Introduction

Landslides are defined as the mass movement of rock, debris or earth down a slope (Cruden 1991) that often cause great damages to human life, property and the natural environment in hilly and mountainous terrains. In active tectonic and erosional settings, landslides are generally considered the dominant hillslope process that permits rapid hillslope adjustment to high rates of rock uplift and erosion (Gallo and Lavé 2014). The eastern Himalayan syntaxis, located in the southeastern Tibetan Plateau, is one of the most tectonically active and fastest uplifting regions on Earth. Landslides are extremely developed in this region due to its special geological, tectonic and geomorphological conditions. Landslides along roads, especially National Highway 318, constantly result in loss of life and property damage (Shang et al. 2005), posing a serious challenge to project planning and construction. However, so far, no landslide susceptibility assessment has been made for this region.

As essential part of hazard assessment, landslide susceptibility mapping is one of most important ways to provide fundamental knowledge on landslide distribution and can help in hazard management. In the last three decades, a lot of techniques and methods have been applied to this effort, which can be roughly categorized into qualitative and quantitative ones (Ayalew and Yamagishi 2005).

The qualitative methods are based on field observations and prior knowledge of experts, in which experts identify judgment rules or assign weighted values for conditioning factor maps and then overlay them to prepare a landslide susceptibility map (Du et al. 2017a). They include the analytical hierarchy process (AHP; Ercanoglu et al. 2008; Ghosh et al. 2011; Kayastha et al. 2013) and weighted linear combination (WLC; Ayalew et al. 2004). Because the weights are assigned based on the field knowledge of experts, a landslide inventory map is not needed. The main problem of such qualitative methods is that they highly depend on the level of expert’s experience, and any different criteria with the consent of the expert can easily be conceded to the assignment of weighted values (Feizizadeh et al. 2014).

The quantitative methods are based on numerical estimates and involve deterministic and statistical approaches (Bui et al. 2011). Deterministic methods are focused on analyzing the stability of a slope and calculating its safety factors (Aleotti and Chowdhury 1999; Godt et al. 2008; Park et al. 2013). Due to the need for exhaustive data from individual slopes, these methods are only applied to areas where landslide types are simple and the geomorphic and geologic properties are fairly homogeneous (Bui et al. 2011). Statistical methods are based on the analysis of the relationships between conditioning factors and existing landslides. These methods require the collection of a large amount of data to produce reliable results. Various statistical methods have been used for landslide susceptibility mapping including bivariate statistical analysis such as frequency ratio (FR; Lee and Pradhan 2006; Yilmaz and Keskin 2009; Mezughi et al. 2011; Regmi et al. 2014), information value (IV) method (Yin and Yan 1988; Lin and Tung 2004; Sarkar et al. 2008; Conforti et al. 2011), weight of evidence (WOE; Sharma and Kumar 2008; Suh et al. 2011; Guo et al. 2015), certainty factor (CF; Binaghi et al. 1998; Lan et al. 2004; Devkota et al. 2013), multivariate statistical analysis such as logistic regression (LR; Park 2010; Pourghasemi et al. 2013; Tsangaratos and Ilia 2016) and stepwise discriminant analyses (Carrara et al. 1991, 2003), and data mining methods such as artificial neural networks (ANNs; Arora et al. 2004; Yilmaz 2009; Pradhan and Lee 2010; Bui et al. 2016) and support vector machines (SVMs; Yao et al. 2008; Bui et al. 2016).

In addition, according to advantages of different methods, some integrated methods, such as LRFR (Umar et al. 2014; Youssef et al. 2015), AHPIV (Fan et al. 2012; Du et al. 2016), LRIV (Du et al. 2017a), AHPFR (Mondal and Maiti 2013), LRWOE (Zhou et al. 2016), have been developed to enhance precision and accuracy of landslide susceptibility mapping.

