Indoor seismology by probing the Earth’s interiorby using sound velocity measurements at highpressures and temperaturesBaosheng Li*† and Robert C. Liebermann*‡

*Mineral Physics Institute and ‡Department of Geosciences, Stony Brook University, Stony Brook, NY 11790

Edited by Russell J. Hemley, Carnegie Institution of Washington, Washington, DC, and approved March 12, 2007 (received for review October 2, 2006)

The adiabatic bulk (KS) and shear (G) moduli of mantle materials athigh pressure and temperature can be obtained directly by mea-suring compressional and shear wave velocities in the laboratorywith experimental techniques based on physical acoustics. Wepresent the application of the current state-of-the-art experimen-tal techniques by using ultrasonic interferometry in conjunctionwith synchrotron x radiation to study the elasticity of olivine andpyroxenes and their high-pressure phases. By using these updatedthermoelasticity data for these phases, velocity and density pro-files for a pyrolite model are constructed and compared with radialseismic models. We conclude that pyrolite provides an adequateexplanation of the major seismic discontinuities at 410- and 660-kmdepths, the gradient in the transition zone, as well as the velocitiesin the lower mantle, if the uncertainties in the modeling and thevariations in different seismic models are considered. The charac-teristics of the seismic scaling factors in response to thermalanomalies suggest that anticorrelations between bulk sound andshear wave velocities, as well as the large positive density anom-alies observed in the lower mantle, cannot be explained fullywithout invoking chemical variations.

elasticity � mantle composition � mantle heterogeneity � ultrasonic

interferometry � pyrolite

Seismological investigations provide the primary source ofinformation about the properties and processes of the

Earth’s interior, especially for depths greater than a few hun-dreds of kilometers (i.e., depths below which rock samples havenot yet reached the Earth’s surface). In addition to regionalstudies that provide detailed velocity structures of the uppermantle and the transition zone, global Earth models of velocityand density profiles versus depths have been generated bycompiling thousands of seismic records and data of differenttypes, e.g., the Preliminary Earth Reference Model (1) andAK135 (2). The variations of compressional wave (P wave) andshear wave (S wave) wave velocities and densities in these modelspresumably reflect radial and lateral variations of chemicalcomposition, mineralogy, pressure, and temperature. Successfulinterpretation of these seismic models in terms of the variablesabove requires experimental and theoretical information on theelasticity of Earth materials under the elevated conditions thatcharacterize the Earth’s interior. One of the petrological modelsthat has been tested extensively in the literature is that ofpyrolite, which was proposed by Ringwood (3) based on thecompositions of mantle peridotites and oceanic basalts (4–8).We use the pyrolite model to compare with seismic models ofboth global and regional nature.

Over the past 40 years or so, the elastic properties of many mantleminerals as well as their high-pressure phases have been studied byusing static and shock compression and various spectroscopictechniques. Such approaches provide important information aboutthe variation of density (hence compressibility) and crystal struc-ture up to the pressure and temperature conditions of the core

mantle boundary; however, they do not directly measure soundvelocities and cannot provide data on the shear elastic properties.

In a manner similar to observational seismology, experimentaltechniques based on physical acoustics provide complete mea-surements of the adiabatic bulk (KS) and shear (G) moduli ofmaterials at high pressure and temperature by directly measuringP and S wave velocities. However, except for those performed inshock wave studies, such acoustic studies still fall short ofachieving the simultaneous pressure and temperature conditionsof the Earth’s deep mantle; consequently, extrapolations of theelastic properties of mantle phases by using finite strain theoryor various equations of states have been required for theinterpretation of seismic data (7, 8).

In this article, we briefly summarize the state-of-the-art inlaboratory studies by using physical acoustics techniques and thendiscuss in detail recent progress in performing measurements ofelastic wave velocities at high pressures and temperatures by usingultrasonic interferometric techniques in conjunction with synchro-tron x radiation. We then present recent data for the polymorphsof olivine and pyroxene and discuss the implications of such data forinterpretation of radial Earth models and also tomographic modelsincorporating lateral variations of velocities and moduli.

