## 6 Loading/Unloading Response Ratio Analysis  
[PERSON] et al. [(58)] defined the stages of earthquake nucleation as stress accumulation, initial weakening, and overall weakening, where core weakening appears in the overall weakening stage. The boundary of the core weakening zone initially expands with time and then contracts in the later period. Finally, it points to the fault block, which is consistent with the changes in rock temperature before the earthquake. It also confirms the transformation of the sub-instability stage from the independent activity of each part of the fault to the overall activity, which was defined by [PERSON] et al. [(52)] on the basis of rock experiments. The overall activity of the fault results from high stress. To verify the high stress at this time, we used the loading/unloading response ratio (LURR) method. The LURR quantitatively reflects the approaching instability of a nonlinear system [(59)]. When the regional stress is in the normal state, the earthquakes in the loading and unloading stages should be about the same. When the region is in a high-stress state, the stress disturbance will cause an earthquake more easily. It is calculated as follows:  
\[Y=\frac{X_{+}}{X_{-}} \tag{6}\]  
where the plus sign (+) and minus sign (-) indicate loading and unloading, respectively. The response rate \(X\) is expressed as  
Figure 6: Electron density changes observed by Zhangheng-1 satellite before Jiashi M6.4 earthquake. (**a**) electron density, (**b**) the orbital position of the study area, and spatial distribution of anomalous area. The pentagram is the epicenter, and the black straight line is the orbit of the satellite in figure b.  
\[X=\lim_{\Delta P\to 0}\left(\frac{\Delta R}{\Delta P}\right) \tag{7}\]  
where \(\Delta R\) and \(\Delta P\) represent the changes in the load \(P\) and response \(R\) under a load \(P\). The formula for using seismic energy E as a response is as follows:  
\[Y=\frac{\left(\sum_{i=1}^{N_{+}}E_{i}^{m}\right)_{+}}{\left(\sum_{i=1}^{N_{-}}E _{i}^{m}\right)_{-}} \tag{8}\]  
When m = 1, \(E^{\text{m}}\) represents the seismic energy, which can be calculated according to the Gutenberg formula; for \(m\) = 1/2, \(E^{\text{m}}\) represents the Benioff strain. In this study, we use the Benioff strain to calculate LURR. \(N^{+}\) and \(N^{-}\) represent the number of earthquakes during loading and unloading, respectively. We classify the earthquakes within 100 km of the epicenter by loading and unloading (Figure 7a) for 200 days before the earthquake. Then we selected the 0 \(<M_{\text{s}}<\) 4 earthquake catalog to calculate LURR. The focal mechanism parameters were selected from the moment tensor results calculated using the Global CMT page: strike: 80\({}^{\circ}\), dip: 71\({}^{\circ}\), slip angle: 124\({}^{\circ}\), focal depth: 12 km. The friction coefficient of the fault was set to 0.4. A window length of 30 days and a step size of 10 days were used to calculate the LURR. The LURR was found to be abnormally high on 31 December 2019 (Figure 7b), and the Jiashi \(M_{\text{s}}\)6.4 earthquake occurred on 19 January 2020. A high-value anomaly also occurred on 8 October 2019; this anomaly preceded the Wushi \(M_{\text{s}}\)5.0 earthquake on 27 October 2019 by 19 days. The magnitude increased with increasing LURR. Figure 7b shows that the ratio is typically approximately one and reaches six before the Jiashi earthquake, indicating a state of high stress before the earthquake. Which indicated that the regional stress level was higher and the load triggered more earthquakes. The green area in Figure 7a shows that the load earthquakes increased.