G.O. Kalygin1, L.A. Kalygina2

1,2 Vladimir State University n.a. A.G. and N.G. Stoletovs (Vladimir, Russia)
1 gkalygin@yandex.ru, 2 lkalygina60@mail.ru

A model for representing data from various geophysical fields is a description in the form of a polyharmonic series with known component frequencies, including the frequencies of solar-lunar gravitational tides. Estimating the parameters of such series is important for studying physical processes in the Earth's crust and near-surface layers of the atmosphere. The use of standard digital spectral analysis methods requires the use of long series, because The frequencies of the components of the series are generally not multiples of each other, the frequency spacing of the neighboring components is of the order of 10-3, the amplitudes of the components are modulated by lower frequency components. An urgent task is to estimate the parameters of a polyharmonic series over a time interval commensurate with the period of the components of the series in order to obtain the dependencies of the series parameters over time. The paper considers the application of the Fourier transform on a limited number of points to estimate the amplitude and initial phase of the components of a polyharmonic series with closely spaced frequencies.

Development of a methodology for estimating the parameters of a polyharmonic series with known frequencies and its application to obtain time dependences of the amplitude and initial phase of the main solar-lunar tides in variations of the vertical component of the Earth's electric field.

Expressions for the values of the amplitude and the initial phase of the sum of the harmonic components are obtained based on the results of calculating the partial sums of the Fourier transform. Estimates of the amplitudes and initial phases of the observational data of the vertical component of the Earth's electric field of the main solar-lunar tides are obtained. Linear changes in the initial phase in neighboring periods make it possible to solve the problem of detecting data of a given frequency. For the observation interval of the vertical component of the Earth's electric field of 1.5 years, the presence of tides S1, P1, S2 and K2, the amplitude modulation of the tide K2 frequency with a period of 1/4 year, was revealed.

The developed technique makes it possible to obtain the parameters of the components of a polyharmonic series with known closely spaced frequencies, and can be used to analyze observational data from various geophysical fields.

Kalygin G.O., Kalygina L.A. Determination of the parameters of a polyharmonic series with closely spaced frequencies. Dynamics of complex systems. 2025. V. 19. № 2. P. 50−56. DOI: 10.18127/j19997493-202502-07 (in Russian).

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