LETTERdoi:10.1038/nature09636

Outer-core compositional stratification fromobserved core wave speed profilesGeorge Helffrich1{ & Satoshi Kaneshima2

Light elements must be present in the nearly pure iron core of theEarth to match the remotely observed properties of the outer andinner cores1,2. Crystallization of the inner core excludes light ele-ments from the solid, concentrating them in liquid near the inner-core boundary that potentially rises and collects at the top of thecore3, and this may have a seismically observable signal. Here wepresent array-based observations of seismic waves sensitive to thispart of the core whose wave speeds require there to be radial com-positional variation in the topmost 300 km of the outer core. Thevelocity profile significantly departs from that of compression of ahomogeneous liquid. Total light-element enrichment is up to fiveweight per cent at the top of the core if modelled in the Fe–O–Ssystem. The stratification suggests the existence of a subadiabatictemperature gradient at the top of the outer core.

Many light elements, namely hydrogen, carbon, nitrogen, oxygen,sulphur and silicon, could plausibly have been included in the coreduring accretion of the early Earth2,4. Among these, oxygen and sul-phur are of interest owing to oxygen’s potentially high solubility in ironat high pressures and the extremely low-temperature eutectic betweeniron and sulphur, which facilitates segregation into the core5–8.Independently of the particular light elements involved, their enrich-ment in the liquid of the outer core is potentially observable because itaffects liquid density and bulk modulus, thereby changing seismicwave speeds. Indeed, a series of past seismic studies focused on thisarea specifically to seek evidence for stratification9–12; many suggestlower seismic wave speeds in the outer core near the core–mantleboundary (CMB) than self-compression of a chemically homogeneousouter core would imply.

Our study uses earthquakes in South America and in the south-western Pacific region that emit shear waves towards the core andconvert to compressional waves that repeatedly reflect from the under-side of the CMB (Fig. 1). The arrivals, SmKS, reflect m 2 1 times fromthe core side of the CMB. Thus most of their travel time is accruedacross the area of potential light-element accumulation, between 80and 400 km below the CMB. We use stacked records of 120–190 indi-vidual observations of SmKS waveforms of three separate earthquakesrecorded by large-scale seismic arrays in Japan and northern Europe tomeasure differential travel times and slownesses between SmKS andSnKS, with m . n, 2 # (m and n) # 5 (Fig. 1). The events are selectedfor their range (separating SmKS multiples with m $ 4) and for theirsampling of different surface and CMB environments. Our array-based measurements on single events yield stacked waveforms whosedifferential times and slownesses are the raw data used. Array mea-surements provide not only direct differential slowness information;more importantly, the stacked waveforms average over source- andreceiver-side near-CMB path effects due to D99 structure.

In the model, named KHOCQ, derived from the observations, wefind that outer-core wave speeds decrease to values a maximum of 0.3%lower than PREM wave speeds13 60 km into the outer core and graduallyreturn to PREM values at a depth of ,300 km (Fig. 2). These small,resolvable differences are significant departures from homogeneous

self-compression of core material1. For two regions with very differentseismic velocity structures in the lowermost mantle, we find a thickeranomalous layer (300 km) than any of the earlier studies, owing to theuse of S4KS and S5KS, which is particularly suitable for investigating theoutermost core but has not yet been extensively used. Isolation of pro-pagation delays accrued at shallowest core levels improves resolution ofdeeper structure.

To interpret the observations, we model seismic wave speeds in Fe–O–S liquids under core conditions14 (Methods). Given composition,pressure and temperature, the model provides liquid bulk modulus, K,density, r, and, thus, seismic wave speed, (K/r)1/2. We calculate com-positional profiles at the top of the outer core that match our wavespeed profile to within 0.02%, have average densities in the top 300 kmof the outer core within 1% of PREM (and thereby obey normal-mode-derived density constraints15), and that merge with PREM wave speeds300 km below the CMB. Feasible variations in iron, oxygen and sul-phur that lead to stable stratification are shown in Fig. 3. The modelledcompositions agree with KHOCQ for oxygen enrichments towards theCMB of 0.8–2 wt% and iron depletions of up to 5 wt%; sulphur may beeither enriched by up to 3 wt% or depleted by 0.8 wt%, depending onthe oxygen content of the liquid. At light-element enrichment of 5% atthe top of the core, the total added light-element mass in the region isabout 11% of the inner core’s mass. We can equate the light-elementmass expelled by inner-core crystallization with light-element enrich-ment in the layer by assuming that the density jump at the inner-coreboundary, DrICB, multiplied by the inner core’s present volume givesthis mass14. Using a previous estimate15 of 610 6 180 kg m23 forDrICB

