# Monitoring of Possible Activities of Yangsan Fault Zone Using GNSS
## 4 Results--Discussion
### Time Series
#### 4.1.3 Stress and Strain Analysis  
The GNSS based approach has an edge over past geological analysis methods for active fault analysis in that it is possible to accurately measure the crustal movement. In this paper, the Yangsan Fault Zone was monitored based on the triangulation network to analyze the stress and strain caused by crustal movement. Therefore, in this study, based on the results of 3 years of precise coordinates, the deformation in stress acting on the Yangsan Fault Zone was analyzed using the triangular network analysis method. To perform this, it is necessary to assume that the target area is deformed on a two-dimensional plane rather than a curved surface. Triangular network analysis calculates the rate of change of a baseline connecting three points of stations as each vertex of a triangle. The formula for calculating the planar strain by trilateration is given as follows:  
\[ \begin{array}{l}\epsilon_{\alpha_{A}}=\epsilon_{\chi}\cos^{2}\alpha_{A}+ \gamma_{xy}\sin\alpha_{A}\cos\alpha_{A}+\epsilon_{y}\sin^{2}\alpha_{A}\\ \epsilon_{\alpha_{B}}=\epsilon_{\chi}\cos^{2}\alpha_{B}+\gamma_{xy}\sin \alpha_{B}\cos\alpha_{B}+\epsilon_{y}\sin^{2}\alpha_{B}\\ \epsilon_{\alpha_{C}}=\epsilon_{\chi}\cos^{2}\alpha_{C}+\gamma_{xy}\sin \alpha_{C}\cos\alpha_{C}+\epsilon_{y}\sin^{2}\alpha_{C}\end{array} \]  
where \(\epsilon_{\chi}\) and \(\epsilon_{y}\) represent the annual axial strains, \(\gamma_{xy}\) represents the annual shear strain, \([\epsilon_{\alpha_{A}},\ \epsilon_{\alpha_{B}},\ \epsilon_{\alpha_{C}}]\) is determined through GNSS stations as the distance change rate of each side, and the symbols \([\alpha_{A},\alpha_{B},\ \alpha_{C}]\) are the azimuth of the geodesic line. A Delaunay triangular network is composed of the GNSS stations around the Yangsan Fault Zone, which is used to calculate the baseline change rate based on the time series  
Figure 6: Displacement of station that GKPG fixed. coordinates. Neglecting the curvature of the earth, the triangular network was assumed to be a two-dimensional plane. No triangle's circumcircle contains any other points except the three vertices of the triangle in this method. The stress strain and area strain of the triangular network was calculated using the baseline distance change rate between the stations. Figure 7 show the stress strain rate for each triangle network calculated for each period. Table 5 shows the calculated principal strain, maximum shear strain, and area strain of the triangle network. From 2018 to 2019, there is a total of four triangles with a maximum shear strain of 200 nstr or more in absolute sense. The triangle with a maximum shear strain is CGUG-HDBG-POSG with the magnitude of 356.5 nstr/year. In addition, the triangular network of BOGG-CGUG-DUCG shows the largest area strain with a scale of 167.2 nstr/year. On the contrary, there was no triangle with a maximum shear strain of 200 nstr or more in the result of 2020 to 2021, but the CGUG-DUCG-GCNG triangle was the largest at 140.2 nstr/year during this period. This triangular network (CGUG-DUCG-GCNG) includes the area where the Gyeongju earthquake, the largest earthquake since the instrumental earthquake, occurred on the Korean Peninsula. According to previous studies, after the Tohoku Earthquake occurred in 2011, the principal stress acting on the Korean Peninsula contracted in the north-south direction and expanded in the east-west direction [21]. Since then, the scale has decreased. Most of the results of this study showed that the stress strain becomes smaller during the period. During the period between 2018 and 2019, many expanding triangles were observed in the network, but the scale has decreased significantly afterwards. Thus, it can be concluded that the stress of the crust around the Yangsan Fault Zone decreases over time based on the results from 2018 to 2021, which might be evidence of a stable state (here, nano-strain is 10\({}^{-9}\) mm/mm and symbolized as nstr).