The GPS position time series have been already shown to reliably describe the geophysical process which happen on or around the Earth’s crust. So far, these data were employed to analyze the Glacial Isostatic Adjustment (GIA, …), post-seismic relaxation (…) and vertical land motion at or near to tide gauges (…).
In all above-mentioned applications the long-term linear trend or a so-called velocity of permanent station has to be estimated with the greatest reliability, as its uncertainty may significantly bias the interpretations. Beyond the trend, the seasonal signatures are also characterizing the GPS position time series. The oscillations arise mainly from environmental loadings (van Dam et al., 2004; Klos et al., 2017) or from thermal expansion of monuments (Munekane, 2008) and these have a tropical period of 365.25 days. Another contributors to seasonal signatures are the artifacts of GPS solution which can be observed as peaks at the draconitic period of 351.
40 days (Amiri-Simkooei et al., 2016). Nowadays, both kinds of oscillations are found to be significant up to their 9th harmonic, meaning a period of few days (Bogusz and Klos, 2016). Lately, Amiri-Simkooei et al. (2016) found that oscillations of draconitic period are smaller of 1.8 times when the latest reprocessing are compared to the old ones. This decrease in amplitude arises mainly from the improvement in the latest models applied at the stage of GPS processing. The parameters of time series, we mentioned, constitute to deterministic or mathematical part of GPS position time series.
When it is modelled and removed, we obtain residuals which contain significant information about noise characterizing certain observations. So far, noises in the GPS position time series were found to follow the power-law noise described by the amplitude and spectral index. Spectral index of 0 means that residuals are a pure white noise uncorrelated in time. Spectral index of -1 is called flicker noise and arises from large-scale phenomena which affect the GPS position time series. It has been found to be preferred to model the residuals of the GPS position time series. Another type of noise, with spectral index of -2, is called random-walk noise and results from the instability of monuments. However, a number of processes may affect the stochastic part of data, leading to wrong conclusions.
As was shown by Williams et al. (2003), if series are too short, the residuals will be estimated to be characterized by pure white noise. Another issue are the offsets which when undetected will mimic a random-walk behavior (Williams, 2003). Moreover, the seasonal signatures, if not recognized properly, will be transferred to residuals and will move the character of preferred flicker noise to more correlated random-walk noise. These processes, affecting the estimates of noise, will cause the over- or under-estimation of uncertainty of velocity.
Lately, Klos et al. (2017) have presented the combined effect of seasonal signals and power-law noise on the estimates of velocity and its uncertainty. They concluded that as the time span of observations becomes longer, the seasonal signatures are less important and noise is what becomes more significant. Bos et al. (2013) found that noise in monthly tide gauge records is best characterized by random-walk process. They cross-compared their findings with the assumption of a pure white noise used so far and found that this wrongly assumed noise model leads to underestimation of velocity uncertainty of up to 2The Global Positioning System (GPS) position time series are characterized within this research to include the velocity term vx, seasonal signatures of nominal periods of 365.
25 days which is called a typical year and of 351.40 days which is called a draconitic year (Amiri-Simkooei et al., 2016). Both of them were modelled with their overtones as described by Bogusz and Klos (2016).Offsets were removed from series using the a priori information from International GNSS Service (IGS) offset file and log files of stations. All epochs of offsets were validated manually. Also, a manual detection of offsets was performed.
A number of 68 offsets was added to those included in the IGS offsets dataset, which were unreported before. For each of the detected offsets, the station position and velocity were estimated individually before and after the occurrence of the offset. In most cases the we tightly constrained the velocities in between offsets at a level of 0.
1mm/yr. Only when the a velocity discontinuity deemed essentially, say due to large earthquakes, we imposed the estimation of different velocity estimate before and after the occurrence if the offsets in the time series.