attributable to light-element release, we find the light-element mass inthe layer agrees (at the 95% confidence level) with the mass expelled bythe inner core if enrichment is 2.5–3 wt% at the top of the outer core.The range of seismically definedDrICB estimates is quite wide, however,so the rough mass balance demonstrates the feasibility of the layer’sformation mechanism rather than providing strong compositionalconstraints.

The lighter material at the top of the core is 5.9% less dense than theliquid 300 km below it (and 1.6% lighter than PREM densities on thecore side of the CMB). The layer’s Brunt–Vaisala frequency, a measureof the strength of density stratification in the core16, is 0.51–1.03 mHz(periods of 1.63–3.43 h), suggesting strong stabilization. The densityexcess in the layer, 20.8 3 1022 to 23.2 3 1022, is about 100 timesgreater than that estimated17 to explain short-period geomagnetic fieldsecular variation and its possible correlation with length-of-day varia-tions. The layer’s density gradient exceeds that in the well-mixed outercore16 by a factor exceeding 1010. Owing to the gradational differencein composition from the bulk of the outer core at the layer’s base,stabilizing it against convective mixing in the outer core is problematic(see Supplementary Information for a discussion). A feasible mech-anism is a subadiabatic gradient at the top of the outer core due to theinability of core heat to escape into the mantle on account of its slowerconvection speeds and low thermal diffusivity18,19. The core liquidmodel (Methods) yields velocities that match our observed profiles

1EarthquakeResearch Institute, University of Tokyo, 1-1-1Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan. 2Earth and PlanetarySciences,University ofKyushu, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581,Japan. {Present address: Earth Sciences, University of Bristol, Wills Memorial Building, Queen’s Road, Bristol BS8 1RJ, UK.

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either for adiabatic temperature gradients in the topmost 300 km of thecore or for an isothermal layer for temperatures between 3,000 and5,500 K, so the results are independent of the temperature structurechosen. Higher temperatures imply a bulk core composition more ironrich by 1–2 wt% and correspondingly larger light-element enrich-ments. This trade-off between core temperature and light-element

S6KS

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Figure 1 | Experiment geometry and paths taken by the seismic wavesthrough the Earth. a, Sources (X) are subduction-zone earthquakes in SouthAmerica (Argentina) and the southwest Pacific Ocean (Fiji) recorded byseismic arrays in Japan (,120 stations) and in Europe (,190 stations). The raypaths are superimposed on tomography maps (SB10L18) of shear-wave speedvariations, dvS, at 2,770 km in the lowermost mantle26. White stars indicaterepresentative core entry points of S3KS. b, SmKS ray paths travel across themantle as shear waves, but across the core as compressional waves. In the core,they reflect m 2 1 times from the underside of the CMB. c, Record section ofobserved (left, recorded by European stations) and predicted (right) SmKSarrivals from the Fiji earthquake. Arrivals and synthetics are aligned on S3KS(0 s), and the Preliminary Reference Earth Model13 (PREM) predictedsuccessive SmKS arrivals shown by dashed lines. Reflectivity synthetics forPREM (right) show that S4KS and S5KS are delayed. S2KS, which arrives beforeS3KS, is not shown, for clarity. PcPPKiKS is the prominent low-slowness arrivalin the synthetics at 163–170u, not observable in the data.

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Figure 2 | Data, velocity profile in the outer core and self-compressionprofile using the velocity profile. a, Raw data are differential travel times (dt)and slownesses measured relative to PREM13 for two regions. Data (and 95%observational uncertainty) for the two Fiji events and one Argentina eventstudied are shown with squares, previous model predictions (see b) are shownwith circles and KHOCQ predictions are shown with stars. Most modelssignificantly overestimate differential travel times relative to observations.b, Outer-core velocity resulting from t–p inversion of differential SmKS traveltimes and slownesses (Methods). Velocities are shown relative to PREM13 andare compared with recent models incorporating similar SmKS data: IASP9127,SP628, AK13529 and model 1 from ref. 11. Lines across the top indicate depthsinto the core travelled by each SmKS path. Higher multiples travel to smallerdepths in the outer core. The KHOCQ error bounds correspond to the range ofinversions with 2s travel-time uncertainties applied—roughly the 95%confidence level. c, Birch’s parameter (and uncertainty bounds) calculated fromKHOCQ departs significantly from self-compression in the range 80–300 kmbelow the CMB, requiring compositional change in the outer-core liquid. Theself-compression line shows the theoretical behaviour of a substance whosecomposition does not vary (Methods). Birch’s parameter for PREM closelyapproximates that for self-compression.

