Nonlinear variability in the geomagnetic secular variation of the last 150 years

Fractals

Volumn 10, Issue 3, 2002, Pages 297-303

  De Santis, A ^a   Barraclough, D ^b   Tozzi, R ^a  

^a ISTITUTO NAZIONALE DI GEOFISICA E VULCANOLOGIA   (Italy)

^b BRITISH GEOLOGICAL SURVEY   (United Kingdom)

Author keywords

Chaos; Geomagnetic Field; Nonlinear Forecasting; Secular Variation

Indexed keywords

EID: 0036758459     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X02001336     Document Type: Conference Paper

References (21)

1. D.R. Barraclough and A. De Santis, "Some Possible Evidence for a Chaotic Geomagnetic Field from Observational Data," Phys. Earth Planet. Int. 99, 207-220 (1997).
2. G. Sugihara and R.M. May, "Nonlinear Forecasting as a Way of Distinguishing Chaos from Measurement Error in Time Series," Nature 344, 734-741 (1990).
3. F. Takens, "Detecting Strange Attractors in Turbulence," in Lecture Notes in Mathematics, ed. D.A. Rand and L.S. Young, Vol. 898 (Springer, Berlin, 1981), pp. 366-381.
4. P. Grassberger and I. Procaccia, "Measuring the Strangeness of Strange Attractors," Physica D9, 189-208 (1983).
5. A.R. Osborne and A. Provenzale, "Finite Correlation Dimension for Stochastic Systems with Power-Law Spectra," Physica D35, 357-381 (1989).
6. I. Procaccia, "Complex or Just Complicated?" Nature 339, 498-499 (1988).
7. W. Marzocchi, F. Mulargia and G. Gonzato, "Detecting Low-Dimensional Chaos in Geophysical Time," J. Geoph. Res. 102(B2), 3195-3209 (1997).
8. J.D. Farmer and J.J. Sidorowich, "Predicting Chaotic Time Series," Phys. Rev. Lett. 59, 845-848 (1987).
9. D.J. Wales, "Calculating the Rate of Loss of Information from Chaotic Time Series by Forecasting," Nature 350, 485-488 (1991).
10. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian and J.D. Farmer, "Testing for Nonlinearity in Time Series: The Method of Surrogate Data," Physica D58, 77-94 (1992).
11. A.A. Tsonis and J.B. Eisner, "Nonlinear Prediction as a Way of Distinguishing Chaos from Random Fractal Sequences," Nature 358, 217-220 (1992).
12. H.D.I. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, New York, 1996).
13. A.D. Fowler and D.E. Roach, "Dimensionality Analysis of Time-Series Data: Nonlinear Methods," Comp. Geosc. 19, 41-52 (1993).
14. L.G. Baker and J.P. Gollub, Chaotic Dynamics (Cambridge University Press, Cambridge), 1990 pp. 182.
15. L. Cafarella, A. De Santis and A. Meloni, "Secular Variation in Italy from Historical Geomagnetic Field Measurements," Phys. Earth Planet. Int. 73, 206-221 (1992).
16. R.G. Currie, "Geomagnetic Time Spectrum," Atmos. Space Sci. 21, 425-438 (1973).
17. N.M. Rotanova, N.Ye. Papitashvili and A.N. Pushkov, "Interpretation of 60-year Variations in the Geomagnetic Field as a Quasi-Harmonic Process," Geomagn. Aeron. 22, 733-735 (1982).
18. N.M. Rotanova, N.Ye. Papitashvili, S.V. Filippov and T.A. Chernova, "Identification and Analysis of 60-Year Variations of the Geomagnetic Field from the Time-Series of Spherical Harmonics," Geomagn. Aeron. 23, 673-679 (1983) (in English translation); pp. 829-836 (in Russian).
19. R.A. Langel, "The Main Field," in Geomagnetism, Vol. 1., ed. J.A. Jacobs (Academic Press, London, 1987), Chap. 4, pp. 249-512.
20. P. De Michelis, G. Consolini and A. Meloni, "Sign Singularity in the Secular Acceleration of the Geomagnetic Field," Phys. Rev. Lett. 81, 5023-5026.
21. K.A. Robbins, "A New Approach to Subcritical Instability and Turbulent Transitions in a Simple Dynamo," Math. Proc. Camb. Phil. Soc. 82, 309-325 (1977).