we avoid noise amplification resulting fromthe downward continuation to the Earth’s surface. Their longwavelength components—which could also be studied fromGRACE data—rely on directional information from the gradientsrather than gradiometer accuracy. Whereas the radial gradient isisotropic, the north and west derivatives emphasize mass anomaliesorthogonal to the differentiation direction. Local mass anomaliesrelated to mountain chains and subduction, oceanic ridges andplateaux leave elongated patterns at small scales. Furthermore,

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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO2063

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Figure 1 | Non-hydrostatic gravitational gradients. Second-order derivatives in the X (north; top row), Y (west; middle) and Z (radially up; bottom)directions of the gravitational potential along the GOCE orbit, in milliEötvös (1 Eötvös = 10−9 s−2). a, Earth’s gravitational gradient anomalies.b, Gravitational gradients from the mantle dynamics model by ref. 20, up to spherical harmonics of degree and order 12. Past subduction geometries16 areindicated by black circles (age: 100–120 Myr), grey circles (age: 64–74 Myr) and white triangles (age: 25–43 Myr). The red stars mark the main upwellingsin the model. The American (S1), West Pacific (S2), Tethyan (S3) and Indonesian (S4) subduction systems are indicated.

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Figure 2 | Gravitational gradients of a subducted slab. a, The present-day North American subduction zone and 4,500-km-long, 400-km-wide and200-km-thick parallelepiped slab elements parallel to the subduction. The depths of the slab elements are 400 km (top), 800 km (middle) and 2,500 km(bottom) below the Earth’s surface. b, Maps of the spatial variations of the second-order derivatives, in the x direction orthogonal to the slab as indicated bythe red arrow, and at 280 km altitude, of the gravitational potential of the three slab elements, calculated up to spherical harmonics of degree and order 75.

large-scale anomalies are clearly observed and, in the following,we focus on these striking features. The north–south elongatedpatterns in the YY gradients over Asia and America follow a belt

of ancient subduction boundaries16,17, where the tectonic platesdescend into the mantle. The negative east–west anomaly in theXX component follows the former Tethys ocean margin18 and the

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NATURE GEOSCIENCE DOI: 10.1038/NGEO2063 LETTERS

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Figure 3 | YY gravity gradients and S40RTS shear-velocity anomalies. a, Second-order derivatives in the Y/west direction, centred on America (top left)and on Asia (top right), of the Earth’s non-hydrostatic gravitational potential along the GOCE orbit, smoothed at 5◦ resolution. Past subduction zonesgeometries16 are drawn as in Fig. 1. C1 marks a deep slab remnant area. b, Contours of the shear-velocity anomalies dVs/Vs from the S40RTS model22 areshown at 1,100 km below America (bottom left), and at 1,900 km below Asia (bottom right), illustrating the north–south directionalities in the tomographicmodel between 900 and 1,600 km below America, and between 1,700 and 2,600 km below Asia.

present-day Indonesian subduction. In the Central Pacific Oceanand south of Africa, positive ZZ anomalies coincide with locationsof deep superplumes in the Earth’s lowermantle10,19.

We analysed the origin of these broad anomalies by using amodel of the lithosphere at isostatic equilibrium, and a mantledynamics model. The comparison with the lithospheric gradientsshows that they are only slightly affected by shallow lithosphericsources at large scales, as the latter rather reflect the ocean–continent dichotomy (see Supplementary Information). We thencomputed the gravitational gradients of a mantle dynamics modelexplaining the Earth’s rotational pole movements over the past120Myr and the geoid20. The mantle mass distribution is obtainedassuming that subducted lithospheric plates sink vertically intothe mantle, with a +80 kgm−3 contrast to the PREM averagedensities21, and includes deep upwellings19 mass anomalies, witha −50 kgm−3 density contrast20. The geometry and sinking rateof the subducted lithosphere is based on a time reconstructionof plate distribution and geometry16; slabs reach the core–

mantle boundary except below North and South America. Theobtained maps of gravitational gradients (Fig. 1b), similar to theobserved ones (Fig. 1a), confirm that the broad satellite gradientanomalies reflect mantle structuring by subduction processes andconvective instability.

To understand how these new data sense the deep hetero-geneities, and in which layers of the Earth’s mantle, we computedthe gradients along theGOCEorbit associatedwith thin slab-shapedand wide spherical cap mass anomalies, at various depths (seeSupplementary Information). Similarly to the dynamic responsefunctions describing the geoid effect of a mass anomaly inside theEarth, the sign of the gradient anomalies changes with the sourcedepth, as a result of deformation of Earth’s internal interfacesby the viscous flow induced by the mass anomaly. With a datanoise level not larger than a few milliEötvös at 1◦ resolution (seeSupplementary Information), the gradiometric signal of a thinsubducted slab can be detected down to at least 1,600 km depth,assuming a +80 kgm−3 density contrast. When the mass anomaly

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dVs/Vs (%)

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Figure 4 | XX gravitational gradients and S40RTS and DR2012 shear-velocity anomalies. a, Second-order derivatives in the X/north direction centred onAsia (left), of the Earth’s non-hydrostatic gravitational potential along the GOCE orbit, smoothed at 5◦ resolution. Past subduction zones geometries16 aredrawn as in Fig. 1. b, Contours of the shear-velocity anomalies dVs/Vs from the S40RTS model22 between 1,300 and 1,400 km are shown (middle), as wellas those from the DR2012 upper mantle model28 at 550 km depth (right). They illustrate the east–west directionalities in the tomographic models between1,000 and 1,500 km, and around 550 km, along the former Tethys margin.

widens (which happens when slabs flatten at the upper–lowermantle boundary or merge in the lower mantle, or for largesuperplumes), our tests show that deeper layers can be reached,down to at least some 2,500 kmdepth for a 4,000-kmwide anomaly.Besides, in contrast to geoid data, the gradients bring an enhancedgeometric characterization of the mass distribution, resulting fromtheir very nature of directional differences, thus facilitating com-parisons with seismic tomography. This is illustrated in Fig. 2,revealing that, besides changing sign between the upper and thelower mantle, the gradients delineate more and more closely theslab borders as depth decreases. For a 4,000-kmwidemass anomaly,significant oscillations at the edges of the mass distribution ap-pear in the signal when the anomaly is shallower than 1,700 km(see Supplementary Information). This is the reason why, for theinvestigated class of signals, smooth gradient variations probablyindicate deep sources.

