Assessment of time-dependent noise in GPS position time series [electronic resource]
Keywords: Geophysics.

This thesis addresses an issue of assessing noise in GPS position time series. Noise, especially time-dependent kind, significantly affects parameters, inferred from the position time series. Some estimates of GPS velocity uncertainties are very low, less than 0.1 mm/yr with 10 years of data. Yet, residual velocities relative to rigid plate models in nominally stable plate interiors can be an order of magnitude larger. This discrepancy could be caused by underestimating low frequency time-dependent noise in position time series, such as random walk. We develop a method for determining representative noise parameters in GPS position time series, by analyzing an entire network simultaneously, that we refer to as the Network Noise Estimator (NNE). The position time series are decomposed into signal (plate rotation and glacial isostatic adjustment (GIA) for central-eastern US), and noise components. NNE simultaneously processes multiple stations with a Kalman filter, and solves for average noise components for the network by maximum likelihood estimation. Synthetic tests show that NNE correctly estimates even low-level random walk, thus providing better estimates of velocity uncertainties than conventional, single station methods. To test NNE on actual data, we analyze a heterogeneous 15 station GPS network from the central-eastern US, assuming the noise is a sum of random walk, flicker, and white noise. For the horizontal time series, NNE finds higher average random walk than the standard individual station based method, leading to velocity uncertainties a factor of 2 higher than traditional methods. Random walk, flicker noise and white noise all affect the uncertainties of velocity calculated from GPS position time series to a different extent. Since white noise is independent of time, it gets averaged over in longer time series. Flicker noise and random walk have higher power at longer periods, so they contribute more significantly to velocity uncertainty. We derive mathematical relationship between estimates of linear trends and noise, and we explore the relationship empirically. We set up the following experiment: for ten years of daily data we calculate velocity uncertainty for time series with typical amplitude of three components of noise. Then we fluctuate each noise value while keeping the two of the rest noise values fixed. We find that random walk's effect on the velocity uncertainty is very profound, flicker noise has a mild effect, and white noise changes barely affect the velocity uncertainty. This has very broad implication: a) if present, random walk completely dominates the velocity uncertainties, b) changes in flicker noise up to 25\% of the value do not affect the velocity uncertainty, c) unaccounted linear trends in the data can trade off with noise estimates, especially random walk. Finally, we apply the method to the real GPS position time-series in the central parts of North American plate. We study 58 stations separated into groups based on the types of monuments. We find that braced monuments have significantly less random walk that the non-braced stations. For braced stations, which are the gold-standard of permanent GPS stations for precise geophysical observations, we find random walk on the order of 0.5 mm/yr$^{0.5}$ and flicker noise just above 2 mm/yr$^{0.25}$ for horizontal time series and random walk on the order of 2 mm/yr$^{0.5}$ and flicker of 7-9 mm/yr$^{0.25}$ for vertical. These noise estimates lead to velocity uncertainties of 0.15-0.2 mm/yr and 0.6-0.8 mm/yr respectively for 10 years of daily position time series.