Integration of Distributed Dense Polish GNSS Data for Monitoring the Low Deformation Rates of Earth’s Crust

Abstract

This research concerns the possibility of monitoring low deformation rates in tectonically stable regions using GPS/GNSS observations. The study was conducted in an area of Poland located in Central and Eastern Europe, where horizontal stress resulting from plate boundary forces in the N–S or NNE–SSW direction has been observed. This stress can translate into deformation of the Earth’s surface. The problem, however, is that it corresponds to strain rate magnitudes of much lower than 10 × 10⁻⁹ per year. This is not much higher than the figure determined using current GNSS observation capabilities. In this study, long-term observations from several GNSS networks were used. The result was a very dense but irregular velocity field. By carefully analyzing and filtering the data, it was possible to eliminate the impact of various errors, creating a more consistent velocity field. This article presents a final GNSS strain rate model for Poland and determines the impacts of the analysis methods on its variation. Regardless of the filtering method adopted, dominant compression rates in the N-S direction are evident. Moreover, this result is consistent despite the use of varying velocity. This shows that even in tectonically stable regions, strain rates can be monitored at 10⁻⁹ per year (below 3 × 10⁻⁹/year).

1. Introduction

With the development of Global Navigation Satellite System (GNSS) technology, more accurate geophysical models, and computational algorithms for use in data processing, it has become possible to detect displacements on the Earth’s surface with single-millimeter accuracy. This allows researchers to study the deformation of the Earth’s crust. Today, thanks to extensive and dense networks of reference stations that provide long-term observations from GNSS, displacement velocities are determined at the required level for kinematic studies [1] of 0.1 mm/year. Such studies are carried out locally in almost all regions of the world, from Antarctica [2,3] to Greenland [4]. With broad access and increased computing capabilities, they are also used on a global scale, as demonstrated by the Global Strain Rate Model [5,6]. GNSS observations play a particularly large role in areas of tectonic activity [7,8,9] due to correlated seismicity [10,11,12,13], which can aid earthquake and tsunami warning systems [14]. Increasingly, using GNSS observations, deformations are studied in regions that are tectonically active [15] but generally considered stable, where tectonic activity and other geodynamic movements do not lead to research in this direction as they are not strongly felt by the public. In Masson’s work [16], based on two decades of GPS observations, the authors were able to extract a first-order tectonic signal over France. They used combined filtering and smoothing methods. The paper [16] found that for detecting small deformations, it is crucial for stations to have adequate spatial resolution so that outlier stations can be excluded.

The current study covered such an area—a region of Poland located in Central and Eastern Europe. It is a region that is practically cut in half by the Teisseyre–Tornquist Zone, which has a NW–SE orientation and separates the East European platform from the West Eurasian platform. In the south, one can also distinguish the Carpathian orogen and the Lower Silesian block with the Sudeten Mountain [17,18] (Figure 1).

One of the first nationwide deformation studies was conducted by a team from the Warsaw University of Technology and the Polish National Geological Institute [19]. However, this study covered only a few locations in Poland and did not give an accurate image of deformation in the region. However, it provided a basis for further work. Following this, a number of geodynamic works were conducted in the Sudeten Mountain area, which is potentially the area with the highest tectonic activity in the region [20,21,22,23]. However, these studies covered a small region. In subsequent years, with the development of observation infrastructure, work was carried out to develop a denser field of horizontal velocities [24,25]. For this purpose, slightly more than 3 years of observations from the first nationwide ASG-EUPOS network were used [26,27], which were managed by the Polish mapping agency—Head Office of Geodesy and Cartography. Further research introduced the first GPS strain rate model for Poland [28], in which the compression rate generally agreed with current knowledge. However, there were discrepancies in the work that resulted from both insufficient filtering of the input data and the use of a segmented method. The authors of [29] show that different methods of determining deformations can give different results. For small areas and a relatively small number of measurement points, good results are obtained using the segmented method. Examples of this include studies of active faults in northern Greece [30] and of the phenomenon of active extension in the Apennines in Italy [31]. However, this method is not suitable for larger areas and larger datasets, as the model does not maintain continuity due to measurement errors. Data filtering is needed here, as confirmed by [32], where the problem of modeling surface deformation in an area of Poland was revisited. This work shows that, especially in the case of stable regions, it is necessary to filter the data so that the resulting model of surface deformation rates maintains adequate continuity and consistency. However, even with proper filtering, the segmented method did not yield satisfactory results. Much better results were obtained using collocation least squares methods [33], which are increasingly popular for studies of large areas and with large amounts of scattered and irregularly distributed data. These methods are especially used for the interpolation of gravity data [34,35], vertical movements [36,37] and, finally, horizontal deformations [29,31,33,38]. There are other methods for carrying out continuous velocity field or strain rate preparation. They are based on various interpolation models, such as statistical methods [39], kriging [25,40], or spline functions [41,42]. In [32], after applying the collocation method, the first deformation model to be consistent with stress measurements was obtained for an area of Poland. Another study on the current tectonics of Poland, where GNSS data were used [43], concerned the most stable part of the region. As noted by the authors, although the magnitude reached the confidence level, the obtained GPS strain rates showed a high correlation with seismological and deep borehole data.

