The velocities of the Global Positioning System (GPS) stations are widely employed for numerous geodynamical studies. The aim of this paper is to investigate the reliability of station velocities and to draw reader’s attention that for proper estimates of velocity, we need to consider the optimal character of noise. We focus on a set of 115 European GPS stations which contributed to the newest release of the International Terrestrial Reference Frame (ITRF), i.e. ITRF2014. Based on stacked Power Spectral Densities (PSDs), we show that amplitudes o f seasonal signals are significant for nine harmonics of tropical year (365.25 days) and two harmonics of draconitic year (351.60 days). The amplitudes of tropical annual signal fall between 0.1-8.4 mm and are much higher for vertical component than for horizontal. Draconitic annual signal reaches the maximum amplitudes of 1.2 and 0.9 mm for North and East, respectively, whereas is slightly higher for the Up component with a maximum of 3.1 mm. We performed a noise analysis with Maximum Like lihood Estimation (MLE) and found that stations in Central and Northern Europe are characterized by spectral index between flicker and random-walk noise, while stations in Southern and Western Europe: between white and flicker noise. Both amplitudes and spectral indices of power-law noise show a spatial correlation for Up component. We compared the uncertainties of velocities derived in this study with a combination of power-law and white noises to the ones offici ally released in the ITRF2014 with a pure white noise. A ratio of the two estimates is larger than 10 for 13 % and 30 % of stations in horizontal and vertical direction, respectively with medians of 6 and 7. The large differences support the fact that at the velocity determination the proper noise characteristic should be taken into account to avoid any mislead interpretation., Anna Klos and Janusz Bogusz., and Obsahuje bibliografické odkazy
We estimated the common seasonal signal (annual oscillation) included in the Global Positioning System (GPS) vertical position time series by using Multichannel Singular Spectrum Analysis (MSSA). We employed time series from 24 International GNSS Service (IGS) stations located in Europe which contributed to the newest ITRF 2014 (International Terrestrial Reference Frame). The MSSA method has an advantage over the traditional modelling of seasonal signals by the Least-Squares Estimation (LSE) and Singular Spectrum Analysis (SSA) approaches because it can extract time-varying and common seasonal oscillations for stations located in the considered area. Having estimated the annual curve with LSE, we may make a misfit of 3 mm when a peak-to-peak variations of seasonal si gnals are to be estimated due to the time-variability of seasonal signal. A variance of data modelled as annual signal with SSA and MSSA differs of 3 % at average what proves that the MSSA-curves contain only time-varying and common seasonal signal and leave the station-specific part, local phenomena and power-law noise intact. In contrast to MSSA, these effects are modelled by SSA. The differences in spectral indices of power-law noise between MSSA and LSE esti mated with Maximum Likelihood Estimation (MLE) are closer to zero than the ones between SSA and LSE, which means that MSSA curves do not contain site-specific noise as much as the SSA curves do., Marta Gruszczynska, Anna Klos, Severine Rosat and Janusz Bogusz., and Obsahuje bibliografické odkazy
The GRID_STRAIN software that runs under the MATLAB® environment helped us in achieving the continuous strain field model. Unfortunately, the program averages the results. Therefore, the authors’ main goal of this paper was to work out a method of good verification of data to avoid falsifying of the results of strain calculations. We decided to use the method of the Delaunay triangulation to build a set of triangles of the data (EPN and ASG-EUPOS stations as the vertexes) and by the use of the velocities of each point and their errors, to estimate the single strain in each triangle. This approach made it possible to exclude the outlying values from the data. Selection of the criteria of the characteristic of insufficiently stable points in order to remove them from further computations is of a great importance for the final results of computations of the deformation field. In such a tectonically stable region, as the area of Poland, the strain values should not be higher than 3 to 4 nanostrains/year. At the low rate of tectonic deformations observed in Poland, the disturbances resulting from insufficient stabilization of the ASG-EUPOS network influence the computations of the deformation field to a significant extent. Improper stabilization of a single permanent station causes unification of the deformation field within 2 to 3 computation triangles having a common vertex at this station. Based on this assumption, nearly 30 of the ASG-EUPOS stations were excluded from further strain calculations. The analysis of the geodynamic consistency of the deformation field for the computation triangles is basis for indicating stations for which the dislocation resulting from insufficient stabilization, significantly exceeds the dislocation resulting from the deformation of the lithosphere. Most of the ASG-EUPOS network stations may be used for analysis of local differentiation of the deformation field in Poland., The regularities of the deformations distribution determined by ASG-EUPOS network stations constitute a new set of data which will be used for further geodynamic interpretation. In case of lower rank disturbances resulting from destabilization of the network stations, this factor’s component cannot be recognized using qualitative analysis of the deformation field., Janusz Bogusz, Anna Klos, Mariusz Figurski, Marek Jarosinski and Bernard Kontny., and Obsahuje bibliografii
This paper presents the results of the application of wavelet decomposition to processing data from the GGP sites (The Global Geodynamics Project). The GGP is an international project within which the Earth's gravity field changes are recorded with high accuracy at a number of stations worldwide using superconducting gravimeters. Data with a 5-second sampling interval from Wettzell and Bad Homburg were used for the research. The wavelet transform enables the investigation of the temporal changes of the oscillation amplitudes or the decomposition of the time series for the analysis of the required frequencies. The wavelet decomposition was performed using the regular orthogonal symmetric Meyer wavelet. The research concerned data from an earthquake period recorded at various locations and a quiet period when the gravimeters worked without any disturbances. The decomposition was followed by the Fast Fourier Transform for signal frequency components and then by correlation analyses of corresponding frequency components (for periods from 10 to 60 000 seconds) for all sensor combinations, for the quiet and the earthquake periods separately. Frequency components defining long term changes for all sensor combinations, as well as combinations between two sensors at the same site for the quiet days are characterised by high correlation coefficients. For the time of the earthquake, the Wettzell site data proved strong correlation for all frequency components, while the Bad Homburg site data showed an unexpected decrease of correlation for the majority of frequency components. The authors also showed that wavelet decomposition can be a good method of data interpolation, especially from the time of earthquakes. Moreover, it is a very useful tool for filtering the data and removing the noises., Janusz Bogusz, Anna Klos and Wieslaw Kosek., and Obsahuje bibliografii