A total of 954 continuous GPS position time series from 414 individual sites in nine different GPS solutions were analyzed for noise content using maximum likelihood estimation (MLE). The lengths of the series varied from around 16 months to over 10 years. MLE was used to analyze the data in two ways. In the first analysis the noise was assumed to be white noise only, a combination of white noise plus flicker noise, or a combination of white noise plus random walk noise. For the second analysis the spectral index and amplitude of the power law noise were estimated simultaneously with the white noise. In solutions where the sites were globally distributed, the noise can be best described by a combination of white noise plus flicker noise. Both noise components show latitude dependence in their amplitudes (higher at equatorial sites) together with a bias to larger values in the Southern Hemisphere. In the regional solutions, where a spatially correlated (common mode) signal has been removed, the noise is significantly lower. The spectral index of the power law in regional solutions is more varied than in the global solutions and probably reflects a mixture of local effects. A significant reduction in noise can be seen since the first continuous GPS networks began recording in the early 1990s. A comparison of the noise amplitudes to the different monument types in the Southern California Integrated GPS Network suggests that the deep drill braced monument is preferred for maximum stability.

We analyze time series of daily positions estimated from data collected by 10 continuously monitoring Global Positioning System (GPS) sites in southern California during the 19‐month period between the June 28, 1992 (M_w=7.3), Landers and January 17, 1994 (M_w=6.7), Northridge earthquakes. Each time series exhibits a linear tectonic signal and significant colored noise. Spectral power at frequencies in the range 5 yr⁻¹to 0.5 d⁻¹is dominated by white noise or possibly fractal white noise and is several orders of magnitude higher than what would be expected from random walk noise (in this short‐period range) attributed by others to geodetic monument motions. Estimating a single slope for the time series' power spectra suggests fractal white noise processes with spectral indices of about 0.4. Site velocity uncertainties assuming this fractal white noise model are 2–4 times larger than uncertainties obtained assuming a purely white noise model. A combination white noise plus flicker noise (spectral index of 1) model also fits the data and suggests that the velocity uncertainties should be 3–6 times larger than for the white noise model. We cannot adequately distinguish between these two noise models, nor can we rule out the possibility of a random walk signal at the lowest frequencies; these questions await the analysis of longer time series. In any case, reducing the magnitude of low‐frequency colored noise is critical and appears to be best accomplished by building sites with deeply anchored and braced monuments. Otherwise, rate uncertainties estimated from continuous GPS measurements may not be improved significantly compared to those estimated from infrequent campaign‐mode measurements.

We use 2.5 to 14 years long position time series from >800 continuous Global Positioning System (GPS) stations to study vertical deformation rates in the Euro‐Mediterranean region. We estimate and remove common mode errors in position time series using a principal component analysis, obtaining a significant gain in the signal‐to‐noise ratio of the displacements data. Following the results of a maximum likelihood estimation analysis, which gives a mean spectral index ~ −0.7, we adopt a power law + white noise stochastic model in estimating the final vertical rates and find 95% of the velocities within ±2 mm/yr, with uncertainties from filtered time series ~40% smaller than from the unfiltered ones. We highlight the presence of statistically significant velocity gradients where the stations density is higher. We find undulations of the vertical velocity field at different spatial scales both in tectonically active regions, like eastern Alps, Apennines, and eastern Mediterranean, and in regions characterized by a low or negligible tectonic activity, like central Iberia and western Alps. A correlation between smooth vertical velocities and topographic features is apparent in many sectors of the study area. Glacial isostatic adjustment and weathering processes do not completely explain the measured rates, and a combination of active tectonics and deep‐seated geodynamic processes must be invoked. Excluding areas where localized processes are likely, or where subduction processes may be active, mantle dynamics is the most likely process, but regional mantle modeling is required for a better understanding.