In this step, to ensure the best possible quality of the time series solutions, we selected stations with uncertainties (sigmas) less than 0.2 mm yr⁻¹ and velocity vectors smaller than 2 mm yr⁻¹. We consider that these criteria guarantee a reliable selection of credible solutions. However, a small number of these sites still exhibit anomalous velocities. These are likely caused by local effects such as landslides, station instability, local geological conditions, subsurface compaction, undocumented antenna changes, and multipath interference. The main reason is that most GPS antennas are mounted on buildings and unstable steel rods. In our analysis, we try to model them as position jumps. The dates of these “unknown” jumps were established using a manual process by examining the “raw” time series plots for each station.

This process automatically eliminates the shorter-lived time series, reducing the number of accepted solutions to 99, with the shortest series extending more than four years. This means that all 99 accepted solutions satisfy the criterion established by Blewitt et al. (2001), who claim that the series should be longer than two and a half years for a reliable estimate of the seasonal terms, which is essential for the reliability of the velocity estimate.

The accuracies (σ) at the 95 % confidence level were estimated using the weighted root mean square (WRMS) of the fit according to the formula: σ=2⋅WRMS2.4⋅Tspan where Tspan is the length of the time series in years. This approach provides estimates of velocities and their uncertainties. This empirical approach relates the scatter of the residuals to the stability of the velocity estimate and provides a practical measure of the combined effect of unmodeled noise sources. A similar approach has been previously applied in geodetic studies (e.g., Muntean et al., 2016).

The use of WRMS-based uncertainties is justified by the relatively long duration of the analyzed time series (all exceeding four years), which reduces the impact of temporally correlated noise on velocity estimation. In addition, careful modelling of discontinuities (e.g., offsets due to equipment changes or local effects) further minimizes bias in the residuals. Under these conditions, the adopted approach provides stable and internally consistent uncertainty estimates across the network. Quantitatively, the mean uncertainty is 0.12 mm yr⁻¹, yielding a mean signal-to-noise ratio of 4.9, with values reaching up to 15. These results indicate that the observed velocities significantly exceed their formal uncertainties and are therefore well resolved (Fig. S4).

We also compared our results with those of Piña-Valdés (2022) for stations with common solutions and found an average difference of less than 0.08 mm yr⁻¹ (Figs. 3 and S4 and S5 in the Supplement). This level of agreement demonstrates general consistency. The results for the 99 accepted sites are summarized in Table S1 in the Supplement.

To create a smooth, coherent representation of the computed time series solutions, we use a spatial gridding approach: we set up an 8×8 grid of latitude and longitude nodes with each node linked to a square search box. The size of these boxes depends on the distance (in km) between nearby nodes, ensuring the north-south and east-west dimensions are equal. The next step we eliminate outliers with a velocity larger than two times the median. Then, we calculate the average of the EW and NS velocity components of the remaining solutions. During this process, 22 of the 99 solutions are excluded as outliers. The final result is a gridded dataset of 47 nodes showing the velocities for each node. The other 17 nodes are not presented since there were no Romanian cGPS stations available in the search area (see Table S2 in the Supplement).

When we include the literature (Piña-Valdés et al., 2022; Serpelloni et al., 2022), solutions for the countries neighbouring Romania, the number of solutions increases to 160. After applying the aforementioned editing step, this number decreases to 133. These solutions are based on a collection of shorter time series from before 2021. Nevertheless, they provide valuable additional information.

For the vertical component, we apply a different approach. This component is hardly affected by horizontal station instabilities, but mostly by undocumented antenna changes. We tackle this problem by estimating vertical position jumps on the dates when they appear in the time series. Furthermore, we select only solutions with an absolute velocity <2 mm yr⁻¹ and an accuracy <1.0 mm yr⁻¹, which we consider credible. Some sites show subsidence, but these are mostly located in coastal areas, on slow landslides, and compacting sedimentary areas. As a result, from the 130 available solutions of the four Romanian permanent networks, 95 solutions were accepted (Fig. 4). The results are presented in Fig. 4 and Table S3 (Supplement). We also compared our solutions with those of Piña-Valdés (2022) and found an average difference of less than 0.03 mm yr⁻¹.

