## 3 Results  
### TSF Characteristics  
Figure 2 and Table 2 display the inversion results of the TSF before the Ms 6.4 Yangbi earthquake. The compromise curve between the stress field inversion fitting error and the length of the model (or the complexity of the model) is shown in Figure 2a. The number marked on the right of the circle in the figure is the value of the damping coefficient, and the cross is the calculated optimal damping coefficient (inflection point). The best stress field inversion result can be obtained at the inflection point, that is, when the optimal dampingcoefficient is 1.2, as shown in Figure 2b. The azimuth of the maximum horizontal principal compressive stress rotates counterclockwise from west to east and rotates clockwise from north to south, which is consistent with the results of previous studies [33; 44; 45]. In the epicentral area (100\({}^{\circ}\) E, 26\({}^{\circ}\) N), the azimuths and plunges of the optimal solutions of \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) are \(-4.4^{\circ}\) and \(2.7^{\circ}\), \(-175.2^{\circ}\)and \(87.3^{\circ}\), \(85.6^{\circ}\)and \(0.4^{\circ}\), respectively, and the corresponding 95% confidence intervals for azimuth of \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) are \(-183.1^{\circ}\)-\(166.8^{\circ}\), \(-355.2^{\circ}\)-\(4.3^{\circ}\), and \(78.2^{\circ}\)-\(91.5^{\circ}\), respectively.  
Figure 2: Results of stress field inversion. (**a**) Tradeoff between the length of the model and data misfit for different values of the damping parameters. The damping values are shown next to each point. The final selected damping parameter is represented by a cross. (**b**) Spatial distribution of the stress field orientation. The axes of the maximum compressive stress, intermediate principal stress and minimum compressive stress are represented as \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\), respectively. The 95% confidence limits of \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) are marked with red, green and blue points, respectively. The best solutions are indicated by black crosses. (**c**) Confidence limits of the \(R\) value corresponding to (**b**). (**d**) Stress field direction and \(R\) value of the Yangbi earthquake using 13 FMSs.  
The relative stress magnitude \(R\) is defined as [7]  
\[R=\frac{\sigma 2-\sigma 1}{\sigma 3-\sigma 1}. \tag{1}\]  
The \(R\) value is the minimum at grid points (100\({}^{\circ}\) E, 27\({}^{\circ}\) N) and (101\({}^{\circ}\) E, 27\({}^{\circ}\) N), and the optimal solution is 0.07; the maximum is at (98\({}^{\circ}\) E, 25\({}^{\circ}\) N), and the optimal solution is 0.45; the optimal solution for the \(R\) value in the epicenteral area (100\({}^{\circ}\) E, 26\({}^{\circ}\) N) is 0.13, and the 95% confidence interval is (0.00-0.30), as shown in Figure 2\(c\).  
We also inverted the TSF in the epicentral region of the Ms 6.4 Yangbi earthquake. The inversion parameters were the same as above, and the results are shown in Figure 2d. The optimal solution of the relative stress \(R\) value is 0.32. The azimuth of \(\sigma_{1}\) is 172.7\({}^{\circ}\) (150.8\({}^{\circ}\)\(\sim\)316.7\({}^{\circ}\)), and the plunge is 6.6\({}^{\circ}\) (\(-\)75.8\({}^{\circ}\)\(\sim\)88.3\({}^{\circ}\)). The azimuth of the minimum principal stress axis \(\sigma_{3}\) is 82.4\({}^{\circ}\) (73.6\({}^{\circ}\)\(\sim\)98.6\({}^{\circ}\)), and the plunge is 2.4\({}^{\circ}\) (\(-\)10.8\({}^{\circ}\)\(\sim\)15.0\({}^{\circ}\)).