GEOPHYSICAL RESEARCH, 2020, vol. 21, no. 2, pp. 5-18. https://doi.org/10.21455/gr2020.2-1

UDC 550.8.05

Abstract  References   Full text (in Russian) Full text (in English)

RESEARCH OF FRACTAL DIMENSION OF TIME SERIES OF GRAVIMETRIC OBSERVATIONS

V.N. Koneshov(1), V.B. Nepoklonov(1,2), M.N. Drobyshev(1), E.S. Spiridonova(2)

(1) Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia

(2) Moscow State University of Geodesy and Cartography (MIIGAiK), Moscow, Russia

Abstract. The article is devoted to the analysis of time series of gravimetric observations using the value of fractal dimension as an indicator of persistence (stability) of the time series. Various numerical methods for assessing this indicator are examined and compared. Using real measuring data, quantitative estimates of the fractal dimension of nine trial time series of gravimetric observations are obtained for two components - the measured values ​​of acceleration of gravity and root mean square deviations of the measurement errors. The obtained estimates are characterized by values ​​from 1.12 to 1.44 for the first component and from 1.26 to 1.42 for the second component, which indicates the stable persistence (inertia) of these time series. The dependence of fractal dimension on the length of the series, the type of the trend-forming polynomial, the estimation method and its settings (using the methods of normalized range and minimum covering) are experimentally studied. Suggestions are given on the method for obtaining fractal dimension estimates and their practical application.

Keywords: gravimetric observations, time series, minimum coverage method, normalized range method, persistence, fractal dimension.

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