Although many methods and techniques have been proposed and implemented for landslide susceptibility mapping, there has been no consensus as to which method and technique are the best. In general, the performance of a method depends on characteristics of different regions (Yang et al. 2015). Thus, comparison of the different methods is important. Yilmaz (2010) compared the landslide susceptibility mapping results produced by LR, SVM and ANN methods and showed the ANN method produced more accurate susceptibility maps than LR and SVM for the case study of Koyulhisar, Turkey. Pourghasemi et al. (2013) compared landslide susceptibility mapping results using LR, AHP and statistical index (SI) for the north of metropolitan Tehran, Iran, and showed that the map obtained from the LR method is more accurate than the other methods. Chen et al. (2016) showed that the IV method enables generating a more accurate susceptibility map than LR for the Zigui-Badong area, China. In addition, the performance of the integrated method and the individual methods have been compared by some researchers. For example, Youssef et al. (2015) showed the LRFR method is better than the LR and FR methods in landslide susceptibility mapping. Zhou et al. (2016) considered that the LRWOE method can provide a more accurate result than the WOE and LR for earthquake-induced landslide susceptibility mapping based on a case study of the April 20, 2013 Lushan earthquake, China. Du et al. (2017a) showed the LRIV method can produce a more accurate susceptibility map than the LR and IV methods for the Bailongjiang watershed, Gansu Province, China. These integrated methods can yield a higher accuracy than individual methods for landslide susceptibility mapping.

Due to the complex topography of and difficult access to the region of the eastern Himalayan syntaxis, landsliding of this region is poorly studied, particularly in the Yarlung Zangbo Grand Canyon zone. To fill this gap, through aerial photograph interpretation and field investigations, we have prepared a landslide inventory map for this region, and then used the AHPIV and LRIV methods to generate a GIS-based landslide susceptibility map. Finally, the performances of the two methods are compared using the area under the receiver operating characteristic (ROC) curves.

Geologic settings

Associated with the collision between the Indian and Eurasian plates, the eastern Himalayan syntaxis is characterized by intensive tectonic deformation, with rapid uplift. This region is laced with many large-scale active faults, such as the Yarlung Zangbo fault, Jiali fault, Dongjiu-Milin fault, Polong-Pangxin fault, Apalong fault and Motuo fault, which control the topography and divide the region into different zones. The outcrop strata of the region range from the Proterozoic to Quaternary. In addition to the Jurassic and Quaternary strata, the others have all undergone different degrees of deterioration. The complex lithology in the region mainly consists of stone, limestone, marble, phyllite, slate, shale and basic, intermediate, intermediate-acidic and acidic magmatic rocks, as well as Quaternary alluvial, and diluvial or morainic materials.

In this region, the rapid uplift of the rock mass, surface erosion and river incision have created the current characteristics of the alpine gorge landscape. The research area is primarily of high mountains and valleys, with an average elevation of more than 3000 m and relative incision depth over 1000 m. Several mountain peaks above 6000 m stand here, such as the Namcha Barwa Peak as the highest one, with an elevation of 7782 m. Around the mountain peaks, the modern glaciers are well developed. The Yarlung Zangbo River basin is the largest watershed in the region, with several major tributaries including the Nyang River and Parlung Zangbo River. The Yarlung Zangbo River cuts through Namcha Barwa area and drops 2 km within the Yarlung Zangbo canyon (Du et al. 2017b). Along this great canyon, warm, moist air flows from the Indian Ocean to south Tibet, which brings abundant rainfall to the region. The annual rainfall is 700–1000 mm (Shang et al. 2005).

The tectonic rock uplifting, complex folding and faulting, coupled with river incision have produced special topographic, geomorphic and tectonic conditions for landslides in this region. Combined with the effect of gravity, earthquakes, rainfalls or glaciation can trigger frequent landslides of varied scales and types. These landslides are a serious challenge to the planning and construction of highways, railways and hydropower projects in this area.

