Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Support vector machine modeling of earthquake-induced landslides susceptibility in central part of Sichuan province, China

Support vector machine modeling of earthquake-induced landslides susceptibility in central part... Background: Support vector machine (SVM) modeling is a machine-learning-based method. It involves a training phase with associated input and a predicting phase with target output decision values. In recent years, the method has become increasingly popular. The aim of this study is to carry out prediction of earthquake-induced landslides distribution in the area affected by the April 20 2013 Lushan earthquake based on GIS and the SVM model. The current study was undertaken to investigate the prevalence of Impaired Fasting Glucose (IFG)/Type 2 Diabetes (T2D) and its risk factors in the adult population in Biyem-Assi-Yaoundé, Cameroon. Results: A detailed inventory map containing 1289 landslides triggered by this earthquake was produced through interpretation of colored aerial photographs and extensive field surveys. Elevation, slope angle, slope aspect, land cover, distance from co-seismic faults, peak ground acceleration and geology unit were selected as the controlling parameters. Cross validation with grid search method were used to search the best modeling parameters. A grid cell size of 60 × 60 m was adopted to produce the landslide susceptibility maps. The study area was divided into 186175 grid cells and each grid consisted of seven layers representing the controlling parameters. 70% of the total landslides (1782 grid cells) were used as positive training samples and 1782 randomly selected points on the stable slopes were treated as negative training samples in concert with four kernel functions: linear, polynomial, radial basis function and sigmoid. These results were further validated using area-under-curve (AUC) analysis of success- rate curves and prediction-rate curves. Comparative analyses of landslide-susceptibility and area relation curves show that both the polynomial and radial basis function suitably classified the input data of both training dataset and validating dataset, though the radial basis function was a bit more successful in success rate curves. Four cases of landslide susceptibility were mapped. The generated landslide-susceptibility maps were compared with known landslide. About 20%-30% of the study area 26 (Linear 34.78%, Polynomial 30.49%, and radial basic 23.83%) was categorized into high and very high susceptible zones during the Lushan earthquake, containing more than 70% occurrence of landslides triggered by the earthquake (Linear 74.16%, Polynomial 85.32%, and radial basic 86.71%). However, in maps with sigmoid function, 62.27% of the area was found to be highly susceptible to landslides during the earthquake with almost the entire landslides occurrence. Conclusion: Most of the high susceptible and very high susceptible area was concentrated along the seism genic faults with a PGA of more than 0.52 g. This paper provide an example for selecting appropriate types of kernel functions for prediction mapping of seismic landslides using support vector machine modeling. The susceptibility maps for earthquake-induced landslides can be useful in landslide hazard mitigation by helping planners understand the probability of landslides in different regions. Keywords: Earthquake-induced landslide; Support vector machine; Susceptibility; Geographic information system * Correspondence: fangligang_csu@163.com Department of Civil Engineering, Central South University, Changsha, Hunan, China Full list of author information is available at the end of the article © 2015 Zhou and Fang; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 2 of 12 Background The results showed that landslide distribution can be Landslide is one of the most severe natural hazards in predicted. Landslides induced by Wenchuan earthquake the world, causing thousands of death and great property were assessed and predicted by Su et al. 2010 using loss per year. Earthquake is a dominant trigger of land- logistic regression models, and were compared with the slides in mountainous and tectonic-active areas. Landslides bivariate statistics, artificial neural networks, and support induced by an earthquake are usually large in number, vector machine models by Xu et al. 2012a. huge in scale and wide in distribution. Earthquake-induced Among these approaches, the support vector machine landslides can bring great damages to property and infra- (SVM) model has become increasingly popular. The structures in developed areas, leading to economic losses SVM was originally developed by [Vapnik, 1995] as a new and fatalities sometimes. For example, more than 20,000 machine learning algorithm for pattern classification and people were killed by landslides induced by the 2008 non-linear regression. The main procedure involved in Wenchuan earthquake with a magnitude of Ms 8.0 and 34 SVM modeling is a training phase with associated input large barrier lakes were produced, which threatened the and target output values. Recently, several authors have residents who lived downstream of these dams [Yin et al. applied the SVM model successfully on landslide suscep- 2009]. In the 2010 Yushu earthquake (Ms 7.1) about 60 tibility mapping. [Gallus et al., 2008] compared several million in damages and 8 deaths were directly caused by classification approaches of SVM, Gaussian process, and earthquake-induced landslides [YP Yin et al., 2010]. LR modeling, with SVM having the best results. [Xu et al., Earthquake-induced landslides were hard to predict, but 2012b] examined the use of SVM model for landslide could be evaluated. Identifying a region’s susceptibility susceptibility mapping in an earthquake zone with com- to landslides during an earthquake was an effective and bination of 4 kernel functions and 3 different training sets most economical way to provide planners with fore- and found that radial-basis and polynomial kernel func- knowledge of dangerous regions thereby helping with tions were suitable for modeling with any input training land management and infrastructure planning. For data. [Xu et al., 2012b] applied 6 different models in earthquake-induced landslide, landslide susceptibility susceptibility mapping of landslides induced by the 2008 assessment was to evaluate location of landslide suscepti- Wenchuan earthquake with SVM having a second best bility zones where landslides could be induced in future results outranked only by logistic regression. [Kavzoglu earthquake shaking. Many different methods and tech- et al., 2013] also made a comparison of susceptibility niques for assessing landslide susceptibility have been results from multi-criteria decision analysis, SVM, and proposed and tested. These have already been systemat- logistic regression and showed that multi-criteria decision ically compared and their advantages and limitations analysis and SVM methods were better than logistic outlined in Carrara et al. 1999, Huabin et al. 2005 and regression in shallow landslides susceptibility mapping. van Westen et al. 2008. Both deterministic and statistical These applications proved that when used properly, SVM methods have been used in earthquake-induced landslide model in landslide susceptibility mapping might produce susceptibility. For deterministic methods, assessment of a good result. Two outstanding advantages of the SVM earthquake-induced landslide susceptibility on a regional are: (a) Based on the principle of minimization structural scale commonly required the employment of an analyt- risk; (b) Guarantee its performance by solving constrained ical slope-stability method and the infinite-slope model quadratic form. Theoretically, it can achieve the optimal [Jibson and Keefer, 1993; Jibson et al., 2000; Refice and prediction result by using the SVM model. Its detailed Capolongo, 2002]. The deterministic method required mathematical formulas are introduced in [Vapnik and calculation to determine the limit-equilibrium of the Cortes 1995]. slope stability given the strength parameters of mass, In this study, we propose the application of SVM failure depth, and groundwater conditions for every model to produce a landslide susceptibility map of the area hit by the April 20, 2013 Lushan earthquake on the calculation point in the study area. This requirement caused immense problems in terms of data acquisition ArcGIS platform. The goal of the study is to produce a and control of spatial variability of the variables ([Carrara relatively accurate landslide susceptibility map with optimal kernel functions. The 4 resultant cases are compared using et al., 1999]. For statistical method, it was most common to use a statistical approach where landslide inventories AUC (area under curve) analysis to verify the susceptibility and causative factors are utilized to build a susceptibility mapping results. This is done by comparisons with known landslide locations to establish the model’s success rate, and model for the prediction of future landslides. For instance, Kamp et al. 2008 carried out spatial prediction of land- its predictive accuracy. slides related to 2005 Kashmir earthquake-induced by use of a multi-criterion method. Lee et al. 2008 applied Study area multivariate statistical methods in a study of shallow On April, 2013, an Ms 7.0 earthquake, with a maximum earthquake-induced landslides in central western Taiwan. source intensity of up to 9.0 on Chinese seismic scale, Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 3 of 12 struck Lushan county, Sichuan province, west China. composition of weathered and fractured superficial soils The epicenter of the main shock was located in 30.3°N, and rocks were widespread throughout the whole study 103.0°E, about 100 km southwest of Chengdu (Figure 1). area, because they could be triggered easily by weak The earthquake occurred on the southern segment of shaking. Rock avalanches are usually originated on a the Longmenshan fault zone. This area was celebrated high place along the river and road banks, with large for steep mountain landscapes and heavy tectonics. The potential energy, resulting in a high speed and a long April 20 earthquake was an strong aftershock of 2008 run-out distance during sliding process. Deep-seated Wenchuan earthquake and were the most devastative landslides