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Determination of the phase projection of a dynamic system from strain field observations

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Abstract

The paper analyzes the possibility of extracting a geophysical field component from a time series considered as a phase projection of a dynamic system. Based on model calculations, the method of averaging of phase trajectories is shown to be applicable for the recovery of time variations of a dynamic system and more reliable determination of its quantitative characteristics if the variations are superimposed by a high-dimension process (a purely random process) and a low-dimension process (linear interpolation). The analysis of the extraction of dynamic system variations from strain records obtained at various points of seismically active regions of China provided the following estimates of dynamic parameters: the phase space dimension is m = 5–7, and the correlation dimension varies, depending on the observation point, within the range d 2 = 2.6–3.5.

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References

  1. A. S. Cherepantsev, “Dimension of the Phase Space of a Dynamic System from Geophysical Data,” Fiz. Zemli, No. 12, 72–81 (2007) [Izvestiya, Phys. Solid Earth 43, 1047–1055 (2007)].

  2. J. F. Gibson, J. D. Farmer, M. Casdagli, and S. Eubank, “An Analytic Approach to Practical State Space Reconstruction,” Phys. D 57, 1 (1992).

    Article  Google Scholar 

  3. G. G. Malinetskii and A. B. Potapov, Contemporary Problems in Nonlinear Dynamics (Editorial URSS, Moscow, 2002) [in Russian].

    Google Scholar 

  4. T. Parker and L. Chua, Practical Numerical Algorithms for Chaotic Systems (Springer, New York, 1989).

    Google Scholar 

  5. A. A. Samarskii, Introduction to Numerical Methods (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

  6. H. G. Shuster, Deterministic Chaos (Springer, Heidelberg, 1982; Mir, Moscow, 1988).

    Google Scholar 

  7. V. B. Smirnov, A. V. Ponomarev, Quian Jiadong, and A. S. Cherepantsev, “Rhythms and Deterministic Chaos in Geophysical Time Series,” Fiz. Zemli, No. 6, 6–28 (2005) [Izvestiya, Phys. Solid Earth 41, 428–448 (2005)].

  8. F. Takens, “Detecting Strange Attractors in Turbulence,” in Lecture Notes in Mathematics (Springer, New York, 1981), Vol. 898, pp. 366–381.

    Google Scholar 

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Authors and Affiliations

  1. Taganrog Institute of Technology, Southern Federal University, Nekrasovskii per. 44, Taganrog, Rostov oblast, 347928, Russia

    A. S. Cherepantsev

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  1. A. S. Cherepantsev
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Correspondence to A. S. Cherepantsev.

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Original Russian Text © A.S. Cherepantsev, 2008, published in Fizika Zemli, 2008, No. 2, pp. 39–58.

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Cherepantsev, A.S. Determination of the phase projection of a dynamic system from strain field observations. Izv., Phys. Solid Earth 44, 119–137 (2008). https://doi.org/10.1134/S106935130802002X

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  • DOI: https://doi.org/10.1134/S106935130802002X

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