## 4 Discussion  
### Seismotectonic Implications of GNSS-Based Strain Tensor Analysis  
Elastic strain fields derived from geodetic observations, such as GNSS data, provide a robust and quantitative basis for assessing tectonic stress accumulation along active fault systems. When interpreted through the framework of elastic dislocation theory, these strain fields serve as proxies for subsurface stress distributions and help identify regions with elevated seismic potential. High-resolution geodetic measurements allow for the detection of subtle crustal deformations and spatial variations in strain rates, which are key to characterizing stress buildup along known faults. Numerous studies have demonstrated that geodetic strain fields correlate well with stress orientations inferred from borehole and seismological data, validating their use in tectonic stress mapping even in complex or intraplate settings [60; 61; 62]. Moreover, inversion of geodetic velocities through elastic dislocation models enables the estimation of deep strain and stress patterns, enhancing our understanding of fault loading and earthquake hazard [63; 64; 65; 66]. The relative displacement vectors observed across multiple baselines are used to construct a planar strain tensor field. Eigenvalue decomposition of this tensor yields  
Figure 10: Formal error ellipses representing the uncertainties in maximum shear strain (\(\gamma\_\)max) estimates for each triangular element, derived from GNSS observations. The upper panel shows results for the 2018–2020 period (blue ellipses), while the lower panel corresponds to the 2019–2020 period (red ellipses). Each ellipse indicates the magnitude and orientation of maximum shear strain, as well as the directional confidence based on the propagated uncertainties from GNSS positioning. Larger ellipses, particularly those associated with triangles 11, 14, and 16, suggest significant strain accumulation and directional consistency, which may imply localized zones of increased seismic hazard. These visualizations facilitate the assessment of spatial variation in deformation and contribute to a more robust understanding of strain distribution along the Yangsan Fault. the principal strains and their orientations, which directly relate to the directions and magnitudes of the dominant compressive and extensional stresses [67]. The maximum shear strain, derived from the differential of principal strains, serves as a critical indicator of fault slip potential. Regions where the principal stress orientation aligns with known fault geometries are often interpreted as seismically unstable and prone to rupture. GNSS-based baselines can detect displacements on the order of millimeters per year, making them particularly effective for monitoring strain accumulation even in tectonically quiet regions [68]. By continuously tracking such subtle changes over time, geodetic baselines can reveal evolving stress conditions and highlight zones experiencing persistent strain accumulation--an essential prerequisite for earthquake nucleation [2]. Moreover, geodetically derived stress field models complement traditional seismic hazard assessments based on historical earthquake catalogs by offering greater spatial resolution and the ability to identify aseismic zones of latent stress. Case studies from Japan, Italy, and North China have demonstrated strong correlations between zones of concentrated geodetic strain and subsequent major seismic events [69; 70]. Elastic strain fields derived from GNSS data provide a physically grounded and quantitative framework for assessing tectonic stress accumulation. When interpreted within the context of elastic dislocation theory, these fields approximate subsurface stress distributions and help delineate regions of elevated seismic potential. Previous studies have confirmed that geodetic strain directions are consistent with stress orientations inferred from borehole breakouts and seismic moment tensors, reinforcing their applicability in regional hazard mapping [60; 61; 62].