Methodology

Analytic hierarchy process information value (AHPIV) method

Analytic hierarchy process (AHP)

As a multi-objective and multi-criteria decision-making approach, the AHP divides a complex decision-making problem into multiple objectives or criteria, expresses the subjective judgement in a quantitative manner and arrives at a scale of preference drawn from a set of alternatives, which makes the decision more reasonable. This method has been widely used in landslide susceptibility assessment (Mondal and Maiti, 2012). The AHP includes the following steps: (i) building a hierarchy model, (ii) establishing a judgment matrix through pairwise comparison (using a scale from 1 to 9), (iii) calculating weights by computation of the normalized principal eigenvector and (iv) testing consistency using the consistency ratio (CR) which must be less than 0.1. The CR is calculated by:

$$ CR=\frac{CI}{RI} $$
(1)
$$ CI=\frac{\lambda_{\mathrm{max}}-n}{n-1} $$
(2)

where CI is the consistency index, RI is the random consistency index, n is the number of parameters and λmax is named the largest eigenvalue.

Information value (IV)

In the 1980s, Yin and Yan (1988) developed the IV method from information theory and used it in landslide spatial prediction for the first time. This method has been widely used since then, especially in landslide susceptibility assessment. It is an indirect statistical approach and can be used to evaluate the spatial relationship between the probability of landslide occurrence and conditioning factor classes (Du et al. 2017a). The information value of conditioning factor classes is calculated as follows (Yin and Yan 1988, 1996; Du et al. 2017a):

$$ {I}_i={\log}_2\frac{S_i/{A}_i}{S/A} $$
(3)

where Si is the area of landslides containing factor class i, Ai is the area of factor class i, S is total area of landslides and A is the total area of the entire study area (Yang et al. 2015; Du et al. 2017a).

AHPIV method

In the AHPIV method, the AHP is used to obtain the factor weights (wi) and the information value method is used to obtain the information value of the conditioning factor class (Ii). The integrated method can be expressed by the following formula:

$$ I=\sum \limits_{i=1}^n{w}_i{I}_i=\sum \limits_{i=1}^n{w}_i{\log}_2\frac{S_i/{A}_i}{S/A} $$
(4)

where I is the comprehensive index of the landslides occurrence, n is the number of the containing factor and wi is the weight of the containing factor (Du et al. 2016; Wang et al. 2017).

Logistic regression information value (LRIV) method

Logistic regression (LR)

As one of the popular multivariate statistical analysis methods, LR can make a multivariate regression relationship between a binary dependent variable and numerous independent variables (Pradhan and Lee 2010). The advantage of LR is that the variables can be either continuous or discrete, or any combination of both types which need not be of a normal distribution (Lee and Pradhan 2006). The LR method has also been widely used in landslide susceptibility mapping. It can be expressed as:

$$ P=\frac{1}{1+{e}^{-z}} $$
(5)

where P is the probability of landslide occurrence, which varies from 0 to 1 on an S-shaped curve, and z is the linear combination of predictors and its value varies from −∞ to +∞ (Eq. 5).

$$ z={\overset{\wedge }{\beta}}_0+{\overset{\wedge }{\beta}}_1{x}_1+{\overset{\wedge }{\beta}}_2{x}_2+{\overset{\wedge }{\beta}}_3{x}_3+\dots \dots +{\overset{\wedge }{\beta}}_n{x}_n $$
(6)

where \( {\overset{\wedge }{\beta}}_0 \) is the intercept of the model, n is the number of independent variables, \( {\overset{\wedge }{\beta}}_i \) (i = 1, 2, 3,…, n) represents coefficients of the model and xi (i = 1, 2,3, …, n) is the independent variable.

LRIV method

The information value method was performed for all the classified conditioning factors. To speed up the convergence and facilitate the final analysis and interpretation in subsequent analysis, the information values should be normalized to a range of 0 to 1 (Du et al. 2017a). The normalized information values are then arranged to corresponding conditioning factor classes and used as independent variables in the LR model. These values can be calculated by a common method as follows:

$$ {\mathrm{x}}_i=\frac{I_i-{I}_{(i)\min }}{I_{(i)\max }-{I}_{(i)\min }} $$
(7)
$$ \mathrm{z}={\overset{\wedge }{\beta}}_0+\sum \limits_{i=1}^n{\overset{\wedge }{\beta}}_i\cdot \frac{I_i-{I}_{(i)\min }}{I_{(i)\max }-{I}_{(i)\min }} $$
(8)

where xi (independent variables in LR) is the normalized values of Ii, and I(i)min and I(i)max are the minimum and maximum information values of the ith conditioning factor, respectively (Du et al., 2017).

