Vestnik КRAUNC. Fiz.-Mat. Nauki. 2026. vol. 54. no. 2. P. 142 – 165. ISSN 2079-6641

PHYSICS
https://doi.org/10.26117/2079-6641-2026-54-2-142-165
Research Article
Full text in English
MSC 86A60, 62M10, 65C20

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Dedicated to the 85th anniversary of Professor P.P. Firstov

Evaluation of the Quality of Periodic Variation Extraction in Model Time Series Under Various Levels of Flicker Noise 1/f^{\alpha}

V.E. Glukhov¹²^{\ast}

¹Kamchatka Branch of the Geophysical Survey of the Russian Academy of Sciences, Piipa Blvd., 9, Petropavlovsk-Kamchatsky, 683006, Russia
²Vitus Bering Kamchatka State University, 4 Pogranichnaya str., Petropavlovsk-Kamchatsky, 683032, Russia

Abstract. A comparison of seven methods for extracting the seasonal component was performed on model data simulating tiltmeter observations in Kamchatka. The seasonal signal was a smoothed meander (period 365 days, duty cycle 0.6), and the noise was flicker noise with exponent \alpha = 2.9. The signal-to-noise ratio (SNR) was varied from –25 to +20 dB, with 30 realizations generated for each of the 12 SNR levels. Quality was assessed using RMSE, correlation, standard deviation ratio, and a developed residual periodicity metric. The mean seasonal function (MSF) method consistently outperformed all other methods across all metrics over the entire SNR range. GPR and FFT showed acceptable results but with limitations (GPR unstable under strong noise; FFT requires precise knowledge of the period). STL, SARIMA, SSA, and the Chebyshev filter are not recommended for standalone seasonal extraction due to systematic distortions or increasing error. For processing Kamchatka data, MSF is optimal. The conclusions are specific to the smoothed meander model, known period, absence of trend, and \alpha = 2.9.

Key words: seasonal component extraction; flicker noise; smoothed meander; tiltmeter observations; Kamchatka; comparison of decomposition methods; mean seasonal function; Chebyshev filter; residual periodicity metric.

Received: 18.05.2026; Revised: 23.06.2026; Accepted: 24.06.2026; First online: 14.09.2026

For citation. Glukhov V.E. Evaluation of the quality of periodic variation extraction in model time series under various levels of flicker noise 1/f^{\alpha}. Vestnik KRAUNC. Fiz.-mat. nauki. 2026, 54: 2, 142-165. EDN: FRTMHZ. https://doi.org/10.26117/2079-6641-2026-54-2-142-165.

Funding. This work used data obtained from the unique research facility “Seismoinfrasound Complex for Monitoring the Arctic Permafrost Zone and the Complex for Continuous Seismic Monitoring of the Russian Federation, Adjacent Territories, and the World” (https://ckp-rf.ru/usu/507436/). The work was funded within the framework of the state assignment of KamGU (Kamchatka State University) of the Ministry of Education and Science of the Russian Federation, Grant No. FSS-2025-0007.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. The author contributed to this article and is solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by the author.

^{\ast}Correspondence: E-mail: glukhov_v@emsd.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Glukhov V.E., 2026

© Institute of Cosmophysical Research and Radio Wave Propagation, 2026 (original layout, design, compilation)

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