are mainly distributed within a short distance earthquake in China since the 2008 Wenchuan earth- from the main co-seismic ruptures, since only a strong quake [Wei-Min et al., 2013]. ground shaking could trigger them. The study area had experienced serious shallow land- This area was very tectonic-active with many folds and slides during this earthquake, since the steep slopes and active faults trending NW–SE (Figure 1). The bedrock jagged ridges were susceptible to landslide while suffer- exposure in the area was dominated by Mesozoic volcanic ing heavy ground shaking. Topography of the study area rocks and Mesozoic group. The volcanic rocks, which ranges from river valley to mountainous. Elevation of comprised tuffs and lavas with intercalated sedimentary the study area ranges from 596 m to 2872 m. Land use rocks. Intrusive rocks consisted mainly of granites, sand- includes mainly cropland distributed on the ridges, slope stone and dykes of various compositions. As a result of wasteland on side-slopes and gullies and town in flat the abundant supply of rainfall and the local rich ground- river valleys. Due to long-term human activity, many parts water, almost all rocks in the study area had undergone a of the natural vegetation have been destroyed. Because certain degree of weathering. In many slopes, weathering it was right time for vegetation, earthquake-induced had penetrated deep into rock masses through joints and landslides were easy to be recognized according to bedding planes (Figure 2). landslide scars on aerial photos. Landslides triggered by the Lushan earthquake can be mainly classified into Methods following types (Figure 2): (1) shallow-disrupted slope Support vector machine (SVM) modeling failures; (2) rock avalanches; and (3) deep-seated rocky Support vector machine (SVM), as the representative’s or soil slides. Shallow-disrupted slope failures with a kernel-based techniques, is a major development in Figure 1 (a) Location of Sichuan Province; (b) Location of the study area; and (c) Geological settings of the study area. Explanation of geology units is listed in Table 2. Unit ‘g’ for Peak ground acceleration (PGA) means acceleration of gravity. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 4 of 12 Figure 2 Typical types of landslides. (a) Rock avalanches, (b) translational slides and (c) shallow-disrupted slope failures. machine learning algorithms. SVM is a group of 1 ϕðÞ w; b; α¼ w − αðÞ y½ w⋅x þ b −1 ð5Þ kk i i supervised learning methods based on the statistical i¼1 learning theory and the Vapnik-Chervonenkis (VC) dimension introduced by [V Vapnik and Cortes, 1995] where α ¼ðÞ α ; α ; …; α ∈R is the Lagrangian multi- 1 2 n and [Chervonenkis, 2013] that can be applied to pattern plier, and the problem can be solved by dual minimization classification or non-linear regression. of Equation (5)withrespect to w and b through standard For the linear separable condition, consider a set of procedures Equation (6). More detail of SVM was discussed training vectors with two classes as follows: in [Vapnik 1995]. D ¼fg ðÞ x ; y ;ðÞ x ; y ; ⋅⋅⋅;ðÞ x ; y ð1Þ 1 2 n 1 2 n ∇ ϕðÞ w; b; α¼ 0 ð6Þ where x ∈ X ⊂ R , y ∈ {1, − 1}, i = 1, 2,⋅⋅⋅,n, that can be sep- ∇ ϕðÞ w; b; α¼ 0 i i arated the two classes [1, −1] by a hyper-plane (Figure 3): Mostly, however, the training vectors are non-separable, ðÞ w⋅x þ b ¼ 0; w∈R ; b∈R ð2Þ [Vapnik 1995] introduced an slack variables ξ modified the constraints as follows: where w is the normal of the hyper-plane, b is a scalar base, and (·) denotes the scalar product operation. yðÞ ðÞ w⋅x þ b ≥1−ξ ; i ¼ 1; 2; ⋅⋅⋅; n; ξ ≥0 ð7Þ i i i After normalization, the geometrical margin between the two groups can be expressed as . The operation of To avoid a high value of ξ , some kind of penalty term C kk w the SVM algorithm is to find the hyper-plane that gives was introduced into the original optimization Equation (3), the largest geometrical margin to the training examples. which can be modified as: The maximum can be expressed as: kk w Minimize kk w þ C ξ ð8Þ 2 2 i¼1 Minimize kk w ð3Þ w;b 2 where C > 0 is the penalty factor to control the trade-off Subjecting to constrains: between the maximum margin and the minimum error. Additionally, a kernel function k(x , x ) is introduced by i j y w x þ b ≥1 i ¼ 1; 2; :::::; n ð4Þ [Vapnik 1995] to transform the originally non-linear data Introducing the Lagrangian multiplier, the cost function pattern to a linear one in higher dimensional feature can be defined as: space (Figure 3). Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 5 of 12 a 2 b Margin = c d Figure 3 Illustration of SVM model. (a) n-dimensional hyperplane differentiating the two classes with maximum gap; (b) non-separable case and the slack variables ξ; (c) transformation using kernel function of the originally non-linear data pattern to a linear one in higher dimensional feature space (d). Selection of the kernel function is the main issue in SVM also have been developed, but their theories are not reach modelling. Theoretically, any function that satisfy the perfection and they produce poor prediction efficiency Mercer criteria can be used as kernel function, however, than two-class SVM [Guo et al., 2005; Yao et al., 2008]. some of them work well in a wide variety of applications. Hence, a two-class SVM modeling is utilized in this study. The mathematical representation of some kernel functions To carry out the two-class SVM modeling, we estab- are listed below: lished a spatial database containing all the landslides triggered by the earthquake and their controlling parame- Linear : Kx ; x ¼ x x ð9Þ i j j ters. Then all the data layers were classified and rasterized p in Arcgis and coded in Matlab7.01. The landslides as well Polynomial : Kx ; x ¼ γx x þ r ; γ > 0 ð10Þ i j j as the same amount of selected stable slopes were ran- domly divided into two groups for training and validation −γ x −x kk i j Radial basis function : Kx ; x ¼ e ; γ > 0 ð11Þ i j purpose, respectively. We use the training dataset as input to train the SVM model, then the testing dataset were Sigmoid : Kx ; x ¼ tanh γx x þ r ð12Þ i j j used to examine the model. Both the training and valid- where γ is the gamma term in all the kernel function ation phase were completed in Matlab 7.01. Finally, all the except linear; p is the polynomial order term in the cells in the study area were input into the established kernel function for the polynomial kernel; r is the bias model for possibility prediction of landslide occurrence. term in the kernel function for the polynomial and sigmoid kernels. Proper parameters, such as the order of Data polynomials and width of radial basis function, play a Two kinds of data were indispensable in the two-class key role in governing the accuracy of the SVM modeling. SVM modeling: (1) Units with landslides and units Of these functions, polynomial and radial basis function supposed to be considered as stable and conditions of (RBF) are the most-used kernels and are utilized in our these units and (2) Conditions of units that needed to be research due to its good generalizing properties. predicted. The former were samples used to train the In reality, the unstable slope cases (with landslides) are two-class SVM model, while the latter were used as the recognized as positive pattern, while stable slope cases input of the trained model to predict risk of region (without landslides) are recognized as negative pattern. including them. All of the data representing a categorical Note that we often commonly have only a one-class attribute should be converted into numeric code before dataset without negative data. One-class SVM models entering the SVM model. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 6 of 12 Landslide inventory Controlling parameters of landslides Institute of Remote Sensing and Digital Earth (RADI) of Seven environmental variables were used to train the the Chinese Academy of Sciences (CAS) took airborne model and to predict the potential distribution for land- images with a high-resolution of 0.6 m covering the slides (Figure 5 and Table 2). These variables included: earthquake-affected area on the morning right after the (1) slope gradient, (2) slope aspect, (3) land cover, (4) earthquake. Except a little part was masked by cloud, distance to fault, (5) peak ground acceleration (PGA) most of earthquake damage in this area was shown clearly distribution of April 20 Lushan earthquake, (6) elevation, on these image. All of these high-resolution images as well (7) geology unit. The above selections were made based as a preliminary interpretation of earthquake-induced on the authors’ knowledge of the physical environment geo-hazards were proposed on Geo-Information Platform and landslides in the study area. Slope gradient, slope as- of Lushan Earthquake [Institute of Mountain Hazard pect, elevation were derived from digital elevation model andEnvironment,C.A.o.S., andGeomatics Center of (DEM). Land cover layer was derived from 1:20,000 scale Sichuan Province 2013] based on Tianditu online map digital vegetation cover maps. For ease of analysis, the service [Chen et al., 2013]. Due to a critical use for rescue 1:20,000 scale superficial and solid geology map covering after earthquake, this preliminary landslide inventory was the study area was divided into 10 groups based on incomplete, only location of suspected landslides were chronostratigraphic unit. Other environmental variables available. were also divided into seven or eight classes manually, The accurate detection of landslides is vital for land- slope gradient was first broken at 15° because very fewer slide susceptibility analysis, so an inventory of landslides landsides were probable on shallower slopes. The PGA triggered by April 20 Earthquake was made with the map is extracted from the United States Geology Survey help of Arcgis server. Firstly, the high resolution images (U.S.G.S) Shakemap (http://earthquake.usgs.gov/earthquakes/ provided by Tianditu map service were invoked into shakemap) (see Table 2). Arcgis through Arcgis server. These images were specified as the based map. Then, an empty vector layer with the Results same coordinate system as the base map was created for There are many free programs for SVM modelling [Chang the storage of landslides. After that, experts in earthquakes and Lin, 2011; Joachims, 1999], which can be downloaded