Construction and analysis of mathematical models describing temporal variations of earth’s gravity field

Background. The study of temporal variations in the Earth’s gravity field is a pressing challenge in modern geophysics, particularly in the context of analyzing the impact of external and internal factors on the gravity force. Conventional approaches to modeling the gravity field are based on predefined theoretical assumptions, which limits their applicability under conditions of high variability of geodynamic processes.

Aim. To develop and test an innovative approach to constructing mathematical models of temporal gravity field variations, which employs empirical data and a phenomenological description of random processes rather than relies on predefined theoretical frameworks.

Materials and methods. The experimental part of the study was carried out at the Ledovo fundamental gravity station using a set of gravimeters of various types. Instrumental measurements of gravity variations were performed. The collected data were analyzed using spectral and statistical methods and Fourier transforms. Special attention was given to comparing readings recorded by different instruments. Additionally, an optimal linear smoothing procedure (OLSP) was applied to construct a generalized model of gravity field variations.

Results. The analysis revealed a high degree of consistency between measurements: the correlation coefficient between GNU-KV and CG-6 gravimeters exceeded 0.9, confirming the similarity of their spectral characteristics and the reliability of the recorded data. At the same time, the study showed that an unambiguous mathematical description of gravity variations is complicated by the influence of poorly understood geodynamic and random factors. The model based on OLSP enables the integration of elements from known theoretical models with consideration of “guest” processes, i.e., external and local factors of uncertain nature that affect the observed gravity variations.

Conclusion. The proposed model-free approach, along with the use of the optimal linear smoothing procedure, offers new possibilities for a more accurate and flexible description of temporal gravity field variations. The developed methodological approach may prove valuable in further geophysical research and in advancing methods for monitoring changes in the Earth’s gravity field.

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