## 4 ETL Susceptibility Assessment in Cephalonia Based on GIS-Based Analytic Hierarchy Process
### Validation of the Model  
The creation of the landslide susceptibility map was followed by the verification of the accuracy of the landslide susceptibility model. The validation of the landslide susceptibility results is usually carried out by applying two methods in the frame of the relevant studies. The first approach involves the comparison of the landslide susceptibility map with an inventory map, which includes landslide events in the study area (e.g., [110; 111; 140; 141; 142]). The second approach involves the use of the receiver operating characteristic (ROC; [143; 144; 145]). The result of this approach is a success rate resulting from the comparison between the earthquake-triggered landslide grid cells and the earthquake-triggered landslide susceptibility grid (e.g., [146]).  
Both approaches were used in this study for Cephalonia. For the first one, the ETL inventory in Cephalonia from 1636 to 2014 was used. The majority of the 67 landslides occurred in areas of high (24/67, 35.82%), very high (16/67, 23.88%) and critically high (15/67, 22.39%) susceptibility (Table 7). In total, 55 out of 67 events (82.09%) occurred in high to critically high susceptibility zones, while 12 occurred in low to medium susceptibility zones (3 in low and 9 in medium susceptibility zones, with a percentage of 4.48% and 13.43%, respectively) (Table 7).  
For the second approach based on the ROC curve, the curves are obtained by plotting in a graph with both axes having values ranging from 0 to 1. The \(x\)-axis comprises values of false positive rate based on the resulting earthquake-triggered landslide susceptibility map and the \(y\)-axis comprises values of true positive rate based on the ETL sites. The accuracy of the model is related to the area under the curve (AUC). The AUC ranges from 0.5 to 1.0 [147; 148] with a value equal to 1.0 corresponding to a perfect model prediction accuracy. A value found along the diagonal line of the graph implies a 50% probability of predicting the generation of landslides. The larger the value of the AUC, the better the landslide susceptibility model predicts susceptible areas and landslides. In the case of Cephalonia, the ROC graph and the AUC have been derived by using the ArcSDM tools in ArcGIS 10.7.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**LSI Class** & **Area (km2)** & **Percentage (\%)** \\ \hline No susceptible & 86.40 & 8.46 \\ Very low & 210.26 & 20.60 \\ Low & 236.42 & 23.16 \\ Moderate & 199.82 & 19.57 \\ High & 152.78 & 14.97 \\ Very high & 99.68 & 9.76 \\ Critically high & 35.52 & 3.48 \\ Total & 1020.87 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Areas of susceptibility map classes.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Landslide Susceptibility** & **ETL** & **Percentage (\%)** \\ \hline No & 0 & 0.00 \\ \hline Very low & 0 & 0.00 \\ \hline Low & 3 & 4.48 \\ \hline Moderate & 9 & 13.43 \\ \hline High & 24 & 35.82 \\ \hline Very high & 16 & 23.88 \\ \hline Critically high & 15 & 22.39 \\ \hline Total & 67 & 100.00 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Distribution of the recorded historical and recent ETL in the detected landslide susceptibility zones of Cephalonia Island.  
The AUC was calculated as 0.803 (Figure 11), which reveals fair to good model prediction accuracy.