Temporal spectrum of spatial correlations between GNSS station position time series

The background noise in Global Navigation Satellite Systems (GNSS) station position time series is known to be both temporally and spatially correlated. Its temporal correlations are well modeled and routinely taken into account when deriving parameters of interest like station velocities. On the other hand, a general model of the spatial correlations in GNSS time series is lacking, and they are usually ignored, although their consideration could benefit several purposes such as offset detection, velocity estimation or spatial filtering. In order to improve the realism of current spatio-temporal correlation models, we investigate in this study how the spatial correlations of GNSS time series vary with the temporal frequency. A frequency-dependent measure of the spatial correlations is therefore introduced and applied to station position time series from the latest reprocessing campaign of the International GNSS Service (IGS), as well as to Precise Point Positioning time series provided by the Nevada Geodetic Laboratory (NGL). Different spatial correlation regimes are thus evidenced at different temporal frequencies. The different levels of spatial correlations between IGS and NGL datasets furthermore suggest that some part of the spatially correlated background noise in GNSS time series consists of GNSS errors rather than aperiodic Earth surface deformation signal.