## 2 Materials and Methods
### Application of Frequency Ratio Model for Landslide Susceptibility Zonation  
The Frequency Ratio (FR) is a geospatial assessment tool used to estimate the susceptibility to landslides in a given research area [13]. It belongs to the bivariate statistical methods, and its value depends on the relationship between the location of landslides and LCFs [27]. For LCFs, weights are assigned based the ratio of the number of observed landslides to the area of the study area. The weights, represented as FRs, can be calculated using landslide inventory and each specific LCF [27]. When \(j\) is the class of a specific LCF (\(i\)), the FR is defined by the following equation:  
\[\text{SCAI}_{i}=\left(\frac{E_{i}}{F_{i}}\right) \tag{1}\]  
where:  
\(A=\) the number of pixels of the landslide in each LCF class  
\(B=\) the total number of pixels of the landslide in the test area  
\(C=\) the number of pixels in each LCF sub-class  
\(D=\) the total number of pixels in the test area [1]  
Accordingly, the FR was calculated by overlying landslide pixels with the thematic layers or LCF layers presented in Section 2.4 Values obtained using this method greater than 1 imply high landslide susceptibility within this class [13] and a strong correlation between the landslide occurrence and LCF class [28]. Values below 1 indicate no or a slight correlation between the LCF and landslide occurrence [13,28].  
Figure 4: Study area division into “Lososina” region and “Grödek” region superimposed on lithostratigraphic units.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Strategy** & **Map** & **Study Area** & \begin{tabular}{c} **No of Landslide in** \\ **Total Study Area** \\ \end{tabular} & \
\begin{tabular}{c} **Landslide Area in Total Study** \\ \end{tabular} &
\begin{tabular}{c} **Percentage of Total** \\ [\%] \\ \end{tabular} \\ \hline
1 st strategy & SOPO & \begin{tabular}{c} Lososina \\ Grödek \\ Total study area \\ \end{tabular} & \begin{tabular}{c} 322 \\ 425 \\ 747 \\ \end{tabular} & \
\begin{tabular}{c} 8.31 \\ 9.94 \\ 18.25 \\ \end{tabular} &
\begin{tabular}{c} 46 \\ 54 \\ — \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 3: Landslides used for landslide susceptibility modeling in various strategies.  
The Landslide Susceptibility Index (LSI) was subsequently calculated for each pixel in the image (\(x\),\(y\)) according to the formula:  
\[\text{LSI}_{xy}=\sum_{i=1}^{n}\text{FR}_{i,j} \tag{2}\]  
Based on natural breaks, [PERSON] [56] developed an optimization method to minimize within-class variance while maximizing between-class variance. This classification method is generally implemented into GIS software, such as ESRI@ ArcGIS software or QGIS (free open source software). The classes are split according to natural clusters inherent in the data, and the boundaries are statistically determined when relatively large jumps occur within the susceptibility indices as determined by their variance. The LSI values were separated based on this method into five susceptible classes. This number of susceptibility zones is commonly used in small-scale landslide susceptibility mapping [57; 58]: very low, low, moderate, high and very high. These are considered adequate for revealing any spatial patterns preserved in a dataset and aiding the interpretation of these LSMs [59].