Seismological investigations provide the primary source of

Indoor seismology by probing the Earth s interior by using sound velocity measurements at high pressures and temperatures Baosheng Li* and Robert C. Liebermann* *Mineral Physics Institute and Department of Geosciences, Stony Brook University, Stony Brook, N 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 (K S ) and shear (G) moduli of mantle materials at high pressure and temperature can be obtained directly by measuring compressional and shear wave velocities in the laboratory with experimental techniques based on physical acoustics. We present the application of the current state-of-the-art experimental techniques by using ultrasonic interferometry in conjunction with synchrotron x radiation to study the elasticity of olivine and pyroxenes and their high-pressure phases. By using these updated thermoelasticity data for these phases, velocity and density profiles for a pyrolite model are constructed and compared with radial seismic models. We conclude that pyrolite provides an adequate explanation of the major seismic discontinuities at 410- and 660-km depths, the gradient in the transition zone, as well as the velocities in the lower mantle, if the uncertainties in the modeling and the variations in different seismic models are considered. The characteristics of the seismic scaling factors in response to thermal anomalies suggest that anticorrelations between bulk sound and shear wave velocities, as well as the large positive density anomalies observed in the lower mantle, cannot be explained fully without invoking chemical variations. elasticity mantle composition mantle heterogeneity ultrasonic interferometry pyrolite Seismological investigations provide the primary source of information about the properties and processes of the Earth s interior, especially for depths greater than a few hundreds of kilometers (i.e., depths below which rock samples have not yet reached the Earth s surface). In addition to regional studies that provide detailed velocity structures of the upper mantle and the transition zone, global Earth models of velocity and density profiles versus depths have been generated by compiling thousands of seismic records and data of different types, e.g., the Preliminary Earth Reference Model (1) and AK135 (2). The variations of compressional wave (P wave) and shear wave (S wave) wave velocities and densities in these models presumably reflect radial and lateral variations of chemical composition, mineralogy, pressure, and temperature. Successful interpretation of these seismic models in terms of the variables above requires experimental and theoretical information on the elasticity of Earth materials under the elevated conditions that characterize the Earth s interior. One of the petrological models that has been tested extensively in the literature is that of pyrolite, which was proposed by Ringwood (3) based on the compositions of mantle peridotites and oceanic basalts (4 8). We use the pyrolite model to compare with seismic models of both global and regional nature. Over the past 40 years or so, the elastic properties of many mantle minerals as well as their high-pressure phases have been studied by using static and shock compression and various spectroscopic techniques. Such approaches provide important information about the variation of density (hence compressibility) and crystal structure up to the pressure and temperature conditions of the core mantle boundary; however, they do not directly measure sound velocities and cannot provide data on the shear elastic properties. In a manner similar to observational seismology, experimental techniques based on physical acoustics provide complete measurements of the adiabatic bulk (K S ) and shear (G) moduli of materials at high pressure and temperature by directly measuring P and S wave velocities. However, except for those performed in shock wave studies, such acoustic studies still fall short of achieving the simultaneous pressure and temperature conditions of the Earth s deep mantle; consequently, extrapolations of the elastic properties of mantle phases by using finite strain theory or various equations of states have been required for the interpretation of seismic data (7, 8). In