## 4 Results  
Using machine learning techniques and Google Earth imagery, we identified and mapped up to 1252 eroded spots from Sentinel 1, Sentinel 2, and Landsat 8 images. Figure 1 depicts the regional distribution of soil erosion. This soil erosion includes many types of soil erosion, including rill erosion, gully erosion, ravine erosion, and stream-bank erosion. We completed three bivariate models in this research to obtain SEM of the study region. Table 2 displays the results of all bivariate approaches in detail. The following is a detailed description of Table 2.  
Altitude, as shown in Table 2, has a significant relationship with soil erosion in the study region. The most important elevation class is 1300-1500 m, followed by \(>\)1500 m, while the least sensitive class of soil erosion is 900 m. In the present investigation, the slope parameter was regarded as the essential element. The slope parameter was essential because, as shown in Table 2, as the slope increased, so did the rate of soil erosion. According to the data in Table 2, \(>\)40\({}^{\circ}\) is the most vulnerable class for erosion phenomena, whereas 10\({}^{\circ}\) and 10-20\({}^{\circ}\) are the most secure and safe zones. The recent survey's analytical findings revealed that SE was the most important class of aspect, followed by NW. According to the tabulated data, S and SW are not major classes for soil erosion. According to the tabulated outcomes, a concave structure is the important class for soil erosion, as shown in Table 2, with 1.32, 2.20, and 0.79 values for the WOE, FR, and IV models, respectively. While the less vulnerable class of curvature parameters was flat, with values of \(-\)2.16, 0.23, and \(-\)1.47 for WOE, FR, and IV, respectively. The statistics of soil erosion and drainage showed that both variables had a positive relationship with each other. The bivariate statistical results suggested that a 25 m drainage buffer is the most vulnerable class for soil erosion, followed by the 25-50 and 50-100 m buffers. According to the table, the WOE, IV, and FR model values for the most vulnerable class are 1.60, 2.87, and 1.49, respectively. The stream study showed that the most vulnerable class of stream parameter was \(>\)250, with \(-\)1.63, 0.60, and \(-\)1.05 for the WOE, FR, and IV models, respectively. In the current research, a rainfall map was generated using CHIRPS satellite data and then divided into five classes to assess the relationship of rainfall parameters with landslide incidents. The precipitation data in Table 2 confirmed the notion that precipitation plays a significant role in soil erosion. The analysis indicated that the precipitation class of 1881-2035 mm/year was the most significant for soil erosion, followed by 1773-1881 and 1681-1773 mm/year. The class 1410-1571 mm/year was the least vulnerable class of current causative factors, with \(-\)0.90, 0.44, and 0.83 for WOE, FR, and IV models, respectively. The tabulated results clearly show that each class of the LULC parameter had varying effects on soil erosion activities. Table 2 shows that the barren land of the current research region is the most sensitive class to soil erosion when compared to other classes of LULC. WOE, FR, and IV analytical values were 0.87, 1.98, and 0.68, respectively. Soil erosion in the built-up class of LULC parameters can be regarded as minimal. The present study's tabulated data demonstrated that faults had no direct influence on soil erosion danger. Table 2 describes the corresponding results of all three models. The findings revealed that the fault's 150-350 m buffer zone was the most vulnerable to soil erosion, while the 25 m buffer was the least vulnerable. The present study's results, as shown in Table 2, highlight that lithology is an important parameter in landslides. The analysis also indicates that Kuzagali Shale is the most vulnerable geological formation to soil erosion, whereas Margalla Hill Limestone is the most resistant. It also indicates that loamy and non-calcareous soils are the most prone to soil erosion.