DOI: 10.1126/Science.285.5431.1231 , 1231 (1999); 285 Science Miaki

Normal-Mode and Free-Air Gravity Constraints on Lateral Variations in Velocity and Density of Earth's Mantle Miaki Ishii and Jeroen Tromp Science 285, 1231 (1999); DOI: 10.1126/science.285.5431.1231

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Updated information and services, including high-resolution figures, can be found in the online version of this article at: on August 27, 2012 http://www.sciencemag.org/content/285/5431/1231.full.html This article cites 23 articles, 1 of which can be accessed free: http://www.sciencemag.org/content/285/5431/1231.full.html#ref-list-1 This article has been cited by 155 article(s) on the ISI Web of Science This article has been cited by 13 articles hosted by HighWire Press; see: http://www.sciencemag.org/content/285/5431/1231.full.html#related-urls www.sciencemag.org This article appears in the following subject collections: Geochemistry, Geophysics http://www.sciencemag.org/cgi/collection/geochem_phys Downloaded from

Science (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. Copyright 1999 by the American Association for the Advancement of Science; all rights reserved. The title Science is a registered trademark of AAAS. R ESEARCH A RTICLES ficient quality. There are density models based on current and past plate motions in which the Normal-Mode and Free-Air sources of heterogeneity are cold subducted slabs (5), and an upper mantle density model, Gravity Constraints on Lateral containing strong high-degree components, has been determined with surface wave data (6). Variations in Velocity and A density model of the mantle is im- portant to geophysics because mantle-flow calculations cannot be performed without Density of Earth’s Mantle it (7, 8). However, a whole-mantle den- Miaki Ishii* and Jeroen Tromp sity model is usually obtained by scaling an S velocity model, which is justifiable With the use of a large collection of free-oscillation data and additional con- if the heterogeneity has a single cause straints imposed by the free-air gravity anomaly, lateral variations in shear that affects both, for example, variations in velocity, compressional velocity, and density within the mantle; dynamic to- temperature. pography on the free surface; and topography on the 660-km discontinuity and In recent years, mainly as a result of the 9 the core-mantle boundary were determined. The velocity models are consistent June 1994 Bolivia earthquake, the quantity and with existing models based on travel-time and waveform inversions. In the quality of normal-mode, or free-oscillation, lowermost mantle, near the core-mantle boundary, denser than average ma- data have improved substantially (9), allowing terial is found beneath regions of upwellings centered on the Paciﬁc Ocean and us to constrain the long-wavelength structure of Africa that are characterized by slow shear velocities. These anomalies suggest Earth. We used this data set, combined with the existence of compositional heterogeneity near the core-mantle boundary. further constraints imposed by Earth’s gravity

Seismologists have produced numerous shear develop a whole-mantle density model because Department of Earth and Planetary Sciences, Harvard (S) and compressional (P) velocity models of short-period body waves are not directly sensi- University, Cambridge, Massachusetts 02138, USA. the mantle based mainly on body-wave data tive to density and long-period normal-mode *To whom correspondence should be addressed. E- (1–4). Unfortunately, they have been unable to observations have been too scarce and of insuf- mail: ishii@seismology.harvard.edu on August 27, 2012 A 0 Fig. 1. Comparison of the BC S part of SPRD6 and SKS12WM13. (A) Relative perturbations in S velocity at (from the top) 100 (Ϯ 4.5%) 600 (Ϯ 1.0%), 1300 (Ϯ 1.0%), 1800 (Ϯ 0.8%), 2300 (Ϯ 1.0%), 1000 and 2850 (Ϯ 3.0%) km, where the values in paren- theses indicate the scale www.sciencemag.org for the maps at each depth. The S part of mod-

Depth (km) el SPRD6 is shown on the left, and model 2000 SKS12WM13 (1) is shown on the right. Blue colors indicate regions of higher than average velocities, and red colors indicate re- Downloaded from gions of slower than average velocities. Coastlines 3000 have been superimposed 0.0 1.0 2.0 0.0 0.5 1.0 for reference. Because the RMS amplitude (%) Correlation maximum harmonic degree in SPRD6 is 6, we truncated degree 12 model SKS12WM13 at the same degree. (B) Root-mean- square (RMS) amplitudes of the S part of SPRD6 and SKS12WM13 as a function of depth. The red line is SPRD6, and the black line is SKS12WM13. (C) Correlation between the S model of SPRD6 and SKS12WM13 as a function of depth. For this number of model parameters, two maps are correlated at the 95% conﬁdence level if the correlation is greater than 0.24.