and geo-hazards were called upon to visually interpret from the internet, providing all kinds of interfaces to other the base map according to their experiences, knowledge software. In this study, LibSVM [Chang and Lin, 2011] as well as previously identified landslide points. High- was employed to finish the computation of the SVM resolution pre-event satellite images of RADARSAT-2 model on Matlab 7.01. The environmental parameters and SPOT-4 (see Table 1) of the study area were were derived and rasterized in ArcGIS 9.3. A grid cell size geometrically rectified and matched to be taken into of 60 × 60 m was adopted to produce the landslide suscep- consideration as a contrast. The boundaries of landslides tibility maps. The study area was divided into 186,230 grid were interpreted on the base map and transformed into cells and each grid consisted of seven layers representing vector format and stored in ArcGIS system. A filed survey the environmental parameters. was finally conducted to check the accuracy of the interpretation, following which the interpreted images Training and validation dataset were modified. The resultant landslide inventory map is The two-class SVM requires both positive and negative shown in Figure 4. Landslide–area ratio(LAR), defined data to train the model. The landslide inventory were as the percentage of the area affected by landslide activity, randomly divided into two groups: 70% of the total (902 and landslide number density (LND) gives the number landslides with 1782 grid cells) were used as positive of landslides per square kilometer. In this study area, training samples. As mentioned before, negative training 2 2 LAR =(4.26 km /674.45 km ) × 100% = 0.63% and LND = data was also needed. 1782 negative training points were 2 − 2 1289landslides/674.45 km =1.91 km . generated within 120 m interval in both north and south direction of the positive points. A validation dataset con- tains 30% of the total landslides (387 landslides with 738 grid cells) and 738 negative points generated using the Table 1 Images used in ArcGIS for interpretation same way as negative training data. A total of 2520 land- No. Type Date Mode/resolution slide points were assigned the value of 1, while the same 1 RADARSAT-2 2012-03-04 WIDE/30 m amount of negative points were assigned the value of 0. 2 SPOT-4 2011-04-09 PAN/6.25 m In SVM modelling, the input of controlling factors 3 SPOT-4 2011-04-09 MS/12.5 m should be as a vector of real numbers. For categorical 4 Airborne images 2013-04-20 0.6 m attributes, a simple 1 of k coding is recommended to Data source can be found on http://www.radi.ac.cn/yaan/yaanphoto/. represent a k-category attribute. For instance, suppose a Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 7 of 12 Figure 4 Distribution of landslides triggered by the April 20, 2013 Lushan earthquake. Figure 5 Controlling factors of landslides as input of the SVM modelling (a) Slope gradient; (b) Aspect; (c) Land cover; (d) Distance to fault; (e) PGA; (f) Elevation; and factors of geology unit can be seen in Figure 2(b). Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 8 of 12 Table 2 Controlling parameters and their classes for this study Controlling parameters Classes Elevation (m) (1)(min)596-800;(2)800-1200(3)1200-1600;(4)1600-2000;(5)2000-2400;(6)24002872(max) Slope gradient (°) (1)< 15;(2)15-20;(3)20-25;(4)25-30;(5)30-35;(6)35-40;(7)40-45;(8)> 45 Aspect (1)F;(2)N;(3)NE;(4)E;(5)SE;(6)S;(7)SW;(8)W;(9)NW; Distance to co-seismic fault (km) (1)< 2;(2)2-4;(3)4-6;(4)6-8;(5)8-10;(6)10-12;(7)12-14;(8)14-16;(9)16-18;(10);18-20 PGA (1)0.24;(2)0.28;(3)0.32;(4)0.36;(5)0.40;(6)0.44;(7)0.48;(8)0.52;(9)0.56;(10);0.58 Land cover (1)Woodland;(2)Wooded Grassland;(3)Closed Shrub land;(4)Open Shrub land;(5)Grassland;(6)Cropland Geology unit (1)Quaternary(2) Paleogene(3)Cretaceous(4)Jurassic(5)Triassic(6)Devonian(7)Silurian (8)Ordovician(9)Sinian(10)Proterozoic 1-dimensional a three-category attribute taking value {a, follows: (1) Set a pair of (C, γ) values for SVM model; (2) b, c}, Just turn it into 3-dimensional numbers such that Randomly divided the training dataset into 5 equal sized a = (1,0,0), b = (0,1,0), c = (0,0,1). If the number of values subsets; (3) Use Four subsets of them to train the SVM in an attribute is not too large, such coding is more model; (4) Validate the trained model using the one stable than using a single number to represent a cat- remaining subset; (5) Repeat step three and four for five egorical attribute ([Hsu et al., 2003]). Therefore, the times for each of the subset; (6) Calculate the overall seven environmental parameters were converted into a accuracy defined as the percentage of data which are vector with 59 bits. Finally, a training dataset containing correctly predicted. 3564 grids with 7 input variables were built through Pairs of (C, γ) were generated through a grid search −8 −7 −6 6 7 8 −8 −7 −6 extracting the value of landslide conditioning factors in with C = 2 ,2 ,2 … 2 ,2 ,2 and γ =2 ,2 ,2 … 6 7 8 every grid. 2 ,2 ,2 . For every pair of (C, γ), we can get an overall accuracy and the optimal C and γ corresponded to the Cross validation and grid search for SVM parameter highest overall accuracy. optimization The best value of C for linear was 2 with the overall The performance of the SVM model is depended on the accuracy 85.5%. The best C and γ for polynomial were choice of kernel functions and their parameters especially found 4 and 1 with the overall accuracy 89.6%. In the the penalty factor C and γ terms. In this study, a grid- case of RBF, the best C and γ were 16 and 1 respectively, search method with 5-folder cross-validation was used to with the overall accuracy 92% while sigmoid used 16 and locate the optimal values of C and γ [Hsu et al., 2003] as 8 as the best C and γ. Figure 6 (a) Success rate curves of the four SVM models; (b) Prediction rate curves of the four SVM models. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 9 of 12 Comparison of landslide susceptibility maps and true positive rate (TPR, defined as TP/(TP + FN)) ROC curve is one of the useful methods for representing as x and y axes respectively. The true-positive rate is the quality of deterministic and probabilistic detection, also known as sensitivity in biomedicine, or recall in especially for landslide susceptibility assessment. The char- machine learning. The false-positive rate is also known acterizes the quality of a forecast system by describing the as the fall-out and can be calculated as 1- specificity. system’s ability to anticipate correctly the occurrence or The area under the ROC curve (AUC) is an important non-occurrence of predefined event (Yesilnacar and Topal measure of the accuracy of the binary classification. 2005). A true positive (TP) means prediction of a landslide AUC values are typically between 0.5 and 1.0. If this area for a point where a landslide does occur, while a false is equal to 1.0 then the roc curve consists of two straight positive (FP) is a prediction of a landslide for a stable lines, one vertical from (0, 0) to (0, 1) and the next point. On the conversely, we can get the true negative horizontal from (0, 1) to (1, 1) this test is 100% accurate (TN) and false negative (FN). A ROC space is defined because both the sensitivity and specificity are 1.0 and by the false positive rate (FPR, defines as FP/(FP + TN)) there was no false positives and no false negatives. On Figure 7 Landslide susceptibility mapping using different kernel functions: (a) Linear; (b) Polynomial; (c) RADIAL basis function; (d) SIGMOID. All the results were classified into five classes: VHS, HS, MS, LS, and VLS. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 10 of 12 the other hand a test that can’t discriminate between was the decision values of each pixel. The results were positive and negative corresponds to an ROC curve that then converted into raster data. Figure 7 showed the is the diagonal line from (0, 0) to (1, 0). The AUC for mapping results for the landslide susceptibility index this line is 0.5. (LSI) ranging from0 to 1. 0 indicates no chance and 1 in- To evaluate the four landslide susceptibility maps, dicates 100% chance for occurrence of landslides. success-rate curves and prediction-rate curves were The LSI values of each grid cell predicted using SVM established, and values of area under curves (AUC) were with the linear, polynomial, radial basis, and sigmoid also calculated [Hasegawa et al., 2009]. Higher AUC value kernel functions were 0.0004-0.9752, 0.0001-0.9999, indicated a higher capacity of correctly classifying the data 0.0007-0.9948, and 0.0047-0.9896 respectively. with existing landslides. The success-rate curve was a A few classification methods, such as natural breaks, measure of goodness of fit for SVM model and training equal intervals and defined interval, were used to distin- data. The curve was obtained by comparing the four guish the susceptibility classes for trial. Equal intervals landslide susceptibility maps with the training dataset, classification was found not to be useful for its emphasis (Figure 6a). Results indicated that RBF and polynomial on the amount of one class value relative to other classes. had the highest AUC values 0.97 and 0.91 respectively, Natural breaks are identified that best group similar values followed by linear (0.77), while model using sigmoid and that maximize the differences between classes and kernel function had the lowest AUC values of 0.58. not useful for comparing multiple maps built from differ- Nevertheless, the success-rate was not a suitable meas- ent underlying information. A series of specified interval ure for the prediction capability of the landslide models sizes can be used to define the classes with different because it was based on the landslide pixels that had ranges in defined interval methods based on a compre- already been used for building the model. To overcome hensive consideration of the data distribution. Moreover, this, prediction-rate curve and corresponding AUC the define interval classification allow comparison of values were obtained by comparing the four susceptibility different maps with similar ranges of attribute value. maps with the validation dataset (Figure 6b). The results The maps with continuous LSI values were then reclas- showed that model using polynomial kernel functions had sified into five landslide