Simultaneous Use of AHP and Fuzzy approaches for Mapping of Landslide Susceptibility in Komroud sub-basin, N Iran

Mohammad Parsa Sadr1, Abbas Maghsoudi2

* Corresponding Author: Mohammad Parsa Sadr

1: Msc of Mining Engineering, Department of Mining and Metallurgy Engineering, Amirkabir University of Technology

2: Assistant Professor of Department of Mining and Metallurgy Engineering, Amirkabir University of Technology

Address:

1, 2: Iran, Tehran, Hafiz Avenue

Email of authors:

1: rouzbehparsasadr@gmail.com

2: a.maghsoudi@aut.ac.ir

Phone and fax number:

0098-21-44169155

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Abstract

In this paper a combination of analytic hierarchy process (AHP) and fuzzy systems was used for landslide susceptibility mapping, in Komroud sub-basin, north of Iran. Landslide is known as a prevalent phenomenon in the study area. Satellite data, field surveys, geological and topographical maps were the origin of data. Remote sensing and GIS techniques were used for manipulating and collecting data. Pairwise matrix comparisons were used for initial ranking of classes. Then, the AHP weighted classes were infused by a fuzzy inference network and landslide susceptibility indexes (LSI) were obtained. Instantaneous break values of LSI were recognized as the boundary of landslide susceptibility classes. Accuracy of generated landslide susceptibility map was assessed by a series of statistical analyses. Results showed a significant relationship between LSI values and the testing data.

Keywords: Landslide Susceptibility, AHP, Fuzzy, GIS, RS, Komroud

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Introduction

Landslide Susceptibility (LS) is defined as the probability of occurrence of a landslide in an area. In other words, LS is a degree to check whether an area can be affected by further mass movements. In a Landslide Susceptibility Zonation map (LSZ), According to the LS values, an area can be divided in to different zones of landslide probability (Sarkar et al. 2004; Kanungo et al. 2006; Chauhan et al. 2010).

Spatial data are provided in a wide range of methods. In comparison with all the data preparation methods, remote sensing is a fast, cheap and simple approach for spatial data set preparation. This spatial data set includes vegetation, land usage, lithology, structural features and the like. Geographical information systems provide us with preservation and processing of spatial data. During the last few years the application of GIS systems has been increasing dramatically (Arnous 2011).

The simultaneous use of GIS and remote sensing can decrease both the period time and operation costs of a project. Combination of RS and GIS techniques has become very common in a variety of studies (Arnous2011). These techniques provide us with the exact location of favorite places. These favorite places include the location of mineral resources (Bonham-Carter 1994), the location of a particular kind of a species, e.g. a plant (Corsi et al. 2000), and the best places for construction of special instruments (Fedra 1999). Particularly, in natural hazard studies, these techniques provide us with the location of vulnerable and susceptible zones to danger. Landslide susceptibility studies are meant to provide civil engineers with the exact location of prone areas of landslides. Therefore, landslide susceptibility zonation is the first step of slope stability operation. Many RS and GIS studies have been handled in order to recognize the susceptible zones of landslide in the last few years (such as Van Westen et al. 2006; Guzzetti et al. 2006; Kanungo et al. 2006; Yalcin 2008; Chauhan et al. 2010; Pradhan et al. 2010; Rossi et al. 2010; Vahidnia et al. 2010; Arnous 2011; Avtar et al. 2011; Akgun 2012; Pourghasemi et al. 2012; Kundu et al. 2013).

Saaty (1980) developed a multi criteria decision making system named Analytic Hierarchy Process. This method is a flexible and easy approach for analyzing complicated problems. AHP is a process for representing the elements of various problems like site selection, suitability analysis and landslide susceptibility analysis (Cengiz et al. 2009). Several authors have utilized AHP for forecasting of landslide hazardous zones, such as Komac 2006. Further, fuzzy approach has been used frequently by many authors such as Pradhan 2011. Pourghasemi et al. 2012 has compared AHP and fuzzy approaches for landslide susceptibility mapping in Haraz watershed, north of Iran. A hybrid AHP- Fuzzy model has been used by Arsalan (2008) for handling public assessments on transportation projects.