www.sciencemag.org SCIENCE VOL 285 20 AUGUST 1999 1231 R ESEARCH A RTICLES ␦␤ ␤ t ␦␣ ␣ t field, to determine lateral variations in S veloc- velocity ( / )s, P velocity ( / )s, density mantle flow, which depend on lateral variations ␦␳ ␳ t ity, P velocity, and density within the mantle, in ( / )s, and topography on discontinuities in density and the relative viscosity of the layers ␦ t addition to dynamic topography on the free ( h/h)s by (12) above and below the discontinuity. Frequently, surface and topography on the 660-km discon- the objective of mantle-flow calculations is to a tinuity (660) and the core-mantle boundary t t t find a viscosity profile and velocity-to-density c ϭ ͵ ͓͑␦␤/␤͒ K␤ ϩ ͑␦␣/␣͒ K␣ (CMB). s s s scaling that reconcile a given velocity model b with the observed gravity anomaly. Here, Theory ϩ ͑␦␳ ␳͒t ϩ ͸͑␦ ͒t we determined lateral variations in density / s K␳]dr h/h s Kd (2) The sensitivity of a normal mode to lateral d and boundary topography simultaneously; heterogeneity is usually visualized in the form The integration over radius r is from the CMB this circumvents the need for a viscosity of a splitting function (10), which represents a with radius b (3480 km) to Earth’s surface with model when fitting the gravity anomaly. local radial average of Earth’s three-dimension- radius a (6371 km), and the summation is over The spherical harmonic coefficients of the t al (3D) heterogeneity. Each mode has its own all discontinuities d. The sensitivity kernels K␤, free-air gravity anomaly, f s (15), are lin- unique splitting function, which at high degrees K␣, K␳, and Kd are given in terms of the eigen- early related to those describing lateral ␦␳ ␳ t corresponds to a surface-wave phase velocity functions of the modes that define the splitting variations in density, ( / ) s, and boundary ␦ t map. An isolated mode of degree l “sees” even- function (12). The number of unknown param- topography, ( h/h) s,by(16) degree structure up to degree 2l, and some eters can be reduced by assuming that lateral clusters of modes have sensitivity to Earth’s variations in P velocity and density are propor- a t ϭ ͑␦␳ ␳͒t Ј ϩ ͸͑␦ ͒t Ј f ͵ / K␳dr h/h K (3) odd-degree heterogeneity (11). A normal-mode tional to lateral variations in S velocity. In the s s s d d splitting function ␴ depends on colatitude ␪ and past, this has been the common approach (12, b ␾ ␦ ␣ ␦ Ј Ј longitude and may be expanded in spherical 13), with typical scaling values of ln / ln The kernels K␳ and Kd describe the sensitiv- t ␤ϭ ␦ ␳ ␦ ␤ϭ harmonics Ys of degree s and order t as (12) 0.55 and ln / ln 0.2 to 0.4 (8, 14). ity of the gravity anomaly to 3D density and s Lateral variations in density, combined with boundary topography, respectively. ␴͑␪ ␾͒ ϭ ͸ ͸ t t ͑␪ ␾͒ , csY s , (1) flow-induced topography on discontinuities, s ϭ 0 tϭϪs determine Earth’s gravity anomaly. Undula- Velocity and Density Models t The splitting-function coefficients cs are lin- tions on boundaries are determined by the den- The splitting functions were corrected for the early related to 3D relative variations in S sity contrast and radial stresses imposed by effects of Earth’s crust with the recent crustal on August 27, 2012 A 0 Fig. 2. Comparison of the P part of SPRD6 and BC P16B30. (A) Relative perturbations in P velocity at six discrete depths throughout the mantle, as in Fig. 1. The scale for the maps at 1000 each depth is (from the top) Ϯ2.5, Ϯ0.8, Ϯ0.5, Ϯ0.5, Ϯ0.5, www.sciencemag.org and Ϯ0.7%. The P part of model SPRD6

Depth (km) is shown on the left, and model P16B30 2000 (3), truncated at degree 6, is shown on the right. The color scheme is the same as in Fig. 1. (B) RMS am- Downloaded from plitudes of the P part of SPRD6 and P16B30 3000 as a function of depth. 0.0 0.5 1.0 1.5 0.0 0.5 1.0 The red line is SPRD6, RMS amplitude (%) Correlation and the black line is P16B30. (C) Correlation between the P model of SPRD6 and P16B30 as a function of depth. For this number of model parameters, two maps are correlated at the 95% conﬁdence level if the correlation is greater than 0.24.