Landslide inventory

Landslide inventory mapping is the most basic step in landslide susceptibility assessment (Hong et al. 2018). A detailed and reliable landslide inventory with 799 landslides as polygons for the study area has been prepared based on interpretation of aerial photographs, extensive field surveys and historical landslide archives (scale: 1:100,000) compiled by the Ministry of Land and Resources of the People’s Republic of China (Fig. 1). According to the material composition category (Liu et al. 2002), these landslides can be divided into two types: soil landslides and bedrock landslides. The soil landslides occurred primarily in the Quaternary loose material layers formed by alluvial deposits, residual slope deposits, collapse deposits, outwash deposits and artificial deposits. Most of them are distributed on the gentle slopes of the valleys. The bedrock landslides are associated with rock composition and structural weaknesses of slopes, which are widely distributed in the study area.

Fig. 1
figure 1

Landslide inventory map of the study area

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The size of the landslides ranges from several thousands to hundreds of millions cubic meters. Most of the large landslides (>106 m3) are bedrock landslides in the study area. The giant landslide at Yigong in 2000 has an approximate length of 10 km and volume of 3.0 × 108 m3 (Fig. 2a). Frequent landslides in this region, such as the 102 landslide (Fig. 2b), Layue landslide and Yigong landslide, have blocked rivers and caused serious damage to roads. Giant ancient landslides in the study area also prevail, such as the Jiaobunong landslide (Fig. 2c) and Wenlang landslide, which are mostly deep-seated. From the landslide inventory map, landslide distribution is of a certain regular pattern, mostly along the Yarlung Zangbo River, Parlung Zangbo River and Layue River (Fig. 1).

Fig. 2
figure 2

Typical landslides in the study area. a Yigong landslide; b 102 landslide; c Jiaobunong ancient landslide

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Landslide conditioning factors

In various references, there is still no clear agreement on the selection of conditioning factors in landslide susceptibility assessment (Hasekiogullari and Ercanoglu 2012; Guo et al. 2015). According to landslide characteristics of the study area, eight main landslide conditioning factors were chosen in this work, including lithology, slope gradient, slope aspect, elevation, curvature, distance to drainages, distance to faults and distance to roads. During map preparation, all of these factors were converted into raster format with a 30 × 30-m pixel size within the ArcGIS platform. They are detailed as follows, emphasized on their relations to landslide occurrence.

Lithology

Lithology is the material basis of landslide occurrence, which reflects the erodibility of the slope rock. Based on 1:200,000 geological maps produced by the Ministry of Land and Resources of China and physical-mechanical properties of rock, the lithology in the study area is divided into seven rock groups: (i) hard solid granite and diorite, (ii) hard layer of sandstone and limestone, (iii) mid-hard solid migmatites, (iv) mid-hard layer of basic-ultrabasic rocks, (v) soft-hard layer of schist and gneiss, (vi) loose sediments and (vii) snow-covered region (Fig. 3a). In the study area, the groups of mid-hard layer of basic-ultrabasic rocks and soft-hard layer of schist and gneiss are relatively more prone to landsliding. The highest density of landslides is present in the group of mid-hard layer of basic-ultrabasic rocks which are mainly distributed along the Yarlung Zangbo suture zone (Fig. 4a). Due to the compression of the Namche Barwa wedge and Gangdise-Nyainqentanglha block, rock mass in this zone is highly broken, serving as a favorable condition for landslide occurrence.

