## 4 Accurate Earthquake Locating
Using the maximum likelihood method [11] and the \(M_{C}\)-varied results from Figure 5a, we generated a \(b\)-value map, setting the sample's lower limit in each grid to 30, with magnitudes exceeding \(Mc\). This map reveals that most areas, including the future Luding \(M_{S}\) 6.8 earthquake's epicenter, fall within a normal range of 0.7-1.1. The only exception is the abnormally low-\(b\)-value area (b \(<\) 0.7) in the southern section of the Longmen Shan fault belt (Figure 5b). Figure 4: The relocated epicentral map in the study region. (**a**) colored by the earthquake-locating method, black: flag = 2, green: flag = 1, purple: flag = 0; (**b**) colored by focal depth, the black solid line indicates the position of the profile line. The yellow star shows the epicenter of the \(M_{S}\) 6.8 Luding earthquake on 5 September 2022. F1: Xianshui He fault belt, F2: Anning He fault belt, F3: Zemu He fault belt, F4: Daling Shan fault belt. Acknowledging the potential for underestimation of the minimum magnitude of completeness (\(M_{C}\)) when using the Maximum Curvature method [62], we opted to set \(M_{C}\) at a conservative \(M_{L}=2.0\). The newly calculated \(b\)-value map (Figure 5c) revealed no significant deviation from the earlier version. To minimize the impact of arbitrary parameter selection on the outcomes, we employed the Hierarchical Space-Time Point-Process Model [63] for recalculating the \(b\)-value map, based on \(M_{C}=M_{L}\) 2.0 (Figure 5d). This approach yielded a smoother distribution of \(b\)-values, yet the overall trend remained consistent with the previous maps. Intriguingly, regardless of the method applied, the epicenter of the impending Luding \(M_{S}\) 6.8 earthquake was not situated in a low-\(b\)-value zone. This observation contradicts conventional wisdom, which typically associates strong earthquakes with low-\(b\)-value areas [6; 7; 64]. To unravel this anomaly, we investigated the stress distribution in the Xianshui He fault zone prior to the Luding \(M_{S}\) 6.8 earthquake, examining the temporal and spatial characteristics of the \(b\)-value. The 2014 Kangding \(M_{S}\) 6.3 earthquake, which occurred north of the Luding \(M_{S}\) 6.8 event on the same fault belt, had exerted a positive Coulomb stress influence on the southern section of the Xianshui He fault belt [65]. To isolate the impact of this earthquake, we divided the study period into two phases, using 2015 as the demarcation point: the first phase spanned from 2009 to 2014, and the second from 2015 to 31 May 2022. We applied a P-test based on the Akaike Information Criterion [66] to quantitatively evaluate the \(b\)-value trends across these two stages. As proposed by [PERSON] [67], the difference in AIC (i.e., \(\Delta\)AIC) for the same statistical window between different stages can be defined as follows:  
\[\Delta AIC=2\left(\sum_{i=1}^{2}N_{i}\ln b_{i}\right)-2 \tag{4}\]  
\(N_{i}\) and \(b_{i}\) are the sample size and \(b\)-value in the \(i\)th window, respectively. The probability that the events in the two sample windows are from the same population can be derived from the AIC:  
\[P=\exp\left(\frac{-\Delta AIC}{2}-2\right) \tag{5}\]  
A significant change in the \(b\)-value is considered to have occurred when \(\Delta\)AIC \(\geq\) 2 (\(P\approx\) 0.05); when \(\Delta\)AIC \(>\) 5 (\(P\approx\) 0.01), it is judged to be highly significant. The results show that, when we choose \(\Delta\)AIC \(\geq\) 2, the southern segment of the Xianshui He fault belt has the only large-scale anomaly area in the study area, with a radius of about 50 km and a \(\Delta\)AIC value of around 5 (Figure 5a), corresponding to \(\Delta\)b \(\leq\)\(-\)0.3, reflecting significant changes in \(b\)-values between the two periods of 2009-2014 and 2015-31  
Figure 5: (**a**) Map of magnitude completeness; (**b**) map of \(b\)-value, derived from an \(M_{C}\)-various mode in (**a**); (**c**) map of \(b\)-value, derived from a fixed \(M_{C}=2.0\); (**d**) map of \(b\)-value, calculated by the HIST-PPM method from a fixed \(M_{C}=2.0\).