Recent studies in the region [32,43] were based on data from the ASG–EUPOS network that, after appropriate filtering, were reduced to about 50 points for the whole country, giving an average density of 1 point per 6500 km². However, the work [32] indicated that even for such a small amount of data, satisfactory results could be achieved. This has led to further research in this direction, as GNSS data have shown great promise for studying neotectonics in Poland, especially since the availability of new data has increased significantly over the years. The purpose of the present study was to develop a new strain rate model for the abovementioned area of Poland based on a larger dataset in order to verify previously obtained results. The research included reprocessing archival GPS observations, analyzing time series data, and estimating station velocities. In the next stages, the spatial consistency of the velocities was checked. Based on the prepared datasets, several variants of the strain rate model were prepared and compared with previous results and the crustal stress directions.

2. Polish GNSS Data Research Infrastructure Center

Poland’s GNSS observation infrastructure (which comprises permanent stations) is spread among scientific, government and private institutions. Before starting our analyses, it was crucial to organize and consolidate the data in one place. All observations were collected from the Polish GNSS Data Research Infrastructure Center (CIBDG) [44], whose purpose is to secure and organize GNSS data and disseminate them to Earth Sciences researchers and others. It was created as part of the implementation of the Polish infrastructure under the international European Plate Observing System program [45], under which national [46,47,48] and European services [49] are being developed. CIBDG was launched in 2022, and is accessed through the services [50] of the Military University of Technology (Warsaw, Poland), hereafter referred to as MUT. CIBDG has archived nearly 3.5 million daily observation files from Polish refereed stations, which have been checked for quality and quantity. For this study, all available GPS observations from 2 June 2008 (when the first Polish ASG-EUPOS network was launched) to the end of 31 December 2021 (GPS weeks 1482_1 to 2186_2) were used. The study included a total of 537 reference stations (Figure 2) belonging to the European EUREF Permanent GNSS Network (50) and local networks (ASG-EUPOS (97), HxGN SmartNet Poland (172), TPI NETpro (123), and VRSnet.pl (83)) as well as other and foreign stations associated with them (12).

2.1. GNSS Data Analysis

To estimate the changes in station positions, GPS observations were used. As the observation period was long and the International GNSS Service (IGS) models changed during the campaign, the study used slightly different computational strategies in the two periods for the release of IGS08 [51] and IGS14 [52]. From 2 June 2008 to 28 January 2017 (GPS weeks: 1482–1933), the models used were consistent with those used by MUT in the EPN-repro2 campaign [53]. After the introduction of IGS14 (GPS weeks: 1934–2186), the antenna models and orbits were changed accordingly. For ground antennas, the EUREF Permanent GNSS Network (EPN) guidelines were applied [54], according to which wherever individual calibrations are available, they should be used instead of IGS-type mean models. Accordingly, for the EPN stations (which, in selected cases (see Figure 1), were the reference stations), the same modeling was used, from which the reference coordinates were calculated. As indicated by [53], the different modeling of the antenna phase center has little effect on the realization of the reference; however, given the purpose of the work, which is to detect a small strain rate, it was decided to directly minimize all potential errors, as well as the distribution of the reference stations, which, as shown in [55], can result in differences in the estimated strain values of about 1 × 10⁻⁹/year in Poland. The use of antennas mounted on ASG-EUPOS stations for which individual calibrations were available was also prioritized. For all others, IGS08- or, at a later stage, IGS14-type mean models were used. The entire processing procedure was performed in daily sessions in cluster mode using Gamit/Globk software [56]. A total of 16 clusters (subnetworks) were created based on Voronoi cells constructed at selected Polish EPN stations. In addition, each subnetwork also contained five stations that belonged to neighboring subnetworks. The list of models used in the analysis was the same as that used by MUT in operational analysis, e.g., in a study of long-term changes in GNSS-derived precipitable water over Poland [57], and is shown in

Table 1. Summary of the processing parameters.

Group	Parameter Notes
Software	GAMIT
Observations	GPS, ionosphere-free code and phase combination
Orbits	IGS08 *, IGS14
Antenna models	transmitters: IGS08 *, IGS14 receivers: individual calibrations for ASG-EUPOS and selected EPN stations; IGS08 *, IGS14 for the rest
Clocks	Estimated
Ionosphere	“iono-free” + higher order
Troposphere	VMF1 as an a priori, 1 h ZTD estimated and 24 h gradient
Tidal displacement	IERS2010, FES2004
Reference frame	ITRF2014 through 25 EPN stations

* For the period from 2 June 2008 to 28 January 2017. VMF1: Vienna Mapping Function; ZTD: zenith total delay.

