# Application of a Hybrid Model in Landslide Susceptibility Evaluation of the Western Tibet Plateau
## 2 Materials and Methods
### Landslide Susceptibility Modeling
#### 2.5.2 Weight of Evidence Method (WoE)  
[PERSON] (1988) first used the WoE to carry out mineral potential assessment [56]. Since then, the WoE has been applied in many fields [57; 58; 59; 60; 61]. The WoE is based on Bayesian statistical analysis, and the specific process of the model is as follows:  
First, the total grid number of the workspace is preset as N[Z]. There is only one geological disaster point in each grid range. The initial probability of a geological disaster occurring in the working area can be obtained as N[L]/N[Z]. Second, the proportion of different factors at different stages in the probability of occurrence of geological disasters can be obtained by presetting \(\text{W}_{i}{}^{+}\) and \(\text{W}_{i}{}^{-}\). \(\text{W}_{i}{}^{+}\) and \(\text{W}_{i}{}^{-}\), respectively, represent the positive and negative effects of factors at this stage on the likelihood of occurrence of geological disasters:  
\[\text{W}_{i}^{+}=\ln\frac{\text{P}\{\text{N}[\text{Xi}]|\text{N}[\text{L}]\}} {\text{P}\{\text{N}[\text{Xi}]|\text{N}[\text{\overline{L}}]\}}=\ln\frac{ \text{N}(\text{Xi}\cap\text{L})/\text{N}(\text{L})}{\text{N}(\text{Xi}\cap \text{\overline{L}})/\text{N}(\text{\overline{L}})}, \tag{2}\]  
\[\text{W}_{i}^{-}=\ln\frac{\text{P}\{\text{N}\left|\text{\overline{Xi}}\right| \text{N}[\text{L}]\}}{\text{P}\{\text{N}\left|\text{\overline{Xi}}\right| \text{N}[\text{\overline{L}}]\}}=\ln\frac{\text{N}(\text{\overline{Xi}}\cap \text{L})/\text{N}(\text{L})}{\text{N}(\text{\overline{Xi}}\cap\text{ \overline{L}})/\text{N}(\text{\overline{L}})}. \tag{3}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Factor** & **TOL** & **VIF** \\ \hline Slope degree & 0.937 & 1.077 \\ Slope aspect & 0.967 & 1.034 \\ Elevation & 0.929 & 1.077 \\ Lithology & 0.695 & 1.439 \\ Distance to faults & 0.867 & 1.154 \\ Distance to roads & 0.832 & 1.203 \\ Distance to rivers & 0.943 & 1.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Conditioning factor categories. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dimensionality**} & \multirow{2}{*}{**Eigenvalue**} & \multirow{2}{*}{\begin{tabular}{c} **Condition** \\ **Index** \\ \end{tabular} } & \multirow{2}{*}{**Slope**} & \multirow{2}{*}{**Aspect**} & \multicolumn{4}{c}{**Variance Proportion**} & \multirow{2}{*}{\begin{tabular}{c} **Distance** \\ **Lithology** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Distance** \\ **to Faults** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Distance** \\ **to Roads** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Distance** \\ **to Rivers** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Slope** \\ **Degree** \\ \end{tabular} } \\ \hline
1 & 1.918 & 1 & 0 & 0.03 & 0.03 & 0.06 & 0.12 & 0.06 & 0.08 & 0.04 \\
2 & 1.13 & 1.303 & 0.41 & 0.14 & 0 & 0 & 0 & 0.19 & 0.05 & 0.02 \\
3 & 1.056 & 1.348 & 0.15 & 0.17 & 0.08 & 0.05 & 0.03 & 0.07 & 0.16 & 0.15 \\
4 & 0.955 & 1.417 & 0 & 0 & 0.67 & 0.02 & 0 & 0.04 & 0.03 & 0.22 \\
5 & 0.896 & 1.463 & 0.07 & 0.36 & 0.03 & 0.53 & 0.01 & 0.01 & 0.01 & 0.01 \\
6 & 0.846 & 1.506 & 0.06 & 0.12 & 0.12 & 0.29 & 0.01 & 0.03 & 0 & 0.47 \\
7 & 0.697 & 1.659 & 0.3 & 0.11 & 0.05 & 0 & 0 & 0.32 & 0.4 & 0.08 \\
8 & 0.503 & 1.953 & 0 & 0.06 & 0.01 & 0.05 & 0.83 & 0.27 & 0.28 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The results of collinearity diagnostics. In the above formulae, the different stages of the different geological disaster impact factors are noted as Xi. The number of grids contained in this stage is written as N[Xi], and the grid number with geological hazard points is N[L]. In the instance where no geological hazard is present, they are denoted as N[\(\overline{X}\)i] and N[\(\overline{L}\)], respectively. N(Xi\(\cap\)L) is the number of grids containing geological hazards of Xi. In the case of everything else, the converse condition is Xi\(\cap\overline{L}\). Then, the contrasting weights can be obtained by addition and subtraction.