Arabian Journal of Geosciences

, Volume 7, Issue 2, pp 725–742

Application of frequency ratio, statistical index, and weights-of-evidence models and their comparison in landslide susceptibility mapping in Central Nepal Himalaya

Authors

  • Amar Deep Regmi
    • Department of Geology, Faculty of ScienceShinshu University
  • Krishna Chandra Devkota
    • Department of GeologyKyungpook National University
  • Kohki Yoshida
    • Department of Geology, Faculty of ScienceShinshu University
    • Geospatial Information Science Research Centre (GISRC), Department of Civil Engineering, Faculty of EngineeringUniversiti Putra Malaysia
  • Hamid Reza Pourghasemi
    • College of Natural Resources and Marine SciencesTarbiat Modares University (TMU)
  • Takashi Kumamoto
    • Department of Earth Sciences, Faculty ScienceOkayama University
  • Aykut Akgun
    • Geological Engineering DepartmentBlack Sea Technical University
Original Paper

DOI: 10.1007/s12517-012-0807-z

Cite this article as:
Regmi, A.D., Devkota, K.C., Yoshida, K. et al. Arab J Geosci (2014) 7: 725. doi:10.1007/s12517-012-0807-z

Abstract

The Mugling–Narayanghat road section falls within the Lesser Himalaya and Siwalik zones of Central Nepal Himalaya and is highly deformed by the presence of numerous faults and folds. Over the years, this road section and its surrounding area have experienced repeated landslide activities. For that reason, landslide susceptibility zonation is essential for roadside slope disaster management and for planning further development activities. The main goal of this study was to investigate the application of the frequency ratio (FR), statistical index (SI), and weights-of-evidence (WoE) approaches for landslide susceptibility mapping of this road section and its surrounding area. For this purpose, the input layers of the landslide conditioning factors were prepared in the first stage. A landslide inventory map was prepared using earlier reports, aerial photographs interpretation, and multiple field surveys. A total of 438 landslide locations were detected. Out these, 295 (67 %) landslides were randomly selected as training data for the modeling using FR, SI, and WoE models and the remaining 143 (33 %) were used for the validation purposes. The landslide conditioning factors considered for the study area are slope gradient, slope aspect, plan curvature, altitude, stream power index, topographic wetness index, lithology, land use, distance from faults, distance from rivers, and distance from highway. The results were validated using area under the curve (AUC) analysis. From the analysis, it is seen that the FR model with a success rate of 76.8 % and predictive accuracy of 75.4 % performs better than WoE (success rate, 75.6 %; predictive accuracy, 74.9 %) and SI (success rate, 75.5 %; predictive accuracy, 74.6 %) models. Overall, all the models showed almost similar results. The resultant susceptibility maps can be useful for general land use planning.

Keywords

LandslidesFrequency ratioStatistical indexWeights-of-evidenceGISHimalaya

Introduction

The Himalayas are one of the most active mountains which have resulted from the collision of the Indian Plate and the Tibetan Plate some 50 million years ago. Since Nepal occupies a major portion of the Himalaya, it has always been recognized as the area prone to natural hazards, e.g., earthquakes and landslides. The annual loss of lives and property due to these natural hazards are significantly high in the Himalayan region. In Nepal itself, the average number of deaths from 1983 to 2007 is about 329 persons, whereas the annual loss of life is as high as 1,336 persons in 1993 (Dhital 2005). The death due to landslides alone is about 111 persons per year.

Intensive rainfall (446 mm in 24 h at Devghat, the confluence of Kali Gandaki and Trishuli River) of July 30 and 31, 2003 triggered hundreds of landslides, slope failures, rock falls, and debris falls along the highway and its surrounding region (Adhikari 2009) (Fig. 1). It was further aggravated by mass movements during the monsoon of 2006, blocking the traffic for several weeks (DWIDP 2009). This road section is one of the busiest strategic roads of Nepal, which connects the Terai with the capital and other central and western mountain districts. Thus, to maintain the traffic as well as to minimize the losses of life and property, landslide susceptibility assessment is essential for this road section.
https://static-content.springer.com/image/art%3A10.1007%2Fs12517-012-0807-z/MediaObjects/12517_2012_807_Fig1_HTML.gif
Fig. 1

Landslide location map of the study area

Landslide susceptibility can be defined as the propensity of an area to generate landslides (Guzzetti et al. 2006). There exists several hazard modeling methodology in literature and can be categorized into heuristic, deterministic, and statistical approaches (van Westen et al. 1997; Aleotti and Chowdhury 1999; Guzzetti et al. 1999; Dai et al. 2002; Alexander 2008; Sharma and Kumar 2008; Wan et al. 2009; Wan and Lei 2009). A heuristic approach (Deoja et al. 1991; Anbalagan 1992; Nagarajan et al. 2000; Saha et al. 2002) is a direct or semidirect mapping methodology in which a relationship is established between the occurrence of slope failures and the causative factors. They are based on the assumption that the relationships between landslide susceptibility and the preparatory variables are known and are specified in the models. A set of variables is then entered into the model to estimate landslide susceptibility (Gupta and Joshi 1990). In this approach, the relative importance of each causative factor for slope instability is evaluated according to subjective expert’s knowledge or statistics of landslide distribution and analysis (van Westen et al. 1999). Therefore, assigning weight values and ratings to the variables is very subjective, and the results are often not reproducible.

In deterministic analysis, the landslide hazard is determined using slope stability models, resulting in the calculation of factor of safety. These models require a large amount of detailed input data, derived from laboratory tests. Hence, these models are applicable in small areas at large scales.

