Modeling of the Vertical Movements of the Earth’s Crust in Poland with the Co-Kriging Method Based on Various Sources of Data

Abstract

The main aim of this study was to evaluate the applicability of the co-kriging method for modeling the vertical movements of the Earth’s crust based on data acquired with the use of precision leveling techniques and measurements conducted by permanent Global Navigation Satellite System (GNSS) stations. Data were processed with the use of empirical, theoretical, and directional variograms (semivariograms), as well as variogram maps. Large-scale spatial variability was determined using polynomial regression. The relationships between the length of the semi-major and semi-minor axes vs. the root mean square (RMS) and the standard error of the estimate were analyzed. The relationships between the anisotropic direction and the number of lags were determined, and other parameters were calculated. Preliminary data fitting produced non-stationary surfaces. The leveling data were anisotropic, and the GNSS data were isotropic. Nugget effects were observed in both datasets, in particular in the GNSS data. The size of the ellipse was strongly correlated with the RMS and σ (average standard deviation of prediction). The anisotropy angle was determined using the number of lags. Co-kriging was found to not be a suitable method for modeling the vertical movements of the Earth’s crust based on data from various sources. The final result was strongly influenced by the initial dataset. The obtained results show how the method of combining data sets (interpolation, network adjustment) affected the final cartographic model.