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Localization of the gravity field and the signature of glacial rebound


The negative free-air gravity anomaly centred on Hudson Bay, Canada, shows a remarkable correlation with the location of the Laurentide ice sheet, suggesting that this gravity anomaly is the result of incomplete post-glacial rebound1,2,3. This region, however, is also underlain by higher-than-average mantle seismic velocities, suggesting that the gravity low might result instead from dynamic topography associated with convective downwellings4,5,6,7. Here we analyse the global gravity field as a simultaneous function of geographic location and spectral content. We find that the Hudson Bay gravity low is unique, with anomalously high amplitude in the spectral band where the power from the Laurentide ice load is greatest2 and the relaxation times predicted for viable models of viscous relaxation are longest8. We estimate that about half of the Hudson Bay gravity anomaly is the result of incomplete post-glacial rebound, and derive a mantle viscosity model that explains both this gravity signature and the characteristic uplift rates for the central Laurentide and Fennoscandian regions6. This model has a jump in viscosity at 670 km depth, comparable to that in dynamic models of the geoid highs over subducted slabs4,9, but lacks a low-viscosity asthenosphere, consistent with a higher viscosity in the upper mantle beneath shields than in oceanic regions.

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Figure 1: Spatio-spectral renditions of the gravity field.
Figure 2: Viscosity model predictions versus observation.


  1. Kaula, W. M. in The Nature of the Solid Earth (ed. Robertson, E. C.) 385–405 (McGraw-Hill, New York, (1972)).

    Google Scholar 

  2. Walcott, R. I. Structure of the earth from glacio-isostatic rebound. Annu. Rev. Earth. Planet. Sci. 1, 15–37 (1973).

    Article  ADS  Google Scholar 

  3. Cathles, L. M. The Viscosity of the Earth's Mantle (Princeton Univ. Press, (1975)).

    Google Scholar 

  4. Hager, B. H. & Clayton, R. W. in Mantle Convection (ed. Peltier, W. R.) 657–763 (Gordon and Breach, New York, (1989)).

    Google Scholar 

  5. Peltier, W. R., Forte, A. M., Mitrovica, J. X. & Dziewonski, A. M. Earth's gravitational field: seismic tomography resolves the enigma of the Laurentian anomaly. Geophys. Res. Lett. 19, 1555–1558 (1992).

    Article  ADS  Google Scholar 

  6. Forte, A. M. & Mitrovica, J. X. New inferences of mantle viscosity from joint inversion of long-wavelength mantle conveciton and post-glacial rebound data. Geophys. Res. Lett. 23, 1147–1150 (1996).

    Article  ADS  Google Scholar 

  7. Pari, G. & Peltier, W. R. The free-air gravity constraint on subcontinental mantle dynamics. J. Geophys. Res. 101, 28105–28132 (1996).

    Article  ADS  Google Scholar 

  8. Hager, B. H. in Glacial Isostasy, Sea-level and Mantle Rheology (eds R. Sabadini, K. L. & Boschi, E.) 493–513 (NATO ASI Ser. C. vol. 334, Kluwer, Dordrecht, (1991)).

    Book  Google Scholar 

  9. Ricard, Y. & Vigny, C. Mantle dynamics with induced plate tectonics. J. Geophys. Res. 94, 17543–17559 (1989).

    Article  ADS  Google Scholar 

  10. O'Connell, R. J. Pleistocene glaciation and the viscosity of the mantle. Geophys. J. R. Astron. Soc. 23, 299–327 (1971).

    Article  ADS  Google Scholar 

  11. Mitrovica, J. X. & Peltier, W. R. Pleistocene deglaciation and the global gravity field. J. Geophys. Res. 94, 13651–13671 (1989).

    Article  ADS  Google Scholar 

  12. Simons, M. thesis, MIT, Cambridge, Massachusetts((1996)).

  13. Simons, M., Solomon, S. C. & Hager, B. H. Localization of gravity and topography: constraints on the tectonics and mantle dynamics of Venus. Geophys. J. Int. 131, 24–44 (1997).

    Article  ADS  Google Scholar 

  14. Hager, B. H. Subducted slabs and the geoid: constraints on mantle rheology and flow. J. Geophys. Res. 89, 6003–6015 (1984).

    Article  ADS  Google Scholar 

  15. Masters, G., Johnson, S., Laske, G. & Bolton, H. Ashear-velocity model of the mantle. Phil. Trans. R. Soc. Lond. A 354, 1385–1411 (1996).

    Article  ADS  Google Scholar 

  16. Van Bemmelen, R. W. & Berlage, H. P. Versuch einer mathematischen behandlung geotektonischer bewegung unter besonderer berucksichtegung der undationstheorie. Beitr. Geophys. 43, 19–55 (1935).

    MATH  Google Scholar 

  17. Haskell, N. A. The viscosity of the asthenosphere. Am. J. Sci. 33, 22–28 (1937).

    Article  ADS  Google Scholar 

  18. Forte, A. M. & Peltier, W. R. Viscous flow models of global geophysical observables. 1. Forward problems. J. Geophys. Res. 96, 20131–20159 (1991).

    Article  ADS  Google Scholar 

  19. Forte, A. M., Woodward, R. L. & Dziewonski, A. M. Joint inversions of seismic and geodynamic data for models of three-dimensional mantle heterogeneity. J. Geophys. Res. 99, 21857–21877 (1994).

    Article  ADS  Google Scholar 

  20. Lambeck, K., Johnston, P. & Nakada, M. Glacial rebound and sea-level change in northwestern europe. Geophys. J. Int. 103, 451–468 (1990).

    Article  ADS  Google Scholar 

  21. Mitrovica, J. X. Haskell [1935] revisited. J. Geophys. Res. 101, 555–569 (1996).

    Article  ADS  Google Scholar 

  22. Mitrovica, J. X. & Forte, A. M. Radial profile of mantle viscosity—results from the joint inversion of convection and postglacial rebound observables. J. Geophys. Res. 102, 2751–2769 (1997).

    Article  ADS  Google Scholar 

  23. Nakada, M. & Lambeck, K. Glacial rebound and relative sea-level variations: a new appraisal. Geophys. J. R. Astron. Soc. 90, 171–224 (1987).

    Article  ADS  Google Scholar 

  24. Nerem, R. S. et al. Gravity model development for TOPEX/Poseidon: joint gravity models 1 and 2. J. Geophys. Res. 99, 24421–24447 (1994).

    Article  ADS  Google Scholar 

  25. Nerem, R. S., Jekeli, C. & Kaula, W. M. Gravity field determination and characteristics: retrospective and prospective. J. Geophys. Res. 100, 15053–15074 (1995).

    Article  ADS  Google Scholar 

  26. Wessel, P. & Smith, W. H. F. New version of the Generic Mapping Tools released. Eos 76, 329 (1991).

    Article  ADS  Google Scholar 

  27. Tushingham, A. M. & Peltier, W. R. Ice-3g: a new global model of late Pleistocene deglaciation based upon geophysical predictions of post-glacial relative sea-level change. J. Geophys. Res. 96, 4497–4523 (1991).

    Article  ADS  Google Scholar 

  28. Hager, B. H. Global isostatic geoid anomalies for plate and boundary layer models of the lithosphere. Earth Planet. Sci. Lett. 63, 97–109 (1983).

    Article  ADS  Google Scholar 

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We thank M. Fang, M. Gurnis and S. Zhong for constructive discussions, as well as J. X. Mitrovica for a thorough review. This work was supported by NASA.

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  1. Correspondence should be addressed to M.S.


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    Correspondence to Mark Simons.

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    Simons, M., Hager, B. Localization of the gravity field and the signature of glacial rebound. Nature 390, 500–504 (1997).

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