The view that the seismic discontinuities bounding the mantle transition zone
at 410- and 660-kilometer depths are caused by isochemical phase transformations
of the olivine structure is debated. Combining converted-wave measurements
in East Asia and Australia with seismic velocities from regional
tomography studies, we observe a correlation of the thickness of, and
wavespeed variations within, the transition zone that is consistent with olivine
structural transformations. Moreover, the seismologically inferred Clapeyron
slopes are in agreement with the mineralogical Clapeyron slopes of the
(Mg,Fe)2SiO4spinel and postspinel transformations

Chevrot, Sébastien

Hilst, R.D. van der

Lebedev, Sergei

The view that the seismic discontinuities bounding the mantle transition zone

at 410- and 660-kilometer depths are caused by isochemical phase transformations

of the olivine structure is debated. Combining converted-wave measurements

in East Asia and Australia with seismic velocities from regional

tomography studies, we observe a correlation of the thickness of, and

wavespeed variations within, the transition zone that is consistent with olivine

structural transformations. Moreover, the seismologically inferred Clapeyron

slopes are in agreement with the mineralogical Clapeyron slopes of the

(Mg,Fe)2SiO4spinel and postspinel transformations

NARCIS 

Seismic evidence for olivine phase changes at the 410- and 660-kilometer discontinuities