Sound Velocity Measurements at High Pressureand TemperatureOver the past half century, various techniques based on physicalacoustics have been used to study the elastic behavior ofmaterials by directly measuring P and S wave velocities underambient and elevated conditions; these include ultrasonic inter-ferometry, Brillouin spectroscopy, impulsive stimulated scatter-ing (ISS), and resonant ultrasound spectroscopy (RUS) (seereviews in refs. 9 and 10). The present state-of-the-art inperforming such measurements at high pressures and tempera-tures characteristic of the Earth’s interior is summarized in Fig.1. Both RUS and Brillouin spectroscopy techniques can achievetemperatures in excess of 1,500 K at room pressure (11, 12).Brillouin spectroscopy and ISS light-scattering techniques haveachieved pressures in excess of 50 GPa at room temperature indiamond-anvil cell apparatus (13, 14). Recent developmentswith ultrasonics and x-rays are described in detail below.

Ultrasonic interferometric methods have been used extensivelyin geophysics since they were developed by McSkimin (15).Progress from the 1960s to the mid-1990s has been summarized inour earlier articles (16, 17). In our laboratory, we have achieved

Author contributions: B.L. and R.C.L. designed research; B.L. and R.C.L. performed research;B.L. and R.C.L. contributed new reagents/analytic tools; B.L. analyzed data; and B.L. andR.C.L. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Abbreviations: P wave, compressional wave; S wave, shear wave; ISS, impulsive stimulatedscattering; RUS, resonant ultrasound spectroscopy.

†To whom correspondence should be addressed. E-mail: bli@notes.cc.sunysb.edu.

© 2007 by The National Academy of Sciences of the USA

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substantial technological progress in enabling sound velocity mea-surements to be conducted under mantle conditions. Among themilestones in the past decade have been the following:

Y Interfacing ultrasonic interferometric techniques with mul-tianvil, high-pressure apparatus for measurements to 10 GPaat room temperature (18) and to simultaneous high pressuresof 10 GPa and temperatures of 1,500 K (19) (Fig. 2).

Y Combining ultrasonic measurements at high pressures and tem-peratures in conjunction with synchrotron x radiation diffractiondeterminations of volumes of sample and pressure standard(20–23) (Fig. 3).

Y Adaptation of x-radiography techniques to monitor directlychanges of sample length under high pressures and temperaturesduring the ultrasonic measurements, allowing for the study ofmaterials undergoing phase transitions and of unquenchablemantle phases (24, 25).

Y Introduction of the transfer function method of ultrasonic inter-ferometry, which allows rapid data collection of acoustic dataand subsequent analysis offline (26).

Y Introduction of simultaneous measurement of both P and S wavevelocities on the same specimen under high pressure and tem-perature by using pure mode transducers (27) and dual-modelithium niobate transducers (25, 28).

Y The ability to measure simultaneously elastic P and S wave traveltimes, density, and sample length in a multianvil apparatusinterfaced with synchrotron x radiation techniques has enabled

direct determination of the cell pressure without relying onsecondary pressure standards (29, 30).

Fig. 2 shows schematically the generation and reception ofacoustic wave signals at high pressures; shown is the arrival of Pand S wave groups analogous to those recorded on seismograms.In Fig. 3, we illustrate the experimental configuration thatenables us to conduct indoor measurements of wave velocities athigh pressures and temperatures by using a Kawai-type, mul-tianvil apparatus at the 13ID beamline operated by GeoSoil-EnviroCARS at the Advanced Photon Source of the ArgonneNational Laboratory (Argonne, IL) (31). By combining theultrasonic measurements with the x-ray diffraction and x-radiography techniques now available at synchrotron facilities,simultaneous measurements of travel times, sample length andvolume, temperature, and pressure can be obtained (see Fig. 3A, C, and D). Additional technical details about each element ofsuch integrated experiments, and the wide range of experimentsthat can be conducted with these updated capabilities can befound in previous publications (32–34). By using these tech-niques, it is now possible to perform high-frequency (20- to80-MHz) measurements of both P and S wave velocities with aprecision of 0.3% on millimeter-sized polycrystalline or single-crystal samples to pressures �20 GPa and simultaneous tem-peratures �1,500 K (Fig. 1).

