References and Notes 1. F. Liebau, Structural Chemistry of Silicates (Springer- Verlag, Berlin, 1985). 2. J. F. Stebbins and P. F. McMillan, J. Non-Cryst. Solids 160, 116 (1993); Am. Mineral. 74, 965 (1989). 3. R. M. Laine et al., Nature 353, 642 (1991); J. Mater. Chem. 6, 1441 (1996). 4. K. Y. Blohowiak et al., Chem. Mater. 6, 2177 (1994). 5. M. L. Hoppe, R. M. Laine, J. Kampf, M. S. Gordon, L. W. Burggraf, Angew. Chem. Int. Ed. Engl. 32, 287 (1993). 6. B. Herreros, S. W. Carr, J. Klinowski, Science 263, 1585 (1994). 7. C. Chuit, R. J. P. Corriu, C. Reye ´, J. C. Young, Chem. Rev. 93, 1371 (1993). 8. G. J. Gainsford, T. Kemmitt, N. B. Milestone, Acta Crystallogr. C 51, 8 (1995); T. Kemmitt and N. B. Milestone, Aust. J. Chem. 48, 93 (1995). 9. J. H. Small, K. J. Shea, D. A. Loy, G. M. Jamison, ACS Symp. Ser. 585, 248 (1995). 10. A. Rosenheim, B. Reibmann, G. Schendel, Z. Anorg. Chem. 196, 160 (1931); I. F. Sedeh, S. Sjo ¨berg, L. O. O ¨ hman, Acta Chem. Scand. 46, 933 (1992); J. Inorg. Biochem. 50, 119 (1993). 11. A. Weiss and D. R. Harvey, Angew. Chem. 76, 818 (1964). 12. S. Sjo ¨berg, N. Ingri, A. M. Nenner, L. O. O ¨ hman, J. Inorg. Biochem. 24, 267 (1985); D. F. Evans, J. Parr, C. Y. Wong, Polyhedron 11, 567 (1992). 13. S. D. Kinrade, K. J. Maa, A. S. Schach, T. A. Sloan, C. T. G. Knight, J. Chem. Soc. Dalton Trans., in press; S. D. Kinrade, C. T. G. Knight, D. L. Pole, R. T. Syvitski, Inorg. Chem. 37, 4272 (1998); ibid., p. 4278; C. T. G. Knight, Zeolites 9, 448 (1989). 14. It has become accepted in the literature that four- coordinate silicate centers are denoted by a “Q” for quadrifunctional. The extent of protonation is ig- nored, and a superscript is used to indicate the num- ber of shared siloxane linkages. Choosing symbols for the five- and six-coordinate centers that are, at once, systematic and practical to use is difficult. The Latin prefix quinti- presents an obvious problem. Herreros et al. (6) used a Roman superscript to indicate five- coordinate sites, for example Si V , but such a system becomes unwieldy describing other than symmetric silicate species. We propose using Greek prefixes to describe the state of Si coordination, obtaining “P” for pentafunctional and “H” for hexafunctional. This terminology is immediately understandable and avoids use of unusual typographical symbols. Over- or underscoring the labels is recommended to avoid confusion with the corresponding elements. Thus, the monomeric species represented by the resonances in Fig. 1 would be labeled as Q 0 ,P 0 , and H 0 . 15. That is, only when there are two adjacent hydroxy groups occurring on opposite sides of the molecule’s Fischer projection (Fig. 3). 16. For low-alkalinity solutions ([OH – ]:[SiO 2 ]  1:1), the 13 C NMR signals corresponding to Si-coordination sites on the polyol shift up-frequency by 1 to 3 ppm from their bulk solution values. Thus, whereas free D-threitol resonates at 62.9 (C-1,4) and 71.8 ppm (C-2,3), the major threitol-Si complex resonates at 64.7, 64.9 (-OSi coordinated C-1,4), 70.7, and 71.7 ppm (C-2,3). Similarly, only the C-2,5 signals of D- mannitol move up-frequency upon silicate complex- ation, shifting from 71.4 ppm to 74.2 and 74.5 ppm. 17. Carbon-13 NMR investigations into the interaction between aqueous borates and polyols reveal similar high-frequency shifts upon complex formation [A. Munoz and L. Lamande ´, Carbohydrate Res. 225, 113 (1991)]. Consistent with our observations, the struc- tural criterion for optimal borate complex formation appears to be that the polyols contain a threo hy- droxy pair. However, the boron center appears to bind across the threo pair itself, rather than at sites adjacent to it. Moreover, boron does not undergo an increase in coordination number. 18. As the [OH – ]:[SiO 2 ] ratio of solutions containing D- threitol is raised above 1:1, new 13 C NMR signals occur at 66.0 (C-1,4) and 70.2 ppm (C-2,3). 19. S. D. Kinrade, J. Phys. Chem. 100, 4760 (1996); I. L. Svensson, S. Sjo ¨berg, L.-O. O ¨ hman, J. Chem. Soc. Faraday Trans. 31, 4558 (1989). 20. J. J. R. Frausto da Silva and R. P. J. Williams, The Biological Chemistry of the Elements (Clarendon, Ox- ford, 1991); R. K. Iler, The Chemistry of Silica (Wiley, New York, 1979). 21. J. D. Birchall, Chem. Soc. Rev. 24, 351 (1995). 