.

Based on the daily solutions, a cumulative solution was prepared. Reference was made to 25 stations of the EPN network (Figure 2) with estimations of translation, rotation, and scale parameters. The received time series data of coordinate changes were analyzed, as discussed in the next section.

2.2. GNSS Velocity Estimation

Depending on the network, the length of the observation session for each station varies significantly and ranges from 1 year to 13 years. The longest time series occur at stations of the ASG-EUPOS network, which was launched in 2008. The next group of stations are those belonging to the HxGN SmartNet Poland and TPI NETpro networks, launched in 2012 and 2013, respectively. The remaining stations have shorter observation sessions due to their shorter operation or data availability in CIBDG. The analyzed time series are, therefore, not homogeneous in length, nor do they cover the same period. Five different time series variants were analyzed, as shown in

Table 2. List of analyzed time series.

Variant	Time Span	Number of Stations	Description
A1	June 2008–December 2021	440	Full period, at least 3 years
A2	January 2014–December 2021	424	Common period, at least 3 years
A3	January 2014–December 2021	344	Common period, at least 5 years
A4	January 2014–December 2021	159	Common period, at least 6.5 years
A5	January 2014–December 2021	392	Common period, at least 3 years, igs14

.

The first variant (A1) covered the entire observation period. Several variants (A2, A3, A4) were then limited to the common period for all three nationwide networks. Only those stations whose observed period exceeded 3 years were considered in the analysis. This was a sufficient period to reliably model and remove the annual signal [58], and, thus, the linear velocity was reliably determined. However, as other work shows, longer time series of at least 4.5 years [59], or even 6 years [59,60], are needed to model small displacements. For this reason, we verified how velocities differ between the variants. Analysis of the time series and determination of velocity were carried out for topocentric coordinates (North, East, and Up) using the least squares method. The time series model is presented in Equation (1).

$$\mathrm{x}\left(\mathrm{t}\right)=x_0+v_x·t+O_A·\sin \left({\omega }_A·t+{\varphi }_A\right)+O_{SA}·\sin \left({\omega }_{SA}·t+{\varphi }_{SA}\right)+{\displaystyle \sum }_{j=1}^m{H}_j·x_j^{off}+{\epsilon }_x\left(t\right)$$

(1)

During the analysis of the time series, the linear trend/velocity ($v_x$) and seasonal fluctuations with annual ($O_A$) and semi-annual ($O_{SA}$) periods were estimated. The process was conducted iteratively, with the removal of outliers (3σ) and low-precision observations (σ > 50 mm). Shifts resulting from hardware changes (${\displaystyle \sum }_{j=1}^m{H}_j·x_j^{off}$) were estimated during the analyses. These shifts were modeled whenever there were equipment changes and other indications of possible spikes (determined through information from site logs and interviews with providers). The effects of improper shift modeling were described in [59], where they showed that this could translate to horizontal velocity bias of about 0.2 mm/year. A time-correlated noise model was used to estimate velocity uncertainties [61,62]. The analysis showed that the velocity discrepancies between the A1 and A5 variants were the largest. The observation period was different in these variants, confirming that the stations do not show linear movement. According to Serpelloni’s work [60], the best variant should be A4, but the number of stations is limited to stations of the ASG-EUPOS network and the EPN network. With this variant, the spatial resolution was not higher than in earlier studies. Thus, this option was rejected as it was not relevant to the main point of the study. For this reason, a time series from the entire period (variant A1) was selected to ensure the longest possible series of ASG-EUPOS stations. This is in line with previous works [59,60], where it was indicated that longer time series should be taken for precise deformation analysis. Finally, 390 stations were used in the analysis, whose velocity uncertainties were estimated to range from 0.03 to 0.28 mm/year for the horizontal component. The mean time series length was 7.9 years (Figure 3). More than 90% of the stations had series longer than 4.5 years. A few stations with shorter periods were left to provide better spatial resolution for further analysis. Finally, the ITRF2014 model [63] was adopted to reduce the plate’s movement. Therefore, the final image (Figure 3) shows slight rotational movement of the region toward the west.