Measurements on Major Mantle MineralsUsing the techniques described above, we have measured theelasticity of many of the most important mantle mineral phasesand high pressures and temperatures, including (MgFe)2SiO4olivine (35, 36), wadsleyite (21), ringwoodite (37), majorite-pyrope garnets (38, 39), MgSiO3 pyroxenes (32, 33, 40), mag-nesiowustite (25), and MgSiO3 perovskite (29). In Table 1, wesummarize these data, including the pressure and temperaturederivatives of the elastic bulk and shear moduli. In the followingsections, we discuss the data for olivine and pyroxenes as theprimary constituents of the upper mantle and for silicate per-ovskite as the dominant mineral in the lower mantle.

Olivine. High-pressure measurements on olivine have been per-formed at progressively higher pressures from 1 to 6 GPa. In the1990s, acoustic data for this important upper mantle phase wereobtained to transition zone pressures (P � 12 GPa) by using ISS,Brillouin scattering, and ultrasonic interferometry. Different data-processing methods used in these studies, such as polynomial fitversus finite strain fit, might have contributed to the apparentdiscrepancies among the reported values for the pressure deriva-tives KS0� and G0� (see ref. 16 for a review). Despite the differencesin experimental techniques, a comparison of the pressure deriva-tives of the bulk modulus derived from finite strain analysis for dataobtained at different pressure ranges suggests a decreasing valuewith increased pressure range, changing from KS0� � 4.8–5 fromexperiments up to 1 GPa to KS0� � 4.2–4.4 for measurements atpressures �10 GPa. Quantitative determination of the secondpressure derivative, K�, however, still requires more accurate datathan those currently available. In addition to these measurementsat high pressures, the elasticity of olivine at high temperature alsohas been measured up to 1,700 K on single crystals by using RUSat room pressure (11).

Most recently, P and S wave velocities at simultaneous pressuresand temperatures have been measured to 8.2 GPa and 1,073 K byusing the techniques described above (36); these data exhibit verysystematic behavior with respect to both pressure and temperature(see figure 1 in ref. 36). The newly measured velocities (VP and VS)and volumes (V) provide sufficient data to obtain the elastic moduliand their pressure and temperature derivatives by fitting finitestrain equations to all of the T–V–VP–VS data, without relying on aninternal pressure standard, yielding KS0 � 130 (�2) GPa, G0 � 77

Pressure (GPa)0 5 10 15 20 25 30

Tem

per

atu

re (

K)

500

1000

1500

2000 GeothermTransition Zone

Ultrasonics+X-ray

RUS

Brillouin Scattering P >50 GPa

Fig. 1. Current experimental pressure and temperature conditions accessi-ble in laboratory acoustic velocity measurements by using different tech-niques. The pressure–temperature range enclosed by the dashed lines repre-sent regions accessible with the combined ultrasonic and x-ray techniques,and solid squares are peak pressure and/or temperature conditions reached inprevious ultrasonic experiments.

Fig. 2. Schematic of acoustic wave propagation in the current experimentalconfiguration for simultaneous measurement of P and S wave velocities inmultianvil high-pressure apparatus (Left) and the acoustic signals generatedand received by using a dual-mode lithium niobate transducer with thetransfer function method of ultrasonic interferometry (Right) to allow rapiddata collection and off-line analysis (Inset).

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(�1) GPa, KS0� � 4.6 (�0.2), G0� � 1.6 (�0.1), �KS/�T � �0.017(�0.001) GPa/K, and �G/�T � �0.013 (�0.001) GPa/K. These dataare consistent with previous experimental results for the ambientelastic moduli and their pressure derivatives from ISS (41) andBrillouin scattering measurements (42, 43). These temperaturederivatives of the adiabatic bulk and shear moduli show closeagreement with the results measured by ref. 11 using the resonantultrasound technique on single-crystal olivine at ambient pressure,although the results of ref. 36 contain explicitly the effect of thecross-derivative with respect to pressure and temperature.

Pyroxenes. By contrast with olivine, the velocity data for MgSiO3

orthopyroxene at high pressure exhibit very anomalous behavior.As pressure increases to 9 GPa, the velocity–pressure behavior is

distinctly nonlinear; above 9 GPa, both P and S velocities exhibitelastic softening, which suggests a transition to a metastable phaseintermediate between orthoenstatite and high-pressure clinoensta-tite (see figure 8 of ref. 32).