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concentration also adds uncertainty to the light-element balancebetween the inner core and the layer discussed earlier.

The liquid model we use only approximates the true composition ofthe core because it includes only iron and accounts for only oxygen andsulphur as light elements. Nickel is also thought to be present in thecore, in concentrations up to ,5 wt% (ref. 4). However, in these con-centrations it seems to act equivalently to iron in sulphur- and oxygen-bearing metallic liquids, in the sense that melt surface energies areunchanged when nickel replaces an equivalent amount of iron20.Furthermore, (Fe,Ni)–(Fe,Ni)S eutectic temperatures are only 20 uClower than Fe–FeS (ref. 21). Thus, except for the minor difference indensity (,0.1%) due to the substitution of nickel for iron, we expect nosignificant effects on liquid properties. Present cosmochemical modelsfor core composition suggest that silicon might also be present inconcentrations of a few weight per cent4. At present, we lack therequisite melting data on Fe–Si alloys to develop an analogous model

for silicon-bearing melts. We suspect that sulphur might decrease inproportion to silicon’s increase22 and lead to a slight decrease in density(,0.1%, due to the slight atomic weight difference), but the bulkmodulus effect on wave speeds cannot yet be assessed owing to thelack of Fe–Si melting data.

If stabilized subadiabatically against convection, core–mantle reac-tion might inject oxygen into the outer core5,7,23. Oxygen diffusionfrom the CMB cannot be responsible for the complete depth rangeof the observed anomaly, however. Anion diffusivities in liquid ironare estimated to be 10211–1029 m2 s21 (refs 3, 24), leading to diffusionlength scales of 10–100 km over the lifetime of the Earth. Thus, theprofile was in large part created by an upward buoyant flux of lightelements from the crystallization of the inner core. The outer core’svelocity profile seems to record the secular evolution of the core’scomposition as the subadiabatic layer grew, possibly modified bycore–mantle reaction. We remark in passing that a subadiabatic layerat the top of the core also has profound implications for the thermalevolution of the core and CMB thermal structure.

METHODS SUMMARYData are broadband records from regional networks in Europe and Japan. Theradial component waveforms are uncorrected for instrument response and corre-spond to ground velocity given typical instrument characteristics (SupplementaryInformation). We measured differential travel times and slownesses of S3KS–S2KS, S4KS–S3KS and S5KS–S3KS on stacked and Hilbert-transformed wave-forms (when required). These are the raw data for the inversion.

We determined velocity profiles by numerical t–p inversion25 using up to six basisfunctions, yielding flattened earth velocity perturbations, dvf/vf, of the form (dvf/vf)(r) 5 60.01max2(0, r 2 rb)/(rCMB 2 rb)2, where r is radius and rb and rCMB arethe minimum perturbation radius and the CMB radius, respectively. SeeSupplementary Information for fitting details and coefficients. The Fe–O–S liquidmodel is from ref. 14 and is based on thermodynamic fits to the melting curves of Fe,FeO and FeS using a 1-bar metallurgical model of liquid free energy. See Methods forthe fitting procedure and computational methods; liquid thermophysical propertiesare listed in Supplementary Information. The model yields high-pressure and-temperature bulk modulus and density, and, therefore, seismic wave speeds inouter-core liquid. Because the model is free-energy based, the liquid heat capacity,thermal expansivity and, thus, the adiabatic gradient in the liquid can also becalculated through thermodynamic identities relating to free-energy derivatives.

Full Methods and any associated references are available in the online version ofthe paper at www.nature.com/nature.

Received 24 May; accepted 29 October 2010.