3. Strain Rates

Based on the obtained velocities, surface strain rate maps were prepared. The method used to estimate surface strain rates for the selected area of Poland was based on the least-squares algorithm presented in [64]. In this method, strain rates are interpolated from a discrete distribution of data points. The method inverts the deformation by keeping the continuity of the model for the entire area. For each station, inversion was performed via the least squares method using the velocities and their covariances. From this, six parameters were determined: velocities ($U_x$, $U_y$), rotation rate ($\omega$), and components of the strain rate tensor (${\epsilon }_{xx}$, ${\epsilon }_{yy}$, ${\epsilon }_{xy}$). The algorithm shown in Equation (2) estimates the deformation at any point (R).

$$\left[\begin{array}{c}{V}_{x1}\\ V_{y1}\\ V_{x2}\\ V_{y2}\\ \cdots \\ V_{xn}\\ V_{yn}\end{array}\right]=\left[\begin{array}{cccccc}1& 0& {\mathsf{\Delta }}_{y1}& {\mathsf{\Delta }}_{x1}& {\mathsf{\Delta }}_{y1}& 0\\ 0& 1& -{\mathsf{\Delta }}_{x1}& 0& {\mathsf{\Delta }}_{x1}& {\mathsf{\Delta }}_{y1}\\ 1& 0& {\mathsf{\Delta }}_{y2}& {\mathsf{\Delta }}_{x2}& {\mathsf{\Delta }}_{y2}& 0\\ 0& 1& -{\mathsf{\Delta }}_{x2}& 0& {\mathsf{\Delta }}_{x2}& {\mathsf{\Delta }}_{y2}\\ \cdots & \cdots & \cdots & \dots & \cdots & \cdots \\ 1& 0& {\mathsf{\Delta }}_{yn}& {\mathsf{\Delta }}_{xn}& {\mathsf{\Delta }}_{yn}& 0\\ 0& 1& -{\mathsf{\Delta }}_{xn}& 0& {\mathsf{\Delta }}_{xn}& {\mathsf{\Delta }}_{yn}\end{array}\right]\left[\begin{array}{c}{U}_x\\ U_y\\ \omega \\ {\epsilon }_{xx}\\ {\epsilon }_{xy}\\ {\epsilon }_{yy}\end{array}\right]+\left[\epsilon \right]$$

(2)

where $V_{xn}$ and $V_{yn}$ are the components of velocity at successive stations. Coordinate increments between R and the nth station are denoted as ${\Delta }_{xn}$ and ${\Delta }_{yn}$. This implies a minimum number of stations of three (with different locations) so that the strain rate can be determined. By solving the model $\mathit{m}={\left(A^T{C}^{-1}A\right)}^{-1}{A}^T{C}^{-1}d$, information about the mean strain rate in the analyzed area was obtained. The model also takes into account the velocity covariance matrix (C), which was originally a diagonal matrix. The applied method uses reconstruction of the covariance matrix $C_i=C_i{G}_i^{-1}$ to include a Gaussian weighting function ($G_i$), which depends on the distance ($L_i$) and spatial resolution ($Z_i$) of the data under analysis, as presented in Equation (3).

$$G_i=L_i\times Z_i$$

(3)

$L_i=exp\left(-\Delta R_i^2/D^2\right)$ is used as the distance weighting function, where ∆R is the distance of consecutive points and D is the smoothing parameter. It defines the size of the interpolated area by reducing the weights of the distant data. This function reduces the weight of the velocity of stations that are more distant from the analyzed point. The higher the value of L, the smoother the model (Figure 3). This can be fixed-defined or estimated through an iterative process [64]. Based on the estimated strains in the coordinate system, the principal strains (${\epsilon }_1,{\epsilon }_2$) and the direction ($\theta$) of maximum strain were calculated using the formula presented in Equation (4).

$${\epsilon }_1,{\epsilon }_2=\frac{{\epsilon }_x+{\epsilon }_y}{2}\pm \frac{1}{2}\sqrt{{\left({\epsilon }_{xx}-{\epsilon }_{yy}\right)}^2+4·{\epsilon }_{zy}^2}, tan2\theta =\frac{2{\epsilon }_{xy}}{{\epsilon }_{xx}-{\epsilon }_{yy}}$$

(4)

The dilatation (volumetric strain), which is the first invariant of the strain tensor, and shear strain were also calculated (see Equation (5)).

$${\epsilon }_{dilation}={\epsilon }_{xx}+{\epsilon }_{yy}; {\epsilon }_{max shear strain}=\sqrt{{\epsilon }_{xy}^2+{\left({\epsilon }_{xx}-{\epsilon }_{yy}\right)}^2/4}$$

(5)

These are helpful in interpreting the observed. The positive dilatation represents expansive deformation (red), while the negative dilatation represents contractive deformation (blue).

