Remote Sensing and Statistical

Analysis of Fracture Populations

Around Lake Thingvallavatn, SW Iceland

Johan Oxenstierna

This study aims at a description and statistical analysis of tectonic and

magmatic fractures in the Western Volcanic Zone (WVZ) on Iceland. Two

fracture populations are studied with respect to their distance to the Hengill

volcano: The southern area is between 0-10 kilometers from the volcano and

the northern area is between 16-25 kilometers from the volcano. The

description and analysis of fractures is carried out separately for the two

areas as well as for the two areas together to test different mapping

procedures, statistical methods and the influence of the volcano on the

properties of the fractures.

There are various reasons for considering this an important study: Firstly, this

is not an extensively researched field and there are many unanswered

methodological questions on how to map and describe the fractures. In this

study, problems such as how maps are stitched and georeferenced, how

fractures are divided into segments and mapped in respect to topography, are

discussed. The potential errors caused by these methodological problems are

concluded to be large enough to significantly affect statistical tests analyzing

fracture populations.

In the analysis part, the properties of the fracture populations are studied

using Kolmogorov Smirnov and χ2 goodness-of-fit tests, scatter-plots, simple

count and ratios among other methods. It was found that the fracture

populations follow distributions that are not easily defined, but that they are

of the same and quantifiable type. With more data their common distribution

could therefore be modeled, and the factor by which the Hengill volcano

affects the strike of fractures per distance unit from the volcano could be

calculated. It was also found that magmatic fractures are formed in a similar,

but not necessarily the same stress-field as tectonic fractures. Therefore

change in magma pressure might change the local stress regime around

magmatic fractures, affecting their strike.

Uppsala universitet, Institutionen för geovetenskaper

Kandidatexamen i Geovetenskap, 180 hp

Självständigt arbete i geovetenskap, 15 hp

Tryckt hos Institutionen för geovetenskaper

Geotryckeriet, Uppsala universitet, Uppsala, 2012.

Självständigt arbete Nr 37

Remote Sensing and Statistical

Analysis of Fracture Populations

Around Lake Thingvallavatn,

SW Iceland

Johan Oxenstierna

Självständigt arbete Nr 37

Remote Sensing and Statistical

Analysis of Fracture Populations

Around Lake Thingvallavatn,

SW Iceland

Johan Oxenstierna

1

Contents Abstract ...................................................................................................................................... 2

Introduction ................................................................................................................................ 3

2. Geological Setting .................................................................................................................. 4

2.1 Iceland .............................................................................................................................. 4

2.2 The Western Volcanic Zone ............................................................................................. 6

2.3 The Thingvallavatn Area .................................................................................................. 6

3. Methods ................................................................................................................................ 11

3.1 Mapping .......................................................................................................................... 12

3.2 Statistical analysis ........................................................................................................... 14

4. Results .................................................................................................................................. 18

4.1 Mapping .......................................................................................................................... 18

4.2 Statistical analysis ........................................................................................................... 19

Frequency and age ............................................................................................................ 19

Frequency of strike ........................................................................................................... 20

Frequency of lengths ......................................................................................................... 25

Length and strike ............................................................................................................... 25

Average deviation of strike from the mean strike and distance to the volcano ................ 26

Length and elevation ......................................................................................................... 27

Elevation of fractures and the distance to the volcano...................................................... 29

Spacing of tectonic fractures and the distance to the volcano .......................................... 30

5. Discussion ............................................................................................................................ 33

5.1 Mapping .......................................................................................................................... 33

5.2 Statistical analysis ........................................................................................................... 34

6. Conclusions .......................................................................................................................... 39

7. References ............................................................................................................................ 40

8. Appendix .............................................................................................................................. 42

Appendix 1: ....................................................................................................................... 42

Appendix 2: ....................................................................................................................... 42

2

Abstract

This study aims at a description and statistical analysis of tectonic and

magmatic fractures in the Western Volcanic Zone (WVZ) on Iceland. Two

fracture populations are studied with respect to their distance to the Hengill

volcano: The southern area is between 0-10 kilometers from the volcano and

the northern area is between 16-25 kilometers from the volcano. The

description and analysis of fractures is carried out separately for the two

areas as well as for the two areas together to test different mapping

procedures, statistical methods and the influence of the volcano on the

properties of the fractures.

There are various reasons for considering this an important study: Firstly,

this is not an extensively researched field and there are many unanswered

methodological questions on how to map and describe the fractures. In this

study, problems such as how maps are stitched and georeferenced, how

fractures are divided into segments and mapped in respect to topography,

are discussed. The potential errors caused by these methodological problems

are concluded to be large enough to significantly affect statistical tests

analyzing fracture populations.

In the analysis part, the properties of the fracture populations are studied

using Kolmogorov Smirnov and χ2 goodness-of-fit tests, scatter-plots,

simple count and ratios among other methods. It was found that the fracture

populations follow distributions that are not easily defined, but that they are

of the same and quantifiable type. With more data their common

distribution could therefore be modeled, and the factor by which the Hengill

volcano affects the strike of fractures per distance unit from the volcano

could be calculated. It was also found that magmatic fractures are formed in

a similar, but not necessarily the same stress-field as tectonic fractures.

Therefore change in magma pressure might change the local stress regime

around magmatic fractures, affecting their strike.

3

Introduction

This study aims at a description and statistical analysis of tectonic and magmatic fractures in

the Western Volcanic Zone (WVZ) on Iceland. There are various reasons for considering this

an important study: Firstly there is the methodological problem of (1) how to map and

describe the fractures and (2) how to analyze them. Furthermore, there is the geological side

with the question of why the fractures are distributed in the way they are. This question can

only be satisfactorily discussed after the methodological issues have been taken into account.

The aim here is thus to test various physical variables of the fractures against each other to get

a better understanding of how they form and develop in rifting zones.

The study area is located around 20 kilometers east of Reykjavik (Iceland) and it is

subdivided into two parts, one located to the SW of Lake Thingvallavatn (southern area) and

one located to the NE of the lake (northern area). The southern area is dominated by the

Hengill volcano. The description and analysis of fractures was carried out separately for the

two areas as well as for the two areas together to test different mapping procedures, statistical

methods and the influence of the volcano on the properties of the fractures.

The study aims at answering the following questions:

1) Mapping: Which mapping methods are most effective when tracing fractures on aerial

photographs?