this article, we briefly summarize the state-of-the-art in laboratory studies by using physical acoustics techniques and then discuss in detail recent progress in performing measurements of elastic wave velocities at high pressures and temperatures by using ultrasonic interferometric techniques in conjunction with synchrotron x radiation. We then present recent data for the polymorphs of olivine and pyroxene and discuss the implications of such data for interpretation of radial Earth models and also tomographic models incorporating lateral variations of velocities and moduli. Sound Velocity Measurements at High Pressure and Temperature Over the past half century, various techniques based on physical acoustics have been used to study the elastic behavior of materials by directly measuring P and S wave velocities under ambient and elevated conditions; these include ultrasonic interferometry, Brillouin spectroscopy, impulsive stimulated scattering (ISS), and resonant ultrasound spectroscopy (RUS) (see reviews in refs. 9 and 10). The present state-of-the-art in performing such measurements at high pressures and temperatures characteristic of the Earth s interior is summarized in Fig. 1. Both RUS and Brillouin spectroscopy techniques can achieve temperatures in excess of 1,500 K at room pressure (11, 12). Brillouin spectroscopy and ISS light-scattering techniques have achieved pressures in excess of 50 GPa at room temperature in diamond-anvil cell apparatus (13, 14). Recent developments with ultrasonics and x-rays are described in detail below. Ultrasonic interferometric methods have been used extensively in geophysics since they were developed by McSkimin (15). Progress from the 1960s to the mid-1990s has been summarized in our 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. and R.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 stimulated scattering; 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 GEOPHSICS SPECIAL FEATURE www.pnas.org cgi doi 10.1073 pnas.0608609104 PNAS May 29, 2007 vol. 104 no. 22 9145 9150

substantial technological progress in enabling sound velocity measurements to be conducted under mantle conditions. Among the milestones in the past decade have been the following: Interfacing ultrasonic interferometric techniques with multianvil, high-pressure apparatus for measurements to 10 GPa at room temperature (18) and to simultaneous high pressures of 10 GPa and temperatures of 1,500 K (19) (Fig. 2). Combining ultrasonic measurements at high pressures and temperatures in conjunction with synchrotron x radiation diffraction determinations of volumes of sample and pressure standard (20 23) (Fig. 3). Adaptation of x-radiography techniques to monitor directly changes of sample length under high pressures and temperatures during the ultrasonic measurements, allowing for the study of materials undergoing phase transitions and of unquenchable mantle phases (24, 25). Introduction of the transfer function method of ultrasonic interferometry, which allows rapid data collection of acoustic data and subsequent analysis offline (26). Introduction of simultaneous measurement of both P and S wave velocities on the same specimen under high pressure and temperature by using pure mode transducers (27) and dual-mode lithium niobate transducers (25, 28). The ability to measure simultaneously elastic P and S wave travel times, density, and sample length in a multianvil apparatus interfaced with synchrotron x radiation techniques has enabled Temperature (K) 2000 1500 1000 500 RUS Transition Zone Ultrasonics+X-ray Geotherm Brillouin Scattering P >50 GPa 0 5 10 15 20 25 30 Pressure (GPa) Fig. 1. Current experimental pressure and temperature conditions accessible in laboratory acoustic velocity measurements by using different techniques. The pressure temperature range enclosed by the dashed lines represent regions accessible with the combined ultrasonic and x-ray techniques, and solid squares are peak pressure and/or temperature conditions reached in previous ultrasonic experiments. Fig. 2. Schematic of acoustic wave propagation in the current experimental configuration for simultaneous measurement of P and S wave velocities in multianvil high-pressure apparatus (Left) and the acoustic signals generated