From the above analysis, confirmed by a comparison with thefast seismic velocity anomalies of the S40RTS model22, we canidentify the mantle structures evidenced in our maps. We interpretthe three-lobe anomaly in the YY gradients over North andCentral America (Fig. 3a, anomaly S1) as tracking the subductedFarallon lithosphere in the upper lower mantle. Consistently, a fastnorth–south seismic velocity anomaly is found between 900 and1,600 km (refs 8,22,23), coinciding with the central negative lobeof the YY anomaly (see Fig. 3b). Over Asia, the broader positiveYY pattern (Fig. 3a, anomaly C1) is probably related to deeperand wider mass anomalies, and we find consistent fast seismicvelocities between 1,700 and 2,600 km depth (see Fig. 3b). This canreflect mid-mantle remnants of subducted Jurassic lithosphere22,24.In these areas, the lower mantle mass signal overprints notonly the lithosphere signal, reduced by isostasy at the gradientscales, but also the upper mantle signal. This arises from thecorrespondence between the differentiation directions and thenorth–south/east–west global structure of the deep Earth, involvinglarge amounts of mass. Formed as a result of the stability of nearlynorth–south subductions around the Pacific region over the past250Myr (ref. 25), the wide downwelling ring of slabs partitioningthe lower mantle is strongly directional and, therefore, naturallyhighlighted by the satellite gradients. Thus, around the Japanesearc, where slabs are thought to stagnate at the transition zone(ref. 26), thereby reducing the upper lower mantle directionalheterogeneity, the gradient signal is low (Fig. 3a, anomaly S2).We finally note that the observed YY gradients are smoother

than those from the mantle model, where the slab density andgeometry do not change with depth. These discrepancies indicatelimits of the model, which does not include the processes ofslab accumulation in the lower mantle, suggested below Asia, norslab stagnation around the transition zone, suggested below theJapanese subduction.

A more complex XX gradients pattern is observed along theformer Tethyan margin (Fig. 4a, anomaly S3), with two differentscales. The directions coincide with those of a fast velocity anomalybetween 1,000 and 1,500 km depth18,27, which may explain thelarge-scale positive lobe of the gradient anomaly in the IndianOcean. Furthermore, the strength of a smaller scale componentmay point to an important east–west structuring in the uppermantle along the former subduction boundary, also suggested by anelongated east–west velocity anomaly at 550 km depth in an uppermantle tomographic model28 (Fig. 4b), resolved at 500 km depthin the model of ref. 29. Because gradient anomalies change signwith the source depth, the observed composite pattern may helpdifferentiate between upper and lower mantle structures, such asthe subducted Indian plate and the earlier subducted Tethys slabs,shedding light on howplatemovements relate tomantle flows.

If the GOCE mission originally targeted the Earth’s shallowlayers, our gravitational gradient maps offer a new scope to gra-diometry from space: mantle dynamics. The geometric consis-tency of gravity gradients and seismic velocities indicates thatthey can be combined to decipher the mantle density and vis-cosity structure30 from global to regional scales, less emphasizedin the smooth geoid, and help identify the physical mechanismsreflected by seismic velocity variations. From this combination,new insights are expected on the mantle temperature and com-position variations associated with density and seismic veloci-ties anomalies. Inconsistencies between the datasets might alsopoint to mechanisms not associated with density variations, suchas anisotropy and stress. Probing the path and chemical evo-lution of the subducted tectonic plates, and the induced vis-cous flows, the gradients should give new clues towards under-standing the mantle vertical mixing. This picture on slab de-scent and accumulation may also help illuminate the deepestmantle structure and geodynamics. This new field of applica-tions of gravity gradients calls for a joint analysis with othergeophysical data, flow models and tectonic plate history recon-structions, opening new avenues to integrated global dynamicmodels of the Earth.

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NATURE GEOSCIENCE DOI: 10.1038/NGEO2063 LETTERSReceived 26 June 2013; accepted 9 December 2013;published online 19 January 2014

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AcknowledgementsWe thank CNES for financial support through the TOSCA committee, and ESA foraccess to the GOCE data. We thank J. Besse, O. de Viron and B. Romanowicz forimportant comments on our manuscript, and G. Hetenyi for discussions on the mantlestructure below Tibet. We thank G. Métris for providing us with software for thedifferentiation of the spherical harmonics, and J. Penguen for assistance in the numericalcomputations. This is IPGP contribution 3470.

Author contributionsI.P. and G.P-M. designed the study. I.P., G.P-M., M.G-L. and L.M. analysed the data andperformed the geophysical modelling. M.D. and M.M. discussed and commented on theresults and implications at all stages. I.P. wrote the manuscript with inputs from allco-authors. L.M. wrote Supplementary Section 2.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints.Correspondence and requests for materials should be addressed to I.P.

Competing financial interestsThe authors declare no competing financial interests.

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