2) Statistical analysis: What are the statistical relationships between the following variables:

frequency and age, frequency and strike, frequency and length, length and strike, average

deviation of strike and distance to the central volcano, length and elevation, elevation and

the distance to the central volcano, distance between fractures and distance to the volcano

of:

-tectonic and magmatic fractures mapped in the southern study area?

-tectonic and magmatic fractures mapped in the northern study area?

-tectonic fractures mapped in the southern and the northern study areas?

Which statistical methods are most suitable to establish the nature of these relationships

and why? What can be inferred from the relationships?

4

2. Geological Setting

2.1 Iceland

Iceland is located on a large submarine platform in the north Atlantic. It has an area of

103,100 km² and reaches a maximum altitude of around 2110 meters. It consists of oceanic

basaltic crust (Weisenberger, 2010).

Iceland has formed due to two main factors, the fact that it is located on top of the Iceland

mantle plume and a Mid Oceanic Ridge (MOR) at the same time. The Mid-Atlantic ridge

started to diverge about 56-53.5 million years ago (Weisenberger, 2010). It is believed that the

first lavas came up from the crust when the Iceland plume, which is slowly moving in a

northwestern direction, coincided with that of the position of the MOR (Saemundsson, 1992).

Over the last 500 years Iceland’s volcanic activity was responsible for around a third of the

total lava produced in the world (Feldmann, 2010). Significant eruptions occur every five to

ten years, today predominantly in the southern areas, at volcanoes such as the Eyjafjallajokull

and Katla, mount Hekla and Laki. The latter was the site of the second largest basaltic lava

eruption in history with its 1783 eruption, leading to the deaths of 20-25% of the Icelandic

population and destruction of crops over large areas in Europe (Foulger, 2005).

Most of the volcanism produces basaltic lava, but large central volcanoes such as Hekla

produce more silicic lava. Another typical feature on Iceland are the volcanic fissures, which

are “linear fracture[s] on the Earth's surface through which lavas, pyroclastics, and gas are

erupted and effused” (Allaby, 1999). These fissures often have the same orientation as the

tectonic fractures of the plate margin and many eruptions. Small fissures can cluster in fissure

swarms that are up to 100 kilometers long and 10 kilometers wide (Saemundsson, 1992).

There are many different variations of eruptive types and products that depend on parameters

such as whether the volcano is on land, subglacial or submarine. One major volcanic area, for

instance, is the Grimsvötn situated under the Vatnajökull glacier, where hyaloclastite, a glassy

and tuff-like breccia, forms due to the rapid cooling of the lava under ice and water. Since the

last three million years have been dominated by glaciations, many of the lavas on Iceland

were deposited subglacially. Today Iceland´s subglacial eruptions amount to a whole 83% of

the world’s total of such eruptions, and large hyaloclastite ridges have formed in the process

(Batsford, 2010).

Based on the age of rocks, Iceland can be divided into three stratigraphic zones (Figure 1).

The Tertiary zone (bright grey) consists of flood basalts up to 10 kilometers thick (Ward,

1971). The Plio-Pleistocene zone (darker grey) is younger than three million years and

consists of flood basalts and hyaloclastites. The Upper Pleistocene-Holocene (dark grey) is

called the Neovolcanic zone, which hosts most of the active volcanoes and where most of the

present day rifting is occurring. This area makes up about one third of Iceland’s area

(Feldmann, 2010).

The volcanism on Iceland is concentrated in the three volcanic zones, The Northern, Western

and Southern. These consist of 30 volcanic systems, of which 12 are mainly comprised of

5

fissure swarms and a central volcano, 7 of only a central volcano, 9 of a fissure swarm and a

central domain, and 2 by a central domain (Thoradson, 2007).

Figure 1: An overview map of Iceland showing the three general stratigraphic zones of the rocks and the

volcanic zones WVZ (Western Volcanic Zone), EVZ (Eastern Volcanic Zone), NVZ (Northern Volcanic Zone),

SISZ (South Iceland Seismic Zone), RVB (Reykjanes Volcanic Belt), SVB (Snaefellsnes Volcanic Belt), ÖVB

(Öraefi Volcanic Belt). Main fault structures are the MIB (Mid-Iceland Belt), TFZ (Tjörnes Fracture Zone), KR

(Kolbeinsey Ridge). Map from Thoradson et al. (2007).

6

2.2 The Western Volcanic Zone

The Western Volcanic Zone (WVZ) is about 170 kilometers long and extends from the

western edge of the Reykjanes peninsula up to the glacier Langjökull (Figure 1). The WVZ

has provided Iceland with some of its largest crustal spreading in the last 6-7 million years,

today the spreading is dominated by the Eastern Volcanic Zone (EVZ) that started to develop

2-3 million years ago (Sigmundsson, 2006). The volcanic activity is focused in four areas: the

Hengill, Langjökull and Prestanjúkur and an area around Mount Kálfstindar. Most of the

eruptions occurred early in post-glacial times. Recent magma production has been low,

leading to a graben formation in the Lake Thingvellir area (Einarsson, 1991). It is believed

that the whole area of western Iceland is experiencing a steady decline in melting, especially

in late postglacial times. The area includes 44 observed locations where eruptions occurred

(Sinton, 2005).

The seismicity of the WVZ is high and predominantly restricted to depths of 1-7 kilometers,

with a high concentration at the Hengill triple junction (Clifton, 2001). There, the Reykjanes

Ridge splits into the WVZ and the South Iceland Seismic Zone (SISZ) (see Figure 1).

A common feature of the WVZ and the other volcanic zones of Iceland are the volcanic

fissures. In the WVZ they are usually found in swarms approximately five kilometers apart

with a general strike to the north-east. Most fissures are small usually less than a hundred

meters. The swarms consist of normal faults, extension fractures with no or little shear

displacement and hybrid fractures (shear and extension) (Saemundsson, 1992).

There are also a number of table mountains and hyaloclastite cones within the zone. These

have been created from isolated vents in sub-glacial eruptions. Lava shields of different

volumes have formed with large shields usually being basaltic in composition and small

shields usually picritic in composition. The last fissure eruption occurred in the thirteenth

century (Thoradson, 2007).