1. Birch, F. Elasticity and constitution of the Earth’s interior. J. Geophys. Res. 57,227–286 (1952).

2. Stevenson, D. J. Models of the Earth’s core. Science 214, 611–619 (1981).3. Fearn, D. R. & Loper, D. E. Compositional convection and stratification of Earth’s

core. Nature 289, 393–394 (1981).4. Wood, B. J., Walter, M. J. & Wade, J. Accretion of the Earth and segregation of its

core. Nature 441, 825–833 (2006).5. Rubie, D. C., Gessmann, C. K. & Frost, D. J. Partitioning of oxygen during core

formation on the Earth and Mars. Nature 429, 58–61 (2004).6. Ozawa, H. et al. Chemical equilibrium between ferropericlase and molten iron to

134 GPa and implications for iron content at the bottom of the mantle. Geophys.Res. Lett. 35, L05308 (2008).

7. Frost, D. J. et al. Partitioning of oxygen between the Earth’s mantle and core. J.Geophys. Res. 115, B02202 (2010).

8. Hilty, D. C. & Crafts, W. Liquidus surface of the Fe-S-O system. J. Metals (Trans.AIME) 4, 1307–1312 (1952).

9. Lay, T.&Young,C.Thestably-stratifiedoutermost core revisited. Geophys.Res. Lett.17, 2001–2004 (1990).

10. Garnero,E. J., Helmberger,D.V.&Grand,S.P.Constraining outermost corevelocitywith SmKS waves. Geophys. Res. Lett. 20, 2463–2466 (1993).

11. Tanaka, S. Possibility of a low P-wave velocity layer in the outermost core fromglobal SmKS waveforms. Earth Planet. Sci. Lett. 259, 486–499 (2007).

12. Alexandrakis, C. & Eaton, D. W. Precise seismic-wave velocity atop Earth’s core: noevidence for outer-core stratification. Phys. Earth Planet. Inter. 180, 59–65 (2010).

13. Dziewonski, A. & Anderson, D. L. Preliminary reference Earth model. Phys. EarthPlanet. Inter. 25, 297–356 (1981).

14. Helffrich, G. & Kaneshima, S. Seismological constraints on core composition fromFe-O-S liquid immiscibility. Science 306, 2239–2242 (2004).

15. Masters, G. & Gubbins, D. On the resolution of density within the Earth. Phys. EarthPlanet. Inter. 140, 159–167 (2003).

16. Loper,D. E. A model of the dynamical structureof theEarth’s outer core.Phys. EarthPlanet. Inter. 117, 179–196 (2000).

a

b

15 0

10

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S

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5

4

3

2

1

0

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O,

S c

oncentr

atio

n c

hang

e (w

t%)

O (PREM ± 1%)

S (PREM ± 1%)

−6 −5 −4 −3 0−2 −1

5 10 15

Figure 3 | Compositional variation in the Fe–O–S liquids that match theobserved wave speed profile and core density constraints. a, Feasiblecomposition profiles are shown by lines linking PREM wave speeds at 300-kmdepth in the outer core to wave speeds at the top of the outer core. Profiles areisothermal in the topmost 300 km and then join an adiabat initiated at the CMBat 4,300 K. For feasibility, core liquid compositions must be within 1% of theaverage PREM density in the top 300 km of the core15 and must match theobserved velocity profile. For comparison with previous core compositionestimates, the filled circle indicates a first-principles core liquid compositionestimate30. b, Compositional variation along feasible profiles for 1% densityagreement with PREM. The compositional difference at the CMB and the baseof each feasible profile shown in a (presumably the well-mixed outer corerepresented by PREM wave speeds 300 km below the CMB) is shown here.Oxygen enrichment by .0.8 wt% is required in all cases and sulphurenrichment is required only at oxygen contents $1 wt%.

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17. Braginsky, S. I. MAC-oscillations of the hidden ocean of the core. J. Geomag.Geoelectr. 45, 1517–1538 (1993).

18. Gubbins, D., Thomson, C. & Whaler, K. Stable regions in the Earth’s liquid core.Geophys. J. R. Astron. Soc. 68, 241–251 (1982).

19. Lister, J. R. & Buffett, B. A. Stratification of the outer core at the core-mantleboundary. Phys. Earth Planet. Inter. 105, 5–19 (1998).

20. Rose, L. A. & Brenan, J. M. Wetting properties of Fe-Ni-Co-Cu-O-S melts againstolivine: implications for sulfide melt mobility. Econ. Geol. 96, 145–157 (2001).

