Schmidt Institute of Physics of the Earth, RAS
Moskva, Russian Federation
Geophysical Center RAS
Space Research Institute
Moscow, Russian Federation
CSCSTI 37.00
CSCSTI 38.00
Russian Classification of Professions by Education 05.00.00
Russian Library and Bibliographic Classification 26
Russian Trade and Bibliographic Classification 63
BISAC SCI SCIENCE
A mathematical technology for digital processing of geophysical signals has been developed for estimating non-stationary parametric functions. Two-stage approximations with local models in the first stage and weighted approximation averaging models in the second stage were used. Algorithms for calculating estimates of parametric amplitude and frequency functions, increment/decrement functions, and frequency dispersions have been developed. Error formulas for estimating parametric pulsation functions have been proposed. Examples of applying the technology to model and experimental observations have been implemented. The technology's capabilities are demonstrated, allowing for the calculation of frequency function estimates and frequency derivative functions for geomagnetic pulsations of the “pearl” type.
Geophysical signals, geomagnetic pulsations, non-stationary parameters, two-stage approximation, local approximations, weighted averaging
1. Afanasyev A. A., Rybolovlev A. A. and Ryzhkov A. P. Digital Signal Processing. — M. : Goryachaya Liniya-Telekom, 2019. — 356 p. — (In Russian).
2. Aleshkevitch V. A. Course in General Physics. Optics. — M. : Fizmatlit, 2011. — 320 p. — (In Russian).
3. Anikeyev D. A., Penkin G. O. and Strijov V. V. Local approximation models for human physical activity classification // Informatics and Applications. — 2019. — Vol. 13, no. 1. — P. 40–48. — https://doi.org/10.14357/19922264190106. — (In Russian).
4. Bioucas-Dias J., Katkovnik V., Astola J., et al. Absolute phase estimation: adaptive local denoising and global unwrapping // Applied Optics. — 2008. — Vol. 47, no. 29. — P. 5358–5369. — https://doi.org/10.1364/ao.47.005358.
5. Fedorov E. N., Pilipenko V. A., Engebretson M. J., et al. Transmission of a Magnetospheric Pc1 Wave Beam Through the Ionosphere to the Ground // Journal of Geophysical Research: Space Physics. — 2018. — Vol. 123, no. 5. — P. 3965–3982. — https://doi.org/10.1029/2018ja025338.
6. Fung L., Bearon R. N. and Hwang Y. A local approximation model for macroscale transport of biased active Brownian particles in a flowing suspension // Journal of Fluid Mechanics. — 2022. — Vol. 935. — A24. — https://doi.org/10.1017/jfm.2022.10.
7. Getmanov V. G. Digital Processing of Non-Stationary Oscillatory Signals Based on Local and Spline Models. — M. : MEPhI, 2011. — 298 p. — (In Russian).
8. Getmanov V. G. Local and spline approximations in digital processing of geomagnetic observations // Chebyshevskii Sbornik. — 2019. — Vol. 19, no. 4. — P. 26–42. — https://doi.org/10.22405/2226-8383-2018-19-4-26-42. — (In Russian).
9. Getmanov V. G. Digital Signal Processing With Applications for Geophysics and Experimental Mechanics. — M. : Tekhnosphera, 2021. — 356 p. — (In Russian).
10. Getmanov V. G., Dabagyan R. A. and Sidorov R. V. Studying geomagnetic pulsation characteristics with the local approximation method // Geomagnetism and Aeronomy. — 2016. — Vol. 56, no. 2. — P. 195–202. — https://doi.org/10.1134/s0016793216020055.
11. Getmanov V. G., Dovbnya B. V. and Kornilov A. S. Estimating the Frequency and Amplitude Parameters of the Serpentine-Emission Type of Geomagnetic Pulsations // Geomagnetism and Aeronomy. — 2018. — Vol. 58, no. 4. — P. 523–532. — https://doi.org/10.1134/s0016793218040060.
12. Getmanov V. G., Gvishiani A. D., Pilipenko V. A., et al. Estimation of Parameters of Non-stationary Geophysical Signals Based on Two-Stage Approximations Using Local Models // Russian Journal of Earth Sciences. — 2025. — Vol. 25. — ES2020. — https://doi.org/10.2205/2025es000979.