In the statistical approach, multivariate and bivariate statistical techniques are used for landslide susceptibility mapping throughout the world. Bivariate statistical analyses involve the idea of comparing a landslide inventory map with maps of landslide influencing parameters in order to rank the corresponding classes according to their role in landslide formation. Ranking is normally carried out using landslide densities. A variety of multivariate statistical approaches exist, but those commonly used to map landslide susceptibility include discriminant analyses and logistic regression (Lee 2007a; Pradhan 2010a). Different other methods have been proposed by several investigators, including weights-of-evidence (WoE) methods (Bonham-Carter 1991; Gokceoglu et al. 2005; Neuhäuser and Terhorst 2007; Mathew et al. 2007; Bui et al. 2008; Zhu and Wang 2009; Regmi et al. 2010a, b; Pourghasemi et al. 2012a), weighting factors, weighted linear combinations of instability factors (Ayalew et al. 2004), landside nominal risk factors (Gupta and Joshi 1990; Saha et al. 2005), probabilistic models (Carranza and Hale 2001, 2002; Chung and Fabbri 2003, 2005; Lee 2005; Lee and Pradhan 2006, 2007; Akgün et al. 2011; Pradhan et al. 2012; Mohammady et al. 2012; Pourghasemi et al. 2012b, d), certainty factors (Binaghi et al. 1998), information values (Saha et al. 2005; Wan et al. 2008), modified Bayesian estimation (Chung and Fabbri 1998). Additionally, there exists some other data mining techniques, such as neuro-fuzzy (Lee et al. 2006; Vahidnia et al. 2010; Oh and Pradhan 2011; Sezer et al. 2011; Bui et al. 2011), fuzzy logic (Ercanoglu and Gokceoglu 2002; Kanungo et al. 2006, 2008; Lee 2007b; Muthu et al. 2008; Pradhan and Lee 2009; Pradhan 2010b, c; Pradhan 2011a, b; Pourghasemi et al. 2012c), artificial neural networks (Kanungo et al. 2006; Melchiorre et al. 2008; Chen et al. 2009; Pradhan and Lee 2009, 2010a, b; Pradhan et al. 2010a, b; Pradhan and Buchroithner 2010; Pradhan and Pirasteh 2010; Poudyal et al. 2010; Yilmaz 2009a, b; Yilmaz 2010a, b; Pradhan 2011c; Zare et al. 2012; Bui et al. 2012a), support vector machine (Yao et al. 2008; Yilmaz 2010a, b; Pourghasemi et al. 2012f; Pradhan 2012; Bui et al. 2012b), decision tree methods (Saito et al. 2009; Yeon et al. 2010; Nefeslioglu et al. 2010a, b; Pourghasemi et al. 2012e; Pradhan 2012), Shannon’s entropy (Devkota et al. 2012; Pourghasemi et al. 2012d, g), general additive model (Xiao et al. 2010), evidential belief function (Althuwaynee et al. 2012; Bui et al. 2012c), and spatial decision support system (Wan 2009). Understanding the differences between the proposed approaches is not always simple. The main differences are the rigor of the approach (Chung and Fabbri 1998) and the method used to estimate the prior probability of landslide occurrence.

There are many literatures available related to the landslide studies from Nepal Himalaya (Deoja et al. 1991; Dhital et al. 1991; Dangol et al. 1993; Dangol 2000; Pantha et al. 2008; Regmi et al. 2012a, b). These studies basically deal with the loss of life and property, physical properties of the landslides, and effect of geological setting in the formation of these landslides, along with recommendations for preventive measures and landslide susceptibility mapping using the geographic information system (GIS). The main purpose of this paper is to develop landslide susceptibility maps of the Mugling–Narayanghat road corridor and its surrounding region using frequency ratio (FR), statistical index (SI), and WoE models in order to find the better model that is more accurate in landslide susceptibility mapping in the study area.

The study area

The Mugling–Narayanghat Highway is 36 km long and is located in a mountain range between Narayanghat and Mugling of Chitwan Districts, Narayani Zone, Central Nepal. The study area lies within longitude 84°25′30″ E to 84°35′30″ E and latitude 27°52′ N to 27°46′ N (Fig. 1) that falls within the topographical map 2784-03C (Mugling) and 2784-02D (Jugedi Bajar). It covers an area of about 138.14 km2. The minimum and maximum altitudes of the area vary between 200 m at Jugedi Bajar and 1,540 m to the north of Bespani.

Subtropical to temperate climate prevail in the study area, with the winter temperatures ranging in between 6 and 25 °C, while that of summer ranging from 25 to 40 °C. The monthly maximum temperature and daily rainfall records from the nearby Bharatpur station during 2002–2006 have given the highest maximum temperature of 41.2 °C in May 2004 and a mean annual rainfall of 2,650 mm (DWIDP 2009). The months of April, May, and June are the hottest, with average maximum temperatures of 37.8, 39.3, and 38.6 °C, respectively. As in other parts of Nepal, summer monsoon is dominant from June to September’s end. The distribution of the drainage network of the study area is shown in Fig. 1. Trishuli River is the main river system in the study area. From chainage 10 (Ch10) to chainage14 (Ch14), the Trishuli River runs toward east to southeast and flows in the Siwaliks rocks. Within this section, there are three major tributaries of the river, i.e., Das Khola at Ch12 + 600, Khahare Khola at Ch11 + 300, and Jugedi Khola at Ch10 + 300 (Fig. 1). Ch14 to Ch36 of the highway is located in the Lesser Himalayan Zone. Along this section, the axis of the Trishuli River winds north to south or east to west. At Ch25 + 500, the Trishuli River meets the Rigdi Khola, the largest tributary of the Trishuli River within the study area (Fig. 1).

Geological setting

Geologically and tectonically, the Nepal Himalaya is divided into five major tectonic zones, namely, Terai, Sub-Himalaya (Siwaliks), Lesser Himalaya, Higher Himalaya, and Tibetan-Tethys Himalaya (Ganser 1964; Upreti 1999).The Tibetan-Tethys Himalayan zones are characterized by the fossiliferous sedimentary rocks, while the Higher Himalayan zones are dominated by the high-grade metamorphic rocks like gneiss, schist, quartzite, marble, and some granite. Limestone, marble, dolomite, sandstone, shale, slate, phyllite, quartzite, and schist are the dominant rock types in the Lesser Himalayan zone. The Sub-Himalayan zone is characterized by conglomerate, sandstone, mudstone, siltstone, and quaternary deposits.