1232 20 AUGUST 1999 VOL 285 SCIENCE www.sciencemag.org R ESEARCH A RTICLES model Crust5.1 (17). We assumed an isostati- ic free-surface topography, and topography on normal-mode and gravity data, explains 92% of cally compensated crust in the calculation of the 660 and the CMB (18). Initially, we invert- the variance in the mode data and 96% of the the gravity field. Our “dynamic topography,” ed for topography on the 410-km discontinuity variance in the gravity data, which correspond ␹2 ϭ ␹2 ϭ ϭ therefore, is the nonisostatic topography of (410) as well but found that undulations on this to /N 2.0 and /Nf 0.07, where Nf 27 the free surface that is produced by density boundary are poorly constrained by the data is the number of free-air gravity coefficients. anomalies within the entire mantle, including (19). Therefore, topographic variations on 410 The fit to the free-air gravity anomaly is excel- the lithosphere. are those determined in a recent travel-time lent; however, it is well known that the gravity In the inversion, we allowed for lateral vari- study (20). The starting model for the inversion anomaly can be relatively easily fit because of ations in S velocity, P velocity, density, dynam- included S velocity model SKS12WM13 (1) its highly nonunique dependence on density and P velocity model P16B30 (3). The density and boundary topography. Therefore, we did component of the starting model was obtained not allow free-air gravity to change models of by scaling velocity model SKS12WM13 by a density and boundary topography substantially factor of 0.2. There was no starting dynamic from models determined with only normal- topography on the free surface or the CMB, mode data. except for its excess ellipticity, which was de- We compared the S model obtained from termined by very long baseline interferometry the normal-mode inversion with a recent model (21). Starting topography on 660 was taken based on body-wave data, SKS12WM13 (1) from Gu et al. (20). This starting model ex- (Fig. 1). In the shallow mantle, continents are plains 74% of the variance in the mode data but characterized by fast velocity anomalies, and has a relatively high ␹2/N of 6.6, where N ϭ mid-ocean ridges correspond with slow ve- 2850 is the number of normal-mode data (22). locity anomalies. There are strong heteroge- Model SPRD6, obtained by an inversion of neities in the lowermost mantle, with a dis- tinct ring of high-velocity anomalies around the Pacific Ocean. The strong negative anom- Table 1. The maximum and minimum values of alies in the lowermost mantle underneath the the density model with the associated error at the Pacific Ocean and Africa are interpreted as given depth. The average value of the model is mantle upwellings. The correlation between always zero because of the absence of a degree 0 coefﬁcient. The errors are uniformly distributed the two models is high in the upper mantle over the sphere, which reﬂects the fact that and near the CMB, but a lower correlation is on August 27, 2012 modes are sensitive to structure everywhere on found in the mid-mantle, which is relatively the globe. The error values are much smaller than poorly constrained by travel-time and wave- the extrema of the model. form data. We compared the P part of model SPRD6 Depth Maximum Maximum Minimum with P velocity model P16B30 (3) (Fig. 2). The (km) error elongated velocity anomalies at mid-mantle 100 0.86 Ϫ0.83 0.12 depths underneath the Americas and Eurasia 600 0.62 Ϫ0.51 0.08 are characteristic of several recent travel-time Ϫ 1300 0.60 0.60 0.10 models (23). The two P velocity models are www.sciencemag.org 1800 0.53 Ϫ0.53 0.10 Ϫ well correlated at the top of the mantle and 2300 0.99 0.79 0.12 around 2500-km depth but show lower correla- 2850 1.7 Ϫ1.5 0.16 tion in the mid-mantle and near the CMB. The