When we include the literature solutions, the pattern does not change much. It mostly adds subsidence sites in the area west and south-west of Romania. The total number of accepted vertical sites increased to 145.

To better understand deformation and seismic hazard in this complex tectonic region, we further estimate strain rate from the interpolated horizontal vector field of GPS velocities (Fig. 3). We use the open-source software STRAINTOOL, which employs the VISR (Velocity Interpolation for Strain Rate) algorithm developed by Shen et al. (2015). This algorithm interpolates our gridded solution to derive horizontal strain rates across the region, using a weighted least squares approach on a denser regular grid. At each grid point, the horizontal velocity field is approximated by a bilinear function, and a Gaussian function based on the distance between the interpolation grid point and the other grid points is used for distance-weighting. This algorithm allows us to obtain the spatial variation of strain rate, including the maximum shear strain rate (which indicates how much the crust is laterally distorted), and the dilatational strain rate (which reflects areas of extension or compression). These are valuable parameters for understanding the tectonic regime, whether a region is being compressed, extended, or sheared, and how this deformation relates to observed earthquake focal mechanisms.

Many horizontal velocity measurements indicate a predominantly southward movement in the MP, with variations spanning approximately ± 20° toward the southeast and southwest (Fig. 3). The IMF appears to mark a slight orientation change from S-SE to S-SW oriented motion vectors. This shift is also reflected in the South Carpathians, which are obliquely thrust over the MP, defined by strong and sometimes sharp lateral variation in rheology across the major faults like IMF or COF, which imposed the formation of tear-faults and oblique ramps into the Carpathian Orogen (Fig. 3). Hence, the magnitude and direction of motion vary significantly across the IMF and COF or other major faults in the MP and foreland units in general, like PCF and NTF, that are defining crustal blocks with different rheologies, thermal history, and response under the orogenic loading. In contrast, vectors in the EEP show a slight northwestward motion relative to the Eurasian plate. This shift occurs across the PCF and NTF, which define the boundaries of the North-Dobrogea Orogen (Fig. 3), a transitional zone between the EEP margin and the MP. As a result, the EEP undergoes a subtle yet persistent movement relative to Eurasia, diverging from the southward-moving MP through a series of crustal-scale faults that accommodate lateral displacement.

The Transylvanian Basin (TB) and the East Carpathians, on the other hand, show minimal horizontal motion. GPS stations in these areas indicate limited deformation, with inconsistent directional patterns and low overall coherence in movement. Small horizontal motions are observed in the Pannonian Basin (PB) in an NNE direction, which reoriented toward different directions near the Apuseni Mountains (see Figs. 1 and 3).

Overall, the foreland region, particularly the MP, appears to be drifting southward, while the other areas remain relatively stable, indicating that the foreland is more dynamically active than the surrounding regions.

The Carpathians predominantly experience uplift (Fig. 4), concentrated in the East Carpathians (e.g., BICA, TPLT) and the South Carpathians (e.g., VAD2, and PITE). While some scattered stations (ROSU, TGTS) indicate subsidence, the overall trend suggests uplift rates ranging between 0.5 and 2 mm yr⁻¹. The Vrancea bend zone is an interesting exception because it only shows a minor uplift (e.g., LACP and VRAP).

The foreland region exhibits an intricate interplay of uplift and subsidence. The Moesian Platform, which occupies the area bounded by the Carpathians, the Balkans, and the Black Sea, shows a north-south dichotomy in vertical motion. In its southern part, across the E-W trending Danube River and towards the Balkans, the crust is predominantly subsiding. Northward and northeastward toward the Carpathians, the Capidava-Ovidiu Fault, the trend gradually transitions to uplift. The most pronounced uplift occurs in Dobrogea, the exposed basement of the Moesian Platform near the Black Sea, where all geodetic stations record consistent uplift along the coast and the Danube. Notably, the Danube changes its course northward across this transition zone.