The Mugling–Narayanghat road and its surrounding region belong to the Precambrian Lesser Himalayan rocks of Nawakot Complex (Stöcklin and Bhattarai 1978; Stöcklin 1980), Miocene Siwaliks, and Quaternary terrace deposits (Fig. 2). The Nawakot Complex is divided into the Lower Nawakot Group and Upper Nawakot Group, and along this road section, the rocks from both groups are observed. Kuncha Formation, Fagfog Quartzite, Dandagaun Phyllite, Nourpul Formation, and Dhading Dolomite are from the Lower Nawakot Group, while Benighat Slate Formation is the only formation exposed from the Upper Nawakot Group. The Siwalik Group in the study area consists of Lower Siwalik and Middle Siwalik. Quaternary deposits consist of river terraces of different ages. The main rock types are mudstone, sandstone, limestone, dolomite, slate, phyllite, quartzite, and amphibolite (Table 1).
https://static-content.springer.com/image/art%3A10.1007%2Fs12517-012-0807-z/MediaObjects/12517_2012_807_Fig2_HTML.gif
Fig. 2

Geological map of the study area

Table 1

Description of geological units of the study area

 

Formation

Geological age

Rock type

 

Quaternary Deposit

Recent

Mainly river terraces

Siwaliks

Middle Siwaliks

Mesozoic

Coarse-grained, salt- and pepper-like massive sandstone

Lower Siwaliks

Mesozoic

Variegated mudstone, with some thick-bedded, light gray, fine-grained sandstones

 

MBT

   

Nawakot complex

Upper Nawakot group

Benighat Slate Formation

Palaeozoic

Dark bluish gray to nearly black, soft-weathering slates and phyllites; many are argillaceous, and subordinately siliceous or finely quartzitic

STF (Simaltal Thrust Fault)

Lower Nawakot group

Dhading Dolomite

Late Precambrian

Dolomite consisting of fine crystalline or dense and light blue–gray in color. It is thinly bedded and platy in the basal part and the beds are thick to massive with common occurrence of columnar stromatolite in some parts. Frequent intercalation of black slate

Nourpul Formation

Late Precambrian

Predominantly phyllitic, but contains a variable amount of quartzitic and calcareous intercalations and dolomites and dolomitic quartzites

Purebesi Quartzite

Late Precambrian

Purple quartzite

Amphibolits

 

Thin beds of greenish amphibolites

Dandagaun Phyllites Jhikhu Carbonate

Late Precambrian

Uniform argillaceous to finely quartzitic phyllites of dark blue–green color

Fagfog Quartzite

Late Precambrian

White quartzite made up of colloidal fine-grained chert to impure coarse orthoquartzite, with occasional reddish to pale orange tints, with some intercalation of phyllite. Ripple marks are present in quartzite

Kuncha Formation

Late Precambrian

Alternation of phyllites, phyllitic quartzites and phyllitic gritstones resembling graywackes

Main boundary thrust (MBT) is the main geological structure in the study area. It separates the Lesser Himalayan rocks from the overlying Siwaliks (Fig. 2). Beside the MBT, other faults in the study area are Jugadi Thrust (JT), Kamalpur Thrust (KT), Simaltal Thrust (ST), and Virkuna Thrust (VT) (Fig. 2) (Devkota et al. 2012). All these thrusts are trending from east to west. MBT crosses the highway near Ch14 of the highway. JT is located to the south of the MBT, and it crosses the highway at around Ch10 and follows the Jugadi Khola. To the north of the MBT, KT, ST, and VT lie and pass through Ch16 + 700, Ch23 + 00, and Ch27 + 600 of the highway, respectively (Fig. 2) (Devkota et al. 2012). Several small-scale normal faults are distributed throughout the study area (Fig. 2). The rocks of the study area are highly deformed and display numerous synclines, anticlines, and sometimes continuous folding. A major syncline (Jalbire Sinclonorium) passes through Jalbire (Fig. 2). Jalbire Syncline is an open, noncylindrical, and slightly plunging fold, with the general trend and plunge of the fold being 112° and 7°, respectively. In the study area, most of the instabilities are observed along the Das Khola, Khahre Khola, and Jugedi Khola valleys and around MBT and immediately north of it. Geomorphologically, the Mugling–Narayanghat road section is within the Mahabharat Range (Hagen 1969; Upreti 1999).

Input data preparation

For landslide susceptibility analysis, the main steps are data collection and construction of a spatial database from which the relevant factors are extracted, followed by assessment of landslide susceptibility using the relationship between landslide and landslide-related factors and validation of the results (Guzzetti et al. 1999; Ercanoglu and Gokceoglu 2004). It is important to construct a digitized database for making the landslide susceptible map using GIS. Data preparation involved the digitization or creation of a GIS database, which includes topographical data, geological data, land use data, etc. For landslide susceptibility assessment, the number of attributes used for rating varies widely. In this study, 11 factors were selected in the first stage: slope gradient, slope aspect, plan curvature, altitude, stream power index (SPI), topographic wetness index (TWI), lithology, land use, distance from faults, distance from rivers, and distance from highway. Topographic maps and aerial photographs provided by the Department of Survey, Government of Nepal were used as the basic data sources for generating these layers. A landslide distribution map was prepared using earlier reports, aerial photographs, and field surveys. These data sources were used to generate various thematic layers using ArcGIS 9.3 and ArcView 3.3 softwares. Brief descriptions of the procedure for the preparation of each data layer are given in the succeeding subsections.

Landslide inventory

The first step in landslide susceptibility assessments is to acquire information about the landslides that have occurred in the past. This stage is considered as the fundamental part of the landslide hazard studies (Guzzetti et al. 1999; Ercanoglu and Gokceoglu 2004). Since landslide occurrences in the past and present are keys to future spatial prediction (Guzzetti et al. 1999), a landslide inventory map is a prerequisite for such a study. A landslide inventory map provides the basic information for evaluating landslide hazards or risk on a regional scale. Accurate detection of the location of landslides is most important for probabilistic landslide susceptibility analysis. For landslide inventory mapping, both the desk study and field study were performed. First of all, the aerial photographs of the area were analyzed and the landslide inventory map was created, and this was rechecked during the field surveys. From this, more than 438 slides were identified and mapped (Fig. 1). From these, 295 (67 %) landslides were randomly selected as training data and the remaining 143 (33 %) were kept for validation purposes. Almost every type of landslides are observed in the study area; however, rotational types are the dominant ones. Rock falls, debris flow, and topples are also observed along the highway.

Geomorphological-related factors

Geomorphological parameters used in this study are slope gradient, slope aspect, plan curvature, altitude, TWI, and SPI. The topographic map was used to prepare the digital elevation model (DEM) of the study area with 20 × 20 m pixel size. Using this DEM and the ArcGIS 9.3 software, the previously mentioned geomorphological thematic data layers were generated.

