Modeling the geoid and polar motion in geological tim

The main objective of our research is to: 1) conduct a correlation analysis of the relationship between geoid heights and topographic heights in the modern era using calculated moving correlation coefficients (MCC); 2) extrapolate the obtained correlation model to past geological epochs and determine the paleogeoid using known surface heights derived from paleoDEM continental reconstruction models (Scotese and Wright, 2018); 3) perform calculations of changes in "True Polar Wander" (TPW) based on the obtained paleogeoid height data sets resulting from the movement of lithospheric plates. Methodology. To investigate the correlation between geoid heights and lithospheric surface heights, data for 1ºx1º trapezoids from the EGM2008 model, topographic heights from ETOPO1, and paleoDEM paleoreconstruction models were used. The center of the moving window was shifted by 1º in both latitude and longitude within grids of 3ºx3º and 9ºx9º, reflecting the global nature of the correlation and mitigating local variations. By extrapolating the modern correlation model to past geological epochs, we investigate the dynamic paleogeographic evolution and its impact on the geoid structure. To study the dynamics of changes in the Earth's lithospheric shape, paleogeoid heights, and pole position, the concept of approximating their surfaces with a semi-parameterized biaxial ellipsoid was used. Results. Based on the calculated MCC values, a map of the correlation between geoid heights and topographic heights for the modern era was constructed. We conducted a detailed correlation analysis for different epochs – 200, 400, and 540 million years ago, as well as for intervals from the modern era to 540 million years ago, in 5 million-year steps, using paleogeoid models. This analysis was used to hypothesize about the secular movement of the Earth's rotational poles and the associated dynamics of the lithosphere. Scientific Novelty. The modeling of paleogeoid heights was performed for further assessment of the Earth's pole displacement. We also discuss the impact of gravitational and rotational forces on the internal structure of the Earth, from the lithosphere to the inner core, suggesting cyclic geodynamic instability manifested as secular variations in the Earth's shape and gravitational field. Our conclusions indicate a subtle understanding of the relationship between tectonic activity and paleogeoid anomalies, suggesting minimal direct influence of lithospheric plate movements on geoid height changes, but significant indirect influence through mantle convection over geological time. Practical significance. This study not only provides deeper insight into the historical configuration of the Earth's geoid and continents but also enhances our understanding of the dynamic processes shaping the current and future geodynamic evolution of the planet.