2.3 The Thingvallavatn Area

The studied area is about 1000 km2 large. The main features of the area are Lake

Thingvallavatn, Iceland´s second largest lake, the graben structures associated and the

volcano mountains to the north and south of the lake. The zone is about 80 km long and 10

km wide and is called the Hengill Volcanic system (Gudmundsson, 2000a)). The area is

considered to be active in terms of volcanism and today nearly half of the area is covered by

postglacial lava. The area has historically been the site of important studies on rifting and

several researchers, for instance Nielsen and Bernauer, applied Wegener´s continental drift

theory long before it was accepted by the majority of scientists (Saemundsson, 1992).

7

Lake Thingvallavatn lies in the middle of a N30-trending graben structure (Saemundsson,

1992). It is asymmetrical with the faults being more tightly spaced and with a larger throw on

the NW side than on the SE side, where the throw is spread out over a larger amount of

smaller faults (Saemundsson, 1992). The dip of the faults is mostly subvertical. The number

and size of faults in different areas depends on the age of the rock they are found in, with

more faults occurring in the older rocks (Saemundsson, 1992). The throw also depends on the

age of the host rock and in some places where the fault passes between different stratigraphic

units the throw suddenly becomes bigger in the older rock. Rifting rates in most cases vary

between 1-3 mm/year (Saemundsson, 1992) with much higher values during active rifting

periods. During the latest active period, in the year 1789, the Almannagjá fault alone rifted by

half a meter or more (Saemundsson, 1992).

In the Thingvallavatn area the Hengill and the Hrömmundartindur volcanoes are proposed as

the main volcanic systems with their respective fissure swarms (Saemundsson, 1992). There

are many different lava flows. Their relative age is usually established by the degree of

faulting or erosion. The oldest sequence in the area is from the Plio-Pleistocene at around 3.1

to 0.7 Myr and consists of basaltic flows and glacial deposits that are up to 400 meters thick

(Saemundsson, 1992). The rock sequence is shown in Figure 2 and the accompanying cross

section is shown in Figure 3. Superimposed on the Plio-Pleistocene sequence is a

discontinuity of around one million years below the next sequence of Upper Pleistocene rocks

(0.7 – 0.01 Myr). These are found northwest and south of Lake Thingvallavatn and consist

mostly of sub-glacial shield-volcano pillow lava and breccia, often covered by glacial

deposits. All of these surface deposits have been exposed to glacial erosion originating from

the Langjökull area in the north (Saemundsson, 1992). There are also end and lateral

moraines. The margins of Lake Thingvallavatn have also changed with time, for instance

during the melting stage in the last glaciation it formed an ice lake at the south margin of the

glacier with a much higher water-level than today and the former shore banks are still visible

on certain locations (Saemundsson, 1992).

8

Figure 2:Plio-pleistocene (3,1-0,01Myr) rock succession around lake Thingvallavatn (from Saemundsson,

1992).

9

Figure 3: Cross sections of the Thingvallavatn graben. The colors are the same as in Figure 2 and Figure 4.

(from Saemundsson, 1992).

The majority of rocks in the area are postglacial and belong to the largest lava flow that

originate from a fissure eruption around 9100 years ago (Saemundsson, 1992) and covers

more than 100 km2 at the northern shores of Lake Thingvallavatn (Eldborgir, see Figure 4). It

10

is evident at the famous Almannagjá fault, which has a maximum throw of 30 to 40 meters

and clearly displays separate layers of lava lobes (Saemundsson, 1992).

Other lava flows were erupted 7000 years ago on the east bank of Lake Thingvallavatn, 5800

years ago south of the bank of Lake Thingvallavatn and then 1880 years ago at a similar

location when a crater row just north of Nesjavellir erupted ( Figure 4). Ash layers are found

in soils from the different periods (Saemundsson, 1992).

Figure 4: The Pleistocene-Holocene geologic rocks around Lake Thingvallavatn (from Saemundsson, 1992).

11

3. Methods

The reason the parameters chosen in study question 2 in the introduction is hereby provided:

Frequency and the age of fractures: One can assume that there should be more fractures in an

older rock than in a young one because the older the rock, the more time it had to acquire

more fractures. This was also concluded in a similar study on northern Iceland (Hjartardóttir

et al., 2009). The assumption is in this study tested in the Thingvallavatn area.

Frequency and the strike of fractures: The aim here is to see whether the fractures are aligned

in any organized fashion that could be used for modeling or estimating the formation of yet to

be located fractures. Clifton et al. (2003), also seek a distribution pattern for frequency and

strike when studying fractures west of the study area. They state that the strike of fractures

exhibit a normal distribution. This claim is tested in the Thingvallavatn area. The type of

distribution is additionally analyzed using a Kolmogorov-Smirnov test to find the degree of

similarity between the strike distributions on both sides of Lake Thingvallavatn. The final aim

is to not just be able to say that the “volcano has a pronounced effect on the regional stress

field” without quantification as done in the Hjartdottir et al. study (2009), but to be able to say

that the “volcano affects the strike of fractures by a factor of x degrees per kilometer distance

from the volcano”.

A similar question can be posed concerning magmatic fractures: Does the strike of magmatic

fractures depend on the strike of tectonic fractures and if so by what degree? This is

interesting to find out whether the form of tectonic fractures is the only variable that governs

the way in which new magmatic fractures align themselves at the surface (for more on

statistical dependence see “correlation and causality”, appendix). This type of causality is

expected because magmatic fractures are supposedly formed in the same stress field as

tectonic fractures. There are, however, factors that could affect this stress field locally around

magmatic fractures, such as magma pressure. Statistics will show whether such factors can be

statistically neglected or if they have to be taken into account when studying the strike of

fractures.

Frequency of fracture length: The population distributions of the length of fractures is

studied.

Length of fractures and strike of fractures: It is assumed that the longer a fracture is the less

their strike deviates from their mean strike (Hjartdottir et al., 2009). This study tests whether

this can be confirmed on the Thingvallavatn area.

Average deviation of strike of fractures as a function of the distance to the volcano of

fractures: According to Hjartdottir et al. (2009), the presence of a volcano “has a pronounced

effect on the regional stress field around the plate boundary, as can be seen from the azimuth

of the volcanic fissures and tectonic fractures in the fissure swarms close to Askja” (Askja

being the volcano). Thereby the average deviation of strike should get larger closer to the

volcano. This argument is tested in the Hengill area.

12

Length and elevation of fractures: Hjartdottir et al. (2009), state that fractures “get fewer and

smaller with increasing elevation” (Hjartardóttir et al., 2009). The argument is tested in the

Thingvallavatn area.