Fig. 4. Shear velocity, A B bulk sound velocity, and density models at 2800- km depth. (A) Map views Downloaded from of shear velocity (top), bulk sound velocity (middle), and density (bottom) from an inversion with these model parameters (model SBRD6). The color scheme is the same as in the previous ﬁgures. The scale for the maps is Ϯ2.5, Ϯ2.0, and Ϯ1.5% for S velocity, bulk sound velocity, and density, respectively. Note the strong Fig. 3. Relative perturbations in even-degree den- anticorrelation between sity at six discrete depths as in Figs. 1 and 2. The shear and bulk sound scale for each map (from the top) is Ϯ1.0, Ϯ0.5, velocity (correlation co- Ϯ0.5, Ϯ0.5, Ϯ0.8, and Ϯ1.0%, respectively. Blue efﬁcient of Ϫ0.63). (B) regions denote higher than average density, and Same as in (A), but red regions denote lower than average density. showing only the de- The maximum and minimum values of the den- gree 2 component. The sity model are summarized in Table 1. scales for the maps are Ϯ0.7, Ϯ0.4, and Ϯ0.5%, respectively.

www.sciencemag.org SCIENCE VOL 285 20 AUGUST 1999 1233 R ESEARCH A RTICLES P velocity part of SPRD6 agrees well with a The last part of model SPRD6 consists of variety of damping schemes, for example, size, recent model obtained by Ka´rason and van der topography on the free surface, the 660, and gradient, and second derivative damping, as Hilst (24). the CMB (Fig. 6). The 660 part of model well as a range of weighting of the gravity The laterally heterogeneous even-degree SPRD6 is compared with two recent travel- anomaly, and found that the pattern of density whole-mantle density model (Fig. 3 and Ta- time models (20, 26), and our CMB model is heterogeneity did not change substantially. Fur- ble 1) is generally poorly correlated with compared with a seismological (27) and a thermore, the number of resolved parameters either the S or P velocity models. Near the geodynamical model (28). for the density model, determined by the trace CMB, high-density anomalies appear in areas of the appropriate portions of the resolution of mantle uplift beneath the central Pacific and Robustness of the Models matrix, is consistently greater than that of the S Africa. To further illustrate the nature of the First, we examined the dependence of our mod- or P velocity models, regardless of the weight- anomalies near the CMB, we inverted for lat- els, especially the density model, on the starting ing of the gravity anomaly (this included an eral variations in S velocity, bulk sound veloc- model used in the inversion. Density models inversion with only normal-mode data). ity, and density. Our results confirm earlier obtained from different starting models (with Resolution in the lower mantle was investi- observations of an anticorrelation between different scaling values) are consistent with one gated with input models peaked at 2700-km shear and bulk sound velocity (25) (Fig. 4). another (supplementary Figs. 1 and 2) (29), and depth (Fig. 7A). In this test, density is the best The root-mean-square (RMS) amplitudes, the strong positive density anomalies near the resolved of the three models. The S velocity is or the power of lateral heterogeneity, of the S, CMB persist regardless of the starting model. also well resolved, but the recovery of the P P, and density models exhibit an increase near The density model can also be influenced by model is poor. We also investigated the com- the surface and the CMB, with the exception of the parameterization of the inversion due to the ponents of Earth structure that contribute to the P model, which is relatively flat in the lower effects of damping. We performed inversions produce an output model with a spike at 2800- mantle (Fig. 5A). The RMS amplitude of den- with three parameterizations: (i) S velocity, P km depth, known as a Backus-Gilbert resolu- sity is comparable to that of P in the lower velocity, and density; (ii) S velocity, bulk sound tion kernel (32) (Fig. 7B). Resolution tests (sup- mantle and exceeds it below 2000-km depth. velocity, and density; and (iii) shear modulus, plementary Fig. 5), Backus-Gilbert kernels As observed in recent travel-time models (3, 4), bulk modulus, and density. The density models (supplementary Fig. 6), and checkerboard res- the S and P parts of model SPRD6 are well obtained on the basis of these three inversions olution tests (supplementary Fig. 7) consistently correlated in the upper mantle but not as well in are compatible with one another, indicating that show that the density structure is well resolved the mid-mantle (Fig. 5B). In the lower mantle, the effect of damping on parameterization is by the data. the correlation peaks around 2500-km depth limited (supplementary Fig. 3). We also inves- The pattern of density heterogeneity that we

