Gravitation smoothing of time series (spectral properties)
https://doi.org/10.22405/2226-8383-2018-19-4-11-25
Abstract
This article continues the cycle of works by authors on the development of mathematical aspects methods of artificial intelligence for the processing of observations conducted under the guidance of academician A.D. Gvishiani, which was began in 2000. It is devoted to a new universal method of smoothing, originally intended for the analysis of geophysical time series. Gravitational smoothing formed the basis for studying the acceleration of the secular course of the Earth’s main magnetic field with using of the observational data of the INTERMAGNET network. But the properties of the smoothing operator have not been studied so far. This aticle is first step to this goal.
About the Authors
S. M. Agayan
Geophysical Center RAS
Russian Federation
Russian Federation
Agayan Sergey Martikovich — D.Sc., Principal research scientist
D. A. Kamaev
Russian Federal Survey for Hydrometeorology and Environmental Monitoring
Russian Federation
Russian Federation
Kamaev Dmitry Alfredovich — D.Sc., Chief of laboratory, NPO Taifu
Sh. R. Bogoutdinov
Geophysical Center RAS; Schmidt Institute of Physics of the Earth RAS
Russian Federation
Russian Federation
Bogoutdinov Shamil Rafekovich — PhD, Leading research scientist GC RAS, Moscow; Senior research scientist Schmidt IPhE RAS
A. S. Pavelev
SHTORM Technology Ltd
Russian Federation
Russian Federation
Pavelev Artem Sergeevich — programmer
References
1. Samarskii A.A. 1982, “Introduction to numerical methods“, Moscow, Nauka, 269 p.
2. Samarskii A.A., Gulin A.V. 1989, “Numerical methods“, Moscow, Nauka, 432 p.
3. Bahvalov N.S., Zhidkov N.P., Kobelkov G.M. 2003, “Numerical methods“, Moscow, Publishing house "Laboratory of Basic Knowledge", 632 p.
4. Pshenichny, B.N., Danilin Yu.M. 1975, “Numerical Methods in Extremal Tasks“, Moscow, Nauka 319 p.
5. Daubechies I. 1992, “Ten Lectures of Wavelets“, Springer-Verlag, 369 p.
6. Mallat S. 1999, “Вэйвлеты в обработке сигналов“, Academic Press, 620 p.
7. Gvishiani, A.D., Diament M., Mikhailov V.O., Galdeano A., Agayan S.M., Bogoutdinov Sh.R., Graeva E.M. 2002, “Artificial Intelligence Algorithms for Magnetic Anomaly Clustering“, Izvestiya, Physics of the Solid Earth. English Translation Copyright by MAIK “Nauka/Interperiodica”, Russia, vol. 38. pp. 545-559.
8. Mikhailov V., Galdeano A., Diament M., Gvishiani A., Agayan S., Bogoutdinov Sh., Graeva E., Sailhac P. 2003, “A Application of artificial intelligence for Euler solutions clustering“, Geophysics, vol. 68, no. 1, pp. 168–180.
9. Bogoutdinov Sh.R., Agayan S.M., Gvishiani A.D., Graeva E.M., Rodkin M.V., Zlotnicki J., Le Mou?l J.L. 2007, “Fuzzy logic algorithms in the analysis of electrotelluric data with reference to monitoring of volcanic activity“, Izvestiya, Physics of the Solid Earth. MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC, vol. 43, pp. 597-609
10. Gvishiani A.D., Agayan S.M., Bogoutdinov Sh.R. 2008, “Fuzzy recognition of anomalies in time series“, Doklady earth sciences, vol. 421, no. 1, pp. 838-842. DOI: 10.1134/S1028334X08050292
11. Bogoutdinov Sh.R., Gvishiani A.D., Agayan S.M., Solovyev A.A., Kihn E. 2010, “Recognition of disturbances with specified morphology in time series. Part 1: Spikes on magnetograms of the worldwide INTERMAGNET network“, Izvestiya, Physics of the Solid Earth, vol. 46, no. 11, pp. 1004-1016.
12. Soloviev A.A., Agayan S.M., Gvishiani A.D., Bogoutdinov Sh.R., Chulliat A. 2012, “Recognition of disturbances with specified morphology in time series: Part 2. Spikes on 1-s magnetograms“, Izvestiya, Physics of the Solid Earth, vol. 48, no. 5, pp. 395–409. DOI: 10.1134/S106935131204009X
13. Gvishiani A.D., Agayan S.M. , Bogoutdinov Sh.R., Kagan A.I. 2011, “Gravitational smoothing of time series“, Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, vol. 17, no. 2, pp. 62–70.
14. Agayan S.M., Bogoutdinov Sh.R., Dobrovolsky M.N., Kagan A.I. 2014, “Weighted gravitational time series smoothing“, Russ. J. Earth Sci., vol. 14. doi: 10.2205/2014ES000543
15. Soloviev A., Chulliat A., Bogoutdinov, Sh. 2017, “Detection of secular acceleration pulses from magnetic observatory data“, Physics of the Earth and Planetary Interiors, pp. 128-142. doi: 10.1016/j.pepi.2017.07.005
16. Gelfond A.O. 1959, “Finite difference calculus“, M: GIFML, 400 p.
17. Wilkinson J.H. 1970, “The Algebraic eigenvalue problem“, M.: Nauka, 564 p.
Review
For citations:
Agayan S.M., Kamaev D.A., Bogoutdinov Sh.R., Pavelev A.S. Gravitation smoothing of time series (spectral properties). Chebyshevskii Sbornik. 2018;19(4):11-25. (In Russ.) https://doi.org/10.22405/2226-8383-2018-19-4-11-25
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