Slope gradient

Slope gradient is one of the most important causes of slope instability (Ayalew et al. 2004; Guzzetti et al. 1999; Kolat et al. 2006; Ohlmacher and Davis 2003; Oyagi 1984). The moisture content and pore pressure could be influenced at local scales, whereas the regional hydraulic behavior could be controlled by slope angle patterns at larger scales (Mancini et al. 2010). The slope in the study area varies from 0° to 73.72°. This map was produced automatically in ArcGIS using the DEM with 20 × 20 m grid size and is divided into five categories (Fig. 3a).
https://static-content.springer.com/image/art%3A10.1007%2Fs12517-012-0807-z/MediaObjects/12517_2012_807_Fig3a_HTML.gifhttps://static-content.springer.com/image/art%3A10.1007%2Fs12517-012-0807-z/MediaObjects/12517_2012_807_Fig3b_HTML.gif
Fig. 3

Various thematic maps used for the present study. a Slope (in degrees), b slope aspect, c plan curvature, d altitude (in meters), e SPI, f TWI, g land use, h distance from faults, i distance from rivers, and j distance from highway

Slope aspect

The slope aspect map was also produced from the DEM and it is defined as the direction of the maximum slope of the terrain surface. The slope aspect is related to the physiographic trends and the main precipitation direction (Ercanoglu and Gokceoglu 2002). In the present study, the aspect direction is divided into ten classes (Fig. 3b).

Plan curvature

Curvature analysis allows dividing the area into concave, convex, and flat surfaces and, consequently, may help to identify zones that exhibit proneness to landslide (Mancini et al. 2010). The curvature was derived from the DEM in ArcGIS. It is reclassified into three classes: concave, flat, and convex (Fig. 3c).

Altitude

The altitude map was produced using the DEM with 20 × 20 m grid size. In the present study area, the altitude ranges from 200 to 1,540 m and is reclassified into seven classes with 200 m interval (Fig. 3c).

Stream power index

SPI measures the erosion power of the stream and is also considered as a factor contributing toward stability within the study area. The SPI can be defined as (Moore and Grayson 1991):
$$ \mathrm{SPI}={A_{\mathrm{s}}}\tan \beta $$
(1)
where As is the specific catchment area and β is the local slope gradient measured in degrees. In the present study, SPI is divided into four classes (Fig. 3e).

Topographic wetness index

Another important topographic factor within the runoff model is the TWI (Beven and Kirkby 1979) defined as:
$$ \mathrm{TWI}=\ln \left( {\frac{a}{{\tan \beta }}} \right) $$
(2)
where a is the cumulative upslope area draining through a point (per unit contour length) and tan β is the slope angle at the point. The \( \ln \left( {\frac{a}{{\tan \beta }}} \right) \) index reflects the tendency of water to accumulate at any point in the catchment (in terms of a) and the tendency of gravitational forces to move that water down slope (expressed in terms of tan β as an approximate hydraulic gradient) (Poudyal et al. 2010). In the present study, TWI is divided into three classes (Fig. 3f).

Lithology

Lithology plays an important role in landslide susceptibility studies because different geological units have different susceptibilities to active geomorphological processes of the Himalaya (Pradhan et al. 2006). Sandstone, mudstone, limestone, dolomite, slate, phyllite, amphibolites, quartzite, and quaternary deposits cover the study area. The lithological map was produced by the help of previous geological map and from detailed field investigation (Fig. 2).

Land use map

Land use also plays a significant role in the stability of the slope. The land covered by forest regulates continuous water flow and water infiltrates regularly, whereas the cultivated land affects the slope stability owing to saturation of covered soil (Devkota et al. 2012). The land use map was provided by the Survey Department of Nepal (Fig. 3g). It consists of nine different land use types; they are cutting, cultivation, forest, orchard, grass, bush, barren, sand, and river. Bush (39 %) covers the highest amount of area followed by cultivation land (33 %) and forest (21 %) (Fig. 3g).

Distance from faults

The spatial distribution of landslides in the study area shows a strong correlation with the tectonic fractures as faults. The landslides occurred mainly along the faults and decreased sharply with distance from it. A buffer map related to the fault with a 100-m buffer zone interval is shown in Fig. 3h. The fault lines were derived from the geological map in 1:100,000 scale.

Distance from rivers

Runoff plays an important role as a triggering factor for landslides. The distance from rivers is represented by the proximity of the rivers in the area. The river map obtained from the Department of Survey of Nepal was used in the ArcGIS 9.3 software to get the proximity to rivers (Fig. 3i).

Distance from highway

Landslides are very common along road cuts. This is mainly due to the fact that the natural condition of the slope is damaged during the process of road construction. Also, the road cut exposes the joints and fractures that make the slope unstable. Road cuts are usually sites of anthropological instability. Also, a given road segment may act as a barrier, a net source, a net sink, or a corridor for water flow, and depending on its location in the area, it usually serves as a source of landslides (Pradhan 2010a, b, c). The Mugling–Narayanghat Highway is buffered with a buffer distance of 100 m in ArcGIS 9.3 to generate the distance in the highway map (Fig. 3j).

Methods

Although there are several methods in the statistical approach of landslide susceptibility mapping, in the present study, we have adopted three approaches: FR, SI, and WoE for the landslide susceptibility assessment of Mugling–Narayanghat road corridor and its surrounding regions. Details of each approach are described in the succeeding subsections.

Frequency ratio model

Among several bivariate statistical methods for landslide susceptibility mapping, the FR model has been adopted for the present study (Pradhan and Lee 2009). The FR model is a simple and understandable probabilistic model, in which the FR is defined as the ratio of the area where landslides occurred in the total study area and is also the ratio of the probabilities of a landslide occurrence to a nonoccurrence for a given attribute (Bonham-Carter 1994; Pradhan and Lee 2009). It can be expressed by the given formula equation:
$$ \mathrm{LSI}=\sum {\mathrm{FR}} $$
(3)
where LSI is the landslide susceptibility index and FR is the frequency ratio. FR is expressed as:
$$ \mathrm{FR}=\frac{{\frac{{{N_{\mathrm{pix}}}\left( {S{X_i}} \right)}}{{\sum {_{i=1}^mS{X_i}} }}}}{{\frac{{{N_{\mathrm{pix}}}\left( {{X_j}} \right)}}{{\sum {_{j=1}^n{N_{\mathrm{pix}}}\left( {{X_j}} \right)} }}}} $$
(4)
where Npix(SXi) is the number of pixels with landslides within class i of parameter variable X, Npix(Xj) is the number of pixels within parameter variable Xj, m is the number of classes in the parameter variable Xi, and n is the number of parameters in the study area. The FR of all the thematic layers used in the present study was calculated in Microsoft Excel and is given in Table 2. Using these FR values, the thematic maps were reclassified by the help of the spatial analyst tool in ArcGIS 9.3. These reclassified layers were then added using the raster calculator of ArcGIS to get the final susceptibility map.
Table 2