As shown in Figure 4, smoothing of the model can be achieved by increasing the value of the distance weighting function. According to [39], in the method we used, it is difficult to objectively determine the optimal value of the smoothing factor. Analyses on the impact of correlation length were also conducted in [65], where the authors proposed a modified LSC algorithm to better interpolate data across different tectonic plates. A correlation length of 150 km was adopted in previous solutions for northern Poland [43], where it corresponded to the mean density of the points and generally did not exceed the size of the tectonic blocks. In this case, it can be seen that depending on the distance weighting function, the picture of the strain rate varies. With L = 50 km, one can see large disturbances in the deformation field, where, locally, deformations exceed 20 × 10⁻⁹/year. However, starting at 100 km, disturbances are present only at the edge of the area, and the mean values are about 3 × 10⁻⁹/year to 5 × 10⁻⁹/year. For the weighting threshold set as W_t = 24 (see [64] for details), the value of the distance weighting function varies from 46 km to 109km, depending on the local density of points. The mean value is 61.9 km, so with the optimal correlation length, the image is close to that depicted in Figure 4a (the result is shown in greater detail in Figure 5a).

Previous work [32] has shown that in the studied region, the strain image based on GNSS measurements is heavily distorted by the measurement errors that occur. This can be seen in Figure 4a. Therefore, it is necessary to filter out station movements that should be treated as erroneous. Today, the problem of input data filtering for velocity and strain modeling is being addressed with increasing frequency, as evidenced by [66], where the method used made it possible to identify outlier stations in the Apennine Terrane region.

For the purposes of the present study, spatial changes in strain rate were assumed to be small and continuous. Consequently, velocity differences between neighboring and nearby stations should be small, and any deviation from this was treated as an indicator that individual stations exhibit anomalous movements, including those caused by local conditions (subsidence, mass movements, fluctuations in hydrology, or building movements) or measurement and velocity estimation errors. Therefore, we used two methods to identify outlier stations.

3.1. Distance-Based Data Filtration (DBF)

The first approach compared the velocity of stations with the mean velocity from a given area. The area was defined by the radius of the circle (r), which was changed from 50 km to 300 km with a step of 50 km. No weights were assumed for distance when calculating mean movements. The same procedure was followed for each r. Based on the obtained deviations, stations exceeding the 97th percentile were excluded. Regardless of the adopted r, the list of excluded stations in the first iteration was practically the same, and included stations with outliers of about 1 mm/year. With a mean distance of 30 km between stations, velocity differences of 1 mm/year correspond to a strain rate of 30 × 10⁻⁹/year, which is practically 10 times the expected strain [28,32]. The procedure continued for the reduced dataset. Twenty-five iterations were carried out in this way, eliminating a total of 266 stations. In the rest of this article, the resulting datasets are denoted as DBF_r-i, where r is the radius used and i is the iteration number.

This work involved a number of calculations for a number of prepared station velocity sets. Using DBF filtering of the data in one iteration, the models showed no significant differences regardless of the radius used. After excluding 130 stations (15th iteration), the models were also generally consistent in terms of strain rate direction. The number of excluded points was generally similar. All models showed a dominant NNW–SSW compression rate direction with slight deviations in individual regions. Therefore, further analysis was based on solutions for r = 100 km. Solutions based on a radius of 50 km in later iterations did not give satisfactory results due to a reduction in the spatial resolution of the dataset, so with a small r, there were not enough data. Figure 5 shows the models for raw data and after 5, 15, AND 25 iterations. In all cases, the correlation lengths were estimated based on the current data distribution and were 61.9 km, 63.3 km, 83.2 km, and 110.8 km, respectively.

The DBF_100-15 model, shown in Figure 5c, shows a similar, though not identical, direction pattern of the main deformation rates to the model developed for the raw data, with a distance weighting function of 100 km (Figure 4d). However, differences can be seen at the boundary of the area, where without filtering of the data, spurious higher strain values appeared. It is important to note the deformation image for the 25th iteration, where stations in the northern part of the country were excluded from the dataset and the size of deformation on the craton decreased significantly. However, the NNE-SSW compression rate direction, which is dominant for the entire region, was preserved (Figure 5d and Figure 6b).

3.2. Strain Pattern-Based Data Filtration (SBF)

The second method was based on comparing the reference strains resulting from the displacement of the central station with the strains estimated for triangles constructed on surrounding stations. This method was previously presented in [32] and made it possible to obtain an image of deformations corresponding to the directions of principal stresses. As the number of stations increased and the distribution of stations was not uniform, the shapes of the triangles formed were very different. In many cases, this was not optimal, for example, due to the very short, and, at the same time, very long triangular edges. Only one station was selected from the group of stations within a 5 km radius. The time series length and the velocity estimation error were taken as a criteria for selecting the station. Based on these criteria, 89 stations were excluded. Next, a triangle mesh was created for this set, and the strain rate was calculated for each segment.

