Application of geostatistical simulation to gravity field modeling and physical geodesy problems

The precise determination of the Earth's gravity field and geoid represents a fundamental challenge in physical geodesy, with direct implications for navigation, mapping, and geodynamic studies. Geostatistical simulation provides a rigorous methodological framework for addressing the spatial heterogeneity of gravimetric data and quantifying uncertainties associated with geodetic models. This study presents geostatistical applications in physical geodesy along three main axes: optimal interpolation of gravity anomalies through kriging and its variants, geostatistical simulation for probabilistic gravity anomalies modeling, and geodetic network optimization for geoid calculation. Geostatistical methods are distinguished by their ability to explicitly model spatial correlation through the variogram and rigorously quantify spatial uncertainty. Practical applications demonstrate effectiveness in integrating multi-source data with heterogeneous precision and resolution (terrestrial, airborne, and satellite measurements), propagating uncertainty in derived quantities, and optimizing the positioning of new gravimetric stations according to objective statistical criteria. Current challenges include processing very large datasets requiring high-performance algorithms and low-rank approximations, modeling anisotropy and non-stationarity of the gravity field, and extending to spatio-temporal approaches to capture temporal variations. Promising perspectives lie in hybridization with machine learning for automatic estimation of complex variograms while preserving the theoretical rigor of geostatistics, establishing this approach as an indispensable complement to classical methods in physical geodesy.

Keywords: gravity field, physical geodesy problems, geostatistical simulation, spatial interpolation, uncertainty quantification.