## 2 Data and Methods
### Stress Field Inversion Method  
The orientation of the fault plane and the direction of fault slip are determined by a set of seismic focal mechanisms, which can be used to calculate the most suitable princi  
Figure 3: Focal mechanism solution classification diagram [32] of seismic activity in this study. The three vertices correspond to pure strike–slip (top, green), reverse (right, blue), and normal fault (left, orange) mechanisms. The curved lines on the figure correspond to the mechanisms having P and B axes with dips of 60\({}^{\circ}\) (left and top) and a T axis with a dip of 50\({}^{\circ}\) (right). Earthquakes are defined as normal, strike–slip, or reverse if the dip of the P or B axes exceeds 60\({}^{\circ}\) or if the dip of the T axis exceeds 50\({}^{\circ}\), respectively [32]. Figure 2: Distribution of the moment tensor solution used [31] shown by the beachballs in the study area. The dashed box shows the 187 selected focal mechanisms. The size of the sphere represents the magnitude of the earthquake. The remaining symbols are represented as shown in Figure 1.  
pal stress direction and relative stress magnitude R (\(R=(\sigma_{2}-\sigma_{1})/(\sigma_{3}-\sigma_{1})\)) under the assumption of uniform stress distribution in the source area (e.g., [34]). In this study, the improved method proposed by [PERSON] [34; 35; 36; 37; 38] is applied to invert the regional stress tensor using focal mechanisms. First, the fault slip direction is assumed to be consistent with the shear direction, and the stress model is searched by a grid. Then, the corresponding regional stress tensor can be inferred through the common constraints of multiple focal mechanism solutions. Stress is a symmetric second-order tensor, so it can be characterized by independent parameters. In this method, four parameters (\(\sigma_{1}\), \(\sigma_{2}\), \(\sigma_{3}\), R) can be calculated to represent the stress tensor. First, two sets of Cartesian coordinate systems are considered: one is a non-primed set fixed by the principal directions of stress with \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) representing the three principal stress axes, and the other is a primed set fixed in the observed geometry of the fault plane, including \(x_{1}^{\prime}\) normal to the fault plane, \(x_{2}^{\prime}\) on the fault plane and parallel to it while normal to the direction of fault slip, and \(x_{3}^{\prime}\) parallel to the slip direction (e.g., [34]). The fault plane and auxiliary plane are assumed. Based on the above assumption, the slip of the fault is in the shear stress direction, which can be expressed as:  
\[\sigma_{12}^{\prime}=0=\sigma_{1}\beta_{11}\beta_{12}+\sigma_{2}\beta_{12} \beta_{22}+\sigma_{3}\beta_{13}\beta_{23}, \tag{1}\]  
where \(\sigma_{12}^{\prime}\) is the shear stress in the normal direction of the fault plane (\(x_{1}^{\prime}\)), which is normal to the slip direction (\(x_{2}^{\prime}\)) and \(\beta_{ij}\) is the cosine angle between the two sets of coordinate axes. Using the orthogonal expression for \(x_{1}^{\prime}\) and \(x_{2}^{\prime}\):  
\[0=\beta_{11}\beta_{12}+\beta_{12}\beta_{22}+\beta_{13}\beta_{23}, \tag{2}\]  
Combined with Equation (1), the following can be obtained:  
\[(\sigma_{2}-\sigma_{1})/(\sigma_{3}-\sigma_{1})=-(\beta_{13}\beta_{23})/(\beta _{12}\beta_{22})=R, \tag{3}\]  
Based on the observed fault plane and assuming that the direction of the principal stress is known, Equation (3) describes the principal stress in the \(x_{3}^{\prime}\) direction consistent with the slip direction, where \(\sigma_{1}\geq\sigma_{2}\geq\sigma_{3}\), and the value of R is limited by \(0\leq R\leq 1\)[34]. R is also known as the stress shape factor, and its relationship with the stress shape ratio \(\varphi\) is \(\varphi=1-R\). When R = 0, the tensile stress axis remains relatively stable, the compressive stress axis and the intermediate stress axis rotate freely in the plane normal to the tensile stress axis, and both of them are in the state of extrusion.