Spatial variations of stochastic noise properties of GPS time series

Abstract:

The noise properties of the daily position time series of 568 GPS stations across North America have been investigated using solutions from two processing centers, namely the Pacific Northwest Geodetic Array (PANGA) and New Mexico Tech. (NMT). We demonstrate that at the low frequencies the power spectral density of the noise exhibit signs of flattening, a continuing increase following with a 1-over-frequency slope or even an increase of power that corresponds to random walk noise. Flattening of the power spectral density roughly halves the uncertainty of the estimated linear motion while random walk doubles it. Various noise models were used to describe this stochastic behaviour and we found that there is a pattern in their spatial distribution. Part of the GPS network is located in tectonically active areas and episodic tremors and slip need to be modelled to avoid that an incorrect trajectory model results in an increase of estimated random walk noise. The selection of the optimal noise model is based on which one has the highest log-likelihood value. Since long time series increase the differences in log-likelihood values between the various fitted noise models, only time series with an observation span of 10 years were used. Next, to reduce the probability of over selecting noise models with many parameters, we employ the Akaike and Bayesian Information Criteria. Finally, we find no obvious spatial correction between the type of monument and the uncertainties of the estimated Tectonic rate.