The aim of this study was to produce a landslide susceptibility map to inform the inhabitants of the region about the landslide endangered zones.

The Komroud basin is located in the Semnan province in the north of Iran. The area is located between the 350 51’ 42” and 350 54’ 26” geographical latitude, and 530 3’ 00’’ and 530 7’ 16’’ geographical longitudes. The district covers an area equal to 1862.2 hectares. The maximum elevation in the Komroud area is about 3690 meters, while the minimum height located at the outlet of the basin is measured at 1535 meters. The region's average precipitation level is measured at 516 mm per year, with 67% relative humidity, and an average temperature of 16 degrees Celsius. The climate in this region is considered to be a semi-humid, cold region. The location of the study area is observable in figure 1.

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Figure 1- Location of study area

Geological and Tectonic characteristics

The eminent geological phenomenon in the area is the presence of Abyek-Shahroud trust fault, which have caused the Miocene bedrock to stay in adjacency of Precambrian basement. The ages of the lithological units of the area varies widely from Precambrian to Quaternary. The lithological units of the area are mentioned in table 1. The geological map of the area is presented in figure 2. Also, figure 3 shows a number of geological units of the area, which are crucial on the scope of this study.

Table 1- Geological units of the study area

Figure 2- Geological map of the study area

Figure 3- a; Sandy shale of Zagun formation, b; black limestone and shale of Barut formation, c; the boundary of Zagun and Barut formation, d; Sandy shale of Zagun formation

Most of the registered mass movements in the area have occurred on the weathered material of Barut and Zagun formation. Generally it has been observed that most of landslides have occurred in terrains with weak material such as shale, clay and etc. While, well bedded massive limestone is not as prone as weathered shale and alluvial fans. Figure 4 shows a number of landslides which have occurred in the study area.

Figure 4- a; Landslide in the Zagun formation, b; a major landslide in the Barut formation and the quaternary deposits, c; Landslide in Zagun formation

Manipulating of the data set

The data which was the source of the study are summarized in table 2. According to the characteristics of the study area, factors of vegetation, geomorphology, Tectonic and Lithology were recognized as causal factors in occurrence of a landslide. Spatial data of these factors were collected from Satellite data, Published maps and field surveying. GIS were used for manipulation and analysis of data. In order to produce a reliable and representative map of landslide susceptible areas, a hybrid AHP-Fuzzy model was designed. In this system, recorded landslides were separated into two separate classes of testing and training data. According to the training data, casual factors were classified to sub-classes. Pairwise comparisons of AHP were utilized for allocation of weights to Sub-classes. Then, according to a fuzzy inference network, data layers were integrated and a LSZ map was generated.

Authors have used various methods for classification of continues data. A number of authors have used equal interval approach for classification of continuous data (Nandy et al. 2009). In this paper, this method was used for classification of proximity to faults and slope angle. Field surveys and sampling were used for classification of vegetation continuous data (NDVI). There are definite classes for discrete data. In this study aspect and lithology were the discrete data.

Table 2- Source of data and their specific usage

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Slope and Aspect

Surface topography is the origin of the mass movements and it guides their direction, thus controlling the density and extent of landslides (Chauhan et al. 2010; Arnous 2011; Avtar et al. 2011). Therefore, a range of features including slope and slope aspect were obtained from DEM. The DEM map was generated using topographical map. Slope is considered to be the most important cause of occurrence of mass movements in an area. On a slope of an isotropic material, any increase in the slope, increases the probability of rupture. To evaluate the effect of the increased slope, initially the examination of spatial distribution of slope is required (Clerici et al. 2002; Van Westen et al. 2003). Based on the obtained information from the DEM map, the spatial distribution of train slopes of the region was classified into five categories of a)- 00 to 10 °, b)- 100 to 200, c)- 200 to 300, d)- 300 to 400,and e)- greater than 400

(Fig 5a) (Chauhan et al. 2010).