Spatial relationship between each factor and landslide by the FR, SI, and WoE models in Nepal

Factor

Class

(a)

(b)

FR (b/a)

SI (W+)

W

C

S2(W+)

S2(W)

S(C)

C/S(C)

Slope degree

0–15°

12.24

3.73

0.30

−1.19

0.09

−1.28

0.09

0.00

0.31

−4.17

15–25°

13.6

12.2

0.90

−0.11

0.02

−0.12

0.03

0.00

0.18

−0.70

25–35°

24.59

31.86

1.30

0.26

−0.10

0.36

0.01

0.00

0.12

2.89

35–45°

28.42

33.56

1.18

0.17

−0.07

0.24

0.01

0.01

0.12

1.95

>45°

13.13

18.64

1.42

0.35

−0.07

0.42

0.02

0.00

0.15

2.79

Slope aspect

Flat

2.96

0

0.00

0.00

0.03

0.00

0.00

0.00

0.00

0.00

North

6.78

4.07

0.60

−0.51

0.03

−0.54

0.08

0.00

0.29

−1.83

Northeast

10.82

11.19

1.03

0.03

0.00

0.04

0.03

0.00

0.18

0.20

East

8.68

10.51

1.21

0.19

−0.02

0.21

0.03

0.00

0.19

1.11

Southeast

10.75

19.32

1.80

0.59

−0.10

0.69

0.02

0.00

0.15

4.66

South

12.59

15.59

1.24

0.21

−0.03

0.25

0.02

0.00

0.16

1.55

Southwest

12.43

12.2

0.98

−0.02

0.00

−0.02

0.03

0.00

0.18

−0.12

West

10.29

9.83

0.96

−0.05

0.01

−0.05

0.03

0.00

0.20

−0.26

Northwest

10.52

10.51

1.00

0.00

0.00

0.00

0.03

0.00

0.19

−0.01

North

6.15

6.78

1.10

0.10

−0.01

0.10

0.05

0.00

0.23

0.45

Altitude (m)

<400

25.55

23.39

0.92

−0.09

0.03

−0.12

0.01

0.00

0.14

−0.85

400–600

24.06

33.9

1.41

0.34

−0.14

0.48

0.01

0.01

0.12

3.92

600–800

19.48

21.36

1.10

0.09

−0.02

0.12

0.02

0.00

0.14

0.81

800–1,000

14.16

13.56

0.96

−0.04

0.01

−0.05

0.03

0.00

0.17

−0.29

1,000–1,200

6.68

7.12

1.07

0.06

0.00

0.07

0.05

0.00

0.23

0.30

1,200–1,400

1.87

0.68

0.36

−1.01

0.01

−1.03

0.50

0.00

0.71

−1.44

>1,400

0.18

0

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Lithology

Quaternary

3.32

0

0.00

0.00

0.03

0.00

0.00

0.00

0.00

0.00

Terrace

9.58

13.56

1.42

0.35

−0.05

0.39

0.03

0.00

0.17

2.31

Middle Siwaliks

0.02

0

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Lower Siwaliks

1.01

2.37

2.34

0.85

−0.01

0.87

0.14

0.00

0.38

2.26

Benighat Slate

11.48

12.88

1.12

0.12

−0.02

0.13

0.03

0.00

0.17

0.76

Dhading Dolomite

10.06

12.2

1.21

0.19

−0.02

0.22

0.03

0.00

0.18

1.22

Nurpul Formation

41.65

47.12

1.13

0.12

−0.10

0.22

0.01

0.01

0.12

1.90

Purebesi Quartzite

4

3.05

0.76

−0.27

0.01

−0.28

0.11

0.00

0.34

−0.83

Amphibolite

0.25

0.34

1.35

0.30

0.00

0.30

1.00

0.00

1.00

0.30

Dandagau Formation

1.68

1.02

0.61

−0.50

0.01

−0.51

0.33

0.00

0.58

−0.87

Fagfog Quartzite

2.03

0.68

0.33

−1.09

0.01

−1.11

0.50

0.00

0.71

−1.56

Kuncha Formation

6.87

6.78

0.99

−0.01

0.00

−0.01

0.05

0.00

0.23

−0.06

Distance from rivers (m)

0–50

31.39

32.2

1.03

0.03

−0.01

0.04

0.01

0.01

0.12

0.30

50–100

38.76

45.08

1.16

0.15

−0.11

0.26

0.01

0.01

0.12

2.22

100–150

9.29

10.17

1.09

0.09

−0.01

0.10

0.03

0.00

0.19

0.52

150–200

5.05

4.41

0.87

−0.14

0.01

−0.14

0.08

0.00

0.28

−0.51

>200

7.48

8.14

1.09

0.08

−0.01

0.09

0.04

0.00

0.21

0.43

Distance from highway (m)

0–100

9.84

5.08

0.52

−0.66

0.05

−0.71

0.07

0.00

0.27

−2.69

100–200

9.56

14.58

1.53

0.42

−0.06

0.48

0.02

0.00

0.16

2.90

200–300

9.16

13.22

1.44

0.37

−0.05

0.41

0.03

0.00

0.17

2.40

300–400

16.75

17.97

1.07

0.07

−0.01

0.08

0.02

0.00

0.15

0.56

>400

46.66

49.15

1.05

0.05

−0.05

0.10

0.01

0.01

0.12

0.86

Distance from faults (m)