and drops toward the CMB. Compared with the tigated results of inversions for density with and obtained from the mode data alone is robust but on August 27, 2012 correlation between P and S, density does not without boundary topography (supplementary has a range of amplitudes that satisfy the data correlate as well with either of the two velocity Fig. 4). Introduction of topography reduced the equally well. Addition of the free-air gravity models. It is substantially decorrelated from the amplitude of density heterogeneity near a anomaly to the data set narrowed the amplitude velocity models in the transition zone (400- to boundary, but it did not substantially influence range and slightly modified the pattern in the 700-km depth). its pattern. mid-mantle. It also introduced a trade-off be- Next, we examined the resolution of the tween density heterogeneity and boundary to- inversion. Resolution is dependent on the pography. Of the three boundary topographic 0 damping scheme (30) and the relative weight- models, which include the free surface, the 660,

ing between the free-air gravity anomaly and and the CMB, the free surface is the least www.sciencemag.org the mode data (31). We experimented with a constrained. There is a wide range of acceptable

1000 ABC Depth (km) Downloaded from 2000

Fig. 6. Topography of the free surface, the 660, and the CMB. AB(A) Map of dynamic free-sur- 3000 0.0 1.0 2.0 -0.5 0.0 0.5 1.0 face topography. Blue colors RMS amplitude (%) Correlation indicate areas of depression, and red colors indicate areas of Fig. 5. RMS amplitude and correlation. (A) S, P, elevation. The scale for the and density RMS amplitudes of model SPRD6 as a map is Ϯ1.0 km. (B) Maps of function of depth. The red curve is the S model, 660 topography. The color the blue curve is the P model, and the green curve scheme is the same as in (A), is the RMS amplitude of the density model. (B) but the scale is Ϯ15.0 km. The Correlations between the S, P, and density parts top map is part of model of SPRD6 as a function of depth. Correlation SPRD6, the middle map is from between S and P is shown by the blue line, that Gu et al. (20), and the bottom between S and density is shown by the red line, map is from Flanagan and Shearer (26). The latter two maps are truncated at harmonic degree 6 to ease and that between P and density is shown by the visual comparison. (C) Maps of CMB topography plotted on a scale of Ϯ5.0 km. The top map is from green line. The black line is the zero line. For this the SPRD6 inversion, the middle map is from Morelli and Dziewonski (27), and the bottom map is from number of model parameters, two maps are cor- Forte et al. (28). The bottom map is based on S velocity model S.F1.K/WM13 (8) and a depth-dependent related at the 95% conﬁdence level if the corre- density scaling proposed by Karato (39). The Morelli and Dziewonski map is expanded in spherical lation is greater than 0.24. harmonics up to degree 4, and the Forte et al. map is truncated at degree 6.

1234 20 AUGUST 1999 VOL 285 SCIENCE www.sciencemag.org R ESEARCH A RTICLES topographic amplitudes with small-ampli- data are insufficient to give a reliable mod- the number of degrees of freedom was in- tude changes to the 3D density model and el by themselves; therefore, the 660 model creased from an S-velocity–only inversion to little change in the gravity fit. To obtain was damped toward the model of Gu et al. model SPRD6, with independent lateral varia- reasonable topography on the free surface, (20) (supplementary Fig. 8A). The data do tions in S, P, density, and boundary topography we damped the amplitude of our dynamic have sufficient sensitivity to undulations of (supplementary Table 1 and supplementary Fig. topography to a size (Ϯ1 km) between the the CMB, although there is a range of 9). The effects of uncertainties in the data on observed dynamic topography (33) and that permissible amplitudes (supplementary model structure were investigated by adding predicted from mantle-flow calculations Fig. 8B). We required the CMB to have an various levels of random noise to the splitting (34). This resulted in dynamic topography overall amplitude of Ϯ5 km to be compat- functions (supplementary Fig. 10). Even when resolution tests that failed to recover any ible with the amplitude determined by Mo- random noise with an RMS of 30% was added input models. Topography on 660 is con- relli and Dziewonski (27). to the data, the resulting models are highly strained better than the free surface, but the The fit to the mode data was monitored as consistent with model SPRD6.