and received by using a dual-mode lithium niobate transducer with the transfer function method of ultrasonic interferometry (Right) to allow rapid data collection and off-line analysis (Inset). direct determination of the cell pressure without relying on secondary pressure standards (29, 30). Fig. 2 shows schematically the generation and reception of acoustic wave signals at high pressures; shown is the arrival of P and S wave groups analogous to those recorded on seismograms. In Fig. 3, we illustrate the experimental configuration that enables us to conduct indoor measurements of wave velocities at high pressures and temperatures by using a Kawai-type, multianvil apparatus at the 13ID beamline operated by GeoSoil- EnviroCARS at the Advanced Photon Source of the Argonne National Laboratory (Argonne, IL) (31). By combining the ultrasonic measurements with the x-ray diffraction and x- radiography techniques now available at synchrotron facilities, simultaneous measurements of travel times, sample length and volume, temperature, and pressure can be obtained (see Fig. 3 A, C, and D). Additional technical details about each element of such integrated experiments, and the wide range of experiments that can be conducted with these updated capabilities can be found in previous publications (32 34). By using these techniques, it is now possible to perform high-frequency (20- to 80-MHz) measurements of both P and S wave velocities with a precision of 0.3% on millimeter-sized polycrystalline or singlecrystal samples to pressures 20 GPa and simultaneous temperatures 1,500 K (Fig. 1). Measurements on Major Mantle Minerals Using the techniques described above, we have measured the elasticity of many of the most important mantle mineral phases and high pressures and temperatures, including (MgFe) 2 SiO 4 olivine (35, 36), wadsleyite (21), ringwoodite (37), majoritepyrope garnets (38, 39), MgSiO 3 pyroxenes (32, 33, 40), magnesiowüstite (25), and MgSiO 3 perovskite (29). In Table 1, we summarize these data, including the pressure and temperature derivatives of the elastic bulk and shear moduli. In the following sections, we discuss the data for olivine and pyroxenes as the primary constituents of the upper mantle and for silicate perovskite as the dominant mineral in the lower mantle. Olivine. High-pressure measurements on olivine have been performed at progressively higher pressures from 1 to 6 GPa. In the 1990s, acoustic data for this important upper mantle phase were obtained to transition zone pressures (P 12 GPa) by using ISS, Brillouin scattering, and ultrasonic interferometry. Different dataprocessing methods used in these studies, such as polynomial fit versus finite strain fit, might have contributed to the apparent discrepancies among the reported values for the pressure derivatives K S0 and G 0 (see ref. 16 for a review). Despite the differences in experimental techniques, a comparison of the pressure derivatives of the bulk modulus derived from finite strain analysis for data obtained at different pressure ranges suggests a decreasing value with increased pressure range, changing from K S0 4.8 5 from experiments up to 1 GPa to K S0 4.2 4.4 for measurements at pressures 10 GPa. Quantitative determination of the second pressure derivative, K, however, still requires more accurate data than those currently available. In addition to these measurements at high pressures, the elasticity of olivine at high temperature also has been measured up to 1,700 K on single crystals by using RUS at room pressure (11). Most recently, P and S wave velocities at simultaneous pressures and temperatures have been measured to 8.2 GPa and 1,073 K by using the techniques described above (36); these data exhibit very systematic behavior with respect to both pressure and temperature (see figure 1 in ref. 36). The newly measured velocities (V P and V S ) and volumes (V) provide sufficient data to obtain the elastic moduli and their pressure and temperature derivatives by fitting finite strain equations to all of the T V V P V S data, without relying on an internal pressure standard, yielding K S0 130 ( 2) GPa, G 0 77 9146 www.pnas.org cgi doi 10.1073 pnas.0608609104 Li and Liebermann