susceptibility categories using the the highest capacity of prediction with the AUC of 0.86, method of define intervals, i.e. very low susceptibility slightly better than RBF (0.82) and Linear (0.78). Same (VLS: less than 0.1), low susceptibility (LS: 0.1-0.3), with success-rate curve, sigmoid had the lowest AUC moderate susceptibility (MS: 0.3-0.5), high susceptibility values. (HS: 0.5-0.7), and very high susceptibility (VHS: more than 0.7) (Figure 7). Discussion The resultant landslide susceptibility maps were also Once the landslide susceptibility models were success- compared with the landslide inventory. The coverage per- fully trained in the training phase, they were then used centages of 5 susceptibility classes and the corresponding to calculate the landslide susceptibility indexes (LSI) for landslide occurrence are shown in Table 3. The results all the pixels. The SVM classification output or result showed that the landslide frequency ratio (defined as the Table 3 Landslide statistical results by different SVM kernel functions Susceptibility class Success Prediction Models rate rate VLS LS MS HS VHS %area 8.39 29.83 27.00 23.87 10.91 Linear %landslide 0.44 6.67 18.73 38.41 35.75 0.77 0.78 LND 0.05 0.22 0.69 1.61 3.28 %area 28.01 27.95 13.56 12.66 17.83 Polynomial %landslide 1.27 4.52 8.89 16.71 68.61 0.91 0.86 LND 0.05 0.16 0.66 1.32 3.85 %area 11.16 54.29 10.09 9.01 14.82 Radial basic %landslide 1.83 5.79 5.67 11.63 75.08 0.97 0.82 LND 0.16 0.11 0.56 1.29 5.07 %area 1.12 7.03 29.56 62.27 0.01 Sigmoid %landslide 0.12 0.71 2.82 96.27 0.08 0.58 0.58 LND 0.11 0.10 0.10 1.55 7.78 Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 11 of 12 ratio of percentage of landslide occurrence in each class on disaster prediction in other regions with potential that of area) gradually increased from the very low to the seismic risks given appropriate kernel functions and high susceptibility class and then suddenly jumped in very model parameters high susceptibility class. Competing interests According to maps, about 20%-30% of the study area The authors declare that they have no competing interests. (Linear 34.78%, Polynomial 30.49%, and RBF 23.83%) were Authors’ contributions categorized into high and very high susceptible zones SZ carried out the susceptibility modeling and drafted the manuscript. LF during the Lushan earthquake, with 70%-80% occurrence arranged the structure of the manuscript and participated in the discussion of landslides triggered by the earthquake (Linear 74.16%, and conclusion of the study. Both authors read and approved the final manuscript. Polynomial 85.12%, and RBF 86.71%). However, in maps with sigmoid function, 62.27% of the area were found to Acknowledgement be highly susceptible to landslides during the earthquake This research is supported by State Key Development Program of Basic Research of China (Grant 2011CB710601) The data used in this paper was provided by the with almost all of the landslides occurrence. Department of Geotechnical Engineering ,Central South University, China. We Most of areas that classified as very high, high and wish to express our sincere appreciation for the generous support. moderate were concentrated along the seism genic faults, Author details suffering a high PGA of more than 0.52 g. This may be- Department of Civil and Structural Engineering, Kyushu University, Fukuoka, cause earthquake is the trigger of the landslides used for Japan. Department of Civil Engineering, Central South University, Changsha, training model to produce the landslide susceptibility map. Hunan, China. Received: 7 August 2014 Accepted: 14 October 2014 Conclusion Based on the statistical learning theory, GIS technology, References SVM model, and four types of kernel functions, including Carrara A, Guzzetti F, Cardinali M, Reichenbach P (1999) Use of GIS technology in linear function, polynomial function, RBF function, and the prediction and monitoring of landslide hazard. Nat Hazards 20(2–3):117–135 sigmoid function, this work has studied the prediction for Chang C-C, Lin C-J (2011) LIBSVM: a library for support vector machines. ACM Transactions on Intelligent Systems and Technology (TIST) 2(3):27 spatial distribution of landslides triggered by the April 20, Chen Y-W, Yap K-H, Lee JY (2013) Tianditu: China’s first official online mapping 2013 Lushan earthquake in Sichuan province of China. service, Media. Culture & Society 35(2):234–249 From the results of this study, the following conclusions Chervonenkis AY (2013) Early History of Support Vector Machines. Festschrift in Honor of Vladimir N. Vapnik, Empirical Inference, pp 13–20 can be drawn: Gallus D, Abecker A, Richter D (2008) Classification of landslide susceptibility in the development of early warning systems. In: Symposium on Headway in (1) Cross validation and grid search was an efficient Spatial Data Handling. Springer: Montpellier, France pp 55–75 Guo Q, Kelly M, Graham CH (2005) Support vector machines for predicting tool for parameters optimization. This method distribution of Sudden Oak Death in California. Ecol Model 182(1):75–90 avoided the subjectivity in parameter selection for Hasegawa S, Dahal RK, Nishimura T, Nonomura A, Yamanaka M (2009) the SVM model. DEM-based analysis of earthquake-induced shallow landslide susceptibility. Geotech Geol Eng 27(3):419–430 (2) The validation results by ROC method showed that Hsu C-W, Chang C-C, Lin C-J (2003) A Practical Guide to Support Vector RBF and polynomial function is the better than Classification. Technical report, Department of Computer Science, National linear and sigmoid for the Lushan earthquake area. Taiwan University. Huabin W, Gangjun L, Weiya X, Gonghui W (2005) GIS-based landslide hazard AUC of RBF shows a high accuracy of 97% (0.97) in assessment: an overview. Prog Phys Geogr 29(4):548–567 case of success rate curves and 82% (0.82) in case of Institute of Mountain Hazard and Environment, C. A. o. S., and Geomatics Center prediction rate curves, and that of polynomial are of Sichuan Province (2013) Geo-Information Platform of Lushan Earthquake. http://scgis.net/LSXEarthquake/ 91% (0.91) and 86% (0.86) respectively. Jibson RW, Keefer DK (1993) Analysis of the seismic origin of landslides: examples (3) According to the landslide susceptibility index of from the New Madrid seismic zone. Geol Soc Am Bull 105(4):521–536 each grid, the study area was divided into 5 classes Jibson RW, Harp EL, Michael JA (2000) A method for producing digital probabilistic seismic landslide hazard maps. Eng Geol 58(3):271–289 of landslide susceptibility, namely very low, low, Joachims T (1999) Svmlight: Support Vector Machine., SVM-Light Support Vector moderate, high and very high and 4 landslide Machine http://svmlight.joachims.org/. University of Dortmund, 19(4) susceptibility maps were generated Comparing with Kamp U, Growley BJ, Khattak GA, Owen LA (2008) GIS-based landslide susceptibility mapping for the 2005 Kashmir earthquake region. Geomorphology all 1289 landslides (2520 grid cells), The results show 101(4):631–642 that the landslide frequency ratio gradually increases Kavzoglu T, Sahin E, Colkesen I (2014) Landslide susceptibility mapping using GIS- from the no to the high susceptibility class. based multi-criteria decision analysis, support vector machines, and logistic regression. Landslides 11(3):425-439 (4) Most of landslide triggered by the earthquake Lee C-T, Huang C-C, Lee J-F, Pan K-L, Lin M-L, Dong J-J (2008) Statistical approach happened in high and very high susceptible zones, to earthquake-induced landslide susceptibility. Eng Geol 100(1):43–58 which were concentrated along the seism genic Refice A, Capolongo D (2002) Probabilistic modeling of uncertainties in earthquake- induced landslide hazard assessment. Comput Geosci 28(6):735–749 faults with a high PGA; Su F, Cui P, Zhang J, Xiang L (2010) Susceptibility assessment of landslides (5) The SVM modelling related to the Lushan caused by the wenchuan earthquake using a logistic regression model. J Mt earthquake landslides can be applied to landslide Sci 7(3):234–245 Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 12 of 12 van Westen CJ, Castellanos E, Kuriakose SL (2008) Spatial data for landslide susceptibility, hazard, and vulnerability assessment: an overview. Eng Geol 102(3):112–131 Vapnik VN (1995) The nature of statistical learning theory. Springer-Verlag New York, Inc, p 188 Vapnik V, Cortes C (1995) Support-vector networks. Mach Learn 20(3):273–297 Wei-Min W, Jin-Lai H, Zhen-Xing Y (2013) Preliminary result for rupture process of Apr. 20, 2013, Lushan Earthquake, Sichuan, China. CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION 56(4):1412–1417 Xu C, Xu X, Dai F, Saraf AK (2012a) Comparison of different models for susceptibility mapping of earthquake triggered landslides related with the 2008 Wenchuan earthquake in China. Comput Geosci 46:317–329 Xu C, Dai F, Xu X, Lee YH (2012b) GIS-based support vector machine modeling of earthquake-triggered landslide susceptibility in the Jianjiang River watershed. China, Geomorphology 145:70–80 Yao X, Tham L, Dai F (2008) Landslide susceptibility mapping based on support vector machine: a case study on natural slopes of Hong Kong, China. Geomorphology 101(4):572–582 Yesilnacar E, Topal T, (2005) Landslide susceptibility mapping: A comparison of logistic regression and neural networks methods in a medium scale study, Hendek region (Turkey). Engineering Geology, 79(3-4):251-266. Yin Y, Wang F, Sun P (2009) Landslide hazards triggered by the 2008 Wenchuan earthquake, Sichuan, China. Landslides 6(2):139–152 Yin Y, Zhang Y, Ma Y, Hu D, Zhang Z (2010) Research on major characteristics of geohazards induced by the Yushu Ms7. 1 earthquake. J Eng Geol 18(3):289–296 Submit your manuscript to a journal and benefi t from: 7 Convenient online submission 7 Rigorous peer review 7 Immediate publication on acceptance 7 Open access: articles freely available online 7 High visibility within the fi eld 7 Retaining the copyright to your article Submit your next manuscript at 7 springeropen.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geoenvironmental Disasters Springer Journals

Support vector machine modeling of earthquake-induced landslides susceptibility in central part of Sichuan province, China

Zhou, Suhua; Fang, Ligang
Geoenvironmental Disasters , Volume 2 (1) – Feb 6, 2015
Download PDF
12 pages

Loading next page...