Fig. 3
figure 3

Maps of landslide conditioning factors. a Lithology: (i) hard solid granite and diorite, (ii) hard layer of sandstone and limestone, (iii) mid-hard solid migmatites, (iv) mid-hard layer of basic-ultrabasic rocks, (v) soft-hard layer of schist and gneiss, (vi) loose sediments and (vii) snow-covered region; b slope gradient (°); c slope aspect; d elevation (m); e curvature; f distance to faults (m); g distance to drainages (m); h distance to roads (m). Maps of landslide conditioning factors (continued)

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Fig. 4
figure 4

Relationships between landslide occurrence and conditioning factor classes. a Lithology: (i) hard solid granite and diorite, (ii) hard layer of sandstone and limestone, (iii) mid-hard solid migmatites, (iv) mid-hard layer of basic-ultrabasic rocks, (v) soft-hard layer of schist and gneiss, (vi) loose sediments and (vii) snow-covered region; b slope gradient (°); c slope aspect; d elevation: (1) <2000 m, (2) 2000~2500 m, (3) 2500~3000 m, (4) 3000~3500 m, (5) 3500~4000 m, (6) 4000~4500 m, (7) 4500~5000 m and (8) >5000 m; e curvature; f distance to faults: (1) <500 m, (2) 500~1500 m, (3) 1000~1500 m, (4) 1500~2000 m, (5) 2000~2500 m, (6) 2500~3000 m, (7) 3000~3500 m, (8) 3500~4000 m and (9) >4000 m; g distance to drainages: (1) <100 m, (2) 100~200 m, (3) 200~300 m, (4) 300~400 m, (5) 400~500 m, (6) 500~600 m, (7) 600~700 m, (8) 700~800 m and (9) >800 m; h distance to roads: (1) <100 m, (2) 100~200 m, (3) 200~300 m, (4) 300~400 m, (5) 400~500 m and (6) >500 m

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Slope gradient

Slope gradient, which affects the gravity-generated stress distribution, surface runoff and the loose material accumulation of the slope, plays an important role in landsliding. In this work, this parameter was obtained from the 30 × 30-m digital elevation model (DEM) and divided into six classes: <10°, 10–20°, 20–30°, 30–40°, 40–50° and >50° (Fig. 3b). The occurrence of landslides within each class in the study area is described in Fig. 4b and Table 1. It is noted that most of these landslides occurred on slopes of 20–50°. The lowest frequencies of landslides were on the very gentle slopes (0–10°).

Table 1 Spatial relationships between each landslide conditioning factor and landslides
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Slope aspect

Slope aspect plays an important role in landslide susceptibility mapping, which is related to weathering, land cover and microclimate. Many scholars use slope aspect as a conditioning factor in landslide susceptibility mapping (Meinhardt et al. 2015; Youssef et al. 2015; Chen et al. 2017). The values of this parameter were also derived from the 30 × 30-m DEM and categorized into nine classes: flat, N, NE, E, SE, S, SW, W and NW (Fig. 3c). Figure 4c shows that landslides are likely to occur on the slopes facing west, southwest and south.

Elevation

Related to soil types, vegetation coverage, rainfall and so on, elevation can influence the landslide distribution. This factor in the study area is divided into eight classes: <2000 m, 2000–2500 m, 2500–3000 m, 3000–3500 m, 3500–4000 m, 4000–4500 m, 4500–5000 m and > 5000 m (Fig. 3d). The spatial relationship between landslides and elevation classes (Fig. 4d) suggests that the slope failures in the study area mainly occurred at places with elevation of <2500 m, which are mostly catchment areas with strong surface runoff, seeming more prone to landsliding.

Curvature

Curvature is another DEM-based derivative, which can affect slope stress field and groundwater distribution. Many researchers use slope curvature as a conditioning factor in preparing landslide susceptibility maps (Umar et al. 2014; Guo et al. 2015; Chen et al. 2017). The slope curvature map was prepared with three classes: concave, flat and convex (Fig. 3e). Figure 4e and Table 1 show that the highest landslide density and area occurred at the localities of convex curvature, followed by area of flat and concave curvatures.

