# Stability Analysis of GNSS Stations Affected by Samos Earthquake
## 3 Results and Discussion
Stations exceeding the critical value were removed after the corresponding iteration until no unstable stations remained. Applying the threshold method based on the coordinate S-transformation model confirmed the instability of the same stations for 3D cartesian coordinates. In Figure 3, red triangles represent the residuals and light blue circles represent the double value of the square root of the sum of the variances. If the residual exceeds the double value of the square root of the sum of the variances of a component of a station, this means the station is unstable. However, in the first stage, the model identified several stations and even stable ones (SAMO, CESM, MNTS, IZMI, NAXO and RODO). A single-point deformation presence on a network can contaminate not only the estimated parameters but also the residual vector; therefore, locating single-point movements can be difficult or sometimes impossible [7]. The large coseismic offset at the SAMO station made it difficult to identify the IKAR station as unstable in the first stage and to include stations with no significant displacements. By excluding the SAMO station, the model was repeated, successfully capturing the deformation at the IKAR GNSS station, while confirming the stability of the other stations (NAXO and RODO). Even though all the unstable stations were determined in the second stage, the author continued to iterate the model, extracting the unstable stations one by one, until none remained. Figure 2: XYZ hypothesis testing results based on coordinate S-transformation model. Each iteration is represented by a different color and geometric symbol, while a corresponding dashed line indicates the critical values for that specific iteration. In Figure 3, the first iteration results are given as an example of the threshold method in the \(X\), \(Y\), \(Z\) components and the \(P\) point. Residuals (red triangles) larger than the T values (blue circles) define unstable points. In the first stage, it is seen that the largest residuals belong to the SAMO GNSS station with the highest red circles in multiple components. In a tectonic sense, determining earthquake characteristics and analyzing crustal deformations are more suitable with a topocentric coordinate system that is aligned with the Earth's surface. This coordinate system allows for easy interpretation of displacement in the north, east and up directions. In Figure 4, theoseismic displacements of the Samos earthquake calculated using GNSS data are illustrated. Figure 4a,b provides visual representations of the horizontal (east and north) and vertical (up) coseismic displacements resulting from the Samos earthquake, respectively. Figure 3: XYZ threshold method initial iteration results based on coordinate S-transformation model. Red triangles and blue circles represent the residual values and the double value of the square root of the sum of the variances, respectively. Figure 4a demonstrates that the horizontal coseismic displacements are dominant, although vertical offsets are required to fit a proper model [21]. The coseismic slip distribution model indicates that the slip reaches approximately 2 km from the surface and particularly in proximity to Samos Island, leading to the largest displacements observed at the SAMO continuous GNSS station. Horizontal displacements indicate (Figure 4a, Table 3) significant displacement at five stations (CESM, MNTS, IZMI, IKAR and SAMO) based on their confidence ellipses, while only SAMO has significant coseismic displacement in the up component (Figure 4b, Table 3). S-transformation model-based hypothesis testing using north and east components identified SAMO as an unstable station in the initial iteration, followed by CESM, MNTS, IZMI and IKAR. The threshold analysis also identified the same stations as unstable. For the up component, similar results were obtained, and the two models determined only the SAMO station as unstable. Regardless of the method used, the results hold true for all dimensions and with different coordinate systems.