13. Getmanov V. G., Sidorov R. V. and Dabagyan R. A. A Method of Filtering Signals Using Local Models and Weighted Averaging Functions // Measurement Techniques. — 2015. — Vol. 58, no. 9. — P. 1029–1036. — https://doi.org/10.1007/s11018-015-0837-5.
14. Gribanova M. S. and Skurikhina E. A. Prediction of Earth Rotation Parameters Using Local Approximation Techniques // Transactions of IAA RAS. — 2020. — No. 54. — P. 11–20. — https://doi.org/10.32876/ApplAstron.54.11-20. — (In Russian).
15. Guglielmi A. V. and Potapov A. S. Problems of the Pc1 magnetospheric wave theory. A review // Solar-Terrestrial Physics. — 2019. — Vol. 5, no. 3. — P. 87–92. — https://doi.org/10.12737/stp-53201910.
16. Guglielmi A. V. and Troitczkaya V. A. Geomagnetics Pulsations and Diagnosis of Magnetosphere. — M. : Nauka, 1973. — 208 p. — (In Russian).
17. Katkovnik V., Egiazarian K. and Astola J. Local Approximation Techniques in Signal and Image Processing. — SPIE, 2006. — 576 p. — https://doi.org/10.1117/3.660178.
18. Katkovnik V. Ya. Nonparametric Identification and Smoothing of Data (Local Approximation Method). — M. : Nauka, 1985. — 336 p. — (In Russian).
19. Kleymenova N. G. Geomagnetics Pulsations // Model of space. Volume 1. — M. : MGU, 2007. — P. 611–626. — (In Russian).
20. Liu J., Shiokawa K., Oyama S.-I., et al. A Statistical Study of Longitudinal Extent of Pc1 Pulsations Using Seven PWING Ground Stations at Subauroral Latitudes // Journal of Geophysical Research: Space Physics. — 2023. — Vol. 128, no. 1. — https://doi.org/10.1029/2021ja029987.
21. Makur A. A Study of Local Approximation in Information Theory. — Massachusetts Institute of Technology, 2015. — 171 p.
22. Mallat S. A wavelet tour of signal processing. Second Edition. — Academic Press, 1999. — 671 p.
23. Matsuda S., Miyoshi Y., Kasahava Y., et al. Multipoint Measurement of Fine-Structured EMIC Waves by Arase, Van Allen Probe A, and Ground Stations // Geophysical Research Letters. — 2021. — Vol. 48, no. 23. — https://doi.org/10.1029/2021gl096488.
24. Mikhailova O. S., Klimushkin D. Yu. and Mager P. N. The current state of the theory of Pc1 range ULF pulsations in magnetospheric plasma with heavy ions: A review // Solnechno-Zemnaya Fizika. — 2022. — Vol. 8, no. 1. — P. 3–18. — https://doi.org/10.12737/szf-81202201. — (In Russian).
25. Nie Y., Wang Y., Sun W., et al. The Local Approximation Method for Structural Optimization // Applied Mechanics and Materials. — 2014. — Vol. 575. — P. 854–858. — https://doi.org/10.4028/www.scientific.net/amm.575.854.
26. Pozdnyakova D. D., Pilipenko V. A., Nose M., et al. Satellite and ground-based observations of Pc1 pulsations during a magnetic storm in March 2023 // Solnechno-Zemnaya Fizika. — 2025. — Vol. 11, no. 2. — P. 56–68. — https://doi.org/10.12737/szf-112202505. — (In Russian).
27. Savelyev I. V. Physics A General Course. Volume 1. Mechanics, Molecular Physics. — M. : Mir, 1979. — 439 p.
28. Time-Frequency Analysis / ed. by F. Hlawatsch and F. Auger. — London UK, Hoboken USA : John Wiley & Sons, 2013. — 472 p.
29. Yin Z.-F., Zhou X.-Z., Hu Z.-J., et al. Westward Excursion of Pc1/EMIC Waves and Their Source Protons: Paradoxical Observations From Ground and Space // Journal of Geophysical Research: Space Physics. — 2024. — Vol. 129, no. 5. — https://doi.org/10.1029/2023ja032317.