Utrecht University Repository

Seismic Evidence for OlivinePhase Changes at the 410- and660-Kilometer DiscontinuitiesSergei Lebedev,1* Se´bastien Chevrot,2 Rob D. van der Hilst1The view that the seismic discontinuities bounding the mantle transition zoneat 410- and 660-kilometer depths are caused by isochemical phase transfor-mations of the olivine structure is debated. Combining converted-wave mea-surements in East Asia and Australia with seismic velocities from regionaltomography studies, we observe a correlation of the thickness of, andwavespeed variations within, the transition zone that is consistent with olivinestructural transformations. Moreover, the seismologically inferred Clapeyronslopes are in agreement with the mineralogical Clapeyron slopes of the(Mg,Fe)2SiO4 spinel and postspinel transformations.The seismic velocity discontinuities at globalaverage depths of 410 and 660 km have beenattributed to isochemical phase transforma-tions, from olivine to wadsleyite (a3b) andfrom spinel to perovskite and magnesiowu¨s-tite (g3pv 1 mw), respectively (1–9). How-ever, some recent in situ studies of thepostspinel transformation suggested that the660-km discontinuity may instead be due tothe transformation of majorite garnet (gt) toperovskite in a pyroxene-garnet–dominanttransition zone (TZ) (10, 11). Tests of theseismic predictions from the olivine modelhave yielded ambiguous results, including asurprisingly weak correlation between thethickness of (HTZ) and seismic velocitieswithin the TZ (12, 13). Here, we show thatthe patterns of S-velocity heterogeneity anddiscontinuity topography in the East Asian–Australian TZ are consistent with olivinetransitions as the prime cause for the 410- and660-km discontinuities (410 and 660).The Clapeyron slopes (of the phaseboundaries in P-T space) of the a3b andg3pv 1 mw reactions are probably positiveand negative, respectively (14). If the seismi-cally inferred Clapeyron slopes g410 and g660are similar (15), the 410 and 660 should bedeflected toward (away from) each other atrelatively high (low) temperatures. HTZwould then correlate with temperature andtemperature-dependent seismic velocitieswithin the TZ (Fig. 1A). If, instead, the 660 iscaused by the gt3pv transition, which has apositive Clapeyron slope (16), the correlationbetween HTZ and the seismic velocitieswould be weak or absent. Pertinent seismicevidence has so far been equivocal (17).We use converted-wave (Pds) delay-timemeasurements along with S-velocity values inthe TZ (VSTZ) estimated from tomographicmodels of East Asia (18) and Australia (19),which were computed with large sets of ver-tical-component seismograms. We measuredtP660s and tP410s arrival times from stacks ofrotated three-component seismograms, de-convolved by the principal component of therecorded P-wave train (12, 20), and obtainedtdiff 5 tp660s 2 tp410s values with “bootstrap”errors (21) for 12 stations in East Asia andAustralia. We rejected traces with a low sig-nal-to-noise ratio, stacks that did not showboth P660s and P410s, and stations for whichthe number of the accepted traces was insuf-ficient to determine tP660s, tP410s, and theiruncertainties (22). Because the paths ofP660s and P410s are essentially the samebelow 660 and above 410 (Fig. 1B), to first-order, tdiff depends only on the thickness ofand seismic velocities within the TZ. The tdiffmeasurements represent lateral averages over’500 km (23).In the tomographic models, the upper 200to 300 km is constrained primarily by long-and intermediate-period Rayleigh waves anddeeper structure, including that in the TZ, bythousands of S and multiple-S waveforms.Dense data coverage (Fig. 2) provides 500- to600-km lateral resolution in the TZ (Fig. 3)(18, 19). However, tomographic imagingmay underestimate the amplitude of TZ1Department of Earth, Atmospheric, and PlanetarySciences, Room 54-512, Massachusetts Institute ofTechnology, Cambridge, MA 02139, USA. 2Observa-toire Midi Pyre«ne«es,14 Avenue Edouard Belin, Tou-louse, France.*To whom correspondence should be addressed. E-mail: sergei@quake.mit.eduFig. 