MgSiO3 pyroxenes transforms to a monoclinic polymorph (high-pressure clinoenstatite, space group C2/c) at pressures above �8GPa at high temperature (44); however, this phase cannot berecovered at ambient conditions. Thus, elasticity data on this phasemust be obtained for samples within its stability field. Ultrasonicinterferometry in conjunction with x radiation described aboveprovides a unique tool to study such phases in situ, allowing for thedetermination of the bulk and shear moduli and their pressure andtemperature derivatives by measuring the specific volume, P and Swave travel times, as well as sample lengths. By using these

SynchrotroSource

SSD/C

CD

Ultrasonic Interferometer

YA

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GX-ray

CCD Camera Transducer

Slits2θθθθ

Al2O3

NaCl+BN

Sample

Glass

Insulator

2mm

BufferRod

MgO

Heater

BN

Tc

WC Anvil

To Transducer

Au

Sample

Au

0.940mm

A B

C D

Fig. 3. Schematic diagram of experimental configuration for ultrasonic interferometry measurements in conjunction with synchrotron x radiation in theKawai-type, multianvil apparatus at the 13ID beamline operated by GeoSoilEnviroCARS at the Advanced Photon Source of the Argonne National Laboratory.(A, C, and D) The three types of raw data obtained in these experiments, providing simultaneous measurements of travel times, sample length and volume,temperature, and pressure. (B) Cell assembly. Detailed description of the cell assembly (B) may be found in ref. 28.

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techniques, P and S wave velocities of high-pressure clinopyroxenehave been determined to �13 GPa and 1,073 K (33). The elasticbulk and shear moduli as well as their pressure and temperaturederivatives subsequently are derived from the measured velocitiesand densities and are included in Table 1. With these data, wecompared the elastic velocities for both high-pressure clinopyrox-ene and olivine phases from 9 to 14 GPa along a 1,673-K adiabatand found that P and S wave velocities of the high-pressureclinopyroxene phase are 2% and 5.3% higher (see Fig. 4), respec-tively, than those of olivine, associated with a 3.5% difference indensity.

MgSiO3 Perovskite. Magnesium silicate perovskite (orthorhombicstructure, space group Pbnm) is believed to be the most abundantconstituent in the lower mantle, representing �75% in volume. Itsthermoelastic properties at high pressure and high temperaturetherefore have significant importance in studying the composition,lateral heterogeneities, and dynamics of the mantle (7, 45–48),which has motivated a number of experimental and theoreticalstudies over the past quarter century to investigate the crystalstructure and elastic properties of (MgFeAl)-silicate perovskite(e.g., refs. 49–54). The extant results, however, still are discrepantwith a range �30 GPa for the isothermal bulk modulus (KT �KS/(1 � ��T)) and the pressure derivative �KT/�P often has beenassumed to be a value of 4. Because �KT/�T in the analysis of static

compression (pressure–volume–temperature) depends largely onKT0, �KT/�P, the thermal expansivity (�) as well as the unit cellvolume at ambient conditions, a wide range of �KT/�T values(0.011–0.050 GPa/K) have been reported in these studies as well asdiscrepant values for the thermal expansion coefficients.

Only a few experimental studies have been conducted to deter-mine the shear modulus of Mg–Pv with acoustic techniques (23, 49,50, 52). Using simultaneous ultrasonic interferometry and x-raydiffraction methods described above, Li and Zhang (29) recentlyconducted measurements on a polycrystalline specimen of MgSiO3perovskite, providing simultaneous determination of P and S wavevelocities as well as the unit cell volumes (density) to 9.2 GPa and873 K. The adiabatic bulk and shear moduli and their pressure andtemperature derivatives derived from this study are KS0 � 253 (�2)GPa, G0 � 173 (�1) GPa, KS0� � 4.4 (�0.1), G0� � 2.0 (�0.1),�KS/�T � �0.021 (�0.002) GPa/K, and �G/�T � �0.028 (�0.002)GPa/K. Compared with other acoustic studies, these bulk and shearmoduli and those from recent Brillouin scattering measurements atambient conditions (49) are in excellent agreement. A recenthigh-pressure Brillouin scattering study to 45 GPa (52) usingpolycrystalline sample of magnesium silicate perovskite containing5.1% wt Al2O3 yielded KS0� � 3.7 (�0.3) and G0� � 1.7 (�0.2),which are slightly lower than the current ultrasonic results. Atpresent, the mismatch in the experimental pressure ranges as wellas the scarcity and scattering of the available Brillouin data in thepressure range of the ultrasonic measurement prohibit us drawingany conclusive inferences about the effect of Al substitution on thepressure derivatives of MgSiO3 perovskite.