0–100

9.52

11.19

1.18

0.16

33.00

0.11

11.19

0.16

0.16

−0.02

100–200

8.75

10.51

1.20

0.18

31.00

0.11

10.51

0.18

0.18

−0.02

200–300

8.13

13.22

1.63

0.49

39.00

0.13

13.22

0.49

0.49

−0.06

300–400

7.43

10.17

1.37

0.31

30.00

0.10

10.17

0.31

0.31

−0.03

>400

58.14

54.92

0.94

−0.06

162.00

0.55

54.92

−0.06

−0.06

0.07

TWI

<5.5

68.75

87.8

1.28

0.24

−0.94

1.19

0.00

0.03

0.18

6.66

5.5–7.2

20.57

12.2

0.59

−0.52

0.10

−0.62

0.03

0.00

0.18

−3.50

>7.2

2.26

0

0.00

0.00

0.02

0.00

0.00

0.00

0.00

0.00

SPI

0–150

23.05

23.39

1.01

0.01

0.00

0.02

0.01

0.00

0.14

0.14

150–300

30.14

35.25

1.17

0.16

−0.08

0.23

0.01

0.01

0.12

1.91

300–450

26.06

31.53

1.21

0.19

−0.08

0.27

0.01

0.00

0.13

2.13

>450

12.72

9.83

0.77

−0.26

0.03

−0.29

0.03

0.00

0.20

−1.48

Land use

Barren

0.45

0

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Bush

37.43

36.95

0.99

−0.01

0.01

−0.02

0.01

0.01

0.12

−0.17

Cultivation

30.34

23.73

0.78

−0.25

0.09

−0.34

0.01

0.00

0.14

−2.46

Cutting

0.36

1.36

3.75

1.32

−0.01

1.33

0.25

0.00

0.50

2.64

Forest

18.65

37.97

2.04

0.71

−0.27

0.98

0.01

0.01

0.12

8.19

Grass

1.17

0

0.00

0.00

0.01

0.00

0.00

0.00

0.00

0.00

Orchard

0.01

0

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

River

2.22

0

0.00

0.00

0.02

0.00

0.00

0.00

0.00

0.00

Sand

1.35

0

0.00

0.00

0.01

0.00

0.00

0.00

0.00

0.00

Plan curvature (100/m)

Concave

42.5

42.03

0.99

−0.01

0.01

−0.02

0.01

0.01

0.12

−0.16

Flat

4.17

0

0.00

0.00

0.03

0.33

0.00

0.58

−2.49

−0.16

Convex

45.3

57.29

1.26

0.23

−0.24

0.01

0.01

0.12

3.98

−0.16

Statistical index model

The second statistical approach used in this study is SI (Wi) model. It was introduced by van Westen et al. (1997) for landslide susceptibility analyses and has been adopted by various researchers. In the SI method, a weight value for a parameter class is defined as the natural logarithm of the landslide density in the class divided by the landslide density in the entire map. This method is based upon the following formula (van Westen et al. 1997):
$$ {W_{ij }}=\ln \left( {\frac{{{f_{ij }}}}{f}} \right)=\ln \left( {\frac{{A_{ij}^{*}}}{{{A_{ij }}}}} \right)\times \ln \left( {\frac{A}{{{A^{*}}}}} \right) $$
(5)
where Wij is the weight given to a certain class i of parameter j, fij is the landslide density within the class i of parameter j, f is the landslide density within the entire map, \( A_{ij}^{*} \) is the area of landslides in a certain class i of parameter j, Aij is the area of a certain class i of parameter j, A* is the total area of landslides in the entire map, and A is the total area of the entire map. To perform the SI modeling, each thematic map is overlaid and crossed separately with the landslides location map (estimation group) using the ArcGIS 9.3 software, and the numbers of pixels forming the landslides that fall into the various classes of the maps of the different factors are calculated. The calculated numbers of pixels are divided by the total number of pixels for that selected parameter to calculate the density of the class. For this, all the cross table obtained in GIS are exported to Microsoft Excel, where all the data required to calculate the weight (Wij) are obtained. The weight is positive when the landslide density is higher than the normal and is negative when it is less than normal. The final weight obtained from the analysis is analyzed using the weighted sum option in the spatial analyst tools of ArcGIS and the final landslide susceptibility map was constructed.

Weights-of-evidence

WoE is a quantitative “data-driven” method used to combine datasets. It uses the Bayesian probability model. In geology, it was originally developed for mineral potential assessment (Bonham-Carter et al. 1988, 1989; Agterberg 1992; Agterberg et al. 1993; Bonham-Carter 2002; Carranza and Hale 2002; Carranza and Castro 2006). Several authors have applied the method to mineral potential mapping using GIS (Carranza and Hale 2000). Cheng (2004) used the method to predict the location of flowing wells and Daneshfar and Benn (2002) used the WoE model to analyze spatial associations between faults and seismicity, whereas Carranza and Castro (2006) used this model for predicting lahar inundation zones. Recently, several researchers have used the WoE model in landslide susceptibility mapping (van Westen et al. 2003; Mathew et al. 2007; Neuhäuser and Terhorst 2007; Bui et al. 2008; Sharma and Kumar 2008; Dahal et al. 2008a, b; Regmi et al. 2010a, b; Pourghasemi et al. 2012a, Mohammady et al. 2012).

A detailed description of the mathematical formulation of the method is available in Bonham-Carter (1991, 1994, 2002) and the mathematical relationship for landslide susceptibility mapping is available in many research articles (Pradhan 2010a, b, c; Dahal et al. 2008b). They have all experimented with Bayes’ conditional probability theorem. Bayes’ probability theorem can be written as:
$$ P\left\{ {\frac{A}{B}} \right\}=\frac{{\left\{ {P\left( {\frac{B}{A}} \right)\times P(A)} \right\}}}{P(B) } $$
(6)
By overlaying landslide locations with each evidence (conditioning factors), the statistical relationship can be measured between them and assessed as to whether and how significant the evidence is responsible for the occurrence of past landslides (Neuhäuser and Terhorst 2007). On the other hand, the WoE model is fundamentally based on the calculation of positive and negative weights W+ and W. The method calculates the weight for each landslide predictive factor (A) based on the presence or absence of the landslides (B) within the area (Bonham-Carter 1994) as follows:
$$ W_i^{+}=\ln \frac{{P\left\{ {B\left| A \right.} \right\}}}{{P\left\{ {B\left| A \right.} \right\}}} $$
(7)
$$ W_i^{-}=\ln \frac{{P\left\{ {\overline{B}\left| A \right.} \right\}}}{{P\left\{ {\overline{B}\left| \overline{A} \right.} \right\}}} $$
(8)
where P is the probability and ln is the natural log. Similarly, B is the presence of potential landslide predictive factor, \( \overline{B} \) is the absence of a potential landslide predictive factor, A is the presence of landslide, and \( \overline{A} \) is the absence of a landslide. A positive weight (W+) indicates that the predictable variable is present at the landslide locations and the magnitude of this weight is an indication of the positive correlation between the presence of the predictable variable and the landslides. A negative weight (W) indicates the absence of the predictable variable and shows the level of negative correlation (Dahal et al. 2008a). In landslide susceptibility mapping, the weight contrast, C(C = W+ − W), measures and reflects the spatial association between the evidence feature and landslide occurrence. C is positive for a positive spatial association and negative for a negative spatial association (Dahal et al. 2008b).
The standard deviation of W is calculated as:
$$ S(C)=\sqrt{{{S^2}{W^{+}}+{S^2}{W^{-}}}} $$
(9)
where S(W+) is the variance of the positive weights and S(W) is the variance of the negative weights. The variances of the weights can be calculated by the following expressions:
$$ {S^2}{W^{+}}=\frac{1}{{N\left\{ {B\cap A} \right\}}}+\frac{1}{{B\cap \overline{A}}} $$
(10)
$$ {S^2}{W^{-}}=\frac{1}{{\left\{ {\overline{B}\cap A} \right\}}}+\frac{1}{{\left\{ {\overline{B}\cap \overline{A}} \right\}}} $$
(11)