21. Usselman, T. M. Experimental approach to the state of the core: part I. The liquidusrelations of the Fe-rich portion of the Fe-Ni-S system from 30 to 100 kb. Am. J. Sci.275, 278–290 (1975).

22. Kilburn, M. R. & Wood, B. J. Metal-silicate partitioning and the incompatibility of Sand Si during core formation. Earth Planet. Sci. Lett. 152, 139–148 (1997).

23. Buffett, B. A. & Seagle, C. T. Stratification of the top of the core due to chemicalinteractions with the mantle. J. Geophys. Res. 115, B04407 (2010).

24. Dobson,D. Self-diffusion in liquid Fe at high pressure. Phys. Earth Planet. Inter. 130,271–284 (2002).

25. Garmany, J., Orcutt, J. A. & Parker, R. L. Travel time inversion: a geometricalapproach. J. Geophys. Res. 84, 3615–3622 (1979).

26. Masters, G., Laske, G., Bolton, H. & Dziewonski, A. in Earth’s Deep Interior: MineralPhysics and Tomography from the Atomic to the Global Scale (eds Karato, S.-I., Forte,A. M., Liebermann, R. C., Masters, G. & Stixrude, L.) 63–87 (Geophys. Monogr. 117,American Geophysical Union, 2000).

27. Kennett, B. L. N. & Engdahl, E. R. Traveltimes for global earthquake location andphase identification. Geophys. J. Int. 105, 429–465 (1991).

28. Morelli, A. & Dziewonski, A. M. Body wave traveltimes and a spherically symmetricP- and S-wave velocity model. Geophys. J. Int. 112, 178–194 (1993).

29. Kennett, B. L. N., Engdahl, E. R. & Buland, R. Constraints on seismic velocities in theEarth from traveltimes. Geophys. J. Int. 126, 108–124 (1995).

30. Alfe, D. Price, G. D. & Gillan, M. J. Iron under Earth’s core conditions: liquid-statethermodynamics and high-pressure melting curve from ab initio calculations.Phys. Rev. B 65, 165118 (2002).

Supplementary Information is linked to the online version of the paper atwww.nature.com/nature.

Acknowledgements This work was supported by an ERI Visiting Professorship to G.H.We thank A. Jackson for comments and O. Lord for experimental references. Data wereprovided by the ORFEUS Data Center, de Bilt, the Netherlands, the J-Array data centre,ERI, Tokyo, Japan, and by NIED, Tsukuba, Japan.

Author Contributions Both authors contributed equally to the project.

Author Information Reprints and permissions information is available atwww.nature.com/reprints. The authors declare no competing financial interests.Readers are welcome to comment on the online version of this article atwww.nature.com/nature. Correspondence and requests for materials should beaddressed to G.H. (george.helffrich@bris.ac.uk).

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METHODSSmKS analysis. We investigate the family of SmKS (m 5 2, 3, 4 and 5) waves usingdifferential travel times between SmKS waves with different values of m. These aresensitive to the velocity structure of the uppermost few hundred kilometres of theouter core (see Fig. 2b for the bottoming depths of SmKS). S4KS and S5KS samplemore predominantly the shallowest 100 km of the core, and their differential traveltimes are insensitive to the velocity structure of the mantle. Robust observations ofS4KS and S5KS have been hampered by their mutual interference, which weameliorate by array analyses of SmKS at large distances, from 140 to 170u, wherethe arrivals separate. We analyse broadband seismograms of two deep earthquakesin Fiji–Tonga observed in Europe and an event in Argentina observed in Japan andTaiwan (Supplementary Table 1). The selected events have quite simple impulsivesource time functions, such that their SmKS phases are separated clearly enoughfrom each other up to m 5 5, as seen in the record sections of the radial componentof the broadband seismograms (Fig. 1c and Supplementary Fig. 2). Comparisonswith the record sections drawn for reflectivity synthetic seismograms31 for thesame event–network pairs (Fig. 1c and Supplementary Fig. 2) show systematicdifferences across the arrays in the SmKS differential travel times (dt) between theobservations and PREM. In particular, S3KS (relative to S2KS) and S4KS and S5KS(both relative to S3KS) all arrive later than those computed for PREM and haveabout the same delay (,1 s). To quantify these observations accurately, differentialtravel times and slownesses are measured by array techniques using either SKKS(called S2KS hereafter, for clarity) or S3KS as the reference phase. Figure 2a showsdifferential travel times that are measured on the linearly stacked waveforms forthe distances at the array centres and corresponding slownesses between threepairs of SmKS waves; S3KS relative to S2KS (called S3KS–S2KS, labelled dt3,2),S4KS relative to S3KS (S4KS–S3KS, dt4,3) and S5KS relative to S3KS (S5KS–S3KS,dt5,3; see Supplementary Table 2 for data).