A C Au CCD Camera SSD/CCD 2θ AG Transducer SSD/CCD B Insulator Ultrasonic Interferometer Heater BN 2mm Slits D MgO Al2O3 NaCl+BN Synchrotro Source X-ray Sample Buffer Glass Rod WC Anvil To Transducer Tc GEOPHSICS SPECIAL FEATURE 0.940 mm Sample Au Fig. 3. Schematic diagram of experimental configuration for ultrasonic interferometry measurements in conjunction with synchrotron x radiation in the Kawai-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. ( 1) GPa, K S0 4.6 ( 0.2), G 0 1.6 ( 0.1), K S / T 0.017 ( 0.001) GPa/K, and G/ T 0.013 ( 0.001) GPa/K. These data are consistent with previous experimental results for the ambient elastic moduli and their pressure derivatives from ISS (41) and Brillouin scattering measurements (42, 43). These temperature derivatives of the adiabatic bulk and shear moduli show close agreement with the results measured by ref. 11 using the resonant ultrasound technique on single-crystal olivine at ambient pressure, although the results of ref. 36 contain explicitly the effect of the cross-derivative with respect to pressure and temperature. Pyroxenes. By contrast with olivine, the velocity data for MgSiO 3 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 exhibit elastic softening, which suggests a transition to a metastable phase intermediate between orthoenstatite and high-pressure clinoenstatite (see figure 8 of ref. 32). MgSiO 3 pyroxenes transforms to a monoclinic polymorph (highpressure clinoenstatite, space group C2/c) at pressures above 8 GPa at high temperature (44); however, this phase cannot be recovered at ambient conditions. Thus, elasticity data on this phase must be obtained for samples within its stability field. Ultrasonic interferometry in conjunction with x radiation described above provides a unique tool to study such phases in situ, allowing for the determination of the bulk and shear moduli and their pressure and temperature derivatives by measuring the specific volume, P and S wave travel times, as well as sample lengths. By using these Li and Liebermann PNAS May 29, 2007 vol. 104 no. 22 9147

Table 1. Elasticity of major mantle minerals Mineral, g/cm 3 GPa K S0, K S0 K S / T, GPa/K G 0, GPa G 0 G/ T, GPa/K Refs. (MgFe) 2 SiO 4 olivine 3.222 1.182 X Fe 130 4.6 0.017 77 1.6 0.014 11, 36, 39, 41 43, 73, 75 (MgFe) 2 SiO 4 wadsleyite 3.472 1.24 X Fe 173 4.5 0.014 108 1.4 0.016 21, 35, 43, 56, 73 (MgFe) 2 SiO 4 ringwoodite 3.548 1.30 X Fe 185 4.5 0.019 119 1.5 0.015 37, 73, 76, 78 (MgFe)SiO 3 clinopyroxene 3.277 0.38 X Fe 117 4.5 0.015 67 1.7 0.014 33, 40, 73, 74 (MgFe)SiO 3 orthopyroxene 3.204 0.799 X Fe 114 6.6 0.013 74 1.6 0.011 40, 73 MgSiO 3 high-pressure clinoenstatite* 3.460 157 5.6 0.017 99 1.5 0.015 33 (MgFe) 3 Al 2 Si 3 O 12 pyrope garnet 3.565 0.76 X Fe 171 4.1 0.016 91 1.5 0.010 39, 73, 77 Mg 4 Si 4 O 12 majorite garnet 3.518 0.97 X Fe 168 4.1 0.015 88 1.5 0.010 38, 39, 77 CaSiO 3 perovskite 4.130 236 4.8 0.027 153 2 0.023 73, 79 (MgFe)SiO 3 perovskite 4.108 1.4 X Fe 253 4.4 0.021 170 2 0.028 28, 29, 46, 49, 50, 51, 52 (MgFe)O magnisiowustite 3.583 2.28 X Fe 166 4.0 0.016 112 1.9 0.024 25, 73 *Results at 6.5 GPa, 300 K. techniques, P and S wave velocities of high-pressure clinopyroxene have been determined to 13 GPa and 1,073 K (33). The elastic bulk and shear moduli as well as their pressure and temperature derivatives subsequently are derived from the measured velocities and densities and are included in Table 1. With these data, we compared the elastic velocities for both high-pressure clinopyroxene and olivine phases from 9 to 14 GPa along a 1,673-K adiabat and found that P and S wave velocities of the high-pressure clinopyroxene phase are 2% and 5.3% higher (see Fig. 4), respectively, than those of olivine, associated with a 3.5% difference in density. MgSiO 3 Perovskite. Magnesium silicate perovskite (orthorhombic structure, space group Pbnm) is believed to be the most abundant constituent in the lower mantle, representing 75% in volume. Its thermoelastic properties at high pressure and high temperature therefore 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 theoretical studies over the past quarter century to investigate the crystal structure and elastic properties of (MgFeAl)-silicate perovskite (e.g., refs. 49 54). The extant results, however, still are discrepant with a range 30 GPa for