Elevation and the distance to the central volcano of fractures: Here the spatial distribution of

fractures is analyzed in respect to their elevation. This is a topographical approach that will

answer whether the fractures are located at any specific elevation more than any other.

Spacing between fractures and distance to the volcano of fractures: In order to study the

shape of the graben the distances between fractures at certain distances from the volcano were

analyzed. According to Scholz and Contreras (1998) faults in a rifting area can be divided into

two classes, the boundary fault system (BFS), and the failed conjugate fault (FCF). If these

can be identified for a fracture set the degree of asymmetry can be estimated for the rifting

area.

3.1 Mapping

The fact that Iceland is covered by around 60% tundra makes remote sensing a good and

efficient method to study geological features at the land surface. For the southern part of the

study area 15 aerial photographs were used most of which were about seven kilometers

across. For the northern part 8 aerial photographs were used. The scale in all photographs is

between 1:25000 to 1:50000 except for the area around Thingvellir where the scale was

1:6000. The aerial photographs in the southern part were stitched together using Adobe

Photoshop that produced a mosaic image of the area with the cost of getting a slightly lower

resolution and a distorted projection. The photomosaic was thereafter transferred to ArcGIS

for analysis. In the northern part the photographs were directly imported into ArcGIS because

one aim of the study (study-question 1) was to compare different methods.

The photomosaic was georeferenced manually using the Universal Transverse Mercator WGS

1984 60o north system. In order to get the photomosaic referenced the ArcGIS

“georeferencing” tool and Google Earth were used. Clear distinguishable points were located

on the photos and assigned with coordinates using Google Earth. 25 georeference points were

used. Since the mosaic was slightly distorted by the stitching process, the georeferencing was

more difficult. There are different algorithms that can be used, 1st, 2

nd or 3

rd etc. polynomial

functions, depending on how many georeferencing points there are. The final average

coordinate error of the photomosaic is ±20 meters, which was considered satisfactory as that

was approximately the precision of Google Earth in the area (in border areas between two

satellite images). The fractures and fissures were drawn using ArcGIS polylines which consist

of three to ten points depending their lengths.

The next step was to map the fractures on the aerial photographs. Various other maps, such as

a geological map (Saemundsson, 1995) of the same area were additionally imported into

ArcGIS. Google Earth with its resolution and 3D function was additionally used for locating

hyaloclastite ridges. The images in Google Earth are however slightly different. They include

13

vegetation and therefore the contrast between fractures and the surrounding landscape was

usually not as good as in the aerial photographs. Also there were some areas that were

covered by clouds, for instance a cloud with 600 meters diameter which partly covered the

area to the north of Thingvellir (see Figure 5).

Figure 5: Perspective view of the southern study area shown in Google Earth. Notice the big cloud (about 600

meters diameter) and its shadow in the lower right corner just above the road.

Since the photomosaic had lost some resolution during the stitching, the aerial photographs

were sometimes studied individually to confirm certain features. Small features, such as

several volcanic fissures, were sometimes too small to be identified on the aerial photographs,

or to distinguish them from tectonic fractures. In those cases the geologic map (Saemundsson,

1995) was used as a reference.

In order to answer the question of a possible correlation between the number of fractures and

elevation a Digital Elevation Model (DEM) of the area was used. The resolution of this DEM,

with a cell size of 90x90 meters, was not optimal but since there were so many fracture

samples it could still be used in statistical analysis.

Similarly, lava flows were mapped on the aerial photographs according to the geological map

(Saemundsson 1995) so that a fracture quantity versus age correlation test could be carried

out. The fractures of each age section were selected on the big map using the ArcGIS tool

“clip”, and then their features were compared to other fracture populations on the map.

14

The fractures were categorized as follows:

Single tectonic fractures striking SW

Single tectonic fractures striking NE

Connected tectonic fractures striking SW

Connected tectonic fractures striking NE

Volcanic fissures

Hyaloclastite ridges

The fractures in the Thingvallavatn area can be described in many ways depending on what

resolution one observes them in. The Almagja-fault could for instance be described as a 7,7

kilometer fault. However, depending on the resolution of the maps, these 7,7 kilometers can

be divided into numerous parts. In this study the Almagja fault was separated into 21 different

segments. One could have increased the number of segments even further. Fractures separated

in a strike-slip fashion by less than approximately five meters were considered as one fracture

whereas a separation larger than that was considered as two fractures. As some maps had

lower resolutions this precision also had to be adjusted to the map in question.

Some differences in mapping between the northern and the southern area can possibly be

attributed to the geological differences between the two. The southern mapping area is

dominated by structures in close proximity to the volcano Hengill. The topography is varied

and there are significant artificial structures. This made it generally harder to spot fractures in

this area so that the geological map was used as a reference. The northern area is more even

topographically. There are less human imprints, and it is generally easier to find fractures

except for the northernmost parts of the area, which are also mountainous.

3.2 Statistical analysis

The statistical methods used to answer the study question are described in the following:

What are the statistical relationships between the following variables: Frequency of the age

of fractures, frequency of the strike of fractures, frequency and length, length and average

deviation of strike, length and elevation, elevation and the distance to the central volcano?

Frequency of age of fractures: The correlativity between these variables could only be tested

in the southern area because there are no significant age differences between the lava flows in

the northern area. In the southern area the lava flows divided into two age categories: Post-

Strangarháls and pre-Strangarháls. The age of the Strangarháls lava has not been established

yet but is probably around 7000-8000 years old and form a sharp border to younger lava flows

(Saemundsson, 1992). The amount of fractures per kilometers square in the post-Strangarháls

areas was counted and compared to the number of fractures in the pre-Strangarháls areas. To

evaluate if the number of fractures in a certain area depends on the age of the host rock a

dependency test is necessary. However this could not be done in this case because the χ2

15

independence test method requires two categorical variables to work. In this case there was

only one categorical variable, age in terms of “pre” or “post”. Additionally the amount of

fractures (27) in the “post” areas is too small to convert them into similar categorical classes

without breaking the conditions of the test. Therefore the result only constitutes a simple

count and ratio.

Frequency of strike of the fractures: To see whether the frequency of strike exhibits a normal

distribution two methods were used: Using a Quantile normality plot method and a

Kolmogorov-Smirnov method. The frequencies are plotted in cumulative histograms and

tested against assigned z-values from standard tables around the mean (z used here since the

control-group data follows a normal distribution under large n).

