## 4 Analysis and Discussion  
### Analysis of the Assessment Results  
On the whole, the evaluation results from both methods demonstrated that the areas posing an extremely high risk of earthquake-triggered landslides were predominantly situated on the western side of the Xianshuie Fault, exhibiting a similar distribution pattern to that of the critical acceleration of the rock-soil masses. Concurrently, the difference method identified elevated earthquake-triggered landslide risks on both sides of the Dadue Fault, aligning with the observed real-world scenario. Conversely, the cumulative displacement method indicated a relatively heightened risk of earthquake-triggered landslides on the western side of the Dadue Fault, accompanied  
Figure 7: Results of the assessment of the risk of earthquake-triggered landslides (using the cumulative displacement method). by isolated high-risk zones on the eastern side. Notably, the actual distribution of seismic landslides deviated somewhat from the assessment results. In general, the proportion of the study area having different earthquake-induced landslide risk levels obtained by the two types of assessment methods showed significant differences (Figure 8). This was due to the different methods used for classifying risk levels, with the difference method employing a natural break classification method to categorize the assessment results, which yielded statistically significant threshold values. In contrast, the cumulative displacement method relied on the findings of previous research and the experience of classifiers to determine the classification breakpoints, resulting in threshold values having physical significance. Although the classification differences were significant, both classification methods have previously achieved good verification results in multiple case studies [6, 15, 17, 18, 20, 22, 23, 26, 32, 33, 48, 49]. In the study area, a comprehensive collection of 476 earthquake-triggered landslides was amassed [39], covering an approximate total area of 17.81 km\({}^{2}\). These data were employed in this study as validation data to facilitate a comparative analysis of the assessment results derived from the two methods. We evaluated the accuracy of the two models using receiver operating characteristic (ROC) curves, which are a comprehensive indicator reflecting the sensitivity and specificity of continuous variables [50]. The evaluation criteria were as follows: when the area under curve (AUC) < 0.5, the prediction results were opposite; when the AUC = 0.5, it indicated a random model; an AUC between 0.5 and 0.7 suggested low accuracy; an AUC between 0.7 and 0.9 indicated high accuracy; when the AUC > 0.9, the model accuracy was very high [51]. We used 476 actual landslides triggered by the earthquake as landslide samples. Additionally, we randomly selected 476 non-landslide samples outside a 100-meter buffer zone from the actual landslide samples, totaling 952 sample points (Figure 9). In order to conduct a quantitative comparison of the two assessment methods, we assigned the five levels of earthquake-triggered landslide risk assessment from low to high as a possibility of 0.2, 0.4, 0.6, 0.8, and 1.0. We defined actual landslide samples as a possibility of 1 and non-landslide samples as a possibility of 0. Then, we statistically analyzed the prediction values of the two assessment methods for landslide and non-landslide samples, respectively, and finally input the statistical results into the Origin 2021 (9.8) software to plot the ROC curve. The ROC curve (Figure 10) displayed the prediction performance of the two assessment methods. The AUC values were 0.804 and 0.762, respectively, indicating that both methods have extremely high predictive abilities and can effectively distinguish between landslide samples and non-landslide samples. In terms of the shape of the ROC curve, both methods were located above the reference line, and the validation curve of the difference method was closer to the upper left corner.