Spatial Variations of Stochastic Noise Properties in GPS Time Series

The noise in position time series of 568 GPS (Global Position System) stations across North America with an observation span of ten years has been investigated using solutions from two processing centers, namely, the Pacific Northwest Geodetic Array (PANGA) and New Mexico Tech (NMT). It is well known that in the frequency domain, the noise exhibits a power-law behavior with a spectral index of around -1. By fitting various noise models to the observations and selecting the most likely one, we demonstrate that the spectral index in some regions flattens to zero at long periods while in other regions it is closer to -2. This has a significant impact on the estimated linear rate since flattening of the power spectral density roughly halves the uncertainty of the estimated tectonic rate while random walk doubles it. Our noise model selection is based on the highest log-likelihood value, and the Akaike and Bayesian Information Criteria to reduce the probability of over selecting noise models with many parameters. Finally, the noise in position time series also depends on the stability of the monument on which the GPS antenna is installed. We corroborate previous results that deep-drilled brace monuments produce smaller uncertainties than concrete piers. However, if at each site the optimal noise model is used, the differences become smaller due to the fact that many concrete piers are located in tectonic/seismic quiet areas. Thus, for the predicted performance of a new GPS network, not only the type of monument but also the noise properties of the region need to be taken into account.