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Pakistan Journal of Science (Vol. 64 No. 2 June, 2012)

SURFACE DEFORMATION THROUGH FRACTAL ANALYSIS OF DEM BASED

SPATIAL DRAINAGE PATTERNS IN GILGIT BALTISTAN REGION (NORTHERN

PAKISTAN)

A. Masood, S. R. Ahmad, S. A. Mahmood*, J. Qureshi*, H. M. Rafique** and M.S. Khan***

Institute of Geology, University of the Punjab, Lahore, Pakistan*Department of Space Science, University of the Punjab, Lahore, Pakistan

**School of Physical Sciences, Department of Physics, University of the Punjab, Lahore, Pakistan***Department of Geological Engineering, University of Engineering and Technology, Lahore, Pakistan

Corresponding authors Email: [email protected]

ABSTRACT: Gilgit Baltistan landscape is a unique tectonic geomorphological composition on theplanet earth. This region is a meeting point of four worlds famous high altitude mountain ranges

(Hindukush, Pamirs, Karakorum and Himalayas). This research examines the Fractal Dimension (FD)

analysis of geometrical spatial drainage patterns to highlight the deformed zone in the study area. One

of the objectives is to delineate zones vigorously affected by anomalies in the drainage pattern based

on FD, Lacunarity (LA) and Succolarity (SA) techniques. Two methods, Box Counting Method

(BCM) and Gliding Box Method (GBM) were used to generate GIS based maps for FD, LA and SA

for the entire drainage network in the region. This endeavor is based on the fact that the drainagenetwork is forced to undergo geometrical changes due to tectonic or lithological control. The low FD

values (closed to 1) in the region are indicative of linearized spatial drainage network due to

neotectonic control. Hence the low FD value of River Indus dictates tectonic control. However the FD

values do not represent the complex meandericity characteristics. A detailed textural investigation was

conducted to analyze linearized drainage network, heterogeneity and connectivity of the drainage

system and its relation to neotectonics. Landsat imagery was found useful to validate the linearization

of Indus River along Raikot fault. The FD, LA and SA maps are very useful to demarcate different

zones where the drainage network is being controlled by Gilgit Baltistan active structures and these

zones are vulnerable to deadly incidents. This study concludes that the fractal analysis is a vital tool to

pinpoint localized areas that can pose potential threats regarding topographic influence and finally

affecting infrastructure and human life.

Keywords: DEM, Drainage Systems, Fractal Dimension, Lacunarity, Succolarity, Neotectonics, Gilgit Baltistan.

INTRODUCTION

In broader sense, fractals are complex patterns

and forms found throughout the natural world. They are

self similar objects, e.g. drainage system, atmospheric

electricity branching patterns, clouds and the leaves of a

tree (see Figure 1). During the last few decades the fractal

complexity and its geometrical distribution have drawn a

great interest of researchers as a genuine model for

investigating natural phenomena. The multiple branching

patterns of a drainage system impart them an impression

of fractal objects (Mandelbrot, 1983). The combined

physical and geological processes are responsible for the

developments of fractal river networks (Dombradi et al.,

2007). The importance of non linear analysis of spatial

patterns is growing in the field of landscape ecology,

forestry, life sciences, food research, information

technology, peripheric system and tectonic morphology

(Dougherty and Henebry, 2002; Melo et al., 2006;

Dombradi et al., 2007; Gloaguen et al., 2007; Martinez et

al., 2007; Feagina et al., 2007; Dong, 2009, Valous et al.,

2010; Shahzad and Gloaguen, 2010; Mahmood and

Gloaguen, 2011).

The main purpose of these methods is to

pinpoint anomalies and diversities in the natural patterns

and their respective causes. In the context of

morphotectonic investigation such anomalies may appear

in the form of linearized, irregular drainage network and

disconnectivity due to physical and geological processes.

Previous studies suggest that the linearization of

individual stream or entire drainage network may be

analyzed to investigate active surface deformation

(Dombradi et al., 2007; Gloaguen et al., 2007; Shahzad

and Gloaguen, 2010; Mahmood and Gloaguen, 2011).Usually the linear analyses focus on the contributing

drainage area, stream length, channel slope, elevation

(secondary parameters) and entirely ignore the fractal

nature of the drainage system. A distinctive linear method

e.g., river profile analysis (wobus et al., 2006; Mahmood

and Gloaguen, 2011) implies the slope area correlation to

generate same results for different causative effect

(Mahmood and Gloaguen, 2011). These effects can be

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reduced if we take spatial distribution of the drainage

network into account.

