Skip to main content


We’d like to understand how you use our websites in order to improve them. Register your interest.

Fractal properties of the IMF and the Earth’s magnetotail field


The time series of the interplanetary and Earth’s magnetotail magnetic fields are analyzed. The data subsets taken by the IMP 8 spacecraft outside and inside of the Earth’s magnetosphere show clearly the fractal properties: their “box dimensions” are found to be close to 1.7 and 1.5 respectively. It is shown that data gaps have a little effect on the results. The magnetic field increment distributions are found to be non-Gaussian, but self-affine.


  1. Burlaga, L. F., Multifractal structure of the interplanetary magnetic field, Geophys. Res. Lett., 18, 69–72, 1991.

  2. Burlaga, L. F. and L. W. Klein, Fractal structure of the interplanetary magnetic field J. Geophys. Res., 91, 347–350, 1986.

  3. Crownover, R. M., Introduction to Fractals and Chaos, 306 pp., Jones and Bartlett Publ., Boston, 1995.

  4. Feynman, J. and A. A. Ruzmaikin, Distribution of the interplanetary magnetic field revisited, J. Geophys. Res., 99, 17,645–17,651, 1994.

  5. Hastings, H. M. and G. Sugihara, Fractals: A User’s Guide for the Natural Sciences, 235 pp., Oxford Univ. Press, Oxford, 1993.

  6. Higuchi, T., Approach to an irregular time series on the basis of the fractal theory, Physica D, 31, 277–283, 1988.

  7. Lighthill, M. J., Introduction to Fourier Analysis and Generalized Func-tions, 79 pp., Cambridge Univ. Press, Cambridge, 1958.

  8. Mandelbrot, B. B. and J. W. van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Review, 10, 422–437, 1968.

  9. Marsch, E., C.-Y. Tu, and H. Rosenbauer, Multifractal scaling of the kinetic energy flux in solar wind turbulence, Ann. Geophys., 14, 259–269, 1996.

  10. Roberts, D. A., Is there a strange attractor in the magnetosphere?, J. Geophys. Res., 96, 16,031–16,046, 1991.

  11. Russell, C. T., Comments on the measurement of power spectra of the interplanetary magnetic field, Solar Wind, NASA SP-308, 365–374, 1972a.

  12. Russell, C. T., Noise in the geomagnetic tail, Planet. Space Sci., 20, 1541–1553, 1972b.

  13. Ruzmaikin, A. A., I. P. Lyannaya, V. A. Stayshkin, and E. Yeroshenko, The spectrum of the interplanetary magnetic field near 1.3 AU, J. Geophys. Res., 98, 13,303–13,306, 1993.

  14. Ruzmaikin, A. A., J. Jeynman, B. E. Goldstein, and E. J. Smith, Intermittent turbulence in solar wind from the south polar hole, J. Geophys. Res., 100, 3395–3403, 1995.

  15. Shlesinger, M., G. Zaslavsky, and U. Frisch (eds.), Lévy Flights and Related Topics in Physics, 347 pp., Springer-Verlag, Berlin, 1995.

  16. Tricot, C., Dimension fractale et spectre, J. de Chimie Phys. et de Physico-Chmie Biol., 85, 379–384, 1988.

  17. Tricot, C., Curves and Fractal Dimension, 323 pp., Springer-Verlag, New York, 1995.

Download references

Author information



Corresponding author

Correspondence to K. Kabin.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kabin, K., Papitashvili, V.O. Fractal properties of the IMF and the Earth’s magnetotail field. Earth Planet Sp 50, 87–90 (1998).

Download citation


  • Solar Wind
  • Fractal Property
  • Interplanetary Magnetic Field
  • Fractional Brownian Motion
  • Solar Wind Turbulence