the isothermal bulk modulus (K T K S /(1 T)) and the pressure derivative K T / P often has been assumed to be a value of 4. Because K T / T in the analysis of static Velocity (km/s) 12 11 10 9 8 7 6 5 4 3 Ol Ol Opx Gt HP-C Opx Gt HP -C Wd Cpx Wd V P V S Cpx Mg-Pv 0 5 10 15 20 25 30 35 Pressure (GPa) Rw Rw Mw Mg-Pv Fig. 4. Acoustic wave velocities of major mantle phases (solid lines) as a function of pressure along a 1,600-K adiabatic geotherm, compared with global 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, magnesiowüstite. Mw compression (pressure volume temperature) depends largely on K T0, K T / P, the thermal expansivity ( ) as well as the unit cell volume at ambient conditions, a wide range of K T / T values (0.011 0.050 GPa/K) have been reported in these studies as well as discrepant values for the thermal expansion coefficients. Only a few experimental studies have been conducted to determine the shear modulus of Mg Pv with acoustic techniques (23, 49, 50, 52). Using simultaneous ultrasonic interferometry and x-ray diffraction methods described above, Li and Zhang (29) recently conducted measurements on a polycrystalline specimen of MgSiO 3 perovskite, providing simultaneous determination of P and S wave velocities as well as the unit cell volumes (density) to 9.2 GPa and 873 K. The adiabatic bulk and shear moduli and their pressure and temperature derivatives derived from this study are K S0 253 ( 2) GPa, G 0 173 ( 1) GPa, K S0 4.4 ( 0.1), G 0 2.0 ( 0.1), K S / T 0.021 ( 0.002) GPa/K, and G/ T 0.028 ( 0.002) GPa/K. Compared with other acoustic studies, these bulk and shear moduli and those from recent Brillouin scattering measurements at ambient conditions (49) are in excellent agreement. A recent high-pressure Brillouin scattering study to 45 GPa (52) using polycrystalline sample of magnesium silicate perovskite containing 5.1% wt Al 2 O 3 yielded K S0 3.7 ( 0.3) and G 0 1.7 ( 0.2), which are slightly lower than the current ultrasonic results. At present, the mismatch in the experimental pressure ranges as well as the scarcity and scattering of the available Brillouin data in the pressure range of the ultrasonic measurement prohibit us drawing any conclusive inferences about the effect of Al substitution on the pressure derivatives of MgSiO 3 perovskite. Implications for the Composition of the Earth s Mantle Calculated Velocity Profiles and Comparison with Radial Seismic Models. With the elastic properties in Table 1, we have calculated the P and S wave velocities of each phase along a 1,600-K adiabat throughout the pressure range of the mantle and have illustrated these results in Fig. 4; we also plotted in Fig. 4 the global model AK135 as a reference. In the upper mantle, the P and S wave velocities of olivine are very close to the seismic velocities; addition of pyrope-rich garnet to this assemblage would increase the velocities, whereas addition of pyroxenes (orthopyroxenes and diopsidic clinopyroxenes) would lower the velocities. Thus, in the depth range below the asthenosphere, a pyrolite-type mantle agrees well with the global seismic models (Fig. 4). The transition from orthopyroxene to high-pressure clinopyroxenes discussed above may be responsible for the seismically observed discontinuities in the depth range of 220 to 300 km (55). In the transition zone, the velocities of both wadsleyite and ringwoodite, the high-pressure polymorphs of olivine, are significantly higher than those for majoritic garnets to which the upper mantle pyroxene phases transform. The gradual diminishing of 9148 www.pnas.org cgi doi 10.1073 pnas.0608609104 Li and Liebermann

garnet component and the formation of calcium perovskite in the transition zone would increase the velocity gradient. As demonstrated by many previous authors, quantitative comparison of velocity jumps with seismic models can provide a means to constrain the olivine content in the upper mantle and the transition zone; such calculations have yielded a wide range of estimates of the olivine content, primarily because of a lack of constraint on the elasticity of wadsleyite at high temperatures (see ref. 56 for an extended discussion). With the iron partitioning in olivine and wadsleyite constrained by the experimental data of ref. 57, Liu and