The East European Platform, forming the eastern foreland of the Carpathians, exhibits only minor vertical movements. Several stations in its northern part record slight uplift, which transitions southward into subsidence toward the Neogene Trotuş Fault, known in literature as the New Trotuş Fault (Maţenco et al, 2007). This subsiding trend extends farther south into parts of the NDO, continuing across the SGF and the PCF, which delineates the boundary with the MP. On the opposite side, the MP is undergoing uplift, reflecting strong differential crustal deformation along these seismically active fault networks.

In the back-arc region relative to the Carpathians, in the Transylvanian and Pannonian basins, estimated crustal motions suggest subsidence relative to stable Eurasia. However, the Apuseni Mountains, a prominent highland dividing the two subsiding basins, exhibit a cluster of stable and slightly uplifted motion vectors. Plotted vectors range between -2 and +2 mm yr⁻¹, with an uncertainty of 1.0 mm yr⁻¹ (Table S3 of the Supplement). This is a general feature for most stations in Europe.

We estimated strain rate variation across Romania (Fig. 5) from the regularized horizontal velocity vector field, and the distribution of maximum shear strain rate and dilatation (Fig. 6a, b). The dilatation rate quantifies the extent to which the Earth's crust is either expanding or contracting. It is derived by combining the principal strain rates, with positive values indicating extension and negative values indicating contraction. High positive dilatation values indicate regions experiencing extension, while negative values suggest compression, as seen in processes such as thrust faulting. On the other hand, the maximum shear strain rate measures the degree of shear deformation within the crust, without affecting its overall volume. This is determined by calculating the difference between the principal strain rates. Elevated shear strain rates are associated with regions undergoing significant shear deformation, such as strike-slip fault zones, while lower values typically occur in areas experiencing predominantly extensional or compressional deformation.

The distribution of strain rates is quite complex (Fig. 5 and Table S4 in the Supplement), which is expected given the region's complicated tectonic framework, with multiple blocks of diverse strengths converging to form a sinuous orogenic track. The highest strain rates were estimated in the southwest, at the border between Romania and Serbia (Fig. 6a). This region also experiences the highest shear strain rate (Krézsek et al., 2013)

Dilatation patterns estimated from the strain tensor show a transition from compression in the PB to extension in the intra-orogenic TB. The South Carpathians and the surrounding foreland regions, including the MP and the EEP, are predominantly characterized by extension (Fig. 6b). However, localized areas of compression are observed in the Eastern and South-East Carpathians, particularly in the Vrancea Zone.

To put our results in a broader context, we plot them against previous GPS-derived velocity vectors (Serpelloni et al., 2022; Piña-Valdés et al., 2022) in Fig. 7. While there is some overlap with the Romanian networks, the differences between datasets are minor. To reduce clutter in the figures and minimize the impact of large tectonic motions in the south, we excluded stations with an absolute horizontal velocity exceeding 7 mm yr⁻¹, as shown in Fig. 7a, horizontal and Fig. 7b, vertical, with the UU-07 seismic tomography model of Amaru et al. (2007), updated based on Wortel and Spakman (2000), at 200 km depth, serving as background.

In the regional plate tectonic context, the observed velocity field highlights the complex interactions between major tectonic plates and blocks that converged in this geodynamically complex region. Seismic tomography shows the high velocity thick cratonic lithosphere to the north-east which is supposed to be tectonically stable, the Vrancea Slab as an elongated high velocity block sinking beneath the Carpathians, and the Adria and the Hellenic slabs subducting beneath the Balkan Peninsula (Fig. 7). To the south, crustal motion velocities increase significantly (Fig. 7), reflecting the rapid motion of the Hellenic subduction system as the African Plate subducts beneath the Eurasian Plate, driving southeastward deformation in Greece. Eastward, the Anatolian Plate is moving westward due to tectonic escape caused by the northward collision of the Arabian Plate with Eurasia. This westward motion is a dominant feature of the eastern Mediterranean and plays a key role in accommodating the overall regional deformation.