Distance to faults

The faults data are based on 1:200,000 geological maps. Apparently, with well-developed cracks, fragmented rock and strong weathering, the slope on both sides of the faults is highly susceptible to landslides. In this work, the distance to faults was calculated in a 500-m interval and is divided into nine classes: <500 m, 500–1500 m, 1000–1500 m, 1500–2000 m, 2000–2500 m, 2500–3000 m, 3000–3500 m, 3500–4000 m and >4000 m (Fig. 3f). The landslide distribution is obviously controlled by the faults, as evidenced by the landslide density decreasing with increasing distance to the faults within 3000 m (Fig. 4f).

Distance to drainages

River undercutting, infiltration and erosion are unfavorable for slope stability along the river banks. The growth level of the surface drainages indicates the cutting level of the surface. The more developed the water system, the more severe the surface cutting. Meng et al. (2004) argued that the rapid uplift of the Tibetan Plateau during the Late Quaternary period led to strong river incision, and thus controlled geological hazards and their distribution. For the study area, the distance to drainages is divided into nine classes: <100 m, 100–200 m, 200–300 m, 300–400 m, 400–500 m, 500–600 m, 600–700 m, 700–800 m and > 800 m (Fig. 4f). Figure 4g shows that the landslide density is the largest in the distance class of 100–200 m, and declines with the growing distance to drainages when exceeding 200 m.

Distance to roads

Due to the micromorphological changes and unloading by road excavation, the slope instabilities often occur along roads in mountainous areas. In addition, the human engineering activities are also generally along roads. These constitute an influence factor for slope failures which depend on the distance to the road. In this work, this parameter was calculated in 500-m intervals and is divided into six classes: <100 m, 100–200 m, 200–300 m, 300–400 m, 400–500 m and > 500 m (Fig. 3h). Analysis shows that in the study area, the landslide density is highest at distances of 0 to 100 m to roads, while lowest for the distances >500 m. The landslide density decreases with the increasing distance to the roads (Fig. 4h).

Results

Landslide susceptibility map using AHPIV

In this method, the judgment matrix (Table 2) was established by the pairwise comparison. The weight values of eight conditioning factors were determined and the consistency test was carried out (Table 2). The CR is 0.025, which is less than 0.1. The results indicated that the judgement matrix satisfies the requirement of the consistency test and the weight values are reasonable.

Table 2 Results of the AHP evaluation
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The information values of eight conditioning factors (Ili = lithology, Isl = slope gradient; Ias = slope aspect; Iss = curvature; Iel = elevation; Ifa = distance to faults; Iri = distance to drainages; Iro = distance to roads) were calculated using Eq. 3. The information values are listed in Table 1. To obtain the landslide susceptibility index, the weight values for each conditioning factor (Table 2) were placed in Eq. 9. Finally, the landslide susceptibility results were divided into five categories using the natural breakpoint method, which are very low, low, moderate, high and very high landslide susceptibility (Fig. 5a).

$$ I=0.169{I}_{\mathrm{li}}+0.259{I}_{\mathrm{sl}}+0.065{I}_{\mathrm{as}}+0.051{I}_{\mathrm{ss}}+0.076{I}_{\mathrm{el}}+0.132{I}_{fa}+0.154{I}_{ri}+0.094{I}_{\mathrm{road}} $$
(9)
Fig. 5
figure 5

Landslide susceptibility maps produced by (a) AHPIV and (b) LRIV methods

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Landslide susceptibility map using LRIV

In order to avoid the bias caused by unequal proportions of landslide and non-landslide pixels when implementing this method, an equal grid cell of non-landslides was randomly selected from the landslide-free area (Bui et al. 2011). The normalized information value layers of conditioning factors were calculated using Eqs. 3 and 7. By analyzing the relationship between the dependent variables (0 is the value of non-landslide and 1 is the landslide) and independent variables (the normalized information values) in SPSS statistics software, the LR coefficients of conditioning factors were obtained. Then, substituting LR coefficients into Eq. 8, the z values were obtained as follows:

$$ {\displaystyle \begin{array}{l}z=-5.788+2.015{I}_{\mathrm{li}}+4.747{I}_{\mathrm{sl}}+1.787{I}_{\mathrm{as}}+2.501{I}_{\mathrm{ss}}\\ {}+0.125{I}_{\mathrm{el}}+0.981{I}_{fa}+1.492{I}_{ri}+0.241{I}_{\mathrm{road}}\end{array}} $$
(10)