Implications of the Models for A Mantle Dynamics We have demonstrated that normal-mode data and the free-air gravity anomaly can constrain independent large-scale lateral variations in S velocity, P velocity, and density. Our velocity models are consistent with existing travel-time models (1–4). The main differences are in the mid-mantle where travel-time and waveform models are least constrained. Our whole-mantle density model has an RMS amplitude that is almost constant through- Fig. 7. Resolution tests. (A) The input is a sharp out the mantle, with a slight increase near the peak in S, P, and density surface and the CMB. In the transition zone, the heterogeneity at 2700- density model is substantially decorrelated from on August 27, 2012 km depth at spherical the velocity models, providing direct evidence harmonic degree 2 and that lateral variations in this region may not be order 1. (Left) Map views entirely due to variations in temperature (35). of models at 2700-km depth. The input models The most prominent features of our density are shown in the ﬁrst model appear near the CMB, where high-den- column, and recovered sity anomalies are found in regions of mantle models are shown in uplift beneath the Pacific and Africa. This ob- the second column. The servation is consistent with convection simula- models are (from the tions where dense material piles up beneath www.sciencemag.org top) S velocity, P veloci- B 0 upwellings because it is too heavy to be en- ty, density, and topogra- SPR phy on the free surface, trained in the uplift (36). Introduction of heavy the 660, and the CMB. core material into the mantle beneath upwell- There is no initial top- ings can also cause such density anomalies ography on any of the (37). These anomalies, combined with the re- boundaries, and the out- gional anticorrelation between shear velocity put shows that there is 1000 virtually no leakage of and density, suggest that compositional as well volumetric structure to as thermal heterogeneity is required to explain Downloaded from topography on bound- lateral variations in the lowermost mantle, es- aries. (Right) Cross sec- pecially near the CMB.

tions of the same reso- Depth (km) lution test for S velocity (top), P velocity (mid- 2000 References and Notes dle), and density (bot- 1. A. M. Dziewonski, X.-F. Liu, W.-J. Su, in Earth’s Deep tom). The models in Interior, D. J. Crossley, Ed. (Gordon and Breach, New- the ﬁrst column are in- ark, NJ, 1997), pp. 11–50. 2. G. Masters et al., Philos. Trans. R. Soc. London A 354, put models; the output 1385 (1996); X.-D. Li and B. Romanowicz, J. Geophys. models in the second Res. 101, 22245 (1996); H. Inoue et al., Phys. Earth column show smearing Planet. Inter. 59, 294 (1990). of structure in the radi- 3000 3. H. Bolton, thesis, University of California, San Diego al direction. (B) Backus- -5.0 0.0Amplitude 5.0 10.0-5Amplitude 0 5-5.0 10 0.0Amplitude 5.0 10.0 (1996). Gilbert resolution ker- 4. G. S. Robertson and J. H. Woodhouse, Geophys. J. Int. nel (32) for structure at 2800-km depth for S velocity (S), P velocity (P), and density (R) heterogeneity 123, 85 (1995). at spherical harmonic degree 2 and order 1. The red curve represents the S velocity, the blue curve 5. Y. Ricard et al., J. Geophys. Res. 98, 21895 (1993); C. represents the P velocity, and the green curve represents density R. The black line is the zero line. A Lithgow-Bertelloni and M. A. Richards, Rev. Geophys. 36, 27 (1998). Backus-Gilbert test indicates where structure in the inverted model has its origin in the real Earth. For 6. T. Tanimoto, J. Geophys. Res. 96, 8167 (1991). example, ideally, the Backus-Gilbert resolution kernels in this ﬁgure should be spiked at 2800-km depth. 7. B. H. Hager, ibid. 89, 6003 (1984); M. A. Richards and Instead, we see that degree 2, order 1 structure at 2800 km in our models is due to Earth’s structure B. H. Hager, ibid., p. 5987; Y. Ricard, C. Vigny, C. between roughly 2400 and 2880 km and that there is a small contribution from heterogeneity near the Froidevaux, ibid. 94, 13739 (1989); B. H. Hager and surface. R. W. Clayton, in Mantle Convection: Plate Tectonics