Fractal analysis is a bonus and powerful tool as

the spatial patterns with different space filling properties

and easily discriminate areas which may yield same

signatures using traditional linear analysis. The space

filling nature of the drainage network is a strong marker

of area vulnerable to active surface deformation. The

drainage systems adjust it selves to get linearized and

recognized as it interact neotectonic deformation

(Mahmood et al., 2009; Shahzad and Gloaguen, 2010;

Mahmood and Gloaguen, 2011). This is why we use non

linear analysis (i.e. FD, LA and SA) to characterize the

irregularity of the drainage network and to calculate the

transformation from a dendiritic pattern into a linearized

and tectonically controlled one.

Figure 1. Self-similarity in nature, identical structures repeating over a wide range of length scales.

The LA is used to understand the textural

representation of the drainage systems by studying their

spatial distribution and size of the vacant spaces between

them. It is a useful tool to discriminate between different

textural patterns which have similar fractal dimension

value. The LA computes the deviation of a fractal object

(e.g. drainage network) from the translational invariance.

The SA is used to compute the orientationregularity of the drainage network and to examine the

rotation of the spatial drainage pattern with the same

translational behavior. The SA computes percolation

capacity of the underline binary image (Melo and Conci,

2008; Shahzad and Gloaguen, 2010; Mahmood and

Gloaguen, 2011) of the spatial drainage pattern both

horizontally (left to right, L2R and right to left, R2L) as

well as vertically (top to bottom, T2B and bottom to top,

B2T). A particular region having low FD value like one

(1) means a region of extreme surface deformation with

more LA value. A low LA values mean less surface

deformation. The SA explains the style of rotation of

drainage network influenced by general patterns and the

rotation of the tectonic structures. Higher mean SA

values represent severely deformed zone.

All these three analyses permit the examination

of textural properties of drainage systems and are quitehelpful to access the delineation and intensity of surface

deformation (Mahmood and Gloaguen, 2011). Drainage

pattern in Gilgit Baltistan (northern Pakistan) is a result

of spatially inconsistent neotectonics and erosinal

processes (Mahmood et al., 2009) and highlights regions

with variable vulnerability to active deformation

(Shahzad and Gloaguen, 2010; Mahmood and Gloaguen,

2011). The anomalous, jumbled and linearized spatial

drainage patterns give motivation for this research.

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Study area: The Gilgit Baltistan (GB) is newly

establishing province in the northern area of Pakistan,

bordering India, China, and Afghanistan. In the North-

South (NS), The Gilgit-Baltisitan extends from

Hindukush Karakorum, with western Himalayas in the

south and the Pamirs in the extreme north (see Figure 2).

Abbreviations of fault names: AM, Alburz

Marmul, CbF, Central Badakhshan Fault, HF, Herat

Fault, CF, Chaman Fault; MoF, Mokar Fault, GzF,

Gardez Fault, KoF, Konar Fault, MBT, Main Boundary

Thrust; MFT, Main Frontal Thrust, MMT, Main Mantle

Thrust, SRT, Salt Range Thrust, MKT, Main Karakoram

Thrust, RF, Reshun Fault, SF, Sarobi Fault and ST,

Spinghar Thrust. (Source: Mahmood and Gloaguen,

2011).

Figure 2. Tectonic map of the Pakistan and neighbouring countries showing reported and newly confirmed faults.

The inset black shape file represents the province of Gilgit Baltistan. GPS velocity vectors (Red) with

respect to Eurasia fixed reference frame (Mohajder et al., 2010), whereas the purple vector is

transformed with respect to India fixed velocities (Wheeler et al., 2005; Mahmood and Gloaguen, 2011).

All these important ranges rendezvous with each

other covering an area of about 43754 sq. km. Primarily

the GB, climatically, biologically and geographically

represents a land of trans-Himalayan character, where

monsoon rains are very rare. The GB holds twelve out of

thirty top peaks of the world with elevation over 7500

meter above sea level and this region is also called the

crown of Pakistan (i.e. second highest peak of the world

K2 or Chogori with elevation 8611 meters).

