Statistical determination and analysis of the Euler pole parameters for NATRF2022

Estimation of Euler pole parameters (EPPs) is a critical step in developing NATRF2022, the upcoming realization of the North American (NA) terrestrial reference frame. These parameters characterize the tectonic motion of the NA plate relative to the ITRF2020/IGS20 reference frame. Improving the accuracy of EPPs reduces residual velocities within the plate, which in turn enhances the stability of geodetic coordinates and extends the validity period of the reference frame. The growing network of consistent, long-term continuously operating GNSS stations provides a robust and reliable source of velocity data for estimating EPPs. Currently, two methods are used for estimating EPPs: (1) solving the classic Euler’s pole theorem in inverse mode, based on the rigid plate assumption, and (2) modeling the deformation field of the tectonic plate to estimate parameters describing the net rotation of the deforming plate, consistent with the deforming plate hypothesis. Both methods are sensitive to the selection of GNSS stations, resulting in slight variations in the estimated EPPs. This sensitivity is further compounded for the NA tectonic plate due to the presence of non-secular and non-stationary deformation induced by glacial isostatic adjustment (GIA) across the plate, as well as the complex dynamics of the diffused boundary zone along its western margin. To address these challenges, a statistical algorithm based on the Maximum Likelihood Estimation (MLE) theory is proposed, offering unbiased parameter estimation for sufficiently large samples. The methodology begins with the selection of stations featuring stable monuments with at least three years of continuous time series. An adaptive grid comprising 50 to 100 cells is considered to ensure a homogeneous spatial distribution of the selected stations. Within each grid cell, one station is randomly selected with place back, and the EPPs are estimated using station velocities. This procedure is repeated many times following the Monte Carlo method to generate a large set of EPP estimates. Histograms of the estimated parameters are then formed to identify the underlying statistical distribution of the EPPs. Finally, the best values corresponding to the maximum likelihood probabilities are selected as the optimized EPPs. The resulting EPPs are then compared with those reported in previous studies, and the significance of the observed differences is evaluated in detail.