Analysis of the Earth’s Free Core Nutation Based on VLBI Observations Processing

R. M. Urunova, S. L. Kurdubov

Transactions of IAA RAS, issue 70, 50–55 (2024)

DOI: 10.32876/ApplAstron.70.50-55

Keywords: Free Core Nutation, Very Long Baseline Interferometry, earth orientation parameters

Abstract

The goal of this research is to study changes in the corrections to the coordinates of Earth’s celestial pole for the period 1979 to 2022, as obtained using VLBI observations. It is supposed that these changes can be described by an empirical model of the Earth’s free core nutation. The current model is based on a single frequency, which corresponds to a period of approximately –430 days, with variable phase and amplitude. The disadvantage of this model is that it predicts correction values only within a limited observation interval on which they were originally based. Therefore, the decision was made to develop a new empirical model that would allow predictions for any moment in time, regardless of the interval on which it was computed. The input data for this model consists of a series of corrections to the coordinates of the celestial pole obtained after secondary processing of VLBI observations using the QUASAR software package. During the research, spectral analysis was employed to extract the frequency characteristics of the changes in the celestial pole coordinates. Since the obtained time series of the corrections is uneven, the Lomba-Scargla periodogram was constructed for its analysis. The spectrum of the series obtained was compared with the spectrum of the uniform time series of the Earth Orientation Parameters (EOP) of finals, as provided by International Earth Rotation and Reference Systems Service (IERS). The spectral analysis of a uniform series included the construction of a Fourier spectrum, which can only be applied to a uniform series. To make the comparison of the spectra of the uniform and uneven series correct, the Lomb-Scargle periodogram was constructed, since it is applicable in both cases. We considered the spectra obtained as the spectrum of the beating that occurred when two harmonics were superimposed. To determine the frequencies and amplitudes of these harmonics, the linear least squares method was applied, and then the nonlinear least squares method was used to refine the calculated values. Next, we compared the resulting model with the generally accepted singlefrequency model having variable phase and amplitude. The Lambert model was used as such a model. As a result, we derived an empirical model of the Earth’s free core nutation, which includes a set of coefficients calculated based on the processed data. The harmonics obtained are described by periods of –422 and –441 days. This model can be utilized to correct predicted correction series for the coordinates of the celestial pole.

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