Implications for the Composition of the Earth’s MantleCalculated Velocity Profiles and Comparison with Radial SeismicModels. With the elastic properties in Table 1, we have calculatedthe P and S wave velocities of each phase along a 1,600-K adiabatthroughout the pressure range of the mantle and have illustratedthese results in Fig. 4; we also plotted in Fig. 4 the global modelAK135 as a reference. In the upper mantle, the P and S wavevelocities of olivine are very close to the seismic velocities; additionof pyrope-rich garnet to this assemblage would increase the veloc-ities, whereas addition of pyroxenes (orthopyroxenes and diopsidicclinopyroxenes) would lower the velocities. Thus, in the depth rangebelow the asthenosphere, a pyrolite-type mantle agrees well withthe global seismic models (Fig. 4). The transition from orthopy-roxene to high-pressure clinopyroxenes discussed above may beresponsible for the seismically observed discontinuities in the depthrange of 220 to 300 km (55).

In the transition zone, the velocities of both wadsleyite andringwoodite, the high-pressure polymorphs of olivine, are signifi-cantly higher than those for majoritic garnets to which the uppermantle pyroxene phases transform. The gradual diminishing of

Table 1. Elasticity of major mantle minerals

Mineral �, g/cm3

KS0,GPa KS0�

�KS/�T,GPa/K

G0,GPa G0�

�G/�T,GPa/K Refs.

(MgFe)2SiO4 olivine 3.222 � 1.182 XFe 130 4.6 �0.017 77 1.6 �0.014 11, 36, 39, 41–43, 73, 75(MgFe)2SiO4 wadsleyite 3.472 � 1.24 XFe 173 4.5 �0.014 108 1.4 �0.016 21, 35, 43, 56, 73(MgFe)2SiO4 ringwoodite 3.548 � 1.30 XFe 185 4.5 �0.019 119 1.5 �0.015 37, 73, 76, 78(MgFe)SiO3 clinopyroxene 3.277 � 0.38 XFe 117 4.5 �0.015 67 1.7 �0.014 33, 40, 73, 74(MgFe)SiO3 orthopyroxene 3.204 � 0.799 XFe 114 6.6 �0.013 74 1.6 �0.011 40, 73MgSiO3 high-pressure clinoenstatite* 3.460 157 5.6 �0.017 99 1.5 �0.015 33(MgFe)3Al2Si3O12 pyrope garnet 3.565 � 0.76 XFe 171 4.1 �0.016 91 1.5 �0.010 39, 73, 77Mg4Si4O12 majorite garnet 3.518 � 0.97 XFe 168 4.1 �0.015 88 1.5 �0.010 38, 39, 77CaSiO3 perovskite 4.130 236 4.8 �0.027 153 2 �0.023 73, 79(MgFe)SiO3 perovskite 4.108 � 1.4 XFe 253 4.4 �0.021 170 2 �0.028 28, 29, 46, 49, 50, 51, 52(MgFe)O magnisiowustite 3.583 � 2.28 XFe 166 4.0 �0.016 112 1.9 �0.024 25, 73

*Results at 6.5 GPa, 300 K.

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Ol

HP -C

Wd

Rw

Gt

Mw

Mw

Mg-Pv

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HP-C

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Opx

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Cpx

VP

Fig. 4. Acoustic wave velocities of major mantle phases (solid lines) as afunction of pressure along a 1,600-K adiabatic geotherm, compared withglobal seismic model AK135 (dotted lines). Ol, olivine; OPx, orthopyroxene;CPx, clinopyroxene; HP-C, high-pressure clinopyroxene; Wd, wadsleyite; Rw,ringwoodite; Gt, garnet; Mg-Pv, magnesium silicate perovskite; Mw,magnesiowustite.

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garnet component and the formation of calcium perovskite in thetransition zone would increase the velocity gradient.