The studentized contrast is a measure of confidence and is defined as the ratio of the contrast divided by its standard deviation. The studentized contrast serves as an informal test that C is significantly different from zero or if the contrast is likely to be “real” (Bonham-Carter 1994).

Results and discussion

Application of frequency ratio model

To determine the level of correlation between the landslide locations and the conditioning factors, i.e., slope degree, slope aspect, altitude, lithology, land use, distance from rivers, distance from highway, distance from faults, TWI, SPI, land use, and plan curvature, the FR method was used. The final landslide susceptibility map obtained by the FR model is shown in Fig. 4. From Table 2, it is seen that landslides are higher in slopes >25°. The FR value is highest for slope class ≥45°, followed by the 25–35° slope class. As the slope angle increases, the shear stress in the soil or other unconsolidated material generally increases. Gentle slopes are expected to have a low frequency of landslides because of the generally lower shear stresses that are associated with low gradients. The steep slopes may not be susceptible to landsliding. The FR from the slope aspect analysis shows that the SE-facing slopes are most affected by landslides, followed by E-, NE-, and S-facing slopes. In the case of altitude, landslide density is highest at the elevation ranging from 400 to 600 m followed by from 600 to 800 m. The FR of the altitude (Table 2) shows that it is >1 at these altitude ranges. For the lithology, it can be seen that Lower Siwaliks, Dhading Dolomite, Dandagau Formation, Nurpul Formation, and Amphibolites have FR values >1 (Table 2). The influence of a drainage system upon the landslide susceptibility was also analyzed by identifying the drainage river line by buffering. The distance in between 0 and 150 m from the drainage river shows higher correlation with the landslides. The highway also has a great influence in landslide formation in the study area. The distance >100 m shows an FR value >1. This value decreases as the distance from the highway decreases. The relation between a landslide and its distance to a drainage line and road shows that, when distance from the drainage (river) line and road increases, the landslide occurrence probability decreases. For that reason, road construction and bank erosion are the most important factors in slope imbalance causing frequent occurrence of landslides.
https://static-content.springer.com/image/art%3A10.1007%2Fs12517-012-0807-z/MediaObjects/12517_2012_807_Fig4_HTML.gif
Fig. 4

Landslide susceptibility map based on the FR model

The distance from the fault map shows that the landslides are highly dependent on these tectonic fractures as the FR value is >1 in between 0 and 400 m from the fault. The FR value decreases with increasing fault distance. The relation between TWI and landslide probabilities showed that the 0–5 classes have the highest FR value and that 300–450 SPI shows high FR value. In the case of land use, higher FR values were for cutting and forest-covered lands. The plan curvature value represents the morphology of the area. The convex curvature has the highest FR value.

Application of statistical index model

The resultant weights for each thematic map for the SI model are given in Table 2. These weights were then analyzed by using the weighted sum option in the spatial analyst tools of ArcGIS to get the final LSI map (Fig. 5). From Table 2 it is seen that, among the Wi for various conditioning factors, slope classes >25° have positive weight values. Thus, it is clear that the slope becomes unstable as the slope becomes steeper. In the case of slope aspect, N, NE, E, SE, and S have positive Wi values. Among all these, SE has the highest value, followed by S, E, N, and NE. The Wi values of altitude are positive within the range of 400 to 800 m, and 1,000 to 1,200 m with the highest value at 400 to 600 m. It slowly decreases with both decreasing and increasing altitudes. Among the Wi calculated for the lithological complexes, Lower Siwaliks has the highest Wi value, followed by terrace deposits, Amphibolites, Dhading Dolomite, Nourpul Formation, and Benighat Slate Formation. The Wi value for the distance from rivers (Drainages) shows that it decreases with the increase in distance from the drainage. From Table 2, it is seen that the distance between 0 and 150 m from the drainage have higher Wi value. The Wi value of distance from highway shows that it is positive for distance >100 m. It decreases as the distance increases. This shows that the highway constructions have a positive influence in landslide occurrence. The Wi value of distance from faults shows that the distance in between 0 and 400 m have positive Wi values, with the highest value occurring at the distance in between 200 and 300 m followed by 300 to 400 m. In the case of TWI and SPI, the 0–5 and 0–450 ranges, respectively, have positive Wi value, showing good correlation with the landslides. In the case of land use, only the cutting and forest-covered lands show good correlation with the landslide formation as these land use system have positive Wi values. Convex slope only consists of positive Wi value.
https://static-content.springer.com/image/art%3A10.1007%2Fs12517-012-0807-z/MediaObjects/12517_2012_807_Fig5_HTML.gif
Fig. 5