1. (A) Schematic depiction of the transition zone in an olivine-dominant mantle. The a3b andg3pv 1 mw phase transformations give rise to the 410- and 660-km discontinuities (1Ð9), and theeffective Clapeyron slopes g410 and g660 have opposite signs. Absent lateral variations in compo-sition, relatively low temperatures (T) cause thickening of the TZ and increase in seismic velocities(VP, VS); high temperatures cause thinning of the TZ and decrease in VP,S. (B) Schematic ray diagramof the P, P410s, and P660s phases.Fig. 2. Ray-path cover-age used in the S-veloc-ity tomography of EastAsia (A) (18) and Austra-lia (B) (19). The tomo-graphic models (Fig. 3)are constrained by parti-tioned waveform inver-sion (PWI) (38) andautomated PWI (18)of multimode Rayleighwaves. Higher modesÑforming the S and mul-tiple S wavesÑare sen-sitive to transition-zonestructure. The stationswith tdiff measurementsare shown with dia-monds. Longitude (hori-zontal axis) is in degrees east, latitude (vertical) is in degrees north (positive) and south (negative).R E P O R T S17 MAY 2002 VOL 296 SCIENCE www.sciencemag.org1300anomalies, and in poorly sampled regions, theretrieved anomalies may be in error due tounresolved trade-offs with structure else-where in the model. We therefore did not takethe models at face value but used a series ofresolution tests (fig. S1) (24) to estimate VSin the TZ beneath the stations that yielded thetdiff measurements. Reliable estimates for theupper (dVS410) and lower (dVS660) parts of theTZ could be obtained for eight stations (plot-ted in Fig. 3), with estimated uncertaintiesranging from 30 to 60 m/s (dVS410) and 40 to80 m/s (dVS660). We recomputed dVS410,660relative to the reference model iasp91 (25)for a reference period of 1 s, assuming aquality factor Q 5 143 (26).The required four independent parameters(tP410s, tP660s, dVS410, dVS660) could be deter-mined for eight stations only. At these sta-tions, tdiff correlates (r 5 0.94) with dVSTZ 5(dVS410 1 dVS660)/2 (Fig. 4A). The best-fittingline was determined by bivariate regressionand has a slope of 0.012 6 0.006 s/(m/s). Fora TZ of constant thickness the differentialtime tdiff would be smaller in high-velocityregions and larger in low-velocity ones. Weobserve the opposite, implying that HTZ var-ies in concert with seismic velocities.Next, we convert dtdiff to transition-zonethickness anomaly dHTZ [using the referenceP and S velocities (VP,S) from iasp91, ourdVSTZ, and assuming R 5 dlnVS/dlnVP 51.7 6 0.7] and dVSTZ to temperature variationdTTZ [using ]lnVS/]T 5 21.35 3 1024 K21(27) and a 0.4 3 1024 K21 uncertainty of thederivative]. HTZ correlates with TTZ (r 50.98), and the slope of the best-fitting line,20.13 6 0.07 km/K, is consistent with the20.13 km/K inferred from the mineralogicalClapeyron slopes of the a3b and g3pv 1mw transformations (14) (Fig. 4B).Encouraged by this result, we use the esti-mates for dVS410 and dVS660 and compute theeffective Clapeyron slopes g410 and g660 direct-ly. Expressing the temperature anomalies dT410and dT660 as functions of dVS410 and dVS660, weobtain one linear equation for each stationdHTZ 5 S ]d]PD660z g660 z]T]lnVSz dlnV S6602 S ]d]PD410z g410 z]T]lnVSz dlnV S410 (1)where (]d/]P)410(660) describes the depth-pressure relationship at the 410(660). Wesolve Eq. 1 for g410 and g660 by minimizingthe chi-square (28) functionx2 5 Oi 5 18SdH TZi 2 dHTZ(g410,g660;(V S410)i,(V S660) i)si D2(2)Fig. 5. (A) The effective Clapeyron slopes at the410- and 660-km discontinuities. x2 misÞt in theg410-g660 plane is plotted in the region aroundthe best-Þt solution (.). The values of the min-eralogical Clapeyron slopes of a3b and g3pv 1mw from (14) [small solid square at (22.0 MPa;2.9 MPa)] and the range of measured values fromthe literature as compiled in (14) (large rectangle)are superimposed as g410 and g660. (B) The mea-sured effective Clapeyron slopes (A) do not de-pend strongly on the measurements at the twostations with largest anomalies (Fig. 4). The starand dark-shaded curve denote the best-Þt valueand 1s error ellipse computed with the completedata set, as in (A). The black and gray circles andlines show the solution of Eq. 1 with one of thetwo stations (equations) excluded; empty circleand dashed line is the solution with both of thestations excluded.Fig. 3. Differential-time(tdiff) measurements ateight stations superim-posed on the tomo-graphic images of theEast Asian (A) and Aus-tralian (B) transitionzones. VS-anomaly val-ues are averaged overthe TZ depth range. TheAsian model (18) wascomputed with 400-kma priori smoothing; theAustralian model (19) issmoothed over 400 kma posteriori. ReferenceVS values are 5291 and5311 m/s for Asia andAustralia, respectively;reference tdiff is 23.9 s(25).Fig. 4. The correlation be-tween (A) S velocity in thetransition zone and the differ-ential time tdiff and between(B) the inferred temperature ofthe transition zone TTZ and itsthickness HTZ. Seismic velocityanomalies dVSTZ are vertical av-erages over the transition-zone depth range, and so arethe estimated temperatureanomalies dTTZ. The data fromthe East Asian stations areshown with dark-shaded sym-bols (BJT, with a square; ENH,triangle; QIZ, inverted triangle;SSE, diamond; XAN, circle).The data from the Australianstations are shown with light-shaded symbols (CTAO, with a square; SA03, inverted triangle; STKA,triangle).R E P O R T Swww.sciencemag.org SCIENCE VOL 296 17 MAY 2002 1301where dHTZi, (VS410)i, and (VS660)i are the data atthe i-th station (i 5 1,. . .,8) and dHTZ(. . .) is afunction of the variables g410 and g660. Thecumulative errors si are computed for dHTZiand account for uncertainties of tdiffi , (VS410,660)i,R, and ]lnVS/]T. The solution (Fig. 5A) isconsistent with the mineralogic Clapeyronslopes of the olivine transformations (14). Thewidth of the error ellipses accounts for ourmeasurement uncertainties as well as for possi-ble lateral variations in R (640%) and dlnVS/dT(630%). Unlike the slope of the straight line inFig. 