coworkers (36) investigated the velocity contrasts between the - and -(MgFe) 2 SiO 4 at the 410-km discontinuity and found that the velocity jumps are 10.9% for V P and 12.2% for V S ; when compared with seismic discontinuities of 5% near 410-km depth, these velocity jumps would suggest an olivine content of 50% in an anhydrous mantle. A hydrous mantle would increase the 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 that the velocity gradients in the vicinity of the discontinuities cannot be taken into account. In a comparison with seismic data from the upper mantle to the bottom of the transition zone, Li and coworkers (21, 56) found that for depths in the upper mantle 200 km, the pyrolite model velocities agree with the seismic data both in absolute values and gradients; the jumps across the 410-km depth region for pyrolite are 6.9% and 7.9% across the 410-km discontinuity for P and S waves, respectively, over a thickness of 10 km. They concluded that compositional models with less olivine than pyrolite might satisfy the 410-km discontinuity, but they will predict velocities that are too slow in the upper mantle above the 410-km discontinuity and in the transition zone near 660-km depth. With the recently updated data set shown in Table 1, we have constructed the velocity and density profiles for pyrolite model along a 1,600-K adiabat following the approaches developed by previous researchers (59); the results are compared with regional seismic models in Fig. 5. The reanalysis of previous wadsleyite data in ref. 36 and the revised pressure and temperature derivatives for pyrope-majorite garnets (39) alter both the calculated velocity jumps at 410-km depth and the velocity gradients in the transition zone. Considering the uncertainties in the current modeling as well as the trade-offs in seismic data, the pyrolite model provides an adequate explanation of the major seismic discontinuities at 410- and 660-km depths, although the pyrolite model has larger velocity jumps (6.2% and 6.7% for P and S waves, respectively) at the 410-km depth, and the velocity gradients in the transition zone still are slightly lower than some regional seismic velocity models. The velocity jumps of the current pyrolite, for instance, are comparable to those reported in ref. 60; the velocity gradient in the transition zone also shows good agreement with the AK135 model in ref. 2 (Fig. 4). On the other hand, the impedance (z V, where V stands for V P or V S ) contrasts from the current pyrolite model ( 9% for P wave, 10% for S wave) at 410-km depth are higher than those from 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 the current pyrolite model therefore is implied. In the lower mantle, using these updated results for the bulk and shear moduli as well as their pressure and temperature derivatives for MgSiO 3 perovskite from recent Brillouin scattering and the simultaneous ultrasonic and x-ray studies (29, 49), Li and Zhang (29) found that the radial velocity and density profiles of pyrolite can reproduce the lower mantle P and S velocities and density of the Preliminary Earth Reference Model within 0.5% from the top to the bottom of the lower mantle (see figure 4 a c in ref. 29). All of these results seem to suggest that radial velocity and density profiles for a pyrolytic composition along 1,600-K adiabatic geotherm are in general agreement with seismic observations, and consequently no chemical or thermal boundary layers at the 410- or 670-km discontinuities are needed. Velocity (km/s) 11 10 9 8 7 6 5 4 5 10 15 20 25 30 Pressure (GPa) 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). Insight on Lateral Heterogeneities in the Lower Mantle. Seismic tomography reveals varying degrees of lateral heterogeneities in seismic velocities in the lower mantle, especially at the bottom of the lower mantle, where long-wavelength anomalies under the Central Pacific and beneath Africa consistently have been observed in studies using different data types (63 66). Although a thermal origin often has been assumed to be the root cause of these lateral variations, it remains to be demonstrated that temperature anomalies are sufficient to explain the seismic observations without involving chemical effects (67, 68). The logarithmic