Quantile normality method:

Every , is assigned to a z-value and table critical values so that:

Equation 1: The range of the values in the quantile normality test.

Kolmogorov Smirnov method:

The Kolmogorov-Smirnov goodness-of-fit test is based on the empirical distribution where N

ordered data points, y1, y2 .... yn are defined by the following function:

Equation 2: The definition of the Kolmogorov-Smirnov empirical distribution.

n(i) represents the number of data point that are less than Yi. Yi increases by 1/N at each

following data point. The empirical distribution function Fn and the Kolmogorov-Smirnov

statistic Dn are given by:

Equation 3: The empirical distribution function and the Kolmogorov-Smirnov statistic.

16

Where sup is the supremum of the distribution variable x, which is the number that is greater

than or equal to Fn.

A Kolmogorov-Smirnov goodness of fit test was also used to test the similarity of the fracture

strike distributions on both sides of Lake Thingvallavatn. The two data samples were plotted

against one another in cumulative histograms and analyzed by the following principle:

Equation 4:The Kolmogorov-Smirnov statistic when applied to a goodness-of-fit test, and its critical value.

where F1 and F2 are the distribution functions of the respective populations and Kα is a table

critical values.

A χ2 independence test was used to test whether the strike of magmatic fractures depend on

the strike of tectonic fractures. First the strike data was categorized into 10o classes. One

condition for the test to work is that each class contains at least 5 values. Tthis could only be

obtained if the data was distributed by 10o classes because the number of magmatic fractures

only amounted to 38, with a large standard deviation in strike.

Hypotheses to be tested:

H0: The strike of volcanic fissures is independent of the strike of tectonic fractures.

H1: The strike of volcanic fissures is not independent of the strike of tectonic fractures.

Degrees of freedom: (r-1)(c-1)

Test function: Rules of rejection: H0 is rejected if

Frequency and length of fractures: To test the distribution of length of fractures around Lake

Thingvallavatn scatter-plots were used. The magmatic fractures were not tested for any

relationship including lengths since the range of lengths covered by them is too small to avoid

a high degree of error.

Length and strike of fractures: Analysis using scatter-plots.

17

Average deviation of strike and distance to the central volcano: Scatter-plots of the average

deviation of strike (residuals) against the distance were used and analyzed using a moving

average trend line.

Length and elevation: Scatter-plots were used. The study was only carried out for the southern

area more significant changes in topography occur there.

Elevation and the distance to the central volcano: Analysis using scatter plots.

Distance between fractures and distance to the volcano: The distances between fractures were

measured using transects at certain distances, 2500, 5000, 7500 meters for the southern area

and 20000, 22500, 25000 meters for the northern area, from the volcano. The distances were

then plotted in a scatter plot and analyzed. The location of the transects and mid-line of the

diagram were chosen where they seemed to best represent the graben.

18

4. Results

4.1 Mapping

In Figure 6 the map of both areas are displayed with the average spatial errors (average

deviation from correct GPS coordinate with Google Earth as reference) shown to the left of

each areas respective map.

Figure 6: Mosaics of the aerial photographs over the southern and northern study areas separated by Lake

Thingvallavatn in the middle. The southern area is built up of 15 aerial photographs that have been stitched

together. The northern area consists of 8 aerial photographs that have not been stitched together. The fractures

were mapped on the aerial photographs.

19

The average spatial error in the northern area is with 17.8 meters slightly lower than in the

southern area, with 23.5 meters. In total 647 tectonic fractures could be identified. The

outlines of the graben can be clearly seen. Furthermore, it can be observed that the Hengill

volcano possibly affects the strike of tectonic fractures close to it. They seem to spread out

from the volcano. In the northern area the strike seems to be more regular.

4.2 Statistical analysis

Frequency and age

Fractures in the southern study area mapped with the aerial photographs on a geologic map

(Figure 7). The number of fractures/km2 was counted within a confined area.

Figure 7: The mapped fractures plotted on a geological map over the southern area (Saemundsson, 1995). The

number of fractures/km2 was counted within a confined area (green box).

20

The total area inside the green confined area is about 110 km2, of which the pre-Strangarháls

area covers about 85 km2

and the post-Strangarháls area 25 km2. Out of the 221 tectonic

fractures 23 were found to be in the post-Strangarháls category, which is about 10%. This

amounts to 0.83 fractures/km2, while in the pre-Strangarháls area 2.33 fractures/km

2 occur.

There are almost three times more fractures/ km2

in the older rocks than in the younger.

Whether there is any statistic relationship between age and frequency for magmatic fractures

one would similarly study the fissures in the pre- and post- areas. However, since there were

only 38 fissures found the number was not considered sufficient for analysis.

Frequency of strike

Normality test

In Figure 8 the strike frequency distributions of tectonic fractures N and S of Lake

Thingvallavatn are displayed in the form of Rose diagrams and histograms.

Figure 8: The frequency distributions of strikes of the tectonic fractures in the northern area ( a) and c) to the

left) and the southern area ( b) and d) to the right).

21

The frequency distributions were tested for normality using a Normal Quantile Plot method

and a Kolmogorov-Smirnov method:

Ho: The strike of faults are not normally distributed around the mean.

H1: The strike of faults are normally distributed around the mean.

Southern area:

The calculated correlation coefficient between the fracture frequency and assigned z-values is

0.8852.

.

√

0.9768

Ho rejected if

Since Ho cannot be rejected; the strikes of the fractures are not distributed

normally around the mean. P-value = 0.37.

Northern area:

The correlation coefficient (in this case altered into ) between the fracture strike

frequency and assigned z-values was found to be 0.9368, which is slightly higher than the

0.8852 coefficient of the southern area. The distribution of the northern area is therefore

closer to normality than in the southern area.

.

√

0.9689

22

Ho rejected if

Since the Ho cannot be rejected: The strikes of the fractures are not

distributed normally around the mean. P value = 0.34. Hence any further statistical testing of

the frequency of strikes of fractures in the northern area that assume normality cannot be

used.

For the magmatic fractures in the southern area, the question of normality could not be

answered due to lack of data. The distribution of the 38 fissures, however, was concluded not

to be normal by looking at the frequency distribution, which is much more scattered than the

non-normal distributions of the tectonic fractures (Compare Figure 8c/d with Figure 9).

Figure 9: The frequency distribution of strikes of the magmatic fractures.

