Skip to main content
Earth, Planets and Space
Download PDF

A Coupled Map Lattice model for geomagnetic polarity reversals that exhibits realistic scaling

Earth, Planets and Space volume 51, pages 395–402 (1999)Cite this article

Abstract

Seki and Ito (1993) showed that the geomagnetic polarity reversals had a power-law distribution and presented a simple model in which the geodynamo was assumed to be a system of magnetic spins in a critical phase-transition state. We present an improved, more realistic model, and obtain a power exponent in agreement with the observed value, which is about −1.5. The revised model is a Coupled Map Lattice (CML). A CML is a dynamical system with discrete time and space, but continuous state. In the present model, elementary dynamo evolves autonomously according to the Lorenz map obtained from Rikitake dynamo dynamics. We examine the behavior of the system and the distribution of polarity reversal intervals for various values of parameters. We find some sets of the parameters which yield a power exponent close to −1.5.

References

  • Bak, P., C. Tang, and K. Wiesenfeld, Self-organized criticality: An explanation of 1/f noise, Phys. Rev. Lett., 59, 381–384, 1987.

    Article  Google Scholar 

  • Bak, P., How Nature Works: the Science of Self-Organized Criticality, 212 pp., Copernicus, New York, 1996.

    Book  Google Scholar 

  • Berge, P., Y. Pomeau, and Ch. Vidal, Order within Chaos: towards a Deterministic Approach to Turbulence, preface by David Ruelle, translated from the French by Laurette Tuckerman, 329 pp., Wiley, New York, Hermann, Paris, 1984.

    Google Scholar 

  • Cande, S. C. and D. V. Kent, Revised calibration of the geomagnetic polarity timescale for the Late Cretaceous and Cenozoic, J. Geophys. Res., 100, 6093–6095, 1995.

    Article  Google Scholar 

  • Channell, J. E. T., E. Erba, M. Nakanishi, and K. Tamaki, Late Jurassic-Early Cretaceous time scales and oceanic magnetic anomaly block models, in Geochronology, Time Scales, and Global Stratigraphic Correlation, edited by W. A. Berggren, D. V. Kent, M. P. Aubry, and J. Hardenbol, pp. 51–63, Society of Sedimentary Geology Special Publication No. 54, SEPM, Tulsa, 1995.

    Chapter  Google Scholar 

  • Cortini, M. and C. C. Barton, Chaos in geomagnetic reversal records: A comparison between Earth’s magnetic field data and model disk dynamo data, J. Geophys. Res., 99, 18021–18033, 1994.

    Article  Google Scholar 

  • Cox, A., Lengths of geomagnetic polarity intervals, J. Geophys. Res., 73, 3247–3260, 1968.

    Article  Google Scholar 

  • de Wijs, G. A., G. Kresse, L. Vočadlo, D. Dobson, D. Alfè, M. J. Gillan, and G. D. Price, The viscosity of liquid iron at the physical conditions of the Earth’s core, Nature, 392, 805–807, 1998.

    Article  Google Scholar 

  • Gaffin, S., Analysis of scaling in the geomagnetic polarity reversal record, Phys. Earth Planet. Int., 57, 284–290, 1989.

    Article  Google Scholar 

  • Harland, W. B., A. V. Cox, P. G. Llewellyn, C. A. G. Pickton, A. G. Smith, and R. Walters, A Geologic Time Scale, pp. 73–75, Cambridge University Press, New York, 1982.

    Google Scholar 

  • Ito, K., Chaos in the Rikitake two-disc dynamo system, Earth Planet. Sci. Lett., 51, 451–456, 1980.

    Article  Google Scholar 

  • Kaneko, K., The coupled map lattice: introduction, phenomenology, Lyapunov analysis, thermodynamics and applications, in Theory and Applications of Coupled Map Lattices, edited by K. Kaneko, pp. 1–49, John Wiley, New York, 1993.

    Google Scholar 

  • Kono, M., Rikitake two-disk dynamo and paleomagnetism, Geophys. Res. Lett., 14, 21–24, 1987.

    Article  Google Scholar 

  • Lorenz, E. N., Deterministic nonperiodic flow, J. Atoms. Sci., 20, 130–141, 1963.

    Article  Google Scholar 

  • Lutz, T. M. and G. S. Watson, Effects of long-term variation on the frequency spectrum of the geomagnetic reversal record, Nature, 334, 240–242, 1988.

    Article  Google Scholar 

  • Marzocchi, W., F. Mulargia, and G. Gonzato, Detecting low-dimensional chaos in geophysical time series, J. Geophys. Res., 102, 3195–3209, 1997.

    Article  Google Scholar 

  • McFadden, P. L., Statistical tools for the analysis of geomagnetic reversal sequences, J. Geophys. Res., 89, 3363–3372, 1984.

    Article  Google Scholar 

  • McFadden, P. L. and R. T. Merrill, Lower mantle convection and geomagnetism, J. Geophys. Res., 89, 3354–3362, 1984.

    Article  Google Scholar 

  • McFadden, P. L. and R. T. Merrill, Inhibition and geomagnetic field reversals, J. Geophys. Res., 98, 6189–6199, 1993.

    Article  Google Scholar 

  • Naidu, P. S., Statistical structure of geomagnetic field reversals, J. Geophys. Res., 76, 2649–2662, 1971.

    Article  Google Scholar 

  • Rikitake, T., Oscillations of a system of disk dynamos, Proc. Cambridge Philos. Soc, 54, 89–105, 1958.

    Article  Google Scholar 

  • Seki, M. and K. Ito, A phase-transition model for geomagnetic polarity reversals, J. Geomag. Geoelectr, 45, 79–88, 1993.

    Article  Google Scholar 

  • Shimizu, M. and Y. Honkura, Statistical nature of polarity reversals of the magnetic field in coupled-disk dynamo models, J. Geomag. Geoelectr, 37, 455–497, 1985.

    Article  Google Scholar 

  • Sornette, D., Critical phase transitions made self-organized: a dynamical system feedback mechanism for self-organized criticality, J. Phys. I France, 2, 2065–2073, 1992.

    Article  Google Scholar 

  • Takayasu, H., Fractals in the Physical Sciences, 170 pp., Manchester University Press, Manchester, 1990.

    Google Scholar 

Download references

Author information

Author notes

  1. Keisuke Ito

    Present address: The Hakodate Wide Area Unification of Public University, 4-13 Shinonome-cho, Hakodate, 040-0036, Japan

Authors and Affiliations

  1. Department of Liberal Arts, Kobe Tokiwa Junior College, 2-6-2 Otani-cho, Nagata, Kobe, 653-0838, Japan

    Masayuki Seki

  2. The Graduate School of Science and Technology, Faculty of Science, Kobe University, Rokkoudai, Nada, Kobe, 657-8501, Japan

    Keisuke Ito

Authors
  1. Masayuki Seki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Keisuke Ito
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Masayuki Seki.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Seki, M., Ito, K. A Coupled Map Lattice model for geomagnetic polarity reversals that exhibits realistic scaling. Earth Planet Sp 51, 395–402 (1999). https://doi.org/10.1186/BF03352243

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03352243

Keywords

  • Lyapunov Exponent
  • Polarity Reversal
  • Dynamo Model
  • Power Exponent
  • Geomagnetic Data