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and Global Dynamics, W. R. Peltier, Ed. (Gordon and size and gradient damping. We also applied damping (1986); U. Hansen and D. A. Yuen, Nature 334, 237 Breach, Newark, NJ, 1989), pp. 657–763. in the radial direction to obtain a smooth model. (1988); P. J. Tackley, in The Core-Mantle Boundary 8. A. M. Forte, R. L. Woodward, A. M. Dziewonski, J. 31. If the gravity anomaly is weighted heavily relative to Region, vol. 28 of Geodynamics Series, M. Gurnis et Geophys. Res. 99, 21857 (1994). the normal-mode data, the resolution of density and al., Eds. (American Geophysical Union, Washington, 9. J. Tromp and E. Zanzerkia, Geophys. Res. Lett. 22, boundary topography improves at the expense of a DC, 1998), pp. 231–253. 2297 (1995); X. He and J. Tromp, J. Geophys. Res. poorer resolution of S and P velocity. 37. E. Knittle and R. Jeanloz, Science 251, 1438 (1991). 101, 20053 (1996); J. S. Resovsky and M. H. Ritz- 32. G. Backus and F. Gilbert, Geophys. J. R. Astron. Soc. 38. M. P. Flanagan and P. M. Shearer, Geophys. Res. Lett. woller, ibid. 103, 783 (1998). Splitting-function co- 16, 169 (1968). 26, 549 (1999). efficients determined in these three studies are used 33. A. Cazenave, A. Souriau, K. Dominh, Nature 340,54 39. S. Karato, ibid. 20, 1623 (1993). in our inversions; duplicate measurements are used as (1989); M. Gurnis, ibid. 344, 754 (1990). 40. We wish to thank R. J. O’Connell, S. Panasyuk, J. X. complementary independent data. 34. A. M. Forte and R. L. Woodward, J. Geophys. Res. 102, Mitrovica, H. J. van Heijst, and G. Masters for numer- 10. D. Giardini, X.-D. Li, J. H. Woodhouse, Nature 325, 17981 (1997). ous discussions and suggestions. This research was 405 (1987). 35. Compositional variations in the transition zone have supported by the David and Lucile Packard Founda- 11. J. S. Resovsky and M. H. Ritzwoller, Geophys. Res. been suggested previously, for example, on the basis tion. M.I. was also supported by a Natural Sciences Lett. 22, 2301 (1995); M. H. Ritzwoller and J. S. of the substantial decorrelation between 410 topog- and Engineering Council of Canada Postgraduate Resovsky, ibid., p. 2305. raphy and velocity (38). Scholarship. 12. X.-D. Li, D. Giardini, J. H. Woodhouse, J. Geophys. Res. 36. U. Christensen, Ann. Geophys. 2, 311 (1984); G. F. 96, 551 (1991); F. A. Dahlen and J. Tromp, Theoretical Davies and M. Gurnis, Geophys. Res. Lett. 13, 1517 30 March 1999; accepted 9 July 1999 Global Seismology (Princeton Univ. Press, Princeton, NJ, 1998). 13. M. Ritzwoller, G. Masters, F. Gilbert, J. Geophys. Res. 93, 6369 (1988); J. S. Resovsky and M. H. Ritzwoller, ibid. 104, 993 (1999). Search for Cross-Species 14. These relations are determined by mineral physics, although the relation between S and P velocity may also be obtained by comparing shear and compressional Transmission of Porcine travel-time models. O. L. Anderson, E. Schreiber, R. C. Liebermann, N. Soga, Rev. Geophys. 6, 491 (1968); D. L. Anderson, Phys. Earth Planet. Inter. 45, 307 (1987); Endogenous Retrovirus in Patients Theory of the Earth (Blackwell, Oxford, UK, 1989). t 15. The free-air gravity anomaly coefficients f s are obtained from the geoid coefficients gt of EGM96 (ref- Treated with Living Pig Tissue s t ϭ erences below) on the basis of the relation f s Ϫ1 Ϫ t 1 1 2 ga (s 1)gs, where g is the gravitational accelera- Khazal Paradis, * Gillian Langford, Zhifeng Long, tion at Earth’s surface with radius a. The reason for 3 3 3 fitting free-air gravity instead of geoid is that the Walid Heneine, Paul Sandstrom, William M. Switzer, 3 2 4