To the west, the Pannonian Basin, a hyper-extended lithosphere back-arc basin, shows relatively low horizontal deformation rates, suggesting it is currently tectonically stable, with mirror positive inversion of its eastern margin. However, the influence of the Adriatic Plate, a promontory of the African Plate, is meaningful. The Adria Plate, subducting eastwards (Fig. 7), exerts a northeastward push on the Carpathian-Pannonian system, contributing to compressional forces and tectonic inversion along the basin (Bada et al., 2007). These larger-scale processes interact with the local tectonic architecture, such as the Vrancea Slab and associated seismicity (orange stars in Fig. 7), resulting in a complex and heterogeneous deformation regime that bridges the stable cratonic lithosphere and the active subduction-driven tectonics to the south and south-west.

The GPS-derived strain rate field across Romania is characterized by a broadly distributed, long-wavelength deformation pattern. At the regional scale, the field is dominated by N-S extension across much of the foreland and the Carpathian chain, transitioning to localized E-W compression in the southwestern and eastern sectors (Fig. 6). While the GPS data provides a smooth representation of the velocity field, the discrete crustal deformation captured by earthquake focal mechanisms (Fig. 5) and stress indicators from the World Stress Map (WSM2016, Heidbach et al., 2007, Fig. 8) or from focal mechanisms inversion (Petrescu et al., 2021) offers a higher-resolution, albeit more heterogeneous, view of how this regional strain is partitioned along inherited structures. This inherent difference in spatial “wavelength” between geodetic and seismic data is essential for interpreting the transition from plate-scale kinematics to fault-specific failure.

Despite these scale differences, we observe some spatial correlations between the strain rate and seismic regimes. In the compressive domains, the negative dilatation rates observed in the Vrancea and the Eastern Carpathians (Fig. 6b) align with clusters of thrust-faulting stress indicators (Fig. 8) and reverse-faulting mechanisms (Fig. 5), confirming localized crustal shortening and compression at the bend zone. Conversely, the extensional signals identified in the foreland and South Carpathians are corroborated by recent normal-faulting earthquake swarms, such as those occurring near the SGF (Fig. 5 and Craiu et al., 2017) and recent intense seismic sequences in the South Carpathians (Radulian et al., 2023; Borleanu et al., 2024). In areas characterized by high shear strain (Fig. 6a), specifically the southwestern Carpathians, the prevalence of strike-slip and oblique-slip focal mechanisms (Fig. 5) reflects a complex regime of strain partitioning along major fault systems. This alignment across multiple independent datasets, GPS, focal mechanisms, and stress indicators, supports the reliability of the derived strain field.

In regions like the Moesian Platform, the relationship between geodetic strain and seismic indicators is more nuanced. This variability in focal mechanisms, especially among smaller-magnitude events (M 3–4), likely reflecting the activation of secondary, oblique faults accommodating local adjustments within the regional stress framework. This complex pattern (Fig. 5) is particularly evident near large-offset faults where differing rheological properties of crustal blocks that make up the MP (Maţenco et al., 2003; Petrescu et al., 2019) and the influence of pre-existing lithospheric heterogeneities (e.g., Bertotti et al., 2003; Tărăpoancă et al., 2004) lead to pronounced strain partitioning. While the smooth GPS field is not intended to resolve every local pocket of shear or compression, the broad agreement between the primary strain axes and the dominant earthquake regimes suggests that the geodetic model reflects the regional-scale deformation patterns characterizing the Romanian crust.

Our results indicate a clear uplift trend in the foredeep basin area, supporting a typical post-collisional rebound and uplift behavior, as observed in many other orogenic systems. These observations differ from previous temporary GPS models (van der Hoeven et al., 2005) and lower resolution geological datasets (Merten et al., 2005, 2010), which suggested that subsidence dominated the evolution of the region as a typical response to slab subduction and retreat (Tărăpoancă et al., 2004). This represents a notable change from earlier interpretations, which tended to highlight uplift in the Dobrogea forebulge while assuming subsidence further towards the Carpathian Orogen. This is also in line with some historical long-term repeated leveling methods (e.g., Popescu and Dragoescu, 1987; Joó et al., 1987) and is further supported by recent InSAR analyses (Poncoş et al., 2022).