Distribution test

The frequency distributions of tectonic fracture strikes on both the N and S sides of Lake

Thingvallavatn were found to be close to normal. The next step was to test whether they

belong to the same distribution. For this purpose a two sided parameter-free Kolmogorov-

Smirnov distribution test was applied with the hypotheses:

H0: The strike of tectonic fractures in the northern and southern areas do not follow the same

frequency distribution.

H1: The strike of tectonic fractures in the northern and southern areas do follow the same

frequency distribution.

0

2

4

6

8

10

12

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Fre

qu

en

cy

Strike[o]

23

Ho rejected if

Figure 10: The approximate normal cumulative frequency line-plot is represented by the thick black line. The

cumulative frequency plots of the strike of the southern fractures (N=274, thin solid line) and the northern

fractures (N=376, dashed line). The population distributions seem to be similar, with a mean around 60o and

with few fractures between 10 o and 40

o. The northern fractures show a better fit to a normal distribution, which

can be seen by the way that more of them are located closer to the middle of the plot.

, p value = 0,025.

Since the Ho is rejected: The strike of tectonic fractures in the northern and

southern areas do follow the same frequency distribution.

24

χ2 independence test

A χ2 independence test (one-sided) was applied to test whether the strike of magmatic

fractures depends on the strike of tectonic fractures with the hypotheses:

H0: The strike of magmatic fractures is independent of the strike of tectonic fractures.

H1: The strike of magmatic fractures depends on the strike of tectonic fractures.

Degrees of freedom: (r-1)(c-1) = 4

Reject H0 if:

Table 1: The χ2 contingency table where the strike of volcanic fissures is tested against the strike of tectonic

fractures. The expected numbers of tectonic and magmatic fractures (expected frqFRA and frq FISS ) are

calculated by using the contingency table (see methods). The observed and expected numbers of tectonic and

magmatic fractures (frqFRA(obs/exp and frqFISS(obs/exp) are displayed for each 10o class.

Since 6.311 < 9.488 H0 cannot be rejected. The strike of volcanic fissures is independent of

the strike of tectonic fractures. The p-value of 0,1771 is, however, indicating a strong trend

towards dependence. Since the strikes had to be narrowed down to five classes the whole test

is simplified and highly contentious (see discussion).

Strike classes(degrees) 40 50 60 70 80 Sum

frqFRA(0bs/exp) 13 34 70 99 42 258

frqFISS(0bs/exp) 1 4 16 8 6 34

Sum 13 38 86 107 48 292

Expected

frqFRA 11.4863 33.5753 75.9863 94.5411 42.411

frqFISS 1.5137 4.42466 10.0137 12.4589 5.58904

Test Sum

frqFRA 0.19948 0.00537 0.47161 0.2103 0.00398 0.89074

frqFISS 0.17433 0.04076 3.57868 1.59579 0.03022 5.41978

6.311

25

Frequency of lengths

The frequency distributions of the length of tectonic fractures in the respective areas can be

seen in Figure 11.

Figure 11: Histograms of the frequency distributions of the lengths of tectonic fractures in the respective study

areas.

The fracture size distribution is dominated by short length values, but the data is highly

scattered. In the northern area most of the fractures are between 100 and 200 meters long. In

the southern area fracture lengths are wider distributed. Most of the fractures are between 100

and 700 meters long. The data was not subjected to a distribution test because of these highly

variable features.

Length and strike

The scatter plots of the variables length and strike of tectonic fractures are displayed in Figure

12 for the two study areas.

26

Figure 12: Length against strike of fractures.

Short fractures have a higher variability in strike than longer fractures. The long fractures

south and north of Lake Thingvallavatn mainly strike between 050 o – 070

o.

Average deviation of strike from the mean strike and distance to the volcano

This analysis was carried out from the data of both study areas. The two variables are plotted

in Figure 13:

Figure 13: N= 649. Average deviation of strike of tectonic fractures from the mean strike and distance from the

Hengill volcano. The southern area is represented on the left side of the diagram and the northern area is on the

right side. The moving average (red line) is calculated over 32 values.

27

The average deviation from the mean strike decrease with increasing distance to the volcano.

For the magmatic fractures no significant change of strike with distance to the volcano could

be visualized from the 38 fissures found (See Figure 14). The strike of the fissures is generally

between 060o -080

o ENE. There are three fissures on the volcano itself, these have a strike of

about 120o SE.

Figure 14: Deviation of strike of magmatic fractures from the mean strike and distance from the Hengill

volcano.

Length and elevation

The relationship between the parameters elevation and length of tectonic fractures in the

southern area is shown in Figure 15.

0

10

20

30

40

50

60

70

0 2000 4000 6000 8000 10000

Stri

ke d

evi

atio

n f

rom

th

e m

ean

str

ike

[o]

Distance from the Hengill volcano [m]

28

Figure 15: Elevation against length of tectonic fractures in the S area. n=312. The mean elevation is 372

meters; the standard deviation is 145 meters.

Most of the fractures are located around the mean elevation of 372 meters. The number of

fractures decrease the further away they are from this mean elevation. The elevation of

fractures was further visualized in ArcScene (Figure 16):

0

100

200

300

400

500

600

700

800

900

0 1000 2000 3000 4000 5000 6000

Elevation[m]

Length [m]

29

Figure 16: Perspective view over the southern area generated in ArcScene using a DEM. Mount Hengill is in the

middle and Lake Thingvallavatn is at the top right corner. Fractures were mapped on top of the DEM.

The ArcScene map shows no hint of any significant correlation between elevation and length

or between elevation of fractures and distance to the volcano of fractures.

Elevation of fractures and the distance to the volcano

The relationship between the parameters elevation and the distance to the volcano is shown in

Figure 17:

30

Figure 17: Elevation of fractures (n=312) against the distance of fractures to the Hengill volcano.

The fractures close to the volcano tend to be located at a higher elevation. Since this increase

in elevation is singularly made up of mount Hengill the variability between fractures elevation

and their distance to the volcano decreases.

Spacing of tectonic fractures and the distance to the volcano

The selected distances from the volcano and their corresponding transects are shown in Figure

18.

31

Figure 18: The spacing of fractures. The yellow lines are the confines of the measurements, with the yellow line

in the middle marking the presumed mid-line of the graben. The black and white lines are the sections, along

which the spacing was measured. The bright spot to the SW of the lowermost transect is mount Hengill.