4B, the solution of Eq. 1 is not sensitive tothe two extremal data points; excluding eitheror both results in a small displacement of thebest-fit point and a slight widening of the 1sellipses (Fig. 5B).The correlation between tdiff and VSTZ(and thus between the TZ thickness and tem-perature) in East Asia–Australia (Fig. 4) con-trasts the weak correlation inferred fromglobal tdiff data sets and tomographic models(12, 13, 29). We suggest that this inconsis-tency is due to differences in spatial resolu-tion of tdiff measurements, on the one hand,and of VPTZ or VSTZ values from global tomog-raphy, on the other. The resolution of globalwavespeed heterogeneity in the TZ is mostuniform (30, 31) at wavelengths that aremuch larger (.3000 km) than the spatialresolution of the tdiff measurements (’500km), and this may obscure existing tdiff – VSTZcorrelations. Our study, in which tdiff andVSTZ relate to the same spatial length scale,corroborates models in which the phase trans-formations in olivine cause both 410 and 660.References and Notes1. J. D. Bernal, Observatory 59, 265 (1936).2. D. L. Anderson, Science 157, 1165 (1967).3. A. E. Ringwood, Earth Planet. Sci. Lett. 5, 401 (1969).4. E. Ito, E. Takahashi, J. Geophys. Res. 94, 10673(1989).5. T. Katsura, E. Ito, J. Geophys. Res. 94, 15663 (1989).6. G. Helffrich, Rev. Geophys. 38, 141 (2000).7. P. M. Shearer, in Earth’s Deep Interior: Mineral Physicsand Tomography from the Atomic to the Global Scale,S. Karato, A. M. Forte, R. C. Liebermann, G. Masters, L.Stixrude, Eds. (Geophysical Monograph 117, Ameri-can Geophysical Union, Washington, DC, 2000), pp.115Ð131.8. S.-H. Shim, T. S. Duffy, G. Shen, Nature 411, 571(2001).9. L. Chudinovskikh, R. Boehler, Nature 411, 574 (2001).10. T. Irifune et al., Science 279, 1698 (1998).11. K. Hirose, Y. Fei, S. Ono, T. Yagi, K. Funakoshi, EarthPlanet. Sci. Lett. 184, 567 (2001).12. S. Chevrot, L. Vinnik, J.-P. Montagner, J. Geophys. Res.104, 20203 (1999).13. M. P. Flanagan, P. M. Shearer, J. Geophys. Res. 103,2673 (1998).14. C. R. Bina, G. R. Helffrich, J. Geophys. Res. 99, 15853(1994).15. Because phase transformations in the Earth occur overdepth intervals in which multiple phases coexist, it is notmeaningful to deÞne the Clapeyron slopes at 410 or 660thermodynamically (14). The discontinuities, however,are seen as sharp interfaces by Þnite-frequency seismicwaves, and measurements of the depths to these appar-ent interfaces can constrain the effective (ÒseismicÓ)Clapeyron slopes at the discontinuities which, althoughweakly dependent on seismic-wave frequency, other-wise are determined only by thermodynamic properties(14). The seismically derived Clapeyron slopes can alsobe affected by isostructural phases with variable chem-istry at the depth of the discontinuities (32), in particularbecause of the exchange of magnesium and iron be-tween olivine and other mantle minerals (33, 34). Ac-cording to the phase diagrams from (5), a 1% increase inthe magnesium number Mg# 5 Mg/(Mg1Fe) wouldraise the pressure of a3b by 0.1 GPa (increasing thedepth to 410 by dd410 ’ 3 km), the same effect as froma 35 K increase in temperature [given g410 5 2.9 MPa/K(14)]. With P and S velocities (VP,S) also growing withMg# (33), lateral variations in Mg# would thus weakenthe thermally induced anticorrelation between d410 andVP,S depicted in Fig. 1A. Our observation that the Òseis-micÓ Clapeyron slopes agree (within uncertainties) withthe mineralogical slopes for Mg2SiO4 is consistent withthe actual effect of composition being small.16. D. J. Weidner, Y. Wang, in Earth’s Deep Interior:Mineral Physics and Tomography from the Atomic tothe Global Scale, S. Karato, A. M. Forte, R. C. Lieber-mann, G. Masters, L. Stixrude, Eds. (GeophysicalMonograph 117, American Geophysical Union, Wash-ington, DC, 2000), pp. 215Ð235.17. A downwarp of 660 and an uplift of 410 have beendocumented beneath the ÒcoldÓ subduction zones (35,36), but these regions represent only a small fraction ofthe upper mantle, possibly with compositional and ki-netic effects affecting the phase transformations (16). Atlarger scales, there is evidence both for and against add410Ðdd660 anticorrelation (6, 7), but this may be incon-clusive owing to the possibly incoherent