The discrepancy may reflect either a shift in the tectonic regime over time or methodological limitations in capturing ongoing geodynamic processes. The observed uplift may be associated with a partial decoupling between the subducting lower lithosphere and the overlying crust (Petrescu et al., 2021), allowing stress relaxation and isostatic rebound of the upper crust in the foreland. This scenario is consistent with the distribution of intermediate-depth seismicity and the focal mechanism patterns observed in the Vrancea Zone. In addition, Mitrofan et al. (2014) suggested a partial transmission of deformation from the slab to the crust, further supporting the idea of vertical stress transfer from the mantle to the surface.

While the continued uplift in Dobrogea is confirmed, the GPS data suggest that this uplift extends into the foredeep, highlighting the presence of vertical motions in the foredeep basin that are not solely driven by active subduction dynamics. Instead, the observed uplift in both regions may be linked to slab break-off, a late-stage process in the subduction and continental collision cycle (Andrews and Billen, 2009). As mentioned before, the Dobrogea uplifted area at the transition to the Black Sea Basin is parallel to the SE Carpathians, again suggesting the interplay between collisional processes affecting the Orogen and the flexural response of the lower plate, with the forebulge outward migration (from the orogen), accompanied by coeval uplift and erosion.

Seismic imaging suggests that the Vrancea Slab has partially torn and rotated at ∼ 150 km depth (Martin et al., 2006), leaving a deeper slab segment (200–310 km) still weakly attached (Heidbach et al., 2007). If break-off continues to be active (Müller et al., 2010), asthenospheric upwelling through the torn slab segment (Petrescu et al., 2023) may be dynamically supporting present-day uplift in both the SE Carpathians and foredeep. Numerical simulations of subduction-collision systems with spontaneous slab break-off (Duretz et al., 2011) predict post-break-off uplift rates of 0.1–0.8 km Myr⁻¹ (0.1–0.8 mm yr⁻¹), which closely match our observed uplift. Additionally, an increase in slab dip may promote low-wavelength lithospheric folding following continental collision (e.g., Cloetingh et al., 2004; Maţenco et al., 2007), contributing further to the uplift observed in both the SE Carpathians and the foredeep.

Our results also reveal a significant uplift in the East Carpathians (Fig. 4), not just the SE Carpathians, raising the question of whether past slab break-off there (Nemcok et al. 1998) could still be influencing present-day vertical motions. Geodynamic reconstructions suggest that the subducted passive margin of the East European Platform progressively broke off from north to south along the East Carpathians (Sperner et al., 1996), culminating in the currently detaching Vrancea Slab (Sperner et al., 2001; Koulakov et al., 2010; Lorinczi and Houseman, 2010). While the initial isostatic response to slab break-off is expected to occur within a few million years (Duretz et al., 2011) or up to 7 million years after convergence stops (Andrews and Billen, 2009), prolonged effects such as mantle flow, residual buoyancy, and lower-crustal flow could be sustaining regional uplift. This interpretation is further supported by Bouguer gravity anomalies (Fig. 8), which show relatively positive values (0–40 mGal) over the mountain belt, suggesting the presence of denser material at depth or incomplete isostatic compensation. The north-to-south younging of post-collisional volcanism (Seghedi et al., 2004) suggests that slab detachment propagated southward over time, with the East Carpathians experiencing earlier break-off than the SE Carpathians. If asthenospheric upwelling and lithospheric weakening occurred during that time, they could have led to prolonged crustal adjustments that continue to manifest as uplift today.

In addition to the SE and East Carpathians, we also identify localized uplift in the South Carpathians. This region marks the collision between the Dacia Block and the Moesian Platform, where oblique thrusting over the thick Moesian lithosphere (Maţenco et al., 1997) may be inducing flexural or isostatic responses (Bertotti et al., 2003). Bouguer gravity anomalies in this area transition from strongly negative values (∼ -100 mGal) near the foredeep in the south to over +100 mGal at the contact with the Transylvanian Basin (Fig. 8), indicating a shift from thick, low-density crust to denser material in the north. This pattern suggests differential isostatic compensation, where northward crustal thinning leads to less mass deficit and reduced buoyancy, potentially causing flexural uplift. This contrast could drive vertical displacements, as observed. Alternatively, deeper mantle processes, such as residual slab dynamics or lithospheric-scale deformation associated with orogenic curvature, may also influence the observed uplift.