The geology of the GB is very ancient with

some oldest rocks forming the highly stratified

Precambrian peak groups (Zain, 2010) such as

Gasherbrum, Mashabrum, Baltoro, Rakaposhi, Ultar,

Diran, Broadpeak, Muztagh towers, Trango Towers,

Batura, Saltoro Kangri and many more. The mountain

ranges of GB from the head waters of major rivers

include the mighty Indus. The Shyok and Indus river flow

though occupied Kashmir into the GB, hundreds of their

tributaries joined them within the GB (see Figure 3).

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There are evidences that the active surface uplift of the

Himalayas and Karakorum has occurred during the

Quaternary and Holocene time. In the GB the record of

the Quaternary sediment is very well preserved in a series

of same interconnecting basins with valley fills more than

500 meters thick. These sediments consist of debry flow,

tills, fluvial, glacilo fluvial and lacuserint sediment. Most

of them have been severely deformed and Local River

terraces appear to be thrusted, folded and inverted.

Figure 3.Location of study area of Gilgit-Baltistan region (northern Pakistan) with Landsat 7, 4, 2 band

combination drapped over shaded relief map along with major rivers (Indus, Gilgit and Hunza), district

and provincial boundary.

This scenario clearly indicates an active tectonic

environment. The aim of this research is to discuss the

neotectonic frame work for the GB Pakistan and to

describe the active surface deformation based on Fractal

analysis of drainage network. This analysis also

facilitates to demarcate severely deformed zones due to

neotectonic and surface processes.

Datasets and methods: Drainage systems were extracted

from SRTM 90 m and binary image was prepared such

that the streams have a pixel value of 1 and rest of the

space is considered as 0 (Melo et al., 2006; Melo and

Conci, 2008; Shahzad and Gloaguen, 2010; Mahmoodand Gloaguen, 2011). In this research we believe that the

drainage network is strained and linearized as the

landscape is strongly controlled by neotectonic processes.

The FD method is a bit vague, as it simply shows the

amount of network complication. The FD does not

demonstrate the spatial pattern interpretation. This is why

the LA and SA techniques are also deployed to further

interpret the spatial drainage pattern recognition.

Fractal dimension and box counting method: Fractals

are entities that are scale invariant. For fractal patterns

this means they look similar at a greater variety of scales,

i.e. they are self similar. The drainage systems exhibit

irregularities with self-similar properties. FD is bonus to

quantify and destroy geomorphic metric features and its

usage has increased frequently in the last couple of

decades (Gloaguen, et al., 2007; Shahzad and Gloaguen,

2010; Mahmood and Gloaguen, 2011). FD quantifies the

degree of irregularity or fragmentation of an object that

shows spatial patterns. This research computes fractal

dimension for three selected rivers (Indus, Hunza and

Gilgit River) and the whole drainage network of GilgitBaltistan region (northern Pakistan). For this purpose we

have used BCM that uses a moving box of variable size

on a binary image and counts the number of drainage

pixels within the box size applied (Mahmood and

Gloaguen, 2011). In each grid, the box sizes s and

relevant number of boxes N(s)are counted.

Computation of FD by BCM is calculated by using the

following formula.

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ssN

FDos /1log

)(loglim

1

Where N(s) is number of boxes and s is the

length of the box size applied (see Figure 4). Slope of the

best fit line for the log plot of N(s) and 1/s is equal to FD.

The FD generated map was generated with color ramp sothat the regions with low FD values can be identified. In

general FD distribution map characterizes picture of

linearity of the drainage system. When FD tends to 1 it

means that the drainage patterns are highly linearized and

the region is highly vulnerable to surface deformation and

vice versa. Spatial distribution of FD can be divided into

three classes.

Figure 4. Calculation of Fractal Dimension (FD) by using Box Counting Method (BCM).

FD values less than 1.3 corresponds to severely

deformed zones while values of FD greater than 1.3 and

less than 1.6 corresponds to medium vulnerability.