22. We thank J. T. Banks for helpful discussions and R. J. Kirkpatrick for the generous loan of isotopically en- riched silica. Funding was provided in part by NIH (PHS 1 S10 RR 10444-01; GM-42208 and RR 01811), NSF (NSF CHE 96-10502), and the Natural Sciences and Engineering Council of Canada (NSERC). Facilities were provided by the NIH-supported Illinois EPR Re- search Center, and the NSERC-supported Prairie Re- gional NMR Centre (Winnipeg). 23 February 1999; accepted 15 July 1999 Seismic Velocity and Density Jumps Across the 410- and 660-Kilometer Discontinuities Peter M. Shearer 1 * and Megan P. Flanagan 2 The average seismic velocity and density jumps across the 410- and 660- kilometer discontinuities in the upper mantle were determined by modeling the observed range dependence in long-period seismic wave arrivals that reflect off of these interfaces. The preliminary reference Earth model (PREM) is within the computed 95 percent confidence ellipse for the 410-km discontinuity but outside the allowed jumps across the 660-kilometer discontinuity. Current pyrolite mantle models appear consistent with the constraints for the 410- kilometer discontinuity but overpredict amplitudes for the 660-kilometer re- flections. The density jump across the 660-kilometer discontinuity is between 4 and 6 percent, below the PREM value of 9.3 percent commonly used in mantle convection calculations. Observed seismic velocity discontinuities near 410- and 660-km depth in Earth’s upper mantle are believed to be caused primarily by phase changes in olivine and other minerals that result from the increasing pressure with increasing depth (1). Resolving the details of the discontinuities is important for modeling the composition of the mantle and for under- standing the effect that the discontinuities may have on mantle convection (2). Recent analyses of reflected seismic phases (3–5) have yielded estimates of the average discon- tinuity depths that agree within 1%; in con- trast, the average P and S velocity increases across the boundaries are known less precise- ly, and differences of a factor of 2 or greater are seen in the velocity jumps obtained in different studies (6 ). The density jumps, crit- ical parameters for modeling of mantle dy- namics, are particularly hard to measure and are often based on velocity versus density scaling relations rather than direct observa- tional measurements. In principle, however, the velocity and den- sity jumps can be separately resolved by study- ing the behavior of reflection coefficients (7 ) as a function of ray angle. Following this ap- proach, we used the observed amplitudes of reflections off the bottom of the 410- and 660- km discontinuities to measure the velocity and density jumps across the interfaces. These re- flections occur as precursors to the phases SS and PP in long-period seismograms (8). Our data consisted of 13,469 transverse-component and 24,667 vertical-component seismograms from the global seismic networks (GDSN, IRIS, and Geoscope) recorded between 1976 and 1997. To enhance the visibility of the dis- continuity reflections, we aligned the seismo- grams on the maximum amplitude of SS (for the transverse components) and PP (for the vertical components) and stacked the data in bins of constant source-receiver range (Fig. 1). The underside reflected phases S410S and S660S were visible in the transverse-component stack, arriving 2 to 4 min before the direct SS phase. The underside P reflection off the 410-km dis- continuity, P410P, was observed in the vertical- component stack between 100° and 145°, but the underside 660-km reflection, P660P, was not seen (9, 10). Additional details concerning the data and our stacking methods may be found in previous studies (4, 11, 12). We measured the relative amplitudes be- tween the discontinuity reflections and the reference phases SS and PP within 1° bins in source-receiver distance across the intervals for which arrivals were visible (112°to 160° for S410S, 118° to 165° for S660S, and 102° to 140° for P410P). Because of interference from PKP, we did not use P410P data be- tween 118° and 130°. Although P660P was not visible, limits could still be placed on its average amplitude between 118° and 122°, where interference from other phases is ab- 1 Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093– 0225, USA. 2 Lawrence Livermore National Laboratory, Post Office Box 808, L-206, Livermore, CA 94551, USA. *To whom correspondence should be addressed. R EPORTS www.sciencemag.org SCIENCE VOL 285 3 SEPTEMBER 1999 1545