SmKS touches an internal caustic and reflects at the underside of the CMB m 2 1times, suffering a phase delay of nearly p(m 2 1)/2 relative to SKS. Consequently,SmKS and S(m 1 1)KS are related by a Hilbert transform and SmKS andS(m 1 2)KS have opposite polarities. To account for the phase shift, we Hilbert-transform linearly stacked S2KS. We then slant-stack the observed broadbandseismograms aligned on S2KS (Supplementary Table 2), and measure the arrivaltime difference between the transformed S2KS and S3KS. For S4KS–S3KS, S3KS isused as the alignment phase. The stacked S3KS is Hilbert-transformed and therelative travel time of S4KS is measured on the slant-stacked waveforms. S5KS–S3KS is measured as the arrival time difference between S3KS and a pulse of theopposite polarity on the slant-stacked trace aligned on S3KS (Supplementary Figs 2and 3 and Supplementary Table 2). Synthetic tests on the reflectivity seismogramsfor several global Earth models show that these measurements give differentialtravel times between SmKS waves that agree with their ray theoretical predictionsto within 0.2 s. Slight differences in instrument responses among the stations hardlyaffect the results of array processing according to a synthetic test, so stacking and dtmeasurements are performed on the broadband seismograms to avoid deconvolu-tion (Supplementary Fig. 3). S3KS–S2KS and S4KS–S3KS are measured by pickingpeaks and cross-correlating the stacked waveforms, whereas S5KS–S3KS is mea-sured by picking peaks only. The errors in those measurements are evaluated on thebasis of the 95% confidence levels derived from stacking (Supplementary Fig. 3 andSupplementary Table 2).Inversion methodology. The measured differential times and differential slow-nesses (dp) relative to those computed from PREM are listed in SupplementaryTable 2 and shown in Fig. 2a, and the vP anomaly as a function of depth is soughtrelative to PREM. The choice of PREM as the reference model is motivated by themany previous studies10,11,32 which showed that PREM agrees with the SmKS dif-ferential travel times better than any other global reference model, such as IASP91,AK135 and SP6. Although previous studies9–11 suggested the presence of a thin layer(50–100 km thick) with a vP 1–2% lower than PREM at the top of the outer core, arecent study12 shows that the deviations from PREM, if any, should be smaller.

We use a t2p inversion method to invert the differential time and slownessmeasurements to determine the optimum velocity profile. A variety of basis func-tions were explored to eliminate parameterization bias. Fit details and coefficientsare provided in Supplementary Table 3.

As a result of the inversion, we find that vP values are slightly slower thanpredicted by PREM for the top 300 km of the outer core. As seen in Fig. 2a, b,the new data of S5KS–S3KS and S4KS–S3KS do not favour a steep and monotonicreduction of vP as proposed in the previous studies, although a moderately lower vP

(by ,0.3%) than predicted by PREM at the CMB is certainly required. Near theCMB, vP is consistent with the range of feasible solutions in ref. 12. According tosynthetic tests, density perturbations up to about 1% from PREM do not affect theobserved relative amplitudes of SmKS above the uncertainty level of the stackedseismograms, so we do not have a tight control over density, unlike that over vP.Our model is consistent with the measurements of S4KS–S3KS obtained for

individual seismograms10 and for a small-aperture array32, although the uncer-tainties in the previous measurements are far larger than ours. The variations inglobal compilations of S3KS–S2KS for individual station–earthquake pairs aremuch larger but are broadly consistent with our model, probably because theyare prone to bias by mantle-side, small-scale velocity heterogeneity.