 
/lp/springer-journals/support-vector-machine-modeling-of-earthquake-induced-landslides-fn3qevs8nb

References (37)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Zhou and Fang; licensee Springer.
Subject
Environment; Environment, general; Earth Sciences, general; Geography (general); Geoecology/Natural Processes; Natural Hazards; Environmental Science and Engineering
eISSN
2197-8670
DOI
10.1186/s40677-014-0006-1
Publisher site
See Article on Publisher Site

Abstract

Background: Support vector machine (SVM) modeling is a machine-learning-based method. It involves a training phase with associated input and a predicting phase with target output decision values. In recent years, the method has become increasingly popular. The aim of this study is to carry out prediction of earthquake-induced landslides distribution in the area affected by the April 20 2013 Lushan earthquake based on GIS and the SVM model. The current study was undertaken to investigate the prevalence of Impaired Fasting Glucose (IFG)/Type 2 Diabetes (T2D) and its risk factors in the adult population in Biyem-Assi-Yaoundé, Cameroon. Results: A detailed inventory map containing 1289 landslides triggered by this earthquake was produced through interpretation of colored aerial photographs and extensive field surveys. Elevation, slope angle, slope aspect, land cover, distance from co-seismic faults, peak ground acceleration and geology unit were selected as the controlling parameters. Cross validation with grid search method were used to search the best modeling parameters. A grid cell size of 60 × 60 m was adopted to produce the landslide susceptibility maps. The study area was divided into 186175 grid cells and each grid consisted of seven layers representing the controlling parameters. 70% of the total landslides (1782 grid cells) were used as positive training samples and 1782 randomly selected points on the stable slopes were treated as negative training samples in concert with four kernel functions: linear, polynomial, radial basis function and sigmoid. These results were further validated using area-under-curve (AUC) analysis of success- rate curves and prediction-rate curves. Comparative analyses of landslide-susceptibility and area relation curves show that both the polynomial and radial basis function suitably classified the input data of both training dataset and validating dataset, though the radial basis function was a bit more successful in success rate curves. Four cases of landslide susceptibility were mapped. The generated landslide-susceptibility maps were compared with known landslide. About 20%-30% of the study area 26 (Linear 34.78%, Polynomial 30.49%, and radial basic 23.83%) was categorized into high and very high susceptible zones during the Lushan earthquake, containing more than 70% occurrence of landslides triggered by the earthquake (Linear 74.16%, Polynomial 85.32%, and radial basic 86.71%). However, in maps with sigmoid function, 62.27% of the area was found to be highly susceptible to landslides during the earthquake with almost the entire landslides occurrence. Conclusion: Most of the high susceptible and very high susceptible area was concentrated along the seism genic faults with a PGA of more than 0.52 g. This paper provide an example for selecting appropriate types of kernel functions for prediction mapping of seismic landslides using support vector machine modeling. The susceptibility maps for earthquake-induced landslides can be useful in landslide hazard mitigation by helping planners understand the probability of landslides in different regions. Keywords: Earthquake-induced landslide; Support vector machine; Susceptibility; Geographic information system * Correspondence: fangligang_csu@163.com Department of Civil Engineering, Central South University, Changsha, Hunan, China Full list of author information is available at the end of the article © 2015 Zhou and Fang; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 2 of 12 Background The results showed that landslide distribution can be Landslide is one of the most severe natural hazards in predicted. Landslides induced by Wenchuan earthquake the world, causing thousands of death and great property were assessed and predicted by Su et al. 2010 using loss per year. Earthquake is a dominant trigger of land- logistic regression models, and were compared with the slides in mountainous and tectonic-active areas. Landslides bivariate statistics, artificial neural networks, and support induced by an earthquake are usually large in number, vector machine models by Xu et al. 2012a. huge in scale and wide in distribution. Earthquake-induced Among these approaches, the support vector machine landslides can bring great damages to property and infra- (SVM) model has become increasingly popular. The structures in developed areas, leading to economic losses SVM was originally developed by [Vapnik, 1995] as a new and fatalities sometimes. For example, more than 20,000 machine learning algorithm for pattern classification and people were killed by landslides induced by the 2008 non-linear regression. The main procedure involved in Wenchuan earthquake with a magnitude of Ms 8.0 and 34 SVM modeling is a training phase with associated input large barrier lakes were produced, which threatened the and target output values. Recently, several authors have residents who lived downstream of these dams [Yin et al. applied the SVM model successfully on landslide suscep- 2009]. In the 2010 Yushu earthquake (Ms 7.1) about 60 tibility mapping. [Gallus et al., 2008] compared several million in damages and 8 deaths were directly caused by classification approaches of SVM, Gaussian process, and earthquake-induced landslides [YP Yin et al., 2010]. LR modeling, with SVM having the best results. [Xu et al., Earthquake-induced landslides were hard to predict, but 2012b] examined the use of SVM model for landslide could be evaluated. Identifying a region’s susceptibility susceptibility mapping in an earthquake zone with com- to landslides during an earthquake was an effective and bination of 4 kernel functions and 3 different training sets most economical way to provide planners with fore- and found that radial-basis and polynomial kernel func- knowledge of dangerous regions thereby helping with tions were suitable for modeling with any input training land management and infrastructure planning. For data. [Xu et al., 2012b] applied 6 different models in earthquake-induced landslide, landslide susceptibility susceptibility mapping of landslides induced by the 2008 assessment was to evaluate location of landslide suscepti- Wenchuan earthquake with SVM having a second best bility zones where landslides could be induced in future results outranked only by logistic regression. [Kavzoglu earthquake shaking. Many different methods and tech- et al., 2013] also made a comparison of susceptibility niques for assessing landslide susceptibility have been results from multi-criteria decision analysis, SVM, and proposed and tested. These have already been systemat- logistic regression and showed that multi-criteria decision ically compared and their advantages and limitations analysis and SVM methods were better than logistic outlined in Carrara et al. 1999, Huabin et al. 2005 and regression in shallow landslides susceptibility mapping. van Westen et al. 2008. Both deterministic and statistical These applications proved that when used properly, SVM methods have been used in earthquake-induced landslide model in landslide susceptibility mapping might produce susceptibility. For deterministic methods, assessment of a good result. Two outstanding advantages of the SVM earthquake-induced landslide susceptibility on a regional are: (a) Based on the principle of minimization structural scale commonly required the employment of an analyt- risk; (b) Guarantee its performance by solving constrained ical slope-stability method and the infinite-slope model quadratic form. Theoretically, it can achieve the optimal [Jibson and Keefer, 1993; Jibson et al., 2000; Refice and prediction result by using the SVM model. Its detailed Capolongo, 2002]. The deterministic method required mathematical formulas are introduced in [Vapnik and calculation to determine the limit-equilibrium of the Cortes 1995]. slope stability given the strength parameters of mass, In this study, we propose the application of SVM failure depth, and groundwater conditions for every model to produce a landslide susceptibility map of the area hit by the April 20, 2013 Lushan earthquake on the calculation point in the study area. This requirement caused immense problems in terms of data acquisition ArcGIS platform. The goal of the study is to produce a and control of spatial variability of the variables ([Carrara relatively accurate landslide susceptibility map with optimal kernel functions. The 4 resultant cases are compared using et al., 1999]. For statistical method, it was most common to use a statistical approach where landslide inventories AUC (area under curve) analysis to verify the susceptibility and causative factors are utilized to build a susceptibility mapping results. This is done by comparisons with known landslide locations to establish the model’s success rate, and model for the prediction of future landslides. For instance, Kamp et al. 2008 carried out spatial prediction of land- its predictive accuracy. slides related to 2005 Kashmir earthquake-induced by use of a multi-criterion method. Lee et al. 2008 applied Study area multivariate statistical methods in a study of shallow On April, 2013, an Ms 7.0 earthquake, with a maximum earthquake-induced landslides in central western Taiwan. source intensity of up to 9.0 on Chinese seismic scale, Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 3 of 12 struck Lushan county, Sichuan province, west China. composition of weathered and fractured superficial soils The epicenter of the main shock was located in 30.3°N, and rocks were widespread throughout the whole study 103.0°E, about 100 km southwest of Chengdu (Figure 1). area, because they could be triggered easily by weak The earthquake occurred on the southern segment of shaking. Rock avalanches are usually originated on a the Longmenshan fault zone. This area was celebrated high place along the river and road banks, with large for steep mountain landscapes and heavy tectonics. The potential