## 3 Research Methods
### Information Entropy Calculation  
The influencing factors of geological hazards are numerous, and the degree of impact of different factors on hazards varies. It is necessary to use the information value method to determine the weights of each region, as shown in Equation (2):  
\[I(Y,x_{1},x_{2},x_{3}\ldots x_{n})=ln\frac{P(Y,x_{1},x_{2},x_{3}\ldots x_{n})}{P (Y)} \tag{2}\]  
Based on conditional probability operations, Equation (2) can be rewritten as Equation (3):  
\[r=\frac{\sum_{i=1}^{n}(X_{i}-\bar{X})(Y_{i}-\bar{Y})}{\sqrt{(\sum_{i=1}^{n}(X_{ i}-\bar{X})^{2})(\sum_{i=1}^{n}(Y_{i}-\bar{Y}^{2}))}} \tag{3}\]  
Specifically, \(I(Y,x_{1},x_{2},x_{3}\ldots x_{n})\) represents the information contribution of the combination of influencing factors \(x_{1},x_{2},x_{3}\ldots x_{n}\) to geological disaster \(Y\); \(P(Y,x_{1},x_{2},x_{3}\ldots x_{n})\) denotes the probability of geological disaster \(Y\) occurring under the combination of influencing factors \(x_{1},x_{2},x_{3}\ldots x_{n}\); \(P(Y)\) represents the probability of occurrence of geological disaster \(Y\); \(I_{x_{1}}(Y,x_{2})\) signifies the information contribution of evaluation metric \(x_{2}\) to geological disaster \(Y\) under the condition of influencing factor \(x_{1}\)[24].  
This equation illustrates that the total information provided by the combination of influencing factors \(I(Y,x_{1},x_{2},x_{3}\ldots x_{n})\) on the occurrence of geological hazards is equal to the total information contributed by \(x_{1}\), the information contributed by \(x_{2}\) under the condition of \(x_{1}\), and so on, up to the sum of the information contributed by \(x_{n}\) under the condition of the presence of \(I(Y,x_{1},x_{2},x_{3}\ldots x_{n-1})\) This indicates that the disaster-susceptibility assessment based on the information value method fully considers the impact and influence of the combined conditions of various contributing factors on the occurrence of geological hazards.  
Taking this study as an example, the information value method based on Geographic Information System (GIS) technology is used to assess the disaster susceptibility of geological hazards, requiring a reliable standard model. The specific establishment method is as follows [25]:  
(1) Calculate the information amount contributed by the evaluation factors using Equation (4):  
\[I(x_{i},D)=ln\frac{P(x_{i}|D)}{P(x_{i})} \tag{4}\]  
In practical scenarios, frequency is typically calculated using Equation (5): \(N\) represents the frequency of geological disasters in the analyzed region, \(S\) denotes the number of assessed units, \(N_{i}\) is the number of disasters, and \(S_{i}\) represents the number of evaluation factors [26].  
\[I(x_{i},D)=ln(\frac{N_{i}/N}{S_{i}/S}) \tag{5}\]  
(2) The total information amount of geological disasters under the conditions of \(n\)-type influencing factors is calculated using Equation (6):  
\[I_{i}=\sum_{i=1}^{n}I(x_{i},D)=\sum_{i=1}^{n}ln(\frac{N_{i}/N}{S_{i}/S}) \tag{6}\]  
(3) The total information amount is denoted as \(\sum I_{i}\), serving as the evaluation criterion. An increase in this value indicates a higher probability of geological disaster occurrence in the evaluation unit. Conversely, a decrease suggests a lower probability of geological disaster occurrence. When the value is less than zero, it indicates that the probability of a geological disaster occurring in the evaluation unit is below the average level of thestudy area during the same period. If the value equals zero, it signifies that the probability matches the average level. When the value is greater than zero, it implies that the probability of geological disaster occurrence in the unit exceeds the average level of the study area during the same period.  
(4) Based on the final ranking results, classification is performed, and each level is analyzed in depth to determine the different levels of disaster susceptibility for geological hazards.