The P values, which ranged from 0.0194 to 0.9869, were obtained by substituting the z values into Eq. 5. To prepare the landslide susceptibility map, the P value map was divided into five classes using the natural breakpoint method, which are very low, low, moderate, high and very high landslide susceptibility (Fig. 5b).

In order to avoid the multicollinearity among the independent variables, a collinearity analysis is necessary. Tolerance (TOL) and variance inflation factor (VIF) are two primary indexes to assess the multicollinearity (Bui et al. 2011). When the TOL is less than 0.1 or the VIF greater than 10, it is regarded as a multicollinearity problem existing. The TOL and VIF values (Table 3) show that there is no multicollinearity among the chosen independent variables. Table 3 lists the P value of each logistic coefficient in the model. It shows that all the conditioning factors have a P value less than 0.05, which demonstrates that the statistical relationship between variables at a 95% confidence level (Bui et al. 2011). All these indicate that the presented model performs quite well.

Table 3 Relevant parameters of conditioning factors used in LRIV method
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Validation

Validation is a fundamental step to assess the effectiveness of the landslide susceptibility map. In this study, the ROC curve was used to verify the performance of the landslide susceptibility map. This curve is a two-dimensional graph that consists of the true positive rate (sensitivity) on the vertical axis and false positive rate (1 = specific) on the horizontal axis. The area under the ROC curve (AUC), which varies from 0.5 to 1.0, is used to evaluate the model. An AUC value close to the 1.0 implies perfect performance of the model (Bui et al. 2011; Umar et al. 2014).

The ROC curve results showed that the AUC is 0.906 using the LRIV method and 0.884 using the AHPIV method (Fig. 6). It is evident that the LRIV method can produce a better landslide susceptibility map than the AHPIV method in the study area. Figure 7 show the landslide density and area for the five landslide susceptibility classes of the two landslide susceptibility maps, on which the landslide density decreases with lowering the landslide susceptibility.

Fig. 6
figure 6

Receiver operating characteristic (ROC) curve

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Fig. 7
figure 7

Statistics of the landslide susceptibility map produced by the AHPIV and LRIV methods

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Sensitivity analysis

Sensitivity analysis permits seeing how the input variables change the output results (Lee and Talib 2005; Fenta et al. 2015; Tahmassebipoor et al. 2016; Du et al. 2017a). In this study, a map-removal sensitivity analysis (Tahmassebipoor et al. 2016) was conducted to examine the effects of removing any of the conditioning factors on the landslide susceptibility results. The relative decrease of AUC values (RD), which is used to examine the solution changes, is calculated as follows:

$$ R{D}_i=\frac{AU{C}_{\mathrm{all}}- AU{C}_i}{AU{C}_{\mathrm{all}}}\times 100\% $$
(11)

where RDi is the relative decrease of AUC values, AUCall is the AUC value obtained from the landslide susceptibility mapping using all conditioning factors and AUCi is the AUC value when the ith conditioning factor is excluded. A high RD value means a high sensitivity to a landslide susceptibility resulted.

Removing each of conditioning factors in turn, the landslide susceptibility assessment was performed using the LRIV method (Table 4) and the corresponding RD value was calculated. The sensitivity analysis (Table 5) shows that the lithology (RD = 3.02%), slope gradient (RD = 12.05%), aspect (RD = 2.99%), elevation (RD = 2.56%), curvature (RD = 2.26%), distance to drainages (RD = 4.15%), distance to faults (RD = 2.65%) and distance to roads (RD = 2.24%) all have a decline in AUC values. The landslide susceptibility map is more sensitive to the slope gradient and less sensitive to the distance to roads in the study area.