Values greater than 1.6 corresponds to almost invariant

regions (see figure 5a)

Lacunarity and Gliding Box Method: The LA

computes the deviation of a fractal object from

translational invariance and can be used to understand thetextural representation of the spatial drainage pattern by

studying the spatial distributions and sizes of the vacant

spaces (Shahzad and Gloaguen, 2010; Mahmood and

Gloaguen, 2011). The LA discriminates different textural

patterns with similar FD values. For the binary images

the LA is computed by GBM method where a square box

of side r is glided along all possible directions of the

drainage texture. The total number of drainage pixels (i.e.

mass s) is calculated throughout the whole gliding

process. GBM is repeated with a growing box size i.e. r+i

(Plotonik et al., 1993). The gliding box should be of size

r=1 to some fraction of image (M). Resultantly a

frequency distribution of mass s with variable box size

r is obtained. This frequency distribution is transformed

into a probability distribution P(s, r). By normalizing

with the total number of boxes N(r) of size r. The

dimensionless lacunarity (r) is computed by first and

second moments of this distribution, as described thefollowing formula (Plotonik et al., 1993).

2

1

1

2

),(

),(

)(

N

r

N

r

rssP

rsPs

r

(2)

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The LA distribution map was generated with a

moving window of 50 arc seconds by 50 arc seconds

(50x50) on a binary image of drainage network. In all

moving window operation, the underneath image of

5050 is taken as a sub image and the box size r = 1to

25 ( greater than 2.5 are related to heterogonous

spatial pattern, which means severe deformation.

Succolarity: penetration and orientation method: The

SA is a vital feature in spatial pattern recognition. It

computes penetration of a binary image that is how much

a given fluid can flow through the binary image

(Mandelbrot 1983; Melo and Conci, 2008). In the contest

of surface deformation the SA calculates the orientation

of the tectonics or geological structures. The succolarting

factors contain the string which permit percolation

(amount of interrelated pixels in the drainage texture).

These textures consist of two types of pixels i.e. vacant

gaps and impassable maps i.e. drainage (Shahzad andGloaguen, 2010; Mahmood and Gloaguen, 2011). The

SA is computed along any possible flow direction (0

degree to 360 degree). To measure the mean SA value of

the drainage pattern we focus on four possible directions,

i.e. along 0o, 90o, 180o and 270o.The rotation image is

prepared at the required angle and SA is calculated as

follow

1) The binary image if flooded by checking all the

boundary pixels coming from T2B. If a pixel

represents vacant gaps on the image, it simply

means that a fluid can pass and flood this area. The

impenetrable mass black drainage lines are

treated as obstacle to the fluid. All the flood areas

have four neighbours for every pixel (top, bottom,

left and right) this process is recursively performed

on every pixel until the fluid encounter the

impenetrable mass.

2) The flooded area was analyzed using BCM. In this

method we place boxes of variable size k (k-1 to

n), where n is the number of possible factors of

division (Melo and Conci, 2008; Shahzad and

Gloaguen, 2010; Mahmood and Gloaguen, 2011)

on the flooded image and the counting the number

of flooding pixels (NP (k)) within the box size k.

3) The sum of the multiplications of the (NP (k)) by the

pressure matrix PR (pc, k), where pc is the

position on x or y of the centroid of the box on the

scale of pressure applied for each box size iscalculated. The pressure matrix is dependent on

the position of the box to show the amount of

pressure correctly over it. The PR (pc, k) consist of

linearly growing weight from T2B. We divide the

value (NP (k)) x PR (pc, k) by PR (pc, k) to make

SA dimensionless like FD and LA. The SA is

calculated as:

n

k

n

k

kpcPR

kpcPRkNP

dir

1

1

).(

),().(

)(

(3)The (dir) represent the peculation direction. The

value of SA ranges from 0 to 1 and are classified as into

three categories i.e. (< less than 0.5 is low), (0.5 to 0.75 is

medium) and (greater than 0.75 is high SA value). The

drainage texture showing highly succolarating behavior

represents the remote location of impenetrable mass,

which means that the streams are at remote location. In a

neotectonic setting, high SA value corresponds to high

venerability to active deformation due to the high

percentage of vacant gaps and existence of lengthy

impenetrable masses (filaments). These filaments show

the presence of neotectonics in the region. The low SA

values in the regions mean that the geological processes

have stopped the development of lineaments and thus a

high drainage density dominates there.