latter is dominated by degree 2 whereas the former Louisa E. Chapman, Chris Lockey, David Onions, on August 27, 2012 has a whiter spectrum that enables a better fit to the 5 2 higher degrees. F. G. Lemoine et al.,inInternational The XEN 111 Study Group, Edward Otto Association of Geodesy Symposia 117, J. Segawa et al., Eds. (Springer-Verlag, Berlin, 1997), pp. 462–469; F. G. Lemoine et al., Eos 79, 117 (1998); F. G. Lemoine Pig organs may offer a solution to the shortage of human donor organs for et al., NASA/TP-1998-206861 (1998). transplantation, but concerns remain about possible cross-species transmission of 16. A. M. Forte and W. R. Peltier, J. Geophys. Res. 92, porcine endogenous retrovirus (PERV). Samples were collected from 160 patients 3645 (1987). who had been treated with various living pig tissues up to 12 years earlier. Reverse 17. W. D. Mooney, G. Laske, T. G. Masters, ibid. 103, 727 (1998). transcription–polymerase chain reaction (RT-PCR) and protein immunoblot anal- 18. Our models are expanded laterally in spherical har- yses were performed on serum from all 160 patients. No viremia was detected in monics up to degree and order 6 and radially in any patient. Peripheral blood mononuclear cells from 159 of the patients were www.sciencemag.org Chebyshev polynomials up to order 13. 19. This is probably because the 410 is dominated by analyzed by PCR using PERV-specific primers. No PERV infection was detected in structure at degree one (20, 26, 38). any of the patients from whom sufficient DNA was extracted to allow complete 20. Y. Gu, A. M. Dziewonski, C. B. Agee, Earth Planet. Sci. PCR analysis (97 percent of the patients). Persistent microchimerism (presence of Lett. 157, 57 (1998). donor cells in the recipient) was observed in 23 patients for up to 8.5 years. 21. C. R. Gwinn, T. A. Herring, I. I. Shapiro, J. Geophys. Res. 91, 4755 (1986). 22. Our data set is dominated by isolated modes that are Hundreds of patients have been exposed to To supplement the data generated in previ- only sensitive to even-degree structure. There are living porcine cells and tissues for a variety of ous studies (1, 17) and to further investigate the 2850 even-degree generalized splitting-function co- experimental therapeutic indications, including potential transmission of PERV to humans, we Downloaded from efficients but only 96 odd-degree coefficients. There- fore, all estimates of misfit are based on the even- pancreatic islet cells, skin, and whole livers and retrospectively collected PBMCs and serum degree splitting functions; the odd degrees in our spleens for extracorporeal blood perfusion (1– from patients who had been treated with living models are similar to those of the starting model. 4). Proposed future therapeutic indications in- pig tissue. The samples were analyzed in mul- 23. S. P. Grand, R. D. van der Hilst, S. Widiyantoro, GSA Today 7, 1 (1997); R. D. van der Hilst, S. Widiyantoro, clude solid organ transplantation from trans- tiple laboratories using recently developed and E. R. Engdahl, Nature 386, 578 (1997). genic pigs as a means of alleviating the human validated assays specific for PERV: PCR (for 24. H. Ka´rason and R. D. van der Hilst, Eos (fall meet. donor organ shortage (5–7). Although most PERV DNA), RT-PCR (for PERV RNA, a suppl.) 79, F656 (1998). potential pathogens can be eliminated from marker for virions), and protein immunoblot 25. W.-J. Su and A. M. Dziewonski, Phys. Earth Planet. Inter. 100, 135 (1997); G. Masters, H. Bolton, G. source animals for xenotransplantation, one that antibody assays (for exposure to PERV anti- Laske, Eos (spring meet. suppl.) 80, S14 (1999). remains is the porcine endogenous retrovirus gens). Testing strategies were also devised to 26. M. P. Flanagan and P. M. Shearer, J. Geophys. Res. (PERV), a C-type retrovirus that is permanently distinguish whether any PERV DNA detected 103, 2673 (1998). 27. A. Morelli and A. M. Dziewonski, Nature 325, 678 integrated in the pig genome (8–13). Recent was due to actual infection or to the presence of (1987). coculture and infectivity experiments have pig cells. This could result from a situation 28. A. M. Forte, J. X. Mitrovica, R. L. Woodward, Geophys. shown that PERV released from pig kidney cell analogous to that frequently observed after al- Res. Lett. 22, 1013 (1995). lines, from mitogenically activated porcine pe- lotransplantation, termed microchimerism, 29. Supplementary data are available at www. sciencemag.org/feature/data/1040466.shl. ripheral blood mononuclear cells (PBMCs), or where cells from the donor organ are known to 30. Throughout our experiments, the same damping was from porcine endothelial cells can infect human traffic through the recipient (18). applied to S and P velocity, and the damping of the cells and cell lines in vitro, raising concerns Study participants and testing labora- density model was required to be the same as, or slightly greater than, that of the velocity models. The about the possibility of cross-species infection tories. A total of 160 patients (83 males and models presented here use a scheme that contains after xenotransplantation (11, 14–16). 77 females, aged 2 to 77 years) participated in

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