Table 4 Regression coefficients of the logistic regression-information value method when the relevant conditioning factor is excluded
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Table 5 Statistics of the sensitivity analysis
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From the results of ROC and sensitivity analysis, it can be concluded that the landslide susceptibility assessment performance is affected not only by the method used, but also by the type and the number of conditioning factors selected.

Hence, we produced the landslide susceptibility map of the eastern Himalayan syntaxis region using the LRIV method with all eight conditioning factors. From the statistical results of the landslide susceptibility map (Table 6), the very high and high landslide susceptibility areas, accounting for 5.98 and 19.10% of the entire area, respectively, are mainly distributed along the narrow valleys of the Yarlung Zangbo, Yigong Zangbo, Parlung Zangbo and Layue Rivers. The moderate landslide susceptibility areas, accounting for 34.33% of the whole study area, are mainly distributed along tributary gullies of the major rivers. Table 6 shows that 23.96% of the landslides occur in these areas, whereas only 10.88% of the landslides are present in the areas with low and very low landslide susceptibility, which accounts for 40.59% of the study area. The low and very low landslide susceptibility zones are mainly in the areas with gentle slopes and less faults.

Table 6 Statistics of the landslide susceptibility map
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Discussion and conclusions

The IV method is a simple and effective tool in landslide susceptibility mapping. Among all bivariate statistical methods, this approach can determine the impact of each conditioning factor class on landslide occurrence, but it does not consider the relationship between these factors and landslide occurrence (Du et al. 2017a). The LR method is capable of performing multivariate statistical analysis between a dependent variable and several independent ones and provides an easy way to analyze the impact of conditioning factors on landslide occurrence, but it does not analyze the influence of classes of each conditioning factor on landslides (Umar et al. 2014). As a main tool in the subjective assessment of qualitative methods, the AHP method can assign the weights of conditioning factors based on the field knowledge of experts. But this method may be strongly influenced by the subjectivity of the involved experts (Bui et al.2011). The AHP and LR methods can be combined with bivariate statistical analysis (BSA) methods such as the IV method (Umar et al. 2014; Yang et al. 2015; Du et al. 2017a). This study produced landslide susceptibility maps in the region of the eastern Himalayan syntaxis using two integrated methods: the AHPIV method and the LRIV method. The methods can generate a complete model to assess the impact of conditioning factors as well as the effect of each conditioning factor on landslide occurrence. However, the AHPIV method assesses the impact of conditioning factors on landslide occurrence based on field observations and prior knowledge of experts, and the LRIV method does the same by virtue of numerical estimates. The performance of susceptibility maps produced by these two methods for the study area was verified by the ROC curves. The AUC value for the LRIV method is 0.906, which is better than the 0.884 of the AHPIV method. The results indicate that the LRIV method is the best optimized model in this study and it can be considered as a promising method for landslide susceptibility mapping in similar cases for better accuracy.

It is worth noting that the conditioning factors play a key role in landslide susceptibility mapping, but there is no universal standard on how to select conditioning factors and how many factors should be selected. Guo et al. (2015) found that the FR model with the 6 variables performed the same as that with the all 11 variables, and better than 8 variables. Meinhardt et al. (2015) compared landslide susceptibility map results using 9 and 13 variables and found that 9 variables led to a higher AUC value than those from all 13 variables. In this study, we considered eight factors for analysis. The sensitivity analyses were performed to find a better input parameter set, and the results showed that all of the conditioning factors had a positive effect on the landslide susceptibility mapping. However, due to the difficulty of obtaining data, other factors such as rainfall, ground water level and weathering that affect the landslide occurrence are not considered. Whether choosing more factors is conducive to landslide susceptibility results of the study area needs further research.

From this study, we suggest using the LRIV method with all eight conditioning factors to map the landslide susceptibility. This paper gives in-depth thought about landslide susceptibility mapping and the results can help managers, planners and decision makers in land use, landslide management and landslide hazard prevention and mitigation in engineering construction.