RESULTS AND DISCUSSIONS

The drainage system in a tectonically

environment is effected by the change of the geometry

type due to most recent tectonic activities of both local

and regional faults. In the region of Gilgit Baltistan (GB)

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in northern Pakistan the entire drainage system is

experiencing neotectonic influence. The network analyses

have great potential to record signals of tectonic and

erosinal process that contribute towards active surface

deformation. The spatial distribution of the drainage

patterns in the GB are of four types i.e., parallel,

rectangular, dendritic and disconnected drainage system.

These changes in geometrical transition and different

stages and development from one spatial pattern to other

is due to the neotectonic, climatic, geological and spatio

temporal phenomena. Parallel drainage pattern develop in

a highly steepened region and it is evidence they are

tectonically controlled. The relative uplift conditions in a

local region also results in high slope forcing the drainage

pattern to get linearzed which means tectonically uplift.

In a very complex tectonic regime, the spatial drainage

pattern takes the form of disconnected and rugged shape.

The drainage networks that follow the basic fractal

geometry and remain undisturbed are discriminated using

various fractal approaches e.g., FD, LA and SA.

The low FD values in GB suggest the presence

of controlling processes (relative tectonic uplift and

differential erosion) on the GB landscape evolution

(Mahmood and Gloaguen, 2011). If the FD values are

lower or close to 1, it simply means that the drainage

patterns is experiencing a transitional change from

natural mendicarity to more linearization due to more

neotectonic deformation. Using BCM, the FD distribution

was generated with the help of specially design Matlab

algorithm and Arc GIS tools. This FD map indicates

some anomalies in the spatial drainage pattern which

means very low FD (see Figure 5a). The FD map shows

that the most of the GB region is categorized by low to

very low FD values that means the region is highly

deformed and the regional tectonic are influencing and

controlling

Figure 5. (a) Distribution map of the study area of FD. The low values of FD correspond to highly deformed

areas. Ten sites with low values of FD are marked in the map.

local drainage. High fractal values are observed North

East (NE) of Skardu and Ghanche, where the drainage

pattern is not linear because the presence of permanent

glaciers and snow covers. These high values indicate the

spatial drainage pattern are more dendiritic and are

controlled mostly by the erosinal process (glacier

erosion) and have low vulnerability to active

deformation. Another high value can be observed west of

Hunza district because of dendiritic drainage and

presence of glacier and snow. The sudden variation in a

spatial drainage pattern results in variety of FD values.

Although with the computation of space filling nature of

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moving, cork-like plug that began approximately 12 -10

Ma. When a spatial drainage patterns show the same style

of occupying gaps and translation invariance, then SA

computes the orientation of these patterns and explains

the further categorization. The purpose of SA distribution

map was to further distinguish the relative vulnerability

to active deformation in those regions which exhibits

similar low FD values (see Figure 5a) and maximum LA

values (see Figures 5b and 5c). In this particular situation,

the drainage texture is not discriminated based on vacant

gaps and translational invariance, but purely on the basis

of drainage texture orientation. Spatial distribution of SA

values for GB region is consistent with the orientation of

regional structure e.g. near NW orientated Raikot fault

(see Figure 6) it shows higher values. SA values also

classifies different zones in GB that show different

structural orientations, therefore extremely low SA values

delineate the approximate boundary of such structure.

Figure.5. (c) SA distribution map with high values highlighting the severely deformed regions with low drainagedensity. The low values of SA indicate less deformed regions with high drainage density.

Figure 6. Map showing junction of Gilgit with Indus Rivers near Raikot fault. The black circle clearly indicates

the linearized Indus River due to neotectonic influence of the Raikot fault.

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Conclusion: The fractal measures (FD, LA and SA) are

valuable tools for the quantitative description of the

spatial drainage network, its evolution and stages of

landscape development in GB regions northern Pakistan.

The lower FD, higher LA and higher mean SA values

shows the spatial anomalies in the spatial drainage

patterns that suggests mostly the tectonic control in the

region and also higher vulnerability to active surface

deformation. All the three fractal analyses have great

potential to forecast the relative distribution of surface

deformation. The drainage patterns of the GB exhibit

linearzed, parallel and disconnected spatial patterns

corresponding to neotectonics. The tectonically uplifted

regions with great amount of variation in homogeneity

and orientation can easily be differentiated by fractal

dimension, lacunarity and succolarity analysis. The three

fractal analyses have concluded the GB region is

neotectonic active region in the context of India Eurasia

collision and has undergone severe surface deformation

in conjunction with deadly earthquakes.

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