The synthetic seismograms are computed by the reflectivity method, with thestacked broadband seismograms of S2KS used for the source time function aftercorrection of phase shift. We emphasize that data for both Fiji events suggestsimilar vP anomalies and that the models (for example KHOCQ; Supplemen-tary Fig. 4) obtained for the Fiji events match the differential travel times for theArgentina event. The D99 region sampled by the data from Fiji to Europe includes aroot of the Pacific super plume, and that for Argentina to Japan is near a subductedplate (Fig. 1a and Supplementary Fig. 1). The synthetic stacked seismograms forthe derived model (KHOCQ) show excellent fits to the observed stacked seismo-grams for both the Fiji and the Argentina events (Supplementary Fig. 3). Thepresence of a layer with a large velocity anomaly in D99 including an ultralow-velocity zone changes S3KS–S2KS, S4KS–S3KS and S5KS–S3KS by about 0.2 s, buttheir relative magnitudes are hardly affected (less than 0.1 s). The minor differencein the models obtained for the two regions may be partly explained by the differ-ence in the vS structure in D99. More extreme and smaller-scale anomalies mightaffect the differential travel times, but piercing points at the CMB of the SmKS raysare spread over 3,000 km and 2,000 km beneath the receiver side and source side,respectively. The differential travel times used, therefore, should reflect the mantleand core structure averaged over a wide area. All of these considerations indicatethat lateral variation in the mantle-side structure has only minor effects on themodel, and that there actually is a velocity anomaly in the outermost core.Core liquid model. The thermodynamic properties of dominantly iron liquidscontaining various impurities are well known owing to their commercial import-ance in steelmaking. One example is the Fe–O–S system. Experimental constraintsare available on room-pressure thermophysical properties, leading to tabulationsof their thermodynamic properties and models for mixing in the liquid state. Formetallurgical and materials science reasons, the high-pressure properties of solidsare also known through pressure–volume equation-of-state measurements.

Liquid properties are not as well characterized at high pressure, however. A ther-modynamic approach is used to obtain the properties of Fe–O–S liquids from themelting curves of Fe, FeO and FeS, which have been determined experimentally33,34,and shock-wave measurements on FeO35. At the melting point, the free energy, G, ofthe solid (s) and liquid (l) are equal. Referring to the standard states, G0, of the solidand liquid at reference temperature and pressure (Tr, Pr), and using the dependenceof free energy on entropy, S, and volume, V, we find that

G P, Tð Þ~G0 Pr, Trð ÞzðP

Pr

V p, Tð Þ dp{

ðT

Tr

S Pr, tð Þ dt

S(T) is available from standard tables at ambient pressure, Pr, and V(Pr, T) may beobtained from thermal expansivity measurements on solids at ambient pressureyielding a(T), through the relation

V Tð Þ~V Trð Þ expðT

Tr

a tð Þ dt

� �

Solid volumetric properties are obtained by a third-order Birch–Murnaghan equa-tion of state. The implicit relation between P and V is through a reference volume, V0,from which the finite strain, f, undergone by compression is expressed as f 5 [(V/V0)2/3 2 1]/2. The equation of state depends on isothermal bulk modulus, K0, and itspressure derivative, K9:

P fð Þ~3K0f 1z2fð Þ5=2 1{3f K ’{4ð Þ=4½ � ð1ÞThe required integral, #V dP, is usually evaluated by integrating equation (1) byparts36, yielding ðP

Pr

V dp~ V{Vrð Þ P{Prð Þ{ðV

Vr

P df =dvð Þ dv

In equation (1), K0 is the bulk modulus at Pr but at high T. The Anderson–Gruneisen parameter, dT, is used to weaken the bulk modulus at high temperature,under the assumption that it is constant above the Debye temperature37. Thus,

K0 Tð Þ~K0 Trð Þ exp {dT

ðT

Tr

a dt

� �. K9 is taken to be independent of temperature,

and, if not otherwise known, K9 < dT (ref. 38).To calculate Gl(P, T), liquid K0, K9 ; dT and a are needed. These are estimated

from the melting curves, where Gl 5 Gs, using solid equation-of-state data tocalculate Gs and matching the experimental melting brackets. Grid search overK0, a and K9 yields the values shown in Supplementary Table 4, and SupplementaryFig. 5 shows the results of the fits to the experimental brackets for the liquids. For

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higher-pressure calculations, entropies of the solid are modified for known phasetransitions shown in Supplementary Fig. 5. These lead to minor changes in thecalculated melting-curve slope but it is unresolvable given the width of the meltingbrackets. For this reason, owing to their minor effect on gross thermodynamicproperties, structural changes in liquids are ignored39. Non-ideal mixing of end-member liquid is required to fit Fe–FeS eutectic composition variation with pres-sure; see Supplementary Information for justification and parameterization.

