Scaling properties of palaeomagnetic reversal sequence

Nonlinear Processes in Geophysics

Volumn 3, Issue 1, 1996, Pages 13-22

  Ivanov, S S ^a  

^a SHIRSHOV INSTITUTE OF OCEANOLOGY   (Russian Federation)

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EID: 5744254538     PISSN: 10235809     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. Barenblatt, G.I. Self-similarity, Intermediate Asymptotics. (Russian edition : Moscow, Gidrometeoizdat, 1978)
2. Chillingworth, D.R.J. and Holmes, P.J. Dynamical systems and models for reversals of the Earth's magnetic field. Mathematical Geology, v.12, No. 1, 41-59, 1980
3. Cortini, M and Barton., Ch. Chaos in geomagnetic reversal records: A comparison between Earth's magnetic field data and model disk dynamo data. J. Geoph. Res., vol.99, No. B9, 18021-18034, 1994
4. Cox, A V. Magnetostratigraphic time scale. In: Harland, W.B. et al, eds, A Geologic Time Scale. Cambridge Univ. Press, Cambridge, 63-84, 1982
5. Dubois, J. and Pambrun, C. Etude de la distribution des inversions du champ magnetique terrestre entre - 160 Ma et l'actuel (echelle de Cox). Recherche d'un attracteur dans le systeme dynamique qui les genere. C.R. Acad. Sci. Paris, t.311, Serie II, 643-650, 1990
6. Feder, J. Fractals. Plenum Press, New York, 1988
7. Forrest, S.R. and Witten, T.A., Jr. Long-range correlation in smoke particle aggregates. J. Phys., A, 12, L109-117, 1979
8. Fraedrich, K. Estimating the dimensions of weather and climate attractors. J. Atm. Sci., 43, No. 5, 419-432, 1986
9. Grassberger, P. Does climatic attractor exist? Nature, 323, 609-612, 1986
10. Grassberger, P. and Procaccia, I. Measuring the strangeness of strange attractors. Physica D, 9, 189-208, 1983
11. Hilgen, F.J. Astronomical calibration of Gauss to Matuyama sapropels in Mediterranean and implication for the Geomagnetic Polarity Time Scale. Earth and Plan. Sci. Letters, v. 104, 226-244, 1991a.
12. Hilgen, F.J. Extension of the astronomically calibrated (polarity) time scale to the Miocene/Pleistocene boundary. Earth and Plan. Sci. Letters, v. 707, 349-368, 1991b.
13. Ivanov, S.S. "Counter-scaling" method for estimation of self-similarity of self-affine objects. In: J.H.Kruhl, ed., Fractals and Dynamic Systems in Geosciences, Springer, Berlin Heidelberg New York, 391-397, 1994.
14. Korvin, G. Fractal Models in Earth Sciences. Elsevier Publ., Amsterdam, 1992
15. Lorenz, F.N. Deterministic nonperiodic flow. J. Atmospheric Sci., v. 20, 130-141, 1963
16. Lowrie, W. Geomagnetic reversal history. Terra Nova, 2, 438-445, 1991
17. Mandelbrot, BB. The Fractal Geometry of Nature. Freeman, New York, 1983
18. Mandelbrot, B.B. Multifractal measures, especially for the geophysicist PAGEOPH, vol. 131, No. 1-2, 5-42, 1989
19. Mazaud, A., Laj, C., de Seze, L., and Verozub, K.L. 15-Myr periodicity in the frequency of geomagnetic reversal record Nature, 334, 328-330, 1983
20. Naidu, P.S. Statistical structure of geomagnetic field reversals. J. Geophys. Res. 76, 2649-2662, 1970
21. Nicolis, C. and Nicolis G. Is there a climatic attractor? Nature, 311, 529-532, 1984
22. Ord, A. The fractal geometry of patterned structures in numerical models of rock deformation. In: J.H.Kruhl, ed., Fractals and Dynamic Systems in Geosciences, Springer, Berlin Heidelberg New York, 131-155, 1994.
23. Prevot, M., Mankinen, E.A., Gromme, C.S., and Coe, R.S. How the geomagnetic field vector reverses polarity. Nature. 316, 230-234, 1985
24. Reif, F. Statistical Physics. McGraw-Hill Book Co., 1968
25. Rikitake, T. Oscillations of a system of disk dynamos. Proc. Cambr. Phil. Soc., v. 54, 89, 1958
26. Robbins, K.A. A moment equation description of magnetic reversals in the Earth. Proc. Natl. Acad. Sci. U.S.A., v.73, 4297-4301, 1976
27. Sagdeyev, R.Z., Usikov, D.A. and Zaslavsky, G.M. Nonlinear Physics - From the Pendulum to Turbulence and Chaos. Charwood, Chur, Switzerland, 1988
28. Schertzer, D., Lovejoy, S. Scaling and multifractal processes. Lecture Notes, Cargese, 1993, 292 p.
29. Shackleton, N., Berger, A. and Peltier W.R. An alternative astronomic calibration of the Lower Pleistocene time scale based on ODP site 677. Trans. Roy. Soc. Edinb.: Earth Sci., v. 81, 251-261, 1990
30. Takens, F. Detecting strange attractors in turbulence. In: Rand, D.A.and Young, L.S. eds. Dynamical Systems and Turbulence.Lecture Notes in Mathematics. 898, Springer, New York, 366-381, 1981
31. Tritton, D.J, Deterministic chaos, geomagnetic reversals, and the spherical pendulum. In: Lowers, F.J. et al, eds. Geomagnetism and Paleomagnetism. Kluwer Acad. Publ., 215-226, 1989
32. Turcotte, D.L. Fractals in Geology and Geophysics. Pure Appl. Geoph., 131, N1/2, 171-195, 1989
33. Turcotte, D.L. Crustal deformation and fractals: a review. In: J.H.Kruhl, ed., Fractals and Dynamic Systems in Geosciences, Springer, Berlin Heidelberg New York, 7-23, 1994.