energy, resulting in a high speed and a long April 20 earthquake was an strong aftershock of 2008 run-out distance during sliding process. Deep-seated Wenchuan earthquake and were the most devastative landslides are mainly distributed within a short distance earthquake in China since the 2008 Wenchuan earth- from the main co-seismic ruptures, since only a strong quake [Wei-Min et al., 2013]. ground shaking could trigger them. The study area had experienced serious shallow land- This area was very tectonic-active with many folds and slides during this earthquake, since the steep slopes and active faults trending NW–SE (Figure 1). The bedrock jagged ridges were susceptible to landslide while suffer- exposure in the area was dominated by Mesozoic volcanic ing heavy ground shaking. Topography of the study area rocks and Mesozoic group. The volcanic rocks, which ranges from river valley to mountainous. Elevation of comprised tuffs and lavas with intercalated sedimentary the study area ranges from 596 m to 2872 m. Land use rocks. Intrusive rocks consisted mainly of granites, sand- includes mainly cropland distributed on the ridges, slope stone and dykes of various compositions. As a result of wasteland on side-slopes and gullies and town in flat the abundant supply of rainfall and the local rich ground- river valleys. Due to long-term human activity, many parts water, almost all rocks in the study area had undergone a of the natural vegetation have been destroyed. Because certain degree of weathering. In many slopes, weathering it was right time for vegetation, earthquake-induced had penetrated deep into rock masses through joints and landslides were easy to be recognized according to bedding planes (Figure 2). landslide scars on aerial photos. Landslides triggered by the Lushan earthquake can be mainly classified into Methods following types (Figure 2): (1) shallow-disrupted slope Support vector machine (SVM) modeling failures; (2) rock avalanches; and (3) deep-seated rocky Support vector machine (SVM), as the representative’s or soil slides. Shallow-disrupted slope failures with a kernel-based techniques, is a major development in Figure 1 (a) Location of Sichuan Province; (b) Location of the study area; and (c) Geological settings of the study area. Explanation of geology units is listed in Table 2. Unit ‘g’ for Peak ground acceleration (PGA) means acceleration of gravity. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 4 of 12 Figure 2 Typical types of landslides. (a) Rock avalanches, (b) translational slides and (c) shallow-disrupted slope failures. machine learning algorithms. SVM is a group of 1 ϕðÞ w; b; α¼ w − αðÞ y½ w⋅x þ b −1 ð5Þ kk i i supervised learning methods based on the statistical i¼1 learning theory and the Vapnik-Chervonenkis (VC) dimension introduced by [V Vapnik and Cortes, 1995] where α ¼ðÞ α ; α ; …; α ∈R is the Lagrangian multi- 1 2 n and [Chervonenkis, 2013] that can be applied to pattern plier, and the problem can be solved by dual minimization classification or non-linear regression. of Equation (5)withrespect to w and b through standard For the linear separable condition, consider a set of procedures Equation (6). More detail of SVM was discussed training vectors with two classes as follows: in [Vapnik 1995]. D ¼fg ðÞ x ; y ;ðÞ x ; y ; ⋅⋅⋅;ðÞ x ; y ð1Þ 1 2 n 1 2 n ∇ ϕðÞ w; b; α¼ 0 ð6Þ where x ∈ X ⊂ R , y ∈ {1, − 1}, i = 1, 2,⋅⋅⋅,n, that can be sep- ∇ ϕðÞ w; b; α¼ 0 i i arated the two classes [1, −1] by a hyper-plane (Figure 3): Mostly, however, the training vectors are non-separable, ðÞ w⋅x þ b ¼ 0; w∈R ; b∈R ð2Þ [Vapnik 1995] introduced an slack variables ξ modified the constraints as follows: where w is the normal of the hyper-plane, b is a scalar base, and (·) denotes the scalar product operation. yðÞ ðÞ w⋅x þ b ≥1−ξ ; i ¼ 1; 2; ⋅⋅⋅; n; ξ ≥0 ð7Þ i i i After normalization, the geometrical margin between the two groups can be expressed as . The operation of To avoid a high value of ξ , some kind of penalty term C kk w the SVM algorithm is to find the hyper-plane that gives was introduced into the original optimization Equation (3), the largest geometrical margin to the training examples. which can be modified as: The maximum can be expressed as: kk w Minimize kk w þ C ξ ð8Þ 2 2 i¼1 Minimize kk w ð3Þ w;b 2 where C > 0 is the penalty factor to control the trade-off Subjecting to constrains: between the maximum margin and the minimum error. Additionally, a kernel function k(x , x ) is introduced by i j y w x þ b ≥1 i ¼ 1; 2; :::::; n ð4Þ [Vapnik 1995] to transform the originally non-linear data Introducing the Lagrangian multiplier, the cost function pattern to a linear one in higher dimensional feature can be defined as: space (Figure 3). Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 5 of 12 a 2 b Margin = c d Figure 3 Illustration of SVM model. (a) n-dimensional hyperplane differentiating the two classes with maximum gap; (b) non-separable case and the slack variables ξ; (c) transformation using kernel function of the originally non-linear data pattern to a linear one in higher dimensional feature space (d). Selection of the kernel function is the main issue in SVM also have been developed, but their theories are not reach modelling. Theoretically, any function that satisfy the perfection and they produce poor prediction efficiency Mercer criteria can be used as kernel function, however, than two-class SVM [Guo et al., 2005; Yao et al., 2008]. some of them work well in a wide variety of applications. Hence, a two-class SVM modeling is utilized in this study. The mathematical representation of some kernel functions To carry out the two-class SVM modeling, we estab- are listed below: lished a spatial database containing all the landslides triggered by the earthquake and their controlling parame- Linear : Kx ; x ¼ x x ð9Þ i j j ters. Then all the data layers were classified and rasterized p in Arcgis and coded in Matlab7.01. The landslides as well Polynomial : Kx ; x ¼ γx x þ r ; γ > 0 ð10Þ i j j as the same amount of selected stable slopes were ran- domly divided into two groups for training and validation −γ x −x kk i j Radial basis function : Kx ; x ¼ e ; γ > 0 ð11Þ i j purpose, respectively. We use the training dataset as input to train the SVM model, then the testing dataset were Sigmoid : Kx ; x ¼ tanh γx x þ r ð12Þ i j j used to examine the model. Both the training and valid- where γ is the gamma term in all the kernel function ation phase were completed in Matlab 7.01. Finally, all the except linear; p is the polynomial order term in the cells in the study area were input into the established kernel function for the polynomial kernel; r is the bias model for possibility prediction of landslide occurrence. term in the kernel function for the polynomial and sigmoid kernels. Proper parameters, such as the order of Data polynomials and width of radial basis function, play a Two kinds of data were indispensable in the two-class key role in governing the accuracy of the SVM modeling. SVM modeling: (1) Units with landslides and units Of these functions, polynomial and radial basis function supposed to be considered as stable and conditions of (RBF) are the most-used kernels and are utilized in our these units and (2) Conditions of units that needed to be research due to its good generalizing properties. predicted. The former were samples used to train the In reality, the unstable slope cases (with landslides) are two-class SVM model, while the latter were used as the recognized as positive pattern, while stable slope cases input of the trained model to predict risk of region (without landslides) are recognized as negative pattern. including them. All of the data representing a categorical Note that we often commonly have only a one-class attribute should be converted into numeric code before dataset without negative data. One-class SVM models entering the SVM model. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 6 of 12 Landslide inventory Controlling parameters of landslides Institute of Remote Sensing and Digital Earth (RADI) of Seven environmental variables were used to train the the Chinese Academy of Sciences (CAS) took airborne model and to predict the potential distribution for land- images with a high-resolution of 0.6 m covering the slides (Figure 5 and Table 2). These variables included: earthquake-affected area on the morning right after the (1) slope gradient, (2) slope aspect, (3) land cover, (4) earthquake. Except a little part was masked by cloud, distance to fault, (5) peak ground acceleration (PGA) most of earthquake damage in this area was shown clearly distribution of April 20 Lushan earthquake, (6) elevation, on these image. All of these high-resolution images as well (7) geology unit. The above selections were made based as a preliminary interpretation of earthquake-induced on the authors’ knowledge of the physical environment geo-hazards were proposed on Geo-Information Platform and landslides in the study area. Slope gradient, slope as- of Lushan Earthquake [Institute of Mountain Hazard pect, elevation were derived from digital elevation model andEnvironment,C.A.o.S., andGeomatics Center of (DEM). Land cover layer was derived from 1:20,000 scale Sichuan Province 2013] based on Tianditu online map digital vegetation cover maps. For ease of analysis, the service [Chen et al., 2013]. Due to a critical use for rescue 1:20,000 scale superficial and solid geology map covering after earthquake, this preliminary landslide inventory was the study area was divided into 10 groups based on incomplete, only location of suspected landslides were chronostratigraphic unit. Other environmental variables available. were also divided into seven or eight classes manually, The accurate detection of landslides is vital for land- slope gradient was first broken at 15° because very fewer slide susceptibility analysis, so an inventory of landslides landsides were probable on shallower slopes. The PGA triggered by April 20 Earthquake was made with the map is extracted from the United States Geology Survey help of Arcgis server. Firstly, the high resolution images (U.S.G.S) Shakemap (http://earthquake.usgs.gov/earthquakes/ provided by Tianditu map service were invoked into shakemap) (see Table 2). Arcgis through Arcgis server. These images were specified as the based map. Then, an empty vector layer with the Results same coordinate