temperaturevariations in the upper and lower TZ (13) and to uncer-tainties of the measurements (errors in the models ofthe heterogeneous mantle above 410 translate into sub-stantial uncertainties in inferred discontinuity depth).The measurements of HTZ are generally more precisethan those of dd410,660, because HTZ can be constrainedwith observables that to Þrst order do not depend onstructure above 410, such as the tdiff 5 tP660s Ð tP410s thatwe use here. However, a recent global compilation ofconverted-wave differential times tdiff 5 tP660s Ð tP410s(which scale with HTZ) showed poor correlation withseismic velocities from global tomographic models (12).A similarly weak correlation was obtained by mappingHTZ with long-period SS precursors (13).18. S. Lebedev, G. Nolet, in preparation.19. F. J. Simons, A. Zielhuis, R. D. van der Hilst, Lithos 48,17 (1999).20. L. P. Vinnik, Phys. Earth Planet. Int. 15, 39 (1977).21. B. Efron, R. Tibshirani, Science 253, 390 (1991).22. For each station, we collected all available traces andinspected them visually, rejecting those with strongbackground noise before the P-wave onset. After therotation and deconvolution, we also discarded traceswith the SV-component amplitude exceeding 15% ofthat of the P wave. Finally, we rejected the data if P410sor P660s arrivals could not be identiÞed on the stacks(presumably due to multipathing caused by strongupper-mantle heterogeneity or small-scale discontinui-ty undulations). The number of records that contributeto the stacks ranges from 13 to 135, with an average of53 (37).23. We stack the records from events at different azi-muths and distances so that the piercing points ofPds waves at the discontinuities are distributed overan area a few hundred kilometers wide (Fig. 1B).Taking into account the 100- to 300-km width of theFresnel zone of the waves at the discontinuities [see(12) for discussion], we estimate the lateral resolu-tion of the measurements at ’ 500 km.24. Supplementary Web material is available on ScienceOnline at www.sciencemag.org/cgi/content/full/296/5571/1300/DC1.25. B. L. N. Kennett, E. R. Engdahl, Geophys. J. Int. 105,429 (1991).26. A. M. Dziewonski, D. L. Anderson, Phys. Earth Planet.Int. 25, 297 (1981).27. S. Karato, Geophys. Res. Lett. 20, 1623 (1993).28. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P.Flannery, Numerical Recipes in FORTRAN (CambridgeUniv. Press, New York, ed. 2, 1992).29. The correlation of global maps of HTZ obtained usingSS precursors with tomographic TZ wavespeeds isweak (13), although consistent with the olivine Cla-peyron slopes from (14).30. Reference Earth Model Web site, http://mahi.ucsd.edu/Gabi/rem.html.31. T. W. Becker, L. Boschi, Geochem. Geophys. Geosyst.3, paper no. 2001GC000168 (2002).32. L. Stixrude, J. Geophys. Res. 102, 14835 (1997).33. T. Irifune, M. Isshiki, Nature 392, 702 (1998).34. C. Bina, Nature 392, 650 (1998).35. J. E. Vidale, H. M. Benz, Nature 356, 678 (1992).36. C. W. Wicks, M. A. Richards, Science 261, 1424(1993).37. S. Lebedev, S. Chevrot, R. D. van der Hilst, inpreparation.38. G. Nolet, J. Geophys. Res. 95, 8499 (1990).39. We thank A. Zielhuis for running the resolution testsfor the tomographic model of Australia. This workwas supported by the David and Lucile Packard Foun-dation through a fellowship awarded to R.D.v.d.H.27 December 2001; accepted 29 March 2002Identity and Searchin Social NetworksDuncan J. Watts,1,2,3* Peter Sheridan Dodds,2 M. E. J. Newman3Social networks have the surprising property of being “searchable”: Ordinarypeople are capable of directing messages through their network of acquain-tances to reach a specific but distant target person in only a few steps. Wepresent a model that offers an explanation of social network searchability interms of recognizable personal identities: sets of characteristics measured alonga number of social dimensions. Our model defines a class of searchable net-works and a method for searching them that may be applicable to manynetwork search problems, including the location of data files in peer-to-peernetworks, pages on the World Wide Web, and information in distributed da-tabases.In the late 1960s, Travers and Milgram (1)conducted an experiment in which randomlyselected individuals in Boston, Massachu-setts, and Omaha, Nebraska, were asked todirect letters to a target person in Boston,each forwarding his or her letter to a singleacquaintance whom they judged to be closerthan themselves to the target. Subsequentrecipients did the same. The average length ofthe resulting acquaintance chains for the let-R E P O R T S17 MAY 2002 VOL 296 SCIENCE www.sciencemag.org1302

Seismic evidence for olivine phase changes at the 410- and 660-kilometer discontinuities

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