Landslide susceptibility map derived from the SI model

Application of weights-of-evidence model

The WoE modeling is mainly based on the W+ and W. From these, the weight contrast C is calculated. C is positive for a positive spatial association and negative for a negative spatial association. The studentized value of C, the ratio of C to standard deviation or C/S(C), serves as a guide to the significance of the spatial association and acts as a measure of the relative certainty of the posterior probability (Bonham-Carter 1991). The weights and contrasts for each predictor pattern are summarized in Table 2. S2W+ and S2W are the variances of W+ and W. S(C) is the standard deviation of the contrast and C/S(C) is the studentized value of the contrast (Table 2). The detailed procedure of calculating C, S(C), S2W+, and S2W is given in the previous section. The relationship between the landslides and the landslide conditioning factors, contrast, and studentized C are presented in Table 2. The C/S(C) derived based on the WoE were assigned to the classes of each thematic layers to produce multiclass weighted maps for all evidence, which were overlaid and numerically added according to Eq. 12 in order to calculate a LSI map (Fig. 6):
$$ \mathrm{LS}{{\mathrm{M}}_{\mathrm{WoE}}}=\mathrm{Wo}{{\mathrm{E}}_{\mathrm{Slope}}}+\mathrm{Wo}{{\mathrm{E}}_{\mathrm{Aspect}}}+\mathrm{Wo}{{\mathrm{E}}_{\mathrm{Curvature}}}+\mathrm{Wo}{{\mathrm{E}}_{\mathrm{Altitude}}}+\mathrm{Wo}{{\mathrm{E}}_{\mathrm{Lithology}}}+\mathrm{Wo}{{\mathrm{E}}_{{\mathrm{Land}\;\mathrm{use}}}}+\mathrm{Wo}{{\mathrm{E}}_{\mathrm{Fault}}}+\mathrm{Wo}{{\mathrm{E}}_{\mathrm{River}}}+\mathrm{Wo}{{\mathrm{E}}_{\mathrm{Highway}}}+\mathrm{Wo}{{\mathrm{E}}_{\mathrm{TWI}}}+\mathrm{Wo}{{\mathrm{E}}_{\mathrm{SPI}}} $$
(12)
https://static-content.springer.com/image/art%3A10.1007%2Fs12517-012-0807-z/MediaObjects/12517_2012_807_Fig6_HTML.gif
Fig. 6

Landslide susceptibility map derived from the WoE model

Based on the value of C/S(C), it can be seen that the slope gradient >25° has a maximum value. Thus, the area occupied by the slope gradient >25° shows maximum susceptibility with reference to landslides in the study area. In the case of slope aspect, NE- to S-trending slope have higher C/S(C) value, indicating that landslide susceptibility is highest in these slopes. In the case of altitude, the range in between 400 and 600 m has highest C/S(C) value, indicating high landslide susceptibility at this range of elevation. Among the different lithological classes terrace and Lower Siwaliks have highest C/S(C) value, followed by variegated mudstone, with some thick-bedded, light gray, fine-grained sandstones have higher value for C/S(C). These lithological units show maximum susceptibility with reference to landslides in the study area. The distance from rivers parameter also has shown positive influence towards slope destabilization as seen from the C/S(C) value. Slope saturation might be the reason for this phenomenon. The C/S(C) value of distance from highway shows that the distances in between 50 and 150 m have the highest value. It decreases as the distance increases. This is mainly due to the unplanned road cutting. In the case of distance from fault, only the fault distance >400 m shows higher C/S(C) value. In the case of TWI, the highest C/S(C) value is for classes 0–5, and for SPI, it is highest at the range of 150–450. Forest-covered land, followed by cutting land, has a higher value of C/S(C), showing maximum susceptibility to landslides. The convex slope has the highest value of C/S(C), indicating high landslide susceptibility in convex slope.

Validation of the landslide susceptibility maps

The overall performance of the analysis is generally judged on the number of correctly classified cells, and so a validation process is required. There exist several methods for validation of the landslide susceptibility maps. In the present study, landslide susceptibility maps were verified by comparing the susceptibility map with both the training data that were used for building the models and with the landslide locations that were not used during the model building process.

The area under the curve (AUC) represents the success rate and prediction rate percentage of the model. Variation from 0.9 to 1.0 is the ideal situation. AUC was calculated from 100 subdivisions of the LSI values of all the cells in the study area and the cumulative percentage of landslide occurrences in the classes. The AUC was obtained for both the training and the validation data (Fig. 7). The result showed that all the three models exhibited similar performance, with the FR model being the better one (success rate, 76.8 %; prediction rate, 75.4 %), followed by the WoE model (success rate, 75.6 %; prediction rate, 74.9 %) and the SI model (success rate, 75.5 %; prediction rate, 74.6 %) (Fig. 7a, b).
https://static-content.springer.com/image/art%3A10.1007%2Fs12517-012-0807-z/MediaObjects/12517_2012_807_Fig7_HTML.gif
Fig. 7

a Success rate of the landslide susceptibility maps. b Prediction rate of the landslide susceptibility maps

Conclusions

Landslides are a serious threat to life and damage property; thus, landslide susceptibility mapping can be one of the preliminary steps in minimizing these damages. In the current research, three statistically based models, such as FR, SI, and WoE, were used for identifying the areas susceptible to landslides at the Mugling–Narayanghat road corridor and its surrounding area of Central Nepal Himalaya. The results of each model were given.

Finally, the performances of these models were compared. Susceptibility mapping was performed using various topographic, geological, structural, land use, and other datasets in GIS. In order to prepare the susceptibility maps, 11 thematic layers (slope gradient, slope aspect, plan curvature, altitude, SPI, TWI, lithology, land use, distance from faults, distance from rivers, and distance from highway) were used as the input data. The landslide inventory map of the study area was created by the analysis of aerial photographs, remote sensing images, from earlier published/unpublished reports, and by repeated field surveys. Among 438 landslides, 295 (67 %) were used as training data and the remaining 143 (33 %) were used for validation purposes. The AUC curves (success rate and prediction rate) were prepared for all the three models to test their accuracy. The validation results showed that all the three models show equal performance, with the FR model being the better one (success rate, 76.8 %; prediction rate, 75.4 %), followed by the WoE model (success rate, 75.6 %; prediction rate, 74.9 %) and the SI model (success rate, 75.5 %; prediction rate, 74.6 %). From this, the authors conclude that all the three models show almost similar results. As most of these landslide susceptibility maps show good prediction capacity, they can be used for planning future development works by avoiding the highly susceptible zones during project implementation.

Acknowledgments

The authors express their gratitude to MEXT (Ministry of Education, Culture, Sports, Science and Technology, Tokyo, Japan) for funding the present study. Dr. Michel Calvelo, Mr. Pravin Kayasta, and Mr. Ananta Man Shingh are sincerely acknowledged for their great help during the process of writing this paper. Also, the authors would like to thank two anonymous reviewers for their helpful comments on the previous version of the manuscript

Copyright information

© Saudi Society for Geosciences 2013