For each station, the strain rate was analyzed according to the procedure described in [32]. Based on the strain distribution, we verified whether the station exhibited self-motion. As the segment method is sensitive to the shapes of the segments, the value of the determined strain was normalized. The normalization process used the ratio factor of the area of the incircle on a triangle to the area of the triangle. As a maximum value, the value for an equilateral triangle was taken. Thanks to the normalization step, the influence of overestimated strains caused by the unfavorable triangle shape was reduced. For each distribution, a sine function was fitted, whose amplitude and fitting error were determined.

In the first iteration, stations whose amplitude exceeded 30 × 10⁻⁹ /year and whose fit error was less than this were excluded. This group included, among others, the BEL1 and RUDN stations (Figure 7), whose self-motion resulted in deformations corresponding to A = 34.8 × 10⁻⁹/year and A = 32.5 × 10⁻⁹/year, respectively. Both stations are located in a region of mining exploitation: BEL1 is located close to an open-pit lignite mine, and RUDN close to a copper mine and a mining waste disposal reservoir. This location explains the different movements of the stations. After excluding the critical stations, a new triangle mesh was created and the procedure was repeated, with the threshold amplitude value reduced by 1.5 × 10⁻⁹/year. After each iteration, each previously excluded station was checked again to verify that its classification as an outlier was not caused by the movement of a neighboring station. The datasets were prepared and used in this way to prepare the strain rate models. For example, for iterations 15 and 25, which are shown in Figure 8 and Figure 9, the correlation lengths were estimated based on the velocity distribution and were 90.5 km and 102.1 km, respectively.

4. Discussion

The prepared strain rate models show a characteristic small rate of shortening in the NNE-SSW direction, which is in line with the general stress direction of the World Stress Model [67] in the investigated region. A quite different image appears in [68], where irregular and alternating areas of contraction and dilation were obtained over the selected area of Poland. Various solutions [69,70,71,72] covering this area were used in [68]. These included observations from different sources, e.g., ASG-EUPOS and/or SmartNet-Poland. Their work also used data filtering, which included analysis of the velocity uncertainty and consistency analysis of neighboring stations, which can generally be compared to the DBF method used in this paper. As a result of filtration, only a few stations were removed from their study area, and, thus, the strain rate image did not resemble what was obtained in the work presented here. In Figure 5a,b, where the number of rejected stations was smaller, one can see areas of positive and negative strain rates that are similar to those in [68].

The final models vary depending on the chosen method and the number of iterations, which is particularly noticeable at the edges of the models. In the present study, in the initial phases of filtering, both methods gave similar results, while for later iterations, the list of stations became progressively different (for example, the 25th iteration in Figure 10). Only about 50% of each dataset that resulted from the two methods (Figure 10a,b) is common (Figure 10c).

Each method is based on a different approach. In the DBF method, the analysis is carried out over a fixed area, regardless of the density in each set/iteration. In the SBF method, the area changes and is limited to neighboring stations (usually 5 to 7). The SBF method has particular limitations at the area boundaries, where the stations cannot be reliably validated due to the lack of foreign stations. For reliable deformation modeling using this method, it would be necessary to include foreign stations within a range of about 100 km around the analyzed area. This corresponds to about two or three rows of stations of similar density, to be verified in several iterations. The model based on the SBF method also shows a higher number of regional distortions (Figure 8 and Figure 9). This is especially true for areas where more than one station shows outlier movement. These stations remain in the dataset. Averaging velocities from a larger area, as in the DBF method, categorizes such stations as outliers. Using a radius of 100 km (or more) in the DBF method makes the model smoother, which is reasonable for modeling a stable part of Poland (northeast), but inadequate for modeling more active regions (Sudetes). Different filtering approaches show that the image can be quite different in this region (Figure 11).

Recent studies on tectonic stress in the Sudeten area show the great complexity of structures and the different max stress orientations, from NNW–SSE to NE-SW to NW–SE [73], which can affect the movement of the area and the possibility of detecting this movement. This is also confirmed by previous work that uses continuous and periodic GNSS observations in the area [20,21,22,23], where it is shown that the individual Sudeten and Moravian-Silesian blocks are influenced by the active dynamics of Alpine and West Carpathian structures. The directions of the dominant shortening rate obtained in this study coincide with those presented in [73]. This is especially true for the dominant NE-SW direction, seen in northern Bohemia, which was obtained using the DBF method (Figure 11e,f). A more detailed comparative analysis is not possible due to the sparsity of data in this region. It is necessary to expand infrastructure in this region, where the location of stations will be determined by the tectonic structure of the region, allowing for more effective planning in the future.

For stations that have been validated using both methods (Appendix A 

Table A1. The station velocities and their sigmas that have passed both tests.