Distances of the transects to the Hengill volcano are for A: 2500 meters, B: 5000m, C: 7500m, D: 20000m, E:

22500m and F: 25000m.

The spacing of tectonic fractures on both sides of the graben and the distance to the volcano

were then plotted in a Figure 19.

32

Figure 19: Spacing of tectonic fractures against distance to the Hengill volcano.

In the southern area from 2500 to 7500 meters from the volcano the spacing of tectonic

fractures to the NW and the SE of the mid line of the graben center is approximately the same

with around 400 to 500 meters. The spacing of the fractures on the SE side of the mid line of

the graben center is slightly larger than the NW fractures in the southern part, and increases

further with increasing distance to the volcano.

33

5. Discussion

5.1 Mapping

Is it more effective to stitch the maps or to not stitch the maps? In this study the average

spatial error produced in the georeferencing procedure was slightly lower for the northern area

where the aerial photographs were not stitched. Moreover, the southern area lost some of its

resolution during the stitching process making it harder to identify and map fractures.

Furthermore, it is more distorted than the northern area image. It was also more difficult and

more time consuming to georeference the southern area. These shortcomings could however

depend on the type of stitching software. Drawbacks with not using stitching were mainly

noted to be uneven borders between the aerial photographs and that it can be cumbersome to

have to deal with dozens of different map-files rather than a single stitched map-file. This

could also be an advantage though as one has more control over the mapping-procedure and

that one can alter an individual map if it is found that this particular map is wrongly projected.

Once the maps have been stitched, however, no local changes can be made. In this study the

approach without stitching is concluded to be more effective.

Can Google Earth be used to successfully map fractures? The present version of Google

Earth provides material of lower quality than the used aerial photographs. In some areas

however, mostly close to settlements, the resolution can be of equally good quality as the

aerial photographs. It is possible to map fractures and to measure their lengths in Google

Earth using a simple drawing tool, but the data cannot be directly transferred to other

programs.

What is the margin of error when mapping fractures from aerial photographs? As evident

from Figure 11 there could be about 100 more tectonic fractures identified in the northern area

even though the northern area is significantly smaller than the southern area. This could to a

large extent depend on the facts that the fractures were much easier to recognize in the

northern area which has a flatter and more even topography and that the southern area had lost

some of its resolution in the stitching process. Additionally, the fractures could be drawn with

a higher precision and split up into more segments since it was easier to see where the

distance between two fracture segments exceeded five meters and hence constituted two

fractures. In the southern area, this was often not possible, and in many cases one had to rely

on the geological map to map the extent of a fracture since it was impossible to see such small

features on the aerial photographs.

There is not much cause to distrust Saemundssons (1995) geological map over the area, which

was produced using remote sensing combined with extensive field work, but it is still hard to

know whether the differences between the mapped properties of fractures in the northern and

southern areas are because of actual physical differences or because of methodological

differences. This is a crucial matter because if the methodological differences are not properly

understood and handled at the mapping stage the statistical tests which follow may very well

be rendered useless.

34

What are the methodological differences? The main problem is the already addressed effect of

topography, which should be studied in a separate investigation: “What effect does

topography have on the appearance of fractures in aerial photographs?” The maps in the

southern study area, compared to Saemundssons geological map (1995), show that the effect

is significant. No calculations were made but it is estimated that around 20% of fractures in

close proximity (~3km) of Mount Hengill displayed on Saemundssons geological map (1995),

could not be identified on the aerial photographs. In the non-mountainous areas, however,

only 5% of the fractures were missed. If this is the actual case, there is not a single statistical

test that could successfully be applied to model or estimate population distributions with the

given variables without adjustment. It would definitely be of interest in future research to

calculate the exact differences to find the margin of error of the mapping and expose the

fragility of the subject.

Another methodological issue is to determine where one fracture ends and another begins. In

this investigation the minimum distance of 5 meters between fracture segments was chosen to

distinguish segments, but this distance was not chosen because of any related research, where

no such number was found, but because it was considered appropriate. It seems very likely

though, again in reference to Saemundssons geological map (1995) that the choice of this

distance varies significantly between different studies. Saemundsson (1995) most likely used

a larger distance than 5 meters.

Comprehensive methodological studies with clear mapping criteria concerning mapping of

fractures are needed before one can satisfactorily carry out statistical tests based on mapping

data. Until then, the statistical results from this investigation, compared to statistical results

from other investigations, cannot be assumed to show the relationships between parameters of

physical properties of fractures without the significant impact of systematic and/or random

error due to the use of different methods.

5.2 Statistical analysis

Frequency and the age of fractures

The claim by Hjartdottir et al. (2009) that an older rock is usually more fractured can be

confirmed by this study´s data: Almost three times more fractures/km2 were observed in the

older rocks. However, it is difficult to draw any wide spanning conclusions from this result

since the measurement area and the age categories were chosen deliberately. It would be

desirable to see whether the number of fractures depends on the age of the host rock to see

whether age is the only governing parameter that controls the number of fractures, with other

variables, such as the mechanical properties of the rock or change of stress regimes being of

35

insignificant importance. Such an investigation requires more specific data but could be

carried out quite easily in ArcGIS together with a χ2 independence test.

Frequency and the strike of fractures

A disturbance in the strike of fractures could be observed close to the Hengill volcano,

especially in the part between the volcano and Lake Thingvallavatn (see Figure 6). The

statistical analysis also showed that there were some differences in the frequency distributions

between the “northern” and “southern” data sets, but however not to the degree of statistical

significance.

A study carried out west of the current study area (Reykjanes Peninsula) conducted statistical

tests on the frequency distributions of the strike of faults (Clifton and Schliese, 2003). They

concluded that “Fracture strikes exhibit a normal distribution with the great majority between

050o and 060

o” (See Figure 20). These distributions seem to look more organized compared

to the ones in this study, but one needs to pay attention to the fact that the distributions are not

using the highest amount of frequency classes and that a claim of normality needs to be

supplemented with a normality test, something not done in the article.

Figure 20: Normal or not normal? The frequency distributions of strike of fractures on the Reykjanes peninsula,

in Clifton et.al. 2003.

36

The strike of fractures in this study were not found to be normally distributed with a large

margin. This does not exclude the possibility of normality for a larger data set with more than

the 278-369 data points in this investigation.