Slope aspect in the region has a significant role in the development of mass movement, because the slopes facing south, southeast, and northeast of the region have less vegetation. Subsequently their surface areas are more exposed to rainfall, which causes rapid loss of gradient in a heavy rainfall. Similar as the slope’s thematic data layer, the slope aspect’s thematic layer was generated by the DEM. The slope aspect of area were divided into 9 categories of: a) - flat, b) - east c) - south east d) - north east, e) - west, f) - southwest, g) - northwest, h) -south, and i) - north, which can be observed in figure 5b (Lee et al. 2002; Chauhan et al. 2010). Initial ranks (pair wise comparisons) were allotted to sub-classes of aspect map based on the percentage of training data in each category.

Lithology

Lithology is one of the most effective factors in occurrences of landslides, because lithological and structural changes alter the strength and permeability of rock and soil (Carrara et al. 1999). The lithology’s thematic map was generated through both digitizing 1:100,000 geological map of study area from Geological Survey of Iran (GSI) and field surveying. The basis of dividing the area to the following lithological units was the engineering geological characteristics of them. These groups were Group a) - Young fans, weathered material, Shale, siltstone and sandstone; Group b) - Thin bedded limestone with weak cement and Group c) - Thick bedded limestone, well consolidated material, well cemented limestone (Fig 5c).

Structural Characteristics and its Data Layers

The location of area’s faults and fractures is the source of released internal energy of the earth, and in these area, fractures and lineaments are correlated with the area’s mass movement. The area’s lineaments were obtained from band 8 of ETM + filtered images. Enhanced directional filters were used for detection of lineaments in this area. Visually, by identifying rapid topographical changes, sharp contrast in tonal colors and straight grain drainages 17 lineaments in the area were recognized (Chauhan et al. 2010). Figure 5d shows the lineaments of the area.

The lineament density map was obtained from lineament processing using the ARC GIS 10 software. Lineament density values based on equal intervals were divided into five categories (fig 5e).

Vegetation

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The root systems of all plants generate the needed mechanical strength in soil. Some roots grow in downward direction in soil or rock in the potentially unstable regions with shallow landslides. Roots of trees increase the confidence level against occurrence of landslide. Root’s resistance allow the forested foothills with a slope angle of greater than 35 degrees to remain stable, while similar hillsides without any trees, and have slope angles of 12 to 14 degrees are prone to landslide. In some forests, the roots of the trees have not penetrated into the lower rocks or do not pass through the landslide areas, but it is possible to create continuity in a network, that link the upper horizons of soil and the soil resistance may act effectively. Tree roots increase apparent soil adhesion, also by absorbing evaporated and transpired water, and lowering the groundwater levels will help increasing the shear strength of soil. Additionally, vegetation by disposing raindrops prevents the drops from hitting the soil surface and ultimately helps reducing decomposition of the soil particles (Varnes et al. 1984).

Normalized difference vegetation index (NDVI) is a non-linear transformation of the visible bands (red) and infrared bands of satellite data. The NDVI index is considered as the difference between total bands in the visible and near-infrared bands of satellite data. These indices represent the factors such as the distribution of vegetation in the area. NDVI relation is defined as equation below (Carlson et al. 1997):

NDVI=( NIR−VV )( NIR+VV )

(1 )

Where NIR is the near infrared value and VV is the visible value. To depict vegetation, a visible band 3 and near-infrared band 4 of Landsat-7 ETM+ were used. The greater the NDVI value, the denser the vegetation cover. Based on field surveys and sampling, the area was divided into three classes of: a) - dense vegetation, b) - moderate vegetation, and c) - poor vegetation (Fig 5f).

Landslide inventory Map

Mass movements in the areas under study were first identified from the satellite imagery. Then field surveys conducted to confirm and complete the information and then the exact location of identified mass movements were recorded. Figure 5g shows landslide inventory map of the area. Further the location of small landslides has been shown in figure 5h (Chau et al. 2004).

Figure 5- a; slope map, b; aspect map, c; lithology, group 1 includes Alluvial fans, weathered material, shale; siltstone and sandstone. Group 2 includes thin bedded limestone with weak cement. Group 3 includes well consolidated material, well cemented material and thick bedded limestone. d; lineaments of the study area, e; lineament density map, f; vegetation cover, g; mass movements of the area, h; location of landslides of the area

Landslide Susceptibility Mapping

The designed model is presented in figure 6. The Whole applied theory of Analytic Hierarchy Process has been introduced by Thomas L. Saaty (1990) in an article entitled "How to make a decision". In this paper the sub-classes of data layers were compared by pairwise matrixes.

Pair-wise matrix is defined as equation (2):

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A=a ij i , j=1,2 ,. . .. , n (2 )

Figure 6- The designed model

Where aij is each of the arrays, which is located in the ith column and jth row; n is the number of criterions. This matrix is reciprocal. It means that:

aij=1

a ji

i , j=1,2, . .. . , n (3 )

There are some key characteristics of a pair-wise matrix. Every array is greater than zero. Also, the pair-wise matrix is a diagonal matrix, it means that:

aij=1 if i= j ( 4 )

The normalized matrix is a matrix which is derived by dividing any array of pairwise matrix by the summation of the values in its column. The priority or weight of each factor is calculated by calculating of the average amount of each row of the normalized matrix. These averages provide an estimate of the relative weights of the criteria being compared. The higher the weight, the more important the criteria (Saaty 1990). The pairwise matrixes and calculated weights are shown in table 3.

In AHP, an index of consistency, known as the consistency ratio (CR), is used to indicate the probability that the matrix judgments were randomly generated (Saaty 1977).

CR=CI / RI (5 )

Where RI is the average of the resulting consistency index depending on the order of the matrix given by Saaty (1977) and CI is the consistency index and can be expressed as:

CI=( λMax−n)

(n−1 )(6 )

Maxis the largest or principal eigenvalue of the matrix and can be easily calculated from the matrix, and n is the order of the matrix. The CR (Consistency Ratio) was calculated. If the CR values were greater than 0.1, the models were automatically discarded (Saaty 1977).

The aim in this study was to find areas susceptible to landslide occurrence. All the maps with shared information on the same scale, are called the fuzzy membership, on a scale of 0 to 1, and are used as a document for the approval of the topic, and these fuzzy sets could be combined by operators.

Table 3- classification of thematic data layers, the pairwise comparison matrix and calculated weights for each class

Zadeh (1973, 1983), and Zimmerman (1991) have provided several fuzzy operators. Ann et al (1991) have presented five different essential functional geological data. These operators

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include; fuzzy AND, fuzzy OR, fuzzy algebraic product, fuzzy algebraic sum, and fuzzy gamma operator, are described as follows:

μAND=Min {μa , μb , μc ,. ..} (7 )

μOR=Max {μa , μb , μc ,. ..} (8 )

μSUM=∏i=1

n

(1−μ i) (9)

μPRODUCT=∏i=1

n

μi (10 )

μGAMMA=(∏i=1

n

μi )1−γ

×(1−(1−∏i=1

n

μi ) )γ

(11)

In map of fuzzy membership values; μA; the value of fuzzy membership for map A given a special occasion, μB: the value of fuzzy membership for B, and so on. And, μ i : fuzzy membership function for map I, where i = 1, 2, … , n, indicating the combination of the maps.

The effect of fuzzy AND function is to generate output maps that are controlled by the smaller values of fuzzy membership for each point. The fuzzy AND operator is a conservative estimate of the fuzzy sets, with a tendency to produce small quantities. The performance of fuzzy OR operator is as such that the output membership value in any situation is controlled by the maximum values of the input maps. Using this operator, the composed value of membership at any situation is only controlled with the maximum values of the input maps. This operator may be a logical operation under some conditions for the purposes of drawing the Landslide Susceptible Zonation (LSZ) map where the favorable indicators of instability are rare, and the existence of favorable evidence is sufficient to prove the compliance.

With the application of fuzzy product operator, the value of combined fuzzy members, tend towards smaller values, besides multiplication of combined participant members, which are between 0 and 1, results in values less than or equal to combined fuzzy members. Subsequently this operator is a digressive operator and because of the nature of formula in this operator, and the nature of numbers being between 0 and 1, this operator is considered to have high degree of sensitivity in placement. The output of fuzzy algebraic sum operator is always greater than or equal to the largest member of the participating members, and hence this operator is an increasing operator. Two components of evidence which both are of favorable hypothesis reinforce one another, and the obtained result is more valuable than any of the two components alone. The influence of additional combination of multi-components, is controlled with the maximum of 1, and will never exceed this value. This operator unlike the other fuzzy multiplication operators has a lesser value of accuracy in placement, where vast areas using this operator are selected as appropriate placement.

Fuzzy Gamma operator is based on fuzzy algebraic product and fuzzy algebraic sum operations. When γ is equal to 1, the combination acts the same as algebraic sum, and when γ

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is equal to zero, the combination acts the same as the fuzzy algebraic product. Wise selection of γ will guarantee the generation of the output value, which is a flexible compromise between the increased trend, fuzzy algebraic sum, and the decreasing effect of fuzzy algebraic product.

To process the data and identify the prone zones of landslide occurrence; the calculated weights, resulted from the previous level, was allotted to each pixel as a fuzzy score. After allocating fuzzy scores as an attribute to each pixel, all of influential data layers were converted to raster images with a cell size of 50m and readied for processing. The fuzzy inference network is illustrated in figure 7. According to this network using fuzzy operators all of the data layers were categorized in three fuzzy sets of continental, geomorphological and geological. Final map was generated by fuzzy gamma operator, with a value of 0.9. Using natural break values the resulted map was classified into five classes of landslide susceptibility. These classes were very low, low, moderate, high and very high susceptibility (Fig 8).

Figure 7- Fuzzy inference network

Figure 8- Landslide susceptibility zonation map of the komroud sub-basin

Discussion

The results of landslide susceptibility analysis were verified using known landslide locations, as it is usually done in related studies ( Remonodo et al. 2003; Lee et al. 2003; Hagus 2012). Testing points of landslide inventory map were used for checking the precision and accuracy of LSZ map. The number of slide pixels and the number of non-slide pixels were evaluated versus susceptibility classes (Fig 9).

Figure 9- Percentage Comparison of area occupied by each landslide susceptibility class and the susceptibility index values, and histogram showing the relative distribution of landslide classes

The rate curve was created and its areas of the under curve were calculated for all cases. The rate explains how well the model and factor predict the landslide. Thus, the area under curve can measure the prediction accuracy qualitatively. To create the validation curve, the computed landslide index values of all cells in the study area were arranged in descending order and divided into 100 equal classes, ranging from very highly susceptible classes to low susceptible classes. Then, the 100 classes were overlaid and intersected with testing data to establish the percentage of landslide incidences in each susceptible class. The rate verification results appear as a line in Figure 10. The fitness of the rate curve can be judged by the fact that more percentage of landslides must occur in very high susceptibility zone as compared to other zones. The greater the gradient in the first part of the curve, the greater its predictive capability (Hagus 2012).

Figure 10- Cumulative frequency diagram showing success rate curve for landslide susceptibility map

As can be observed in Figure 10, 20% class of the study area where the Landslide Susceptibility Index (LSI) had a very higher rank could explain roughly 50 % of the total landslides. In addition, the 40 % class of the study area where the LSI had a higher rank could explain approximately 70 % of the landslides.

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Further, the prediction of the map was validated more accurately in a quantitative manner using the Area under the Curve (AUC) by considering that the ideal prediction will have highest AUC of 1. In this study, the AUC value was found to be 0.782. Accordingly, it indicates that the prediction precision of the acquired map 81.02 % as compared to the ideal value of 100%, which is comparatively satisfying (Hagus 2012).

It was resulted from the generated LSZ map, that lithology is one of the most important causes of land sliding in the area. Weathering is one of the key factors of slope failure in the area. On the slope of weathered material of Zagun and Barut formation and also quaternary deposits in the area, particularly where the slope gradient increases, occurrences of mass movements are highly probable. The high susceptibility class of LSZ map was checked in the field and it was observed that these areas were generally covered by weak or weathered material. Results of the field surveying confirmed that the hybrid AHP- Fuzzy inference system was successful at identification of landslide-prone terrains.

Conclusion

In this study, a hybrid AHP-Fuzzy inference system was applied to assess the landslide susceptibility of Komroud sub-basin in Semnan province, north of Iran. To achieve this objective, five major landslide inducing factors were taken into consideration which includes Lithology, Proximity to lineament, vegetation, Slope and Aspect. The landslide inventory map was randomly split into two different classes. 60 per cent of landslides were selected for training of the system. The training data was used for classification of continuous data. These continuous data were slope angle and proximity to lineaments. The instantaneous changes in cumulative value of pixels with training data were considered as the boundary of different classes of these data. Analytic hierarchy process was used for weighting of classes of influential factors. The weights which were resulted from AHP approach were specified to pixels as initial fuzzy values. Then, a fuzzy inference network was designed for the integration of these factors. With respect to the natural breaks of the output map, the area was divided in to three classes. The accuracy of generated map was checked by correlation of results with the testing data. It was understood from the verification that the results of hybrid model had a significant correlation with the former landslides in the area.

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Table 4- Geological units of the study area

Geological unit Age Description

QS Quaternary Alluvial fan deposits

EM Eocene Marl and limestone

PgC Paleocene Fajan Formation, sandstone and conglomerate

K2Ch Upper Cretaceous Irregularly bedded

limestone with weathered chert nodules

C1 Cambrian Lalun formation, Sandstone with shale members

PCZ Precambrian Zagun formation, Shale, Sandy shale and red micaceous

PCbt Precambrian Barut formation, alternation of shale and highly weathered black limestone

PCS Precambrian Soltanieh formation; Thick bedded massive Limestone

PCK Precambrian Kahar formation; Salty siltstone, Shale

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Table 5- Source of data and their specific usage

data type Attributes specific usage

Description/ source

Date of acquisition

Spatial resolution/ scale

Satellite data Landsat7 ETM+ imageries

2003 30m/15m Vegetation cover, lineaments and landslides

Geological map

Geological survey of Iran map of Semnan

2006 1:100,000 Lithology, faults

Topographical map

National Cartographic center of Iran

2007 1:50,000 DEM, drainage network, places

Field investigations

Surveying - - Geological formations, landslide distribution, checking the accuracy of final map, defining ranks

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Table 6- classification of thematic data layers, the pairwise comparison matrix and calculated weights for each class

Factors 1 2 3 4 5 6 7 8 9 Weights

Slope

1) >40⁰ 1 0.5

2) 30⁰-40⁰ 1/3 1 0.26

3) 20⁰- 30⁰ 1/5 1/3 1 0.13

4) 10⁰- 20⁰ 1/7 1/5 1/3 1 0.06

5) 0⁰- 10⁰ 1/9 1/7 1/5 1/3

1 0.03

Aspect

1) Southeast 1 0.31

2) South 1/2 1 0.25

3) East 1/3 1/2 1 0.15

4) Northeast 1/4 1/3 1/2 1 0.11

5) North 1/5 1/4 1/3 1/2

1 0.08

6) Southwest 1/6 1/5 1/4 1/3

1/2 1 0.05

7) West 1/7 1/6 1/5 1/4

1/3 1/2 1 0.04

8) Northeast 1/8 1/7 1/6 1/5

1/4 1/3 1/2

1 0.03

9) Flat 1/9 1/8 1/7 1/6

1/5 1/4 1/3

1/2 1 0.02

Lithology

1)Alluvial fans, weathered material, shale; siltstone and sandstone 1 0.72

2)Thin bedded limestone with weak cement 1/5 1 0.19

3)well consolidated material, well cemented material, thick bedded limestone 1/7 1/3 1 0.08

Lineament density

1) very dense 1 0.5

2) dense 1/3 1 0.26

3) Moderate 1/5 1/3 1 0.13

4) sparse 1/7 1/5 1/3 1 0.06

4) very sparse 1/9 1/7 1/5 1/3

1 0.03

Vegetation cover

1)poor 1 0.63

2)moderate 1/3 1 0.26

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3)dense 1/5 1/3 1 0.11

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Figure 1

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Figure 2

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Figure3

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Figure 4

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Figure5

22

Figure6

23

Figure 7

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Figure 8

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Figure 9

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Figure 10

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