system as the base map was created for There are many free programs for SVM modelling [Chang the storage of landslides. After that, experts in earthquakes and Lin, 2011; Joachims, 1999], which can be downloaded and geo-hazards were called upon to visually interpret from the internet, providing all kinds of interfaces to other the base map according to their experiences, knowledge software. In this study, LibSVM [Chang and Lin, 2011] as well as previously identified landslide points. High- was employed to finish the computation of the SVM resolution pre-event satellite images of RADARSAT-2 model on Matlab 7.01. The environmental parameters and SPOT-4 (see Table 1) of the study area were were derived and rasterized in ArcGIS 9.3. A grid cell size geometrically rectified and matched to be taken into of 60 × 60 m was adopted to produce the landslide suscep- consideration as a contrast. The boundaries of landslides tibility maps. The study area was divided into 186,230 grid were interpreted on the base map and transformed into cells and each grid consisted of seven layers representing vector format and stored in ArcGIS system. A filed survey the environmental parameters. was finally conducted to check the accuracy of the interpretation, following which the interpreted images Training and validation dataset were modified. The resultant landslide inventory map is The two-class SVM requires both positive and negative shown in Figure 4. Landslide–area ratio(LAR), defined data to train the model. The landslide inventory were as the percentage of the area affected by landslide activity, randomly divided into two groups: 70% of the total (902 and landslide number density (LND) gives the number landslides with 1782 grid cells) were used as positive of landslides per square kilometer. In this study area, training samples. As mentioned before, negative training 2 2 LAR =(4.26 km /674.45 km ) × 100% = 0.63% and LND = data was also needed. 1782 negative training points were 2 − 2 1289landslides/674.45 km =1.91 km . generated within 120 m interval in both north and south direction of the positive points. A validation dataset con- tains 30% of the total landslides (387 landslides with 738 grid cells) and 738 negative points generated using the Table 1 Images used in ArcGIS for interpretation same way as negative training data. A total of 2520 land- No. Type Date Mode/resolution slide points were assigned the value of 1, while the same 1 RADARSAT-2 2012-03-04 WIDE/30 m amount of negative points were assigned the value of 0. 2 SPOT-4 2011-04-09 PAN/6.25 m In SVM modelling, the input of controlling factors 3 SPOT-4 2011-04-09 MS/12.5 m should be as a vector of real numbers. For categorical 4 Airborne images 2013-04-20 0.6 m attributes, a simple 1 of k coding is recommended to Data source can be found on http://www.radi.ac.cn/yaan/yaanphoto/. represent a k-category attribute. For instance, suppose a Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 7 of 12 Figure 4 Distribution of landslides triggered by the April 20, 2013 Lushan earthquake. Figure 5 Controlling factors of landslides as input of the SVM modelling (a) Slope gradient; (b) Aspect; (c) Land cover; (d) Distance to fault; (e) PGA; (f) Elevation; and factors of geology unit can be seen in Figure 2(b). Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 8 of 12 Table 2 Controlling parameters and their classes for this study Controlling parameters Classes Elevation (m) (1)(min)596-800;(2)800-1200(3)1200-1600;(4)1600-2000;(5)2000-2400;(6)24002872(max) Slope gradient (°) (1)< 15;(2)15-20;(3)20-25;(4)25-30;(5)30-35;(6)35-40;(7)40-45;(8)> 45 Aspect (1)F;(2)N;(3)NE;(4)E;(5)SE;(6)S;(7)SW;(8)W;(9)NW; Distance to co-seismic fault (km) (1)< 2;(2)2-4;(3)4-6;(4)6-8;(5)8-10;(6)10-12;(7)12-14;(8)14-16;(9)16-18;(10);18-20 PGA (1)0.24;(2)0.28;(3)0.32;(4)0.36;(5)0.40;(6)0.44;(7)0.48;(8)0.52;(9)0.56;(10);0.58 Land cover (1)Woodland;(2)Wooded Grassland;(3)Closed Shrub land;(4)Open Shrub land;(5)Grassland;(6)Cropland Geology unit (1)Quaternary(2) Paleogene(3)Cretaceous(4)Jurassic(5)Triassic(6)Devonian(7)Silurian (8)Ordovician(9)Sinian(10)Proterozoic 1-dimensional a three-category attribute taking value {a, follows: (1) Set a pair of (C, γ) values for SVM model; (2) b, c}, Just turn it into 3-dimensional numbers such that Randomly divided the training dataset into 5 equal sized a = (1,0,0), b = (0,1,0), c = (0,0,1). If the number of values subsets; (3) Use Four subsets of them to train the SVM in an attribute is not too large, such coding is more model; (4) Validate the trained model using the one stable than using a single number to represent a cat- remaining subset; (5) Repeat step three and four for five egorical attribute ([Hsu et al., 2003]). Therefore, the times for each of the subset; (6) Calculate the overall seven environmental parameters were converted into a accuracy defined as the percentage of data which are vector with 59 bits. Finally, a training dataset containing correctly predicted. 3564 grids with 7 input variables were built through Pairs of (C, γ) were generated through a grid search −8 −7 −6 6 7 8 −8 −7 −6 extracting the value of landslide conditioning factors in with C = 2 ,2 ,2 … 2 ,2 ,2 and γ =2 ,2 ,2 … 6 7 8 every grid. 2 ,2 ,2 . For every pair of (C, γ), we can get an overall accuracy and the optimal C and γ corresponded to the Cross validation and grid search for SVM parameter highest overall accuracy. optimization The best value of C for linear was 2 with the overall The performance of the SVM model is depended on the accuracy 85.5%. The best C and γ for polynomial were choice of kernel functions and their parameters especially found 4 and 1 with the overall accuracy 89.6%. In the the penalty factor C and γ terms. In this study, a grid- case of RBF, the best C and γ were 16 and 1 respectively, search method with 5-folder cross-validation was used to with the overall accuracy 92% while sigmoid used 16 and locate the optimal values of C and γ [Hsu et al., 2003] as 8 as the best C and γ. Figure 6 (a) Success rate curves of the four SVM models; (b) Prediction rate curves of the four SVM models. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 9 of 12 Comparison of landslide susceptibility maps and true positive rate (TPR, defined as TP/(TP + FN)) ROC curve is one of the useful methods for representing as x and y axes respectively. The true-positive rate is the quality of deterministic and probabilistic detection, also known as sensitivity in biomedicine, or recall in especially for landslide susceptibility assessment. The char- machine learning. The false-positive rate is also known acterizes the quality of a forecast system by describing the as the fall-out and can be calculated as 1- specificity. system’s ability to anticipate correctly the occurrence or The area under the ROC curve (AUC) is an important non-occurrence of predefined event (Yesilnacar and Topal measure of the accuracy of the binary classification. 2005). A true positive (TP) means prediction of a landslide AUC values are typically between 0.5 and 1.0. If this area for a point where a landslide does occur, while a false is equal to 1.0 then the roc curve consists of two straight positive (FP) is a prediction of a landslide for a stable lines, one vertical from (0, 0) to (0, 1) and the next point. On the conversely, we can get the true negative horizontal from (0, 1) to (1, 1) this test is 100% accurate (TN) and false negative (FN). A ROC space is defined because both the sensitivity and specificity are 1.0 and by the false positive rate (FPR, defines as FP/(FP + TN)) there was no false positives and no false negatives. On Figure 7 Landslide susceptibility mapping using different kernel functions: (a) Linear; (b) Polynomial; (c) RADIAL basis function; (d) SIGMOID. All the results were classified into five classes: VHS, HS, MS, LS, and VLS. Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 10 of 12 the other hand a test that can’t discriminate between was the decision values of each pixel. The results were positive and negative corresponds to an ROC curve that then converted into raster data. Figure 7 showed the is the diagonal line from (0, 0) to (1, 0). The AUC for mapping results for the landslide susceptibility index this line is 0.5. (LSI) ranging from0 to 1. 0 indicates no chance and 1 in- To evaluate the four landslide susceptibility maps, dicates 100% chance for occurrence of landslides. success-rate curves and prediction-rate curves were The LSI values of each grid cell predicted using SVM established, and values of area under curves (AUC) were with the linear, polynomial, radial basis, and sigmoid also calculated [Hasegawa et al., 2009]. Higher AUC value kernel functions were 0.0004-0.9752, 0.0001-0.9999, indicated a higher capacity of correctly classifying the data 0.0007-0.9948, and 0.0047-0.9896 respectively. with existing landslides. The success-rate curve was a A few classification methods, such as natural breaks, measure of goodness of fit for SVM model and training equal intervals and defined interval, were used to distin- data. The curve was obtained by comparing the four guish the susceptibility classes for trial. Equal intervals landslide susceptibility maps with the training dataset, classification was found not to be useful for its emphasis (Figure 6a). Results indicated that RBF and polynomial on the amount of one class value relative to other classes. had the highest AUC values 0.97 and 0.91 respectively, Natural breaks are identified that best group similar values followed by linear (0.77), while model using sigmoid and that maximize the differences between classes and kernel function had the lowest AUC values of 0.58. not useful for comparing multiple maps built from differ- Nevertheless, the success-rate was not a suitable meas- ent underlying information. A series of specified interval ure for the prediction capability of the landslide models sizes can be used to define the classes with different because it was based on the landslide pixels that had ranges in defined interval methods based on a compre- already been used for building the model. To overcome hensive consideration of the data distribution. Moreover, this, prediction-rate curve and corresponding AUC the define interval classification allow comparison of values were obtained by comparing the four susceptibility different maps with similar ranges of attribute value. maps with the validation dataset (Figure 6b). The results The maps with continuous LSI values were then reclas- showed that model using polynomial kernel functions had sified into five landslide susceptibility categories using the the highest capacity of prediction with the AUC of 0.86, method of define intervals, i.e. very low susceptibility slightly better than RBF (0.82) and Linear (0.78). Same (VLS: less than 0.1), low susceptibility (LS: 0.1-0.3), with success-rate curve, sigmoid had the lowest AUC moderate susceptibility (MS: 0.3-0.5), high susceptibility values. (HS: 0.5-0.7), and very high susceptibility (VHS: more than 0.7) (Figure 7). Discussion The resultant landslide susceptibility maps were also Once the landslide susceptibility models were success- compared with the landslide inventory. The coverage per- fully trained in the training phase, they were then used centages of 5 susceptibility classes and the corresponding to calculate the landslide susceptibility indexes (LSI) for landslide occurrence are shown in Table 3. The results all the pixels. The SVM classification output or result showed that the landslide frequency ratio (defined as the Table 3 Landslide statistical results by different SVM kernel functions Susceptibility class Success Prediction Models rate rate VLS LS MS HS VHS %area 8.39 29.83 27.00 23.87 10.91 Linear %landslide 0.44 6.67 18.73 38.41 35.75 0.77 0.78 LND 0.05 0.22 0.69 1.61 3.28 %area 28.01 27.95 13.56 12.66 17.83 Polynomial %landslide 1.27 4.52 8.89 16.71 68.61 0.91 0.86 LND 0.05 0.16 0.66 1.32 3.85 %area 11.16 54.29 10.09 9.01 14.82 Radial basic %landslide 1.83 5.79 5.67 11.63 75.08 0.97 0.82 LND 0.16 0.11 0.56 1.29 5.07 %area 1.12 7.03 29.56 62.27 0.01 Sigmoid %landslide 0.12 0.71 2.82 96.27 0.08 0.58 0.58 LND 0.11 0.10 0.10 1.55 7.78 Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 11 of 12 ratio of percentage of landslide occurrence in each class on disaster prediction in other regions with potential that of area) gradually increased from the very low to the seismic risks given appropriate kernel functions and high susceptibility class and then suddenly jumped in very model parameters high susceptibility class. Competing interests According to maps, about 20%-30% of the study area The authors declare that they have no competing interests. (Linear 34.78%, Polynomial 30.49%, and RBF 23.83%) were Authors’ contributions categorized into high and very high susceptible zones SZ carried out the susceptibility modeling and drafted the manuscript. LF during the Lushan earthquake, with 70%-80% occurrence arranged the structure of the manuscript and participated in the discussion of landslides triggered by the earthquake (Linear 74.16%, and conclusion of the study. Both authors read and approved the final manuscript. Polynomial 85.12%, and RBF 86.71%). However, in maps with sigmoid function, 62.27% of the area were found to Acknowledgement be highly susceptible to landslides during the earthquake This research is supported by State Key Development Program of Basic Research of China (Grant 2011CB710601) The data used in this paper was provided by the with almost all of the landslides occurrence. Department of Geotechnical Engineering ,Central South University, China. We Most of areas that classified as very high, high and wish to express our sincere appreciation for the generous support. moderate were concentrated along the seism genic faults, Author details suffering a high PGA of more than 0.52 g. This may be- Department of Civil and Structural Engineering, Kyushu University, Fukuoka, cause earthquake is the trigger of the landslides used for Japan. Department of Civil Engineering, Central South University, Changsha, training model to produce the landslide susceptibility map. Hunan, China. Received: 7 August 2014 Accepted: 14 October 2014 Conclusion Based on the statistical learning theory, GIS technology, References SVM model, and four types of kernel functions, including Carrara A, Guzzetti F, Cardinali M, Reichenbach P (1999) Use of GIS technology in linear function, polynomial function, RBF function, and the prediction and monitoring of landslide hazard. Nat Hazards 20(2–3):117–135 sigmoid function, this work has studied the prediction for Chang C-C, Lin C-J (2011) LIBSVM: a library for support vector machines. ACM Transactions on Intelligent Systems and Technology (TIST) 2(3):27 spatial distribution of landslides triggered by the April 20, Chen Y-W, Yap K-H, Lee JY (2013) Tianditu: China’s first official online mapping 2013 Lushan earthquake in Sichuan province of China. service, Media. Culture & Society 35(2):234–249 From the results of this study, the following conclusions Chervonenkis AY (2013) Early History of Support Vector Machines. Festschrift in Honor of Vladimir N. Vapnik, Empirical Inference, pp 13–20 can be drawn: Gallus D, Abecker A, Richter D (2008) Classification of landslide susceptibility in the development of early warning systems. In: Symposium on Headway in (1) Cross validation and grid search was an efficient Spatial Data Handling. Springer: Montpellier, France pp 55–75 Guo Q, Kelly M, Graham CH (2005) Support vector machines for predicting tool for parameters optimization. This method distribution of Sudden Oak Death in California. Ecol Model 182(1):75–90 avoided the subjectivity in parameter selection for Hasegawa S, Dahal RK, Nishimura T, Nonomura A, Yamanaka M (2009) the SVM model. DEM-based analysis of earthquake-induced shallow landslide susceptibility. Geotech Geol Eng 27(3):419–430 (2) The validation results by ROC method showed that Hsu C-W, Chang C-C, Lin C-J (2003) A Practical Guide to Support Vector RBF and polynomial function is the better than Classification. Technical report, Department of Computer Science, National linear and sigmoid for the Lushan earthquake area. Taiwan University. Huabin W, Gangjun L, Weiya X, Gonghui W (2005) GIS-based landslide hazard AUC of RBF shows a high accuracy of 97% (0.97) in assessment: an overview. Prog Phys Geogr 29(4):548–567 case of success rate curves and 82% (0.82) in case of Institute of Mountain Hazard and Environment, C. A. o. S., and Geomatics Center prediction rate curves, and that of polynomial are of Sichuan Province (2013) Geo-Information Platform of Lushan Earthquake. http://scgis.net/LSXEarthquake/ 91% (0.91) and 86% (0.86) respectively. Jibson RW, Keefer DK (1993) Analysis of the seismic origin of landslides: examples (3) According to the landslide susceptibility index of from the New Madrid seismic zone. Geol Soc Am Bull 105(4):521–536 each grid, the study area was divided into 5 classes Jibson RW, Harp EL, Michael JA (2000) A method for producing digital probabilistic seismic landslide hazard maps. Eng Geol 58(3):271–289 of landslide susceptibility, namely very low, low, Joachims T (1999) Svmlight: Support Vector Machine., SVM-Light Support Vector moderate, high and very high and 4 landslide Machine http://svmlight.joachims.org/. University of Dortmund, 19(4) susceptibility maps were generated Comparing with Kamp U, Growley BJ, Khattak GA, Owen LA (2008) GIS-based landslide susceptibility mapping for the 2005 Kashmir earthquake region. Geomorphology all 1289 landslides (2520 grid cells), The results show 101(4):631–642 that the landslide frequency ratio gradually increases Kavzoglu T, Sahin E, Colkesen I (2014) Landslide susceptibility mapping using GIS- from the no to the high susceptibility class. based multi-criteria decision analysis, support vector machines, and logistic regression. Landslides 11(3):425-439 (4) Most of landslide triggered by the earthquake Lee C-T, Huang C-C, Lee J-F, Pan K-L, Lin M-L, Dong J-J (2008) Statistical approach happened in high and very high susceptible zones, to earthquake-induced landslide susceptibility. Eng Geol 100(1):43–58 which were concentrated along the seism genic Refice A, Capolongo D (2002) Probabilistic modeling of uncertainties in earthquake- induced landslide hazard assessment. Comput Geosci 28(6):735–749 faults with a high PGA; Su F, Cui P, Zhang J, Xiang L (2010) Susceptibility assessment of landslides (5) The SVM modelling related to the Lushan caused by the wenchuan earthquake using a logistic regression model. J Mt earthquake landslides can be applied to landslide Sci 7(3):234–245 Zhou and Fang Geoenvironmental Disasters (2015) 2:2 Page 12 of 12 van Westen CJ, Castellanos E, Kuriakose SL (2008) Spatial data for landslide susceptibility, hazard, and vulnerability assessment: an overview. Eng Geol 102(3):112–131 Vapnik VN (1995) The nature of statistical learning theory. Springer-Verlag New York, Inc, p 188 Vapnik V, Cortes C (1995) Support-vector networks. Mach Learn 20(3):273–297 Wei-Min W, Jin-Lai H, Zhen-Xing Y (2013) Preliminary result for rupture process of Apr. 20, 2013, Lushan Earthquake, Sichuan, China. CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION 56(4):1412–1417 Xu C, Xu X, Dai F, Saraf AK (2012a) Comparison of different models for susceptibility mapping of earthquake triggered landslides related with the 2008 Wenchuan earthquake in China. Comput Geosci 46:317–329 Xu C, Dai F, Xu X, Lee YH (2012b) GIS-based support vector machine modeling of earthquake-triggered landslide susceptibility in the Jianjiang River watershed. China, Geomorphology 145:70–80 Yao X, Tham L, Dai F (2008) Landslide susceptibility mapping based on support vector machine: a case study on natural slopes of Hong Kong, China. Geomorphology 101(4):572–582 Yesilnacar E, Topal T, (2005) Landslide susceptibility mapping: A comparison of logistic regression and neural networks methods in a medium scale study, Hendek region (Turkey). Engineering Geology, 79(3-4):251-266. Yin Y, Wang F, Sun P (2009) Landslide hazards triggered by the 2008 Wenchuan earthquake, Sichuan, China. Landslides 6(2):139–152 Yin Y, Zhang Y, Ma Y, Hu D, Zhang Z (2010) Research on major characteristics of geohazards induced by the Yushu Ms7. 1 earthquake. J Eng Geol 18(3):289–296 Submit your manuscript to a journal and benefi t from: 7 Convenient online submission 7 Rigorous peer review 7 Immediate publication on acceptance 7 Open access: articles freely available online 7 High visibility within the fi eld 7 Retaining the copyright to your article Submit your next manuscript at 7 springeropen.com

Journal

Geoenvironmental Disasters – Springer Journals

Published: Feb 6, 2015

There are no references for this article.