ratios (i.e., scaling factors) R SP lnv S / lnv P, R CS lnv C / lnv S (where V C is the bulk sound speed), and R S ln / lnv S often are used as diagnostics for the origin of mantle heterogeneities because these ratios, derived from seismic and geodynamical inversions, are less ambiguous than the absolute values of the anomalies (64). To calculate these ratios for the current pyrolite model (primarily magnesium silicate perovskite and magnesiowüstite at the pressures and temperatures of the lower mantle) (67), we calculated the velocity and density profiles of the lower mantle following the procedures in ref. 29 but along two different adiabatic geotherms; a numerical differentiation of the results from the two temperatures yielded (1/V P )( V P / T) P, (1/V S )( V S / T) P, (1/V C )( V C / T) P, and (1/ )( / T) P at each depth (pressure), from which the results for R SP, R CS, and R S attributable to lateral temperature variations were obtained (Fig. 6). For anomalies of purely thermal origin, R SP increases from 1.8 at 1,000-km depth to 2.0 at 2,600-km depth in the lower mantle (67, 69). R CS remains positive, decreasing from 0.3 to 0.2 with increasing depth. R S remains positive throughout the lower mantle, changing Amplitude 2.500 2.000 1.500 1.000 0.500 0.000 V P V S dlnvs/dlnvp dlnr/dlnvs dlnvc/dlnvs S-25 GCA TNA SNA Pyrolite 700 1000 1300 1600 1900 2200 2500 Depth (km) Fig. 6. Values of seismic scaling factors in response to lateral variation of temperatures at lower mantle depths. GEOPHSICS SPECIAL FEATURE Li and Liebermann PNAS May 29, 2007 vol. 104 no. 22 9149

from 0.4 to 0.2 from the top to the bottom of the lower mantle; these values are close to those inferred from tomographic and geodynamical inversions (66). A recent review (65) indicated that seismic R SP increases from 1.5 to 2.0 in the depth range from 1,000 to 2,500 km together with highly correlated seismic P and S wave anomalies ( 0.8); these observations seem to support a thermal origin for lateral heterogeneities at these depths. On the other hand, the observation of R SP 2.0 in the lower mantle (66, 70), the negative R CS in the mid-lower mantle (63), and R SP 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, such as iron enrichment and silica enrichment (67 69). Conclusions We have presented the current state-of-the-art experimental techniques for measuring elastic wave velocities at high pressures and temperatures by using ultrasonic interferometric techniques in conjunction with synchrotron x radiation and their applications to the polymorphs of olivine and pyroxene. Based on the updated thermoelasticity of these phases, velocity and density profiles for a pyrolite model were constructed and compared with radial seismic models. Current data provide an adequate explanation of the major seismic discontinuities at 410- and 660-km depths, the gradient in the transition zone, as well as the velocities in the lower mantle, if the uncertainties in the modeling as well as the variations in different seismic models are considered. However, further investigations of the water content in the mantle and its effect on the elastic properties, as well as consideration of other mantle compositional models (e.g., piclogite), are still needed. In the deep lower mantle, the characteristics of the seismic scaling factors in response to thermal anomalies suggest that anticorrelations between bulk sound and S wave velocities, as well as the large positive density anomalies, observed in the lower mantle cannot be explained fully without invoking chemical variations. We appreciate the constructive comments and suggestions of the anonymous reviewers. This research was supported by National Science Foundation Grants EAR00135550 (to B.L.) and EAR02-29704 (to R.C.L.). The experimental data used in this study were obtained by using the facilities at X17B1/B2 of the National Synchrotron Light Source in Brookhaven National Laboratory (Upton, N), which is supported by the Consortium for Materials Properties Research in Earth Sciences under funding from National Science Foundation Grant EAR01-35554 and U.S. Department of Energy, Basic Energy Sciences, and Office of Energy Research Contract No. DE-AC02-76CH00016. 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