As demonstrated by many previous authors, quantitative com-parison of velocity jumps with seismic models can provide a meansto constrain the olivine content in the upper mantle and thetransition zone; such calculations have yielded a wide range ofestimates of the olivine content, primarily because of a lack ofconstraint on the elasticity of wadsleyite at high temperatures (seeref. 56 for an extended discussion). With the iron partitioning inolivine and wadsleyite constrained by the experimental data of ref.57, Liu and coworkers (36) investigated the velocity contrastsbetween the �- and �-(MgFe)2SiO4 at the 410-km discontinuity andfound that the velocity jumps are 10.9% for VP and 12.2% for VS;when compared with seismic discontinuities of �5% near 410-kmdepth, these velocity jumps would suggest an olivine content of50% in an anhydrous mantle. A hydrous mantle would increasethe estimates of the olivine content toward pyrolytic compositions(55–60%), according to data for hydrous wadsleyite of (58).

The disadvantage of comparing the velocity jumps alone is thatthe velocity gradients in the vicinity of the discontinuities cannot betaken into account. In a comparison with seismic data from theupper mantle to the bottom of the transition zone, Li and coworkers(21, 56) found that for depths in the upper mantle �200 km, thepyrolite model velocities agree with the seismic data both inabsolute values and gradients; the jumps across the 410-km depthregion for pyrolite are 6.9% and 7.9% across the 410-km discon-tinuity for P and S waves, respectively, over a thickness of �10 km.They concluded that compositional models with less olivine thanpyrolite might satisfy the 410-km discontinuity, but they will predictvelocities that are too slow in the upper mantle above the 410-kmdiscontinuity and in the transition zone near 660-km depth.

With the recently updated data set shown in Table 1, we haveconstructed the velocity and density profiles for pyrolite modelalong a 1,600-K adiabat following the approaches developed byprevious researchers (59); the results are compared with regionalseismic models in Fig. 5. The reanalysis of previous wadsleyite datain ref. 36 and the revised pressure and temperature derivatives forpyrope-majorite garnets (39) alter both the calculated velocityjumps at 410-km depth and the velocity gradients in the transitionzone. Considering the uncertainties in the current modeling as wellas the trade-offs in seismic data, the pyrolite model provides anadequate explanation of the major seismic discontinuities at 410-and 660-km depths, although the pyrolite model has larger velocityjumps (6.2% and 6.7% for P and S waves, respectively) at the410-km depth, and the velocity gradients in the transition zone stillare slightly lower than some regional seismic velocity models. Thevelocity jumps of the current pyrolite, for instance, are comparableto those reported in ref. 60; the velocity gradient in the transitionzone also shows good agreement with the AK135 model in ref. 2(Fig. 4). On the other hand, the impedance (z � �V, where V standsfor VP or VS) contrasts from the current pyrolite model (�9% forP wave, 10% for S wave) at 410-km depth are higher than thosefrom seismic studies in ref. 61 (5.3% for P wave, 7.8% for S wave)and ref. 62 (6.9% for S wave) for which olivine content less than thecurrent pyrolite model therefore is implied.

In the lower mantle, using these updated results for the bulk andshear moduli as well as their pressure and temperature derivativesfor MgSiO3 perovskite from recent Brillouin scattering and thesimultaneous ultrasonic and x-ray studies (29, 49), Li and Zhang(29) found that the radial velocity and density profiles of pyrolitecan reproduce the lower mantle P and S velocities and density of thePreliminary Earth Reference Model within 0.5% from the top tothe bottom of the lower mantle (see figure 4 a–c in ref. 29). All ofthese results seem to suggest that radial velocity and density profilesfor a pyrolytic composition along 1,600-K adiabatic geotherm arein general agreement with seismic observations, and consequentlyno chemical or thermal boundary layers at the 410- or 670-kmdiscontinuities are needed.

Insight on Lateral Heterogeneities in the Lower Mantle. Seismictomography reveals varying degrees of lateral heterogeneities inseismic velocities in the lower mantle, especially at the bottom of thelower mantle, where long-wavelength anomalies under the CentralPacific and beneath Africa consistently have been observed instudies using different data types (63–66). Although a thermalorigin often has been assumed to be the root cause of these lateralvariations, it remains to be demonstrated that temperature anom-alies are sufficient to explain the seismic observations withoutinvolving chemical effects (67, 68).