Station	Longitude	Latitude	vE	vN	sVE	sVN
	[Degree]		[mm/Year]
0014	14.33130	51.73680	−0.22	+0.29	0.04	0.02
BOGO	21.03530	52.47590	−0.65	+0.03	0.06	0.03
BPDL	23.12740	52.03530	−0.36	+0.06	0.05	0.06
BYTO	17.48810	54.15720	−0.59	−0.44	0.11	0.16
CFRM	18.35320	49.68480	−0.01	+0.37	0.03	0.04
CHOJ	17.55240	53.69520	−0.61	−0.33	0.04	0.04
DABI	23.34530	53.65660	−0.84	−0.11	0.07	0.08
DZIA	20.16740	53.23030	−0.65	+0.07	0.08	0.05
GARW	21.61200	51.89810	−0.49	−0.10	0.06	0.04
GDPG	18.61630	54.37150	−0.71	−0.32	0.08	0.05
GOL2	14.98200	53.82610	−0.35	−0.26	0.12	0.06
GOPE	14.78560	49.91370	+0.02	+0.05	0.05	0.05
GRAJ	22.45230	53.65100	−0.76	−0.09	0.04	0.06
GRAN	16.53140	52.21600	−0.55	+0.12	0.05	0.12
GUBI	14.73860	51.94600	−0.45	+0.20	0.04	0.12
JAKU	15.43330	50.81710	−0.18	+0.45	0.04	0.08
KALI	18.09520	51.75390	−0.25	+0.21	0.03	0.02
KAM1	14.77740	53.96310	−0.50	−0.27	0.03	0.04
KEDZ	18.33080	50.37450	−0.12	+0.30	0.07	0.06
KEPN	17.98360	51.28020	−0.32	+0.40	0.05	0.05
KLCE	20.62970	50.87580	−0.39	+0.27	0.03	0.03
KLOB	18.93690	50.90550	−0.14	+0.31	0.04	0.11
KONI	18.25400	52.22810	−0.27	+0.03	0.07	0.04
KRSN	22.17570	50.95990	−0.43	+0.17	0.04	0.04
KUTN	19.37500	52.22600	−0.35	−0.02	0.06	0.12
LACK	19.60970	52.46600	−0.46	−0.07	0.05	0.05
LAZY	18.89260	49.82300	−0.09	+0.50	0.04	0.03
LBNC	18.75280	50.71390	−0.21	+0.33	0.05	0.08
LESZ	16.57850	51.84040	−0.35	−0.08	0.06	0.06
LOMA	22.06230	53.17980	−0.62	−0.12	0.06	0.06
LUBL	22.55470	51.25090	−0.56	+0.17	0.04	0.04
NAMY	17.74250	51.07480	−0.11	+0.28	0.04	0.04
NIDZ	20.41760	53.36380	−0.59	−0.08	0.06	0.05
NTML	16.11800	52.32080	−0.29	+0.11	0.07	0.05
OPLU	21.97590	51.14930	−0.47	+0.20	0.03	0.04
PISC	23.36700	51.97630	−0.57	+0.11	0.06	0.04
POLA	16.68400	54.12080	−0.48	−0.50	0.12	0.04
PPIL	16.73830	53.15700	−0.54	−0.26	0.04	0.07
RADM	21.16380	51.39140	−0.46	+0.25	0.08	0.08
RYKI	21.92720	51.62450	−0.58	+0.11	0.11	0.04
RZEC	17.11240	53.75640	−0.58	−0.27	0.08	0.07
SANO	22.20080	49.55980	−0.25	+0.20	0.09	0.05
SIDZ	18.71760	51.57300	−0.22	+0.07	0.08	0.06
SIED	22.29420	52.15740	−0.48	+0.00	0.07	0.03
SIEM	22.86270	52.42400	−0.40	+0.07	0.16	0.08
SKCE	20.14130	51.95500	−0.54	−0.07	0.04	0.04
SKSK	21.57090	49.30820	−0.05	+0.29	0.08	0.06
STRO	20.50530	52.51860	−0.65	−0.19	0.06	0.06
SWKI	22.92820	54.09860	−0.96	−0.13	0.07	0.13
SYOW	17.74790	51.30480	−0.36	+0.26	0.05	0.07
SZAM	16.57210	52.61980	−0.61	−0.02	0.07	0.14
TKRN	17.68370	50.09170	−0.12	+0.52	0.08	0.04
TORZ	15.07410	52.31320	−0.33	+0.11	0.05	0.11
TUBO	16.59280	49.20590	+0.16	+0.59	0.08	0.07
TUCH	17.86030	53.58520	−0.58	−0.44	0.09	0.13
TUCZ	16.15760	53.23390	−0.39	−0.21	0.07	0.04
TUPI	16.01090	50.50710	−0.19	+0.33	0.05	0.05
TVID	17.18540	50.37290	−0.26	+0.50	0.06	0.10
USDL	22.58580	49.43290	−0.05	+0.31	0.09	0.09
USTA	16.87380	54.57750	−0.46	−0.47	0.16	0.06
WART	18.62490	51.70760	−0.39	+0.33	0.03	0.06
WAT1	20.90380	52.25380	−0.49	+0.00	0.11	0.05
WLOD	23.55760	51.54480	−0.34	+0.18	0.04	0.04
WRKI	16.37110	52.70560	−0.29	−0.12	0.07	0.08
ZLOT	17.04090	53.36760	−0.44	−0.31	0.04	0.09
ZWIE	22.96250	50.61550	−0.45	+0.01	0.10	0.06

