# Characterization of the Solution of the Seismic Source Mechanism in Southeastern Sichuan
## 4 Stress Field Inversion
### Stress Field Spatial Characteristics  
The determination of stress-field orientation through the analysis of earthquake focal mechanisms serves as a critical tool for comprehending crustal mechanics and seismological phenomena [55]. The inversion process yields the orientations of the three principal stress axes and the relative stress magnitude, \(R\), which is calculated using the following equation:  
\[R=(\sigma_{1}-\sigma_{2})/(\sigma_{1}-\sigma_{3})\]  
in which \(\sigma_{1}\)-\(\sigma_{3}\) are the magnitudes of the three principal stress axes obtained from the deviatoric stress tensor. The relative stress magnitude quantifies whether the magnitude of the intermediate principal stress \(\sigma_{2}\) is closer to the magnitude of the most compressive (\(\sigma_{1}\)) or the least compressive principal stress (\(\sigma_{3}\)). Concurrently, to investigate the spatial distribution characteristics of the regional stress field in southeastern Sichuan, we conducted an inversion and analysis of the regional stress field utilizing MSATSI software (Version 1.0.9) [56; 57], based on the focal mechanism solutions obtained from our study. Figure 5: Principal stress axes inversion in different tectonic regions of southeastern Sichuan. (**a**) Region A: The \(\sigma_{1}\) axis exhibits a near-horizontal orientation trending approximately E-W. (**b**) Region B: The \(\sigma_{1}\) axis reflects NW-SE compression. (**c**) Region C: The inversion results show significant dispersion of the principal stress axes. The inversion results indicate that the comprehensive stress fields of the three regions share some common features (Figure 5), such as the near-horizontal maximum principal stress axis \(\sigma_{1}\)(with a plunge close to 0\({}^{\circ}\)) and the near-vertical minimum principal stress axis \(\sigma_{3}\) (with a plunge close to 90\({}^{\circ}\)). According to the classification criteria of [PERSON] [58], this region is controlled by nearly horizontal extrusion, and the seismogenic structures are dominated by thrust faulting, consistent with the classification result of the last section. Subtle variations in stress orientations are observed across different regions. Region B, positioned in the northern segment of the study area (Figure 5b), exhibits a \(\sigma_{1}\) orientation that corresponds with the principal compressive stress field direction of the Sichuan Basin, as depicted in the stress map by [PERSON] et al. [59] and the velocity direction of GNSS stations [59]. This stress direction is a legacy of the southeastward escape of the Tibetan Plateau [60], which exerts a compressive force in the northwest-southeast direction on the Sichuan Basin. Conversely, Region A, located in the southern part of the study area (Figure 5a), features a \(\sigma_{1}\) orientation that is more aligned with the east-west direction. In situ borehole stress measurements, as reported by [PERSON] et al. [61], indicate that the \(\sigma_{1}\) orientation in Region A is counterclockwise-rotated relative to the background stress field of the Sichuan Basin, implying that a perturbation superimposed on the regional stress field has influenced the local stress orientation. For Region C, Figure 5c illustrates that the principal stress axes are dispersed during the bootstrap resampling process. This dispersion is generally attributed to an insufficient number of samples, which leads to unstable constraints. Consequently, we refrain from a detailed analysis of the stress field directionality in this region. To delineate the finer spatial characteristics of the stress field within the study area, we implemented a mesh grid with a resolution of 0.1\({}^{\circ}\) and conducted a statistical sampling of seismic mechanism solutions within a window of 0.2\({}^{\circ}\). MSATSI software was utilized for 2D stress field inversion, as it provides a well-established and robust framework for resolving discontinuities and ambiguities in the inverted stress field directions, a challenge commonly encountered in traditional inversion algorithms.