The logarithmic ratios (i.e., scaling factors) RSP � �lnVS/�lnVP,RCS � �lnVC/�lnVS (where VC is the bulk sound speed), andR�S � �ln�/�lnVS often are used as diagnostics for the origin ofmantle heterogeneities because these ratios, derived from seismicand geodynamical inversions, are less ambiguous than the absolutevalues of the anomalies (64). To calculate these ratios for thecurrent pyrolite model (primarily magnesium silicate perovskiteand magnesiowustite at the pressures and temperatures of the lowermantle) (67), we calculated the velocity and density profiles of thelower mantle following the procedures in ref. 29 but along twodifferent adiabatic geotherms; a numerical differentiation of theresults from the two temperatures yielded (1/VP)(�VP/�T)P,(1/VS)(�VS/�T)P, (1/VC)(�VC/�T)P, and (1/�)(��/�T)P at each depth(pressure), from which the results for RSP, RCS, and R�S attributableto lateral temperature variations were obtained (Fig. 6).

For anomalies of purely thermal origin, RSP increases from 1.8 at1,000-km depth to 2.0 at 2,600-km depth in the lower mantle (67,69). RCS remains positive, decreasing from 0.3 to 0.2 with increasingdepth. R�S remains positive throughout the lower mantle, changing

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Pressure (GPa)

Vel

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ty (

km/s

)

S-25

GCA

TNA

SNA

Pyrolite

VP

VS

Fig. 5. Comparison of P and S wave velocities of pyrolite model (dashed lines)with seismic models S25 (80), GCA (81), and SNA and TNA (82) (solid lines).

0.000

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700 1000 1300 1600 1900 2200 2500

Depth (km)

Am

plitu

de dlnVs/dlnVp

dlnr/dlnVs

dlnVc/dlnVs

Fig. 6. Values of seismic scaling factors in response to lateral variation oftemperatures at lower mantle depths.

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from 0.4 to 0.2 from the top to the bottom of the lower mantle; thesevalues are close to those inferred from tomographic and geody-namical inversions (66). A recent review (65) indicated that seismicRSP increases from 1.5 to 2.0 in the depth range from 1,000 to 2,500km together with highly correlated seismic P and S wave anomalies(�0.8); these observations seem to support a thermal origin forlateral heterogeneities at these depths. On the other hand, theobservation of RSP � 2.0 in the lower mantle (66, 70), the negativeRCS in the mid-lower mantle (63), and RSP 1.5 in the lower mantle(71), as well as the large positive density anomalies observed in ref.72, cannot be explained without invoking chemical variations, suchas iron enrichment and silica enrichment (67–69).

ConclusionsWe have presented the current state-of-the-art experimentaltechniques for measuring elastic wave velocities at high pressuresand temperatures by using ultrasonic interferometric techniquesin conjunction with synchrotron x radiation and their applica-tions to the polymorphs of olivine and pyroxene. Based on theupdated thermoelasticity of these phases, velocity and densityprofiles for a pyrolite model were constructed and comparedwith radial seismic models. Current data provide an adequateexplanation of the major seismic discontinuities at 410- and

660-km depths, the gradient in the transition zone, as well as thevelocities in the lower mantle, if the uncertainties in the modelingas well as the variations in different seismic models are consid-ered. However, further investigations of the water content in themantle and its effect on the elastic properties, as well asconsideration of other mantle compositional models (e.g.,piclogite), are still needed. In the deep lower mantle, thecharacteristics of the seismic scaling factors in response tothermal anomalies suggest that anticorrelations between bulksound and S wave velocities, as well as the large positive densityanomalies, observed in the lower mantle cannot be explainedfully without invoking chemical variations.

We appreciate the constructive comments and suggestions of the anon-ymous reviewers. This research was supported by National ScienceFoundation Grants EAR00135550 (to B.L.) and EAR02-29704 (toR.C.L.). The experimental data used in this study were obtained by usingthe facilities at X17B1/B2 of the National Synchrotron Light Source inBrookhaven National Laboratory (Upton, NY), which is supported bythe Consortium for Materials Properties Research in Earth Sciencesunder funding from National Science Foundation Grant EAR01-35554and U.S. Department of Energy, Basic Energy Sciences, and Office ofEnergy Research Contract No. DE-AC02-76CH00016. This article isMineral Physics Institute publication no. 367.

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