The degree of similarity of the frequency distributions were tested with a Kolmogorov-

Smirnov test and they were passed as coming from the same distribution, confirming the

visual impression that the fractures on both sides of Lake Thingvallavatn are part of the same

graben and therefore share similar properties. More data would allow quantifying the degree

by which the volcano affects the strike of fractures as a function of distance from the volcano.

This would allow making reliable assumptions about the strike of newly forming fractures.

Regarding the question of whether the strike of magmatic fractures depends on the strike of

tectonic fractures, the statistical answer was no, which means that we cannot exclude the

possibility of other parameters having a significant impact on the strike of magmatic fractures.

The strike of tectonic fractures is quite probably the main parameter, but other variables such

as features of the host rock (e.g. brittleness), magma pressure, elevation or distance to the

central volcano (the deviation of strike from the mean of magmatic fractures was largest on

top of Mount Hengill), are also possible to significantly affect the strike. Therefore it can be

concluded that magmatic fractures in general do align themselves parallel to tectonic fractures

because they form in the same stress field, but that there are other factors as well that affect

the process.

The χ2 independence test of this question that was used to test dependence was flawed with

various problems and thus did not produce significant results. The Kolmogorov-Smirnov test

on the other hand proved itself more suitable in handling these types of statistical problems

although the tests were not used in the same way.

Frequency and the length of fractures

The length is expected to be highly affected by the methodological differences in the mapping

of both study areas. The lengths of tectonic fractures measured in the northern area is

significantly shorter than in the southern area (Figure 11). This could be at least partly

explained by a systematic error.

A geological explanation could be that the northern area consists mostly of the 9100 years old

Eldborgir lava that is different in respect to the mechanical properties of the southern area,

consisting mostly of hyaloclastites and a bigger variation of lava flows. Hyaloclastites are

comparatively soft with a low tensile strength and therefore a tectonic fracture can grow

“longer” in this material, whereas the Eldborgir lava flows are more stiff (Friese, 2008).

However, this would imply that the average deviation of strike of tectonic fractures should

also be greater in the Eldborgir area, but this could not be confirmed in this study.

The type of frequency distribution which the length of fractures might follow has been

discussed using various models (Exponential model: Bohnestiehl and Kleinrock, 1999, 2000;

Carbotte and Macdonald, 1994. Power-law model: Gudmundsson, 1987, 2000) but the

37

different findings may to a significant extent depend on local stress regimes or

methodological differences. In this study neither model could be supported since the number

of data points and the size of the study was not considered to be large enough to draw any

such conclusions.

Strike and length/distance to the volcano

In general it was found that the shorter the tectonic fracture, the larger the variability of the

strike of the fracture. In addition, the northern fractures which were measured to be shorter in

average deviated less from the average strike than the southern fractures. So even if the

Eldborgir lava is in fact more brittle and has led to longer fractures breaking up into more

segments, the strike does not deviate more from the average in the southern area ( Figure 13).

Elevation/length, elevation/distance to the volcano

There is no correlation between any of these variables which were plotted to give a 2D

representation of the fractures. The theory that there should be fewer fractures on top of the

volcano because of the distance to a magmatic dyke is greater (Hjartdottir et al., 2009), could

therefore not be supported.

Spacing of fractures and distance to the volcano

The spacing of fractures was found to be larger on the SE side of the graben (Figure 19).

Consequently the graben is asymmetrical.

The spacing of fractures was also measured to exhibit a larger change on the SE side of the

graben than the SW side (Figure 19). The reason for this type of this asymmetry is unclear,

but might be related to the fact that the area is located on the triple junction between the

WVZ, the SIVZ and the Reykjanes peninsula, so that conflicting stress regimes have affected

the distance between fractures. Bergerat et al., (1999), linked different types of normal and

strike-slip faults to different stress directions and reached the conclusion that as many as four

stress regimes are represented in the area, where some fractures are more affected by one and

other fractures are more affected by another stressfield. The two main stress regimes (Figure

21) are extensions in NE-SW and NW-SE directions.

38

Figure 21: Two conflicting stress mechanisms caused by local stress permutations. (From Bergerat et al., 1998).

It is at the same time questionable whether contrasting stress regimes can account for the large

differences of spacing between fractures that could be seen on both sides of Lake

Thingvallavatn. Hjartdottir et al., (2009), propose that occasional lava intrusions in fractures

under and close to a volcano could create a general stress relief in the area for long periods of

time, reducing the amount of fractures created. The volcano therefore decreases the amount of

rifting in the area close to it so that the spacing between fractures is reduced. This does not

explain, however, why the same change in fracture spacing could not be seen on the NW side

of the graben.

39

6. Conclusions

The strike of fractures is more varied close to the volcano. The frequency distributions

of the strike of fractures were found not to be normal, but they were found to be of the

same and quantifiable type. With more data their common distribution could therefore

be modeled, and the factor by which the Hengill volcano affects the strike of fractures

per distance unit from the volcano could be calculated.

The strike of magmatic fractures was found to be similar to but not dependent on the

strike of tectonic fractures. Therefore change in magma pressure might change the local

stress regime around the fissure, affecting the strike.

Clear mapping criteria are needed in order to conduct remote sensing of fractures in a

systematic way. Otherwise there is a large risk of methodological differences between

studies. The mapping of fissures needs better methods in particular. In this study it was

difficult to locate magmatic fractures on the aerial photographs and the ones located

were too few to analyze in detail.

The study area should be as large as possible to provide a reliable amount of data for the

statistical analysis. It should also be compared to artificial models so that results can be

viewed in a broader perspective. If features are studied on a larger scale the limits of the

resolutions of the aerial photographs will also be a lesser problem.

The non-parametric Kolmogorov-Smirnov statistical test was found to be more suitable

than the categorical χ2 test in this type of study. In order to satisfy χ

2 test conditions

more data than available in this study is required.

40

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42

8. Appendix

Appendix 1:

Correlation and causality (dependence): Dependency is a type of correlation where the

correlation is only and exclusively between two variables. So if one variable is passed as

being dependent on another, say “coffee tasting sweet” depends on “amount of sugar” that

means that “coffee tasting sweet” can only be correlated to one and only one other variable,

namely “amount of sugar”. But if the variable “coffee tasting sweet” is not found to be

dependent on “amount of sugar” that means that there can be a correlation between “coffee

tasting sweet” and “amount of sugar”, but there can also be a correlation between “coffee

tasting sweet” and some other variable, such as “amount of sugar free sweetener”.

Appendix 2: