Deformation at Katla Volcano, Iceland, 2003-2009

Deformation at Katla volcano, Iceland, 2003-2009: Disentangling surface displacements due to ice load reduction and magma movement using InSAR time series analysis Cover images from left to right: Lava ﬂow from the 2010 Eyjafjallajökull eruption, by Kristján Freyr Þrastarson Interferogram of the 2010 Eyjafjallajökull eruption Ice ﬂoating in Jökulsárlon glacial lake, by Júlía Runólfsdóttir Deformation at Katla volcano, Iceland, 2003-2009: Disentangling surface displacements due to ice load reduction and magma movement using InSAR time series analysis

M.Sc. Thesis

Karsten H. Spaans March 2011

Delft University of Technology Faculty of Aerospace Engineering Department of Earth Observation and Space Systems

This report was written as part of the thesis work required for the Aerospace Engineering Master program at Delft University of Technology. I enrolled in the Earth and Planetary Observation master track in September 2008, after struggling through the Bachelor phase, which I had started in 2001. During the Bachelor program, the Earth and Planetary Ob- servation minor program is what rekindled my interest in finishing both my Bachelor and Master degrees at the faculty of Aerospace Engineering. Looking back, the decision to get into the field of Earth Observation was the single best decision I made during my University years. My interest mainly went out to remote sensing and its applications, specifically how additional layers of information can be extracted from seemingly very simple measurements. So when the time came to choose a thesis subject, it was radar interferometry that caught my eye. Although geophysical processes were initially not my main interest, a topic dealing with surface deformations around a volcano in Iceland, Katla, appealed to me most. The topic combined technical work on InSAR processing with interpretation work on a specific application, which was exactly what I was looking for. An added bonus of the thesis subject was that it could be combined with an internship in Iceland. The internship is also part of the Master program of Aerospace Engineering. Working at the University of Iceland for three months allowed me to improve my geophysical understanding of volcanic and tectonic processes, as well as get experience in doing fieldwork. The combined work done during my internship and thesis forms the culmination of all my years spent at the faculty of Aerospace Engineering, and gave me the sense of achievement often missing during the previous years. This report contains the account of the achievements obtained during my thesis work.

i The guidance and support of my supervisor, Dr. Andy Hooper, was invaluable to complete the project successfully. Also, I am grateful to Dr. Freysteinn Sigmundsson and Prof. Ramon Hanssen for their advice throughout the project. I would like to thank Peter Schmidt and Björn Lund from Uppsala University, as well as Þóra Árnadóttir from the University of Iceland for letting me use their glacio-isostacy model. Halldór Geirsson from the Iceland Meteorological Office, now at Penn State University, kindly provided me with processed GPS data from three continuous GPS stations in Iceland, for which I am grateful. For the wonderful discussions and overall great time I would like to thank all the people at the Nordic Volcanological Institute. All the people at the radar group in Delft have my grat- itude for their input, advice and support, as well as the very enjoyable radar meetings. A special mention is reserved here for my officemates during my thesis work, David Bekaert, Lennert van den Berg, Jochgem Gunneman, Anneleen Oyen and Piers van der Torren. The MGP department is thanked for funding my visit to the Dutch Earthscience Conference (NAC10), and allowing me to present my work there. A very special thank you goes out to my parents, for keeping their faith in me, even when no progress was being made, during my years at University, and for supporting me throughout. Finally I would like to thank Amandine, who had the misfortune of becoming my girlfriend during the last months of my thesis. Her unwavering support and endless reviewing of my thesis have helped me keep my sanity through difficult days of coding and writing.

Delft, The Netherlands March 2010 Karsten H. Spaans

ii CONTENTS

Preface i

Abstract v

Nomenclature ix

1 Introduction 1

2 Study area 5 2.1 Iceland ...... 5 2.1.1 Tectonic setting and volcanic zones ...... 6 2.1.2 Volcanism ...... 6 2.1.3 Glacio-Isostatic Adjustment ...... 8 2.2 Katla ...... 8

3 Radar interferometry 11 3.1 Real and Synthetic Aperture Radar ...... 12 3.2 InSAR ...... 14 3.2.1 DORIS processing ...... 17 3.2.2 StaMPS processing ...... 19

4 Partial persistent scatterer processing methodology 27 4.1 Motivation ...... 28 4.2 Interferogram selection ...... 29 4.3 Partial PS selection ...... 31 4.3.1 Gamma estimation ...... 31 4.3.2 Selection ...... 32

iii 4.3.3 Random point reduction ...... 34 4.3.4 Weeding ...... 35 4.4 Displacement estimation ...... 36 4.4.1 Phase unwrapping ...... 37 4.4.2 Nuisance term estimation ...... 38 5 Partial Persistent Scatterer testcases 41 5.1 Simulated data ...... 42 5.1.1 Simulated dataset ...... 42 5.1.2 Processing ...... 42 5.1.3 Selection comparison ...... 46 5.1.4 Phase unwrapping ...... 53 5.2 Eyjafjallajökull eruption ...... 57 5.2.1 TerraSAR-X satellite and data ...... 57 5.2.2 Processing ...... 59 5.2.3 Selection comparison ...... 60 5.2.4 Phase unwrapping ...... 69 6 Katla 73 6.1 Data selection ...... 74 6.2 InSAR processing ...... 77 6.3 Long wavelength signals ...... 83 6.4 Comparison to GPS data ...... 87 6.5 Discussion ...... 91 7 Conclusions and recommendations 97

A Line-of-sight conversion 101 A.1 Incidence angle ...... 101 A.2 Bearing ...... 101 A.3 LOS unit vector ...... 103

iv ABSTRACT

The Katla volcano is one of the most active volcanoes in Iceland. It is partly covered by Mýrdalsjökull icecap, and is in close proximity to three smaller ones. Furthermore, Vatna- jökull icecap, the largest in Europe, is only 80km away. Ongoing ice mass loss from these icecaps, which started over a century ago, has resulted in an uplift of up to 15 mm/yr in the area around Katla, accompanied by smaller horizontal displacements. This displacement signal sums with deformation caused by magma movements, landslides and plate spreading. Disentangling the different contributions in the surface deformation signal around Katla volcano is essential to asses volcanic processes occurring beneath the surface. Measurements at two continuous GPS stations on Katla’s south ﬂank have shown unexpected horizontal movements, compared to the expected plate spreading rates. These movements were initially attributed to a magma source beneath Katla’s icecap. This hypothesis has since become less plausible, due to the long timespan in which this signal was detected, from 2000 up to the summer of 2009. After this, deformations related to the 2010 Eyjafjallajökull eruptions affected the measurements. Alternative hypotheses for the residual horizontal movements are surface displacements due to ice load reduction, local landslides and gravitational sliding. The spatial extent of deformation signals provides valuable clues to the origin of the displacements. GPS measurements in the area however do not have sufﬁcient spatial sampling to differentiate between different deformation sources. In this study, I applied radar interferometry techniques on data over the Katla area, using its superior spatial sampling to discriminate between different contributions to the surface deformation signal in the area. Not only is it important to determine if the residual horizontal motions indicate increased volcanic activity of Katla, the results also add to the understanding of ice mass unloading and other processes going on around Katla and

v the surrounding volcanic systems.

Satellite radar interferometry is a technique that uses two or more radar images to infer surface deformations with centimeter to millimeter accuracy. After processing, the spatial sampling of the deformation measurements is in the order of tens of meters in many areas, allowing for a detailed overview of the spatial behaviour of deformation signals. Current InSAR techniques allow the use of timeseries analysis of interferometry data to increase the quality of results and evaluate deformation behaviour in space and time. Radar images taken over Iceland during (near-)winter time are often affected by snow cover, which reduces the quality of the results signiﬁcantly. Not only are the affected measurements themselves noisier, they also inﬂuence the overall results, reducing the number of accepted measurements in all epochs. I mitigated these effects by processing the high quality data in the conventional way, and developed an extension to the current processing methodology, which allowed me to process the low quality data separately, extracting as much deformation information from them as possible. In doing this, I obtained 21 epochs of surface displacement measurements around Katla with dense sampling and large coverage. During the analysis of the interferometry results, I used a model of the ice load reduction deformation around Iceland to remove this signal from the displacement measurements, leaving only deformation signals that had a relatively small spatial extent. The interferometry results were validated using GPS data from three continuous stations, located south of Katla.

I find no indications of deformation signals that could be related to magma movements on Katla’s south flank, nor do I find these on any other part of the volcano. Furthermore, local causes of the residual movements at the two stations, like land sliding, are not probable, as I detect no variations in the deformation signal in the area surrounding the stations. A more widespread phenomenon is therefore likely to be the source of the residual horizontal motion seen in the GPS data. The direction of these residuals indicates that it is most likely the horizontal component of the ice load reduction displacements, coming from Mýrdal- sjökull and Vatnajökull icecaps, that caused them. At the neighbouring Eyjafjallajökull volcano, I find a deflating signal on its south flank, possibly the result of cooling magma volumes, intruded during events in 1994 and 1999. Another deflating signal is found at Törfajökull, a volcanic system north of Katla. I attribute this deflation to the cooling of a

vi large solidiﬁed magma chamber below it, the presence of which was inferred from seismic studies. Finally, in the area south of Katla, I ﬁnd relatively large residuals between the InSAR results and the model used to remove the ice load reduction deformation signal. These residuals were also detected by GPS, but only on part of the southern side. My results imply that the residuals are consistently large over the area south of Katla, and that the model could be improved here.

vii viii NOMENCLATURE

List of acronyms ASAR Advanced Synthetic Aperture Radar ASTER Advanced Spaceborne Thermal Emission and Reﬂection Radiometer DEM Digital Elevation Model DLR German Aerospace Center DORIS Delft Object-oriented Radar Interferometric Software Envisat European (Space Agency) Environmental Satellite ERS European Remote-Sensing Satellite EVRZ Eastern Volcanic Rift Zone ESA European Space Agency FFT Fast-Fourier Transform GIA Glacio-Isostatic Adjustment GPS Global Positioning System IMO Icelandic Meteorological Ofﬁce InSAR Interferometric Synthetic Aperture Radar JPL Jet Propulsion Laboratory LOS Line-Of-Sight MAR Mid-Atlantic Ridge METI Ministry of Economics, Trade and Industry(Japan) NASA National Aeronautics and Space Administration (United States)

ix NVZ Northern Volcanic Zone PDF Probability Density Function PRF Pulse Repetition Frequency PS Persistent Scatterer PSc Persistent Scatterer candidate Radar Radio direction and ranging ROI_PAC Repeat Orbit Interferometry Package RP Reykjanes Peninsula oblique rift SAR Synthetic Aperture Radar SISZ South Iceland Seismic Zone SLC Single-Look Complex SNR Signal-to-Noise Ratio StaMPS Stanford Method for Persistent Scatterers TFZ Tjörnes Fracture Zone WVZ Western Volcanic Zone

List of symbols

βa Angular resolution [rad] γ Coherence [-] δ Phase estimation residuals [rad]

∆a Azimuth resolution [m]

∆r Range resolution [m] λ Wavelength [m]

σA Amplitude standard deviation [-] τ Pulse length [s]

τeff Effective pulse length [s]

φθ Look angle error phase [rad] u φθ Spatially uncorrelated component of look angle error phase [rad]

φA Atmospheric phase [rad]

φD Interferometric deformation phase [rad]

φN Phase noise [rad]

x φS Orbit inaccuracy phase [rad] ψ Interferometric phase [rad] ψsc Spatially correlated interferometric phase [rad]

A¯ Mean amplitude [m] B Baseline [m]

Bc Chirp bandwidth [Hz]

Bperp Perpendicular baseline [m]

DA Amplitude dispersion [-]

LA Antenna length [m] T Temporal baseline [days] c Speed of light [m/s] fDC Doppler centroid frequency [Hz] N Number of interferograms [-] ncoh Number of coherent PS points selected in an area [-] nrand Threshold on semi-coherent PS points selected in an area [-] rthres Range covered by phase noise threshold [rad]

xi xii CHAPTER ONE

INTRODUCTION

Volcanoes have a split personality. In times of inactivity, one can picture a beautiful mountain surrounded by fertile land, land which feeds masses of people. This picturesque scene is violently disturbed at times of eruptive activity. Lava ﬂows, ash fall, pyroclastic clouds and other eruptive consequences form a very potent threat to human and animal well-being alike. Volcanoes are unpredictable, and our understanding of the processes going on inside them is limited. It is precisely this unpredictable aspect of volcanic eruptions that makes increasing our understanding of the inner workings of volcanoes so vital. Predicting volcanic eruptions accurately and reliably is the holy grail of volcanic research. This research is meant to take us one step further towards the ultimate goal: Predicting the unpredictable.

Our understanding of volcanoes can only be increased by monitoring and studying them carefully. There are different ways in which magma movements and stress changes deep within volcanoes can be detected. Surface deformations provide valuable clues to what is happening below the volcano’s surface. There are many geodetic techniques available to measure these surface deformations. Especially spaceborne remote sensing techniques have made their impact in the geodetic ﬁeld. Interferometric Synthetic Aperture Radar (In- SAR) is one of these remote sensing techniques, which uses high resolution satellite radar images to infer relative surface deformation measurements from phase information. InSAR has in the last two decades been used to monitor earthquakes, dikes and mines, but has also been very successful in monitoring volcanoes, mainly due to its high spatial coverage and

1 1. Introduction

Figure 1.1: Map showing the landmass of Iceland. Katla is indicated by the red box. Eyjafjallajökull icecap can be seen just to the west of Katla. Image courtesy of the National Land Survey of Iceland.

sampling density, precise measurements and the technique not requiring ﬁeldwork. The recent eruption of Eyjafjallajökull has woken up Europe once again to the consequences a volcano can have. Besides Eyjafjallajökull, Iceland is the home of approximately 30 active volcanoes. Volcanic eruptions occur in Iceland on average every few years, and form a very real threat to its population. One of the most active volcanoes is Katla, which is directly connected to Eyjafjallajökull to the east, and has erupted 20 times in the last 1100 years. The location of Katla within Iceland can be seen in Fig. 1.1.

The last major activity of Katla occurred in 1999, when a ﬂood of water came down one of its outlet glaciers, indicating a small eruption below its icecap [Sturkell et al., 2006]. Af- ter this time, the network of continuous GPS stations started to expand rapidly in Iceland, allowing volcanoes to be monitored continuously. Around Katla, three continuous stations have been in operation since the year 2000, at Þorvaldseyri (THEY), Sólheimaheiði (SOHO) and Láguhvolar (HVOL). After several years of measurements, it was noticed that SOHO and HVOL stations moved differently in the horizontal directions compared to the plate spreading velocities [Geirsson et al., 2006; Sturkell et al., 2008]. Fig. 1.2 shows a map of the Katla area, including the three continuous stations in question, with the residual

2 1. Introduction

Figure 1.2: Map of the Katla area, showing residual horizontal GPS velocities compared to the movement of the Eurasian plate, assuming a ﬁxed North-American plate. Plate velocities were calculated using the Revel model. Mýrdalsjökull is the icecap that partly covers Katla. Adapted from [Geirsson et al., 2006]. horizontal velocities indicated. A fourth station is indicated on the map, on the Vestman- naeyjar (VMEY). The residual velocities at SOHO and HVOL were at the time attributed to a local source [Sturkell et al., 2008], most likely magma intrusion. However, the residual velocities per- sisted for several years, which is quite long for deformation signals caused by a local magma source. Also, the direction of the residual velocity at HVOL is nearly parallel to SOHO, and does not point away from Katla’s caldera, as might be expected. All this points to a possible other source of the residual velocities. As alternative causes to magma intrusion, land sliding, gravitational spreading and ice load reduction have been suggested. Bet- ter spatial coverage and higher spatial sampling of deformation measurements was needed to distinguish between different deformation sources, and provide a more satisfying explanation for the residual motion. InSAR satisﬁes these requirements.

3 1. Introduction

The objectives of this study were therefore deﬁned as:

1. Use current InSAR techniques to extract a timeseries showing the deformation signals in the Katla area.

2. Explain the residual movement at SOHO and HVOL GPS stations using the timeseries InSAR data.

This report describes the work done to achieve these objectives, and presents the results obtained.

In order to familiarize the reader with some necessary background, this report starts of with a review of the study area in Chapter 2. Iceland and some of its deﬁning geodynamical properties are introduced here, and a more detailed description of Katla is given. The main geodetic technique used during this study, radar interferometry, is presented in Chap- ter 3. Some basic principