## 3 Materials and Methods
### Methods
#### 3.2.3 Soil Erosion Susceptibility Mapping Techniques  
In the present work, we employed WOE and FR approaches to compute LSM for the study region. The following are the specifics of the approaches stated. **(i)**: **Weight of Evidence:** WOE is a GIS-based quantitative model that uses the Bayes rule to combine data to estimate the likelihood of occurrences [51]. The WOE approach was initially intended to assess mineral potential mapping using geospatial modelling [52]. The WOE model employs statistical techniques to measure the comparative significance established on the log-linear approach of Bayesian probability. In the case of the WOE model, the positive (W\({}^{+}\)) and negative (W\({}^{-}\)) weights are identified as the most important components. The weight of both causative parameters (B) established on the existence or non-existence of soil erosion (C) of research area is evaluated [53] using the equations below. \[\mathrm{W}^{+}=\ln\frac{\mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{C}}\right)}{ \mathrm{h}\left(\frac{\mathrm{B}}{\mathrm{C}}\right)} \tag{1}\]  
\[\mathrm{W}^{-}=\ln\frac{\mathrm{h}\left(\frac{\mathrm{B}}{\mathrm{C}}\right)}{ \mathrm{h}\left(\frac{\mathrm{B}}{\mathrm{C}}\right)} \tag{2}\]  
\[\mathrm{L}=\mathrm{W}^{+}-\mathrm{W}^{-} \tag{3}\]  
P is the probability, and \(\mathrm{ln}\) is the natural log, whereas BB and \(\mathrm{B}^{-}\mathrm{B}^{-}\) are the presence and absence of the causal factors, respectively. Similarly, the presence and absence events are represented by CC and C\({}^{-}\)C\({}^{-}\)[54]. The presence of the predisposing factor at the occurrence sites is represented by W+. Its magnitude demonstrates the positive relationship between the presence of the causative parameter and disaster incidence. A negative weight  
Figure 5: Soil erosion causative factors: (**a**) Fault; (**b**) Soil; (**c**) NDVI; (**d**) Road. (W) indicates the absence of the causal component of soil erosion and indicates the degree of detrimental association. The difference between W+ and W is known as the weight contrast, and demonstrates the spatial link between the causative parameter and the event [55]. In this equation, C stands for both positive and negative spatial associations based on positive and negative values. Figure 6a depicts the final LSM of WOE. **(ii) Frequency Ration (FR):** The FR model has been widely considered as one of the most effective GIS-based models for determining the spatial relationship between two variables [56]. This methodology is a fairly consistent experimental method for producing LSM for the investigated area [57]. The 2.12 algorithm was used to calculate the FR for each predisposing parameter. \[\text{FR}=\frac{\text{N}_{\text{i}}\text{P}_{\text{x}}/\text{N}}{\text{N}_{ \text{i}}\text{Q}/\text{N}\text{I}} \tag{4}\]  
where FR is the Frequency Ratio, \(\text{N}_{\text{i}}\text{P}_{\text{x}}\) is the number of pixels in each landslide conditioning factor class, N is the total number of pixels in the study area, \(\text{N}_{\text{i}}\text{P}_{\text{i}}\) is the number of landslide pixels in each landslide conditioning factor, and N is the total number of landslide pixels in the study area. To create LSI for the area of interest, the following mathematical algorithm was used. \[\text{LSI}=\sum_{i=1}^{\text{n}}\text{FR}_{\text{ij}} \tag{5}\]  
FR_ij is the frequency ratio value for \(\tilde{\gamma}\) class of factor \(\tilde{\gamma}\), and n is the total number of factors. After performing these steps, the LSM map were produced as shown in Figure 6b. **(iii) Information Value:** This approach was used in the current study to generate LSM of the research region. This model, which is based on GIS and RS, was used to forecast the geographical connection between landslide inventory and several types  
Figure 6: Final LSM of the study area: (**a**) LSM by WOE; (**b**) LSM by FR, and (**c**) LSM by IV. of predisposing variables [57]. The following computation formula was used to do this evaluation.