Abstract
The applications of the tools of nonlinear time-series analysis to measurements obtained by digital ionosonde “PARUS,” created at IZMIRAN, is considered. Small-scale structure of the electron density Ne at F-region of ionosphere is examined by exploring observables of reflected high-frequency radio wave.
Time series corresponding to given transmitter frequency f and virtual height h and conforming to usual, not perturbed, day ionogram are examined. Using the standard correlation algorithm, we have determined that for an embedding dimension n = 15, computed correlation dimension D2(n) reaches its saturation, D2 ≃ 4.
Reliability of the estimation of the correlation dimension was confirmed by applying to our sets of measurements J. Theiler's modification of standard algorithm. The test of time difference, smoothing procedure, calculation of the largest Liapounov exponent, and analysis of the surrogate data were employed in our study of data sets. Although our sets of measurements contain a significant “random noise”, nonlinear time-series analysis clear up, that the dynamics of unperturbed ionosphere, generating this time series, exhibits low-dimensional behavior.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Eckman J-P, Ruelle D (1985) Ergodic theory of chaos and strange attractors. Rev Mod Phys 57:617–656
Grassberger P, Procaccia I (1983a) Measuring the strangeness of strange attractors. Physica D 9 N1–2:189–208
Grassberger P, Procaccia I (1983b) Estimation of Kolmogorov entropy from a chaotic signal. Phys Rev A 28:2592–2593
Karpenko AL, Manaenkova NI (1995) Fractal analysis of the measurements obtained by digital ionosonde “Parus”. Tr J Phys 19 N3:526–532
Nerenberg MA, Essex C (1986) Correlation dimension and systematic geometric effects. Phys Rev A 42
Osborne AN, Provenzale A (1989) Finite correlation dimension for stochastic systems with power-law spectra. Physica D 35:357–381
Packard NH, Crutchfield JG, Farmer JD, Shaw RS (1980) Geometry from a time series Phys Rev Lett 45:712–716
Prichard D, Price CP (1992) Spurious dimension estimation from time series of geomagnetic indices. Geophys Res Lett 19 N15:1623–1626
Provenzale A, Smith LA, Vio R, Murante G (1992) Distinguish low-dimensional dynamics and randomness in measured time series. Physica D 58:31–49
Roberts DA, Baker DN, Klimas AJ, Bargatze LF (1991) Indications of low dimensionality magnetospheric dynamics. Geophys Res Lett 18 N2:151
Ruelle D (1990) Deterministic chaos: the science and the fiction. Proc R Soc Lond Ser A 427:241–245
Shan LH, Hansen P, Goertz CK, Smith RA (1991) Chaotic appearance of the AE index. Geophys Res Lett 18 N2:147
Takens F (1981) Detecting strange attractors in turbulence. In: Lect Notes in Math 898. Springer, Berlin Heidelberg New York, pp 366–381
Theiler J (1986) Spurious dimension from correlation algorithms applied to limited time-series data. Phys Rev A 34:2427
Vassiliadis DV, Sharma AS, Eastman TE, Papadopoulos K (1990) Low-dimensional chaos in magnetospheric activity from AE time series. Geophys Res Lett 17:1841
Wolf A, Swift JB, Swinney HL, Vastano J (1985) Determining Lyapounov exponents from a time series. Physica D 16:285–317
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Karpenko, A.L., Manaenkova, N.I. Nonlinear time series analysis of the ionospheric measurements. Geol Rundsch 85, 124–129 (1996). https://doi.org/10.1007/BF00192070
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00192070