Landslide susceptibility mapping of Kan using index of Entropy and LSM

Landslide susceptibility mapping (LSM) is a proper method to predicting landslide hazard risk in order to reducing its consequences. We prepared the LSM mapping of Kan basin by used of index of Entropy model and SVM-S. The validation of the produced maps is evaluated by used of the area under the curve ROC. Study area The study area is located on the north west of Tehran Province, between 35°46′ and 35°58′ N latitude and 51°10′ to 51°23′ E longitude. The area of the basin is 204.385 km2 (Figure. 2 (a)). Material and methods In the present study we used of 8 parameters consisting the distance from river, distance from fault, distance from road, land use, rainfall, aspect, slope, elevation, and lithology. Distance from the road was computed from the road at the interval 200 m using ArcGIS software (Fig.2f). The distance from road and distance from fault was calculated in same way (Figure. 2 d, h). The land use map has reclassified to 5 class (Figure.2g). The lithology parameter has been obtained by the reclassification of the geological map of Tehran at the scale of 1:100000 (Figure.2h). The digital elevation model (DEM) was extracted from the 1:50000 scale topographic maps. The parameters of slope degree (whit 5 classes), aspect layer were produced by used of the digital elevation model. (Figure.2c & d). The topography layer was reclassified into 5 class (Fig.2a). the introduced layers were used in this study according to the type of the models to produce of LSM maps. Entropy index Entropy is a measurement of the instability, imbalance, and uncertainty of a system (yang et al, 2010). The equations used to calculate the information coefficient dj representing the weight value for the parameter as a whole, are given as follows: pij=xij/(∑_(i=1)^m▒xij ) (1) (2) Ej= -k+∑_(i=1)^m▒pij ln⁡(pij) K=〖c(lnm)〗^(-1) (3) ((4 dj = EJ – 1 After calculating the total weight (wj) using Equation 5, the landslide risk of the case study is evaluated: (5) Hi = ∑_(i=1)^m▒xij In equation 5, H is the coefficient of landslide risk, wj is the final weigh of all the factors and Xij is the weight of each factor (zongji et al, 2010). The final landslide susceptibility map was prepared by the summation of weighted products of the secondarily parametric maps. H = (S×0/54) + (Df × 0/74) + (E × 0/082) + (Dr × 0/51) + (Dri × 0/51) + (A × 0/066) + (lu × 0/16) + (Lt × 0/0064) Support Vector Machine SVM algorithm as one of the most popular methods for solving regression problems has had significant results in landslide sensitivity zoning. consider a set of linear separable training vectors Xi (i = 1, 2, . . ., n). The training vectors consist of two classes, which are denoted as Yi = ±1. The goal of SVM is to search an n-dimensional hyperplane differentiating the two classes by their maximum gap. Mathematically, it can be expressed as: 1⁄2=∥w^2∥ (6) Y_i=((W.X_i )+)≥1 (7) A Lagrangian formulation is introduced to solve the problem (equation 8). Thus, the goal is now to minimize the Lagrangian L with to W and b and maximize with respect to λi. For this reason, we used of following equation: L=1/2∥w^2∥-∑_(i=1)^n▒Y^i ((W.X_i )+b)-1) (8) four types of SVM is existed: linear, polynomial, radial basis function (RBF) and sigmoid. The mathematical representation of each kernel (linear, polynomial, radial basis function, and sigmoid) is listed below, respectively: K (X_j 〖.X〗_i )= X_j^i.X_j K (X_j 〖.X〗_i )=(γ∙ X_j^i+r) ._ γ>0 K (X_j 〖.X〗_i )=e^(-γ〖(X_i-X_j)〗^2 ) ._ γ>0 tanh (γ .X_i^T. X_j+r) γ, d, and r are user-controlled parameters, as their correct definition significantly increases the accuracy of the SVM solution. In the present research we used of Sigmoid function. To measure the validation of the models, we used of a relative ROC by comparing the existing landslide location with the two landslide susceptibility maps. The success rate curves were obtained by used of the 70% training dataset (29 landslide locations). ROC curve (AUC) represents the quality of the probabilistic model (it is ability to predict the occurrence or nonoccurrence of an event). Result and discussion The area of the low, moderate, and high classes based on the SVM model were found to be 109.485 km2, 38.7 km2, and 56.2 km2, respectively, whereas based on landslide susceptibility map by used of index of entropy, the 118.175 of the study area has low susceptibility risk, and the moderate, and high susceptibility zones have the 41.2 km2, 45.02 km2 of the study area, respectively (Fig. 3). Based on the entropy model, the 8 numbers of the landslides points located on the high-risk zone and the 8 numbers of the landslide points located on the moderate risk zone and low risk zone have 10 of the landslide points. Based on the LSM map produced by the SVM-S model, the 13 numbers of the landslide points located on the high risk zone and the 5 number of the landslide point located on the moderate-risk zone. The ROC plot assessment reveals that the AUC in the susceptibility map based on the index of entropy model was 0.86 and the AUC in the susceptibility map based on the Logistic Regression model was 0.91 (Fig. 5). Conclusion The high-risk zone on the LSM map produced by the SVM model is located in the north east and the west and south of the basin and based on the LSM map produced by the Entropy model is located in the north east and the south of the basin. The LSM map has produced in a regional scale, so further study need be carried out at the site-specific level to determine the exact extent site of the slope instability. Keywords: LSM, Index of Entropy model, Kan basin, Support Vector Machine, Sigmoid function, SVM-SIGMOID.