A resonance in the Earth's obliquity and precession overthe past 20 Myr drivenbymantle convection

Abstract

The motion of the Solar System is chaotic to the extent that the precise positions of the planets are predictable for a period of only about 20 Myr (ref. 1). The Earth's precession, obliquity and insolation parameters over this time period1,2,3,4,5,6 can be influenced by secular variations in the dynamic ellipticity of the planet which are driven by long-term geophysical processes, such as post-glacial rebound5,7,8,9,10. Here we investigate the influence of mantle convection on these parameters. We use viscous flow theory to compute time series of the Earth's dynamic ellipticity for the past 20 Myr and then apply these perturbations to the nominal many-body orbital solution of Laskar et al.5. We find that the convection-induced change in the Earth's flattening perturbs the main frequency of the Earth's precession into the resonance associated with a secular term in the orbits of Jupiter and Saturn5, and thus significantly influences the Earth's obliquity. We also conclude that updated time series of high-latitude summer solar insolation diverge from the nominal solution for periods greater than the past 5 Myr. Our results have implications both for obtaining precise solutions for precession and obliquity and for procedures that adopt astronomical calibrations to date sedimentary cycles and climatic proxy records.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Predicting past variations in the Earth's dynamic ellipticity.
Figure 2: Precession and obliquity parameters determined from orbital integrations.
Figure 3: An Earth model sensitivity analysis.
Figure 4: A comparison of predicted insolation time series.

References

  1. 1

    Laskar, J. The chaotic motion of the solar system: A numerical estimate of the size of the chaotic zones. Icarus 88, 266–291 (1990).

    ADS  Article  Google Scholar 

  2. 2

    Laskar, J. Secular evolution of the solar system over 10 million years. Astron. Astrophys. 198, 341–362 (1988).

    ADS  Google Scholar 

  3. 3

    Berger, A. & Loutre, M. F. Insolation values for the climate of the last 10 m.y. Quat. Sci. Rev. 10, 297–317 (1991).

    ADS  Article  Google Scholar 

  4. 4

    Quinn, T. R., Tremaine, S. & Duncan, M. Athree million year integration of the Earth's orbit. Astron. J. 101, 2287–2305 (1991).

    ADS  Article  Google Scholar 

  5. 5

    Laskar, J., Joutel, F. & Boudin, F. Orbital, precessional, and insolation quantities for the Earth from −20 Myr to +10 Myr. Astron. Astrophys. 270, 522–533 (1993).

    ADS  Google Scholar 

  6. 6

    Sussman, S. J. & Wisdom, J. Chaotic evolution of the solar system. Science 257, 56–62 (1992).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  7. 7

    Dehant, V., Loutre, M.-F. & Berger, A. Potential impact of the northern hemisphere Quaternary ice sheets on the frequencies of the astroclimatic orbital parameters. J. Geophys. Res. 95, 7573–7578 (1990).

    ADS  Article  Google Scholar 

  8. 8

    Mitrovica, J. X., Pan, R. & Forte, A. M. Late Pleistocene and Holocene ice mass fluctuations and the Earth's precession constant. Earth Planet. Sci. Lett. 128, 489–500 (1994).

    ADS  CAS  Article  Google Scholar 

  9. 9

    Mitrovica, J. X. & Forte, A. M. Pleistocene glaciation and the Earth's precession constant. Geophys. J. Int. 121, 21–32 (1995).

    ADS  Article  Google Scholar 

  10. 10

    Mitrovica, J. X., Forte, A. M. & Pan, R. Glaciation-induced variations in the Earth's precession frequency, obliquity and insolation over the last 2.6 Ma. Geophys. J. Int. 128, 270–284 (1997).

    ADS  Article  Google Scholar 

  11. 11

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

    ADS  Article  Google Scholar 

  12. 12

    Glatzmaier, G. A. Numerical simulations of stellar convective dynamos. 1. The model and method. J. Comp. Phys. 55, 461–484 (1984).

    ADS  Article  Google Scholar 

  13. 13

    Steinberger, B. M. & O'Connell, R. J. Changes in the Earth's rotation axis inferred from advection of mantle density heterogeneities. Nature 387, 169–173 (1997).

    ADS  CAS  Article  Google Scholar 

  14. 14

    Gordon, R. J. & Jurdy, D. M. Cenozoic global plate motions. J. Geophys. Res. 91, 12389–12406 (1986).

    ADS  Article  Google Scholar 

  15. 15

    Richards, M. A. & Engebretson, D. C. Large-scale mantle convection and the history of subduction. Nature 355, 437–440 (1992).

    ADS  Article  Google Scholar 

  16. 16

    Ricard, Y., Richards, M. A., Lithgow-Bertelloni, C. & Le Stunff, Y. Ageodynamic model of mantle density heterogeneity. J. Geophys. Res. 98, 21895–21909 (1993).

    ADS  Article  Google Scholar 

  17. 17

    Richards, M. A., Ricard, Y., Lithgow-Bertelloni, C., Spada, G. & Sabadini, R. An explanation for Earth's long-term rotational stability. Science 275, 372–375 (1997).

    CAS  Article  Google Scholar 

  18. 18

    Spada, G., Ricard, Y. & Sabadini, R. Excitation of true polar wander by subduction. Nature 360, 452–454 (1992).

    ADS  Article  Google Scholar 

  19. 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).

    ADS  Article  Google Scholar 

  20. 20

    Karato, S.-I. Importance of anelasticity in the interpretation of seismic tomography. Geophys. Res. Lett. 20, 1623–1626 (1993).

    ADS  Article  Google Scholar 

  21. 21

    Forte, A. M., Mitrovica, J. X. & Woodward, R. L. Seismic-geodynamic determination of the origin of excess ellipticity of the core-mantle boundary. Geophys. Res. Lett. 22, 1013–1016 (1995).

    ADS  Article  Google Scholar 

  22. 22

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

    ADS  Article  Google Scholar 

  23. 23

    Imbrie, J. Astronomical theory of the Pleistocene ice ages: A brief historical review. Icarus 50, 408–422 (1982).

    ADS  Article  Google Scholar 

  24. 24

    Lourens, L. J. et al.Evaluation of the Plio-Pleistocene astronomical timescale. Paleoceanography 11, 391–413 (1996).

    ADS  Article  Google Scholar 

  25. 25

    Néron de Surgy, O. & Laskar, J. On the long term evolution of the spin of the Earth. Astron. Astrophys. 318, 975–989 (1997).

    ADS  Google Scholar 

  26. 26

    Forte, A. M., Dziewonski, A. M. & Woodward, R. L. Aspherical structure of the mantle, tectonic plate motions, nonhydrostatic geoid, and topography of the core–mantle-boundary, in Dynamics of the Earth's Deep Interior and Earth Rotation (ed. Le-Mouel, J.-L., Smylie, D. E. & Herring, T.) 135–166 (Geophys. Monogr. 72, AGU, Washington, DC, (1993)).

    Google Scholar 

  27. 27

    Li, X.-D. & Romanowicz, B. Global mantle shear-velocity model developed using nonlinear asymptotic coupling theory. J. Geophys. Res. 101, 22245–22272 (1996).

    ADS  Article  Google Scholar 

  28. 28

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

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank K. Cheng, S. Shettleworth, S. Yoerg, J. Templeton, A. Bond, K. Gould-Beierle, B. Gibson and C. Cink for comments on previous drafts of this paper, and D. W. Stephens for assistance with data analysis. The research was supported by The National Science Foundation and the Howard Hughes Medical Institute.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Alessandro M. Forte.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Forte, A., Mitrovica, J. A resonance in the Earth's obliquity and precession overthe past 20 Myr drivenbymantle convection. Nature 390, 676–680 (1997). https://doi.org/10.1038/37769

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.