Velocities in the liquid are calculated from the adiabatic bulk modulus, Ks, anddensity, r, at high P and T using the relation vP~

ffiffiffiffiffiffiffiffiffiffiKs=r

p. The adiabatic bulk

modulus is obtained from the isothermal one using Ks 5 K(1 1 Tac). The core liquidGruneisen parameter, c, is 1.52 (ref. 30). The high-pressure thermal expansivity usedhere depends on the compressed volume40 via dln(a)/dln(V) 5 dT(V/V0)k, withk 5 1.4.

Calculation of the adiabatic gradient in the core, dT/dz 5 ga/Cp requires valuesfor gravitational acceleration, g, and heat capacity, Cp. We calculate g at any depth inthe core by linear interpolation between its value at the CMB given by PREM13 andzero at the Earth’s centre. The high-pressure heat capacity is obtained from Gl(P, T)through the thermodynamic identity Cp 5 2T(h2G/hT2), evaluated numerically.Adiabatic compression of a homogeneous core liquid. When a homogeneousliquid is adiabatically compressed, W rð Þ~v2

P rð Þ varies approximately with radiusas follows1:

1{1g

dW

dr~

LKLP

� �T

z 2LKLP

� �T

{1zc{3dT

� �Tac

Here dT 5 2(1/aK)(hK/hT)P and K, c and a are the isothermal bulk modulus, theGruneisen parameter and the thermal expansion coefficient, respectively. K(P) iscomputed using the third-order Birch–Murnaghan equation. To demonstrate the

smoothness of a profile of 1 2 (1/g)dW/dr for a compressed homogenous liquid,we present an example that fits PREM well (Fig. 2c). The following parameters areused for the computation: K0 5 100 GPa, K9 5 4.75, r0 5 6,280 kg m23, c 5 0.8,TCMB 5 4,300 K, dT/dr 5 20.3 K km21 and dT 5 3.33. The thermal expansioncoefficient, a, decreases linearly from 5 3 1026 K21 at the CMB to 3 3 1026 K21

at 1,700 km below the CMB.

31. Kind, R. Extensions of the reflectivity method for a buried source. J. Geophys. 45,373–380 (1979).

32. Eaton, D. W. & Kendall, J.-M. Improving seismic resolution of outermost corestructure by multichannel analysis and deconvolution of broadband SmKSphases. Phys. Earth Planet. Inter. 155, 104–119 (2006).

33. Boehler, R. Melting of the Fe-FeO and the Fe-FeS systems at high-pressure -constraints on core temperatures. Earth Planet. Sci. Lett. 111, 217–227 (1992).

34. Boehler, R. Temperatures in the Earth’s core from melting-point measurements ofiron at high static pressures. Nature 363, 534–536 (1993).

35. Svendsen,B., Anderson,W. W., Ahrens, T. J.& Bass, J.D. Ideal Fe-FeS, Fe-FeO phaserelations and Earth’s core. Phys. Earth Planet. Inter. 55, 154–186 (1989).

36. Fei, Y., Saxena, S. K. & Navrotsky, A. Internally consistent thermodynamic data andequilibrium phase relations for compounds in the system MgO-SiO2 at highpressure and high temperature. J. Geophys. Res. 95, 6915–6928 (1990).

37. Anderson, O. L., Isaak, D. & Oda, H. High-temperature elastic constant data onminerals relevant to geophysics. Rev. Geophys. 30, 57–90 (1992).

38. Bina, C. R. & Helffrich, G. Calculation of elastic properties from thermodynamicequation of state principles. Annu. Rev. Earth Planet. Sci. 20, 527–552 (1992).

39. Morard, G. et al. Structure of eutectic Fe-FeS melts to pressures up to 17 GPa:implications for planetary cores. Earth Planet. Sci. Lett. 263, 128–139 (2007).

40. Anderson, O. L., Oda, H., Chopelas, A. & Isaak, D. A thermodynamic theory of theGruneisen ratio at extreme conditions: MgO as an example. Phys. Chem. Miner. 19,369–380 (1993).

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