), the model exhibits high continuity (Figure 12a). It can be seen that for the entire area, the compression rate in the NNE-SSW direction dominates. The mean dilatation rate is −1.7 × 10⁻⁹/year, and the mean azimuth of the most compressional rate is 205.4 °CW from north. Slightly lower strain rates (−1.4 × 10⁻⁹/year) occur on the East European Platform. On the West European Platform, the rate of deformation is almost 50% higher (−1.9 × 10⁻⁹/year) (except the strain rates of almost zero in the Sudeten Mountains). The West European Platform also shows much higher shear strain rates (up to 1.5 × 10⁻⁹/year), especially north of the Bohemian Masif, while the East European Platform exhibits rates of less than 0.5 × 10⁻⁹/year (Figure 12b). The model is very simplified and reflects the general field of strain rates. However, it retains high correspondence with the stress directions from the World Stress Map. There are still inconsistencies at the boundary of the model, which would need to be explained using a more detailed analysis based on a larger dataset. For more comprehensive analyses, other models can be used where fewer stations are excluded and the model is more heterogeneous. An example is the model developed for stations that have been validated using at least one method (Figure 12b).

5. Conclusions

This paper presents a discussion on the GNSS deformation rate models for a selected area of Poland. In this work, observations from the Polish GNSS Data Research Infrastructure Center were used. As part of the center’s creation, GNSS observations from the selected area of Poland were processed homogeneously. Analysis of the velocity fields at different stages of filtering allowed us to define areas with highly consistent station movement and those where station movement appeared to be constantly chaotic. Depending on the data filtering method used, the strain rate models differ slightly. The analyses show that for the selected area of Poland, the final image of strain rates is strongly influenced by the choice of source data. However, Poland’s GNSS infrastructure seems sufficient for the analyses discussed. The stabilization of reference stations on buildings may raise questions of interpretation, but there is no direct indication that they have lower value. In the absence of stations directly mounted in the ground (in Poland, there are only six such stations: BOGI, JOZE, LAMA, BOGE, DZWE, and HOLO), the use of stations on rooftops is the only possibility. The analysis of velocity uncertainties does not show that such stations are less stable. Nevertheless, when evaluating station movements, it is necessary to consider available information about the station’s installation and time series characteristics (including whether the station has a tendency to exhibit nonlinear motion). As part of the study, various strain rate models were prepared, which enabled us to conduct comparative analyses. Several conclusions can be drawn from this analysis:

• The small degree of shortening (−1.7 × 10⁻⁹/year) in the NNE-SSE direction dominates in most of the Polish territory and in the NNE-SSW direction (azimuth of 205.4°), which is consistent with the direction of maximum stress in Poland from local measurements and the World Stress Map.
• A slightly slower rate of deformation occurs on the East European Platform (−1.4 × 10⁻⁹/year) than on the West European Platform (−1.9 × 10⁻⁹/year). There are differences in both dilatation and shear deformation.
• Surprisingly little deformation was obtained for the Sudetes region, where deformations are practically absent. This is most likely due to inadequate station placement and the methodology adopted.
• The results of this work confirm the hypotheses of the paper [16], and it was also shown that dense data and appropriate filtering are necessary for detecting small deformations.

It can be concluded that the monitoring of GNSS station movements, in the context of studies of present tectonic activity, is reasonable and promising, even in regions with low tectonic activity. The new strain rate model for the selected area of Poland could be developed in 2025 at the earliest. Based on this, recommendations can be made for future analysis:

• Due to the small number of stations stabilized directly in the ground, it is necessary to try to acquire more points with similar characteristics outside Poland in order to increase the reliability of the obtained results. It is advisable that future studies use as many stations as possible in a zone of up to 100 km from the Polish borders, with a sufficiently long observation period.
• Deformation analysis should be carried out on the basis of the new velocities determined after the reprocessing campaign using the new IGS20 frame and models [76]. At this point, detailed analysis and the selection of stations whose movement is least questionable should be carried out.
• Regions for which results diverged depending on the adopted filtering method should be analyzed in detail. These are mainly border regions for which adequate surface filtration was not possible.
• Due to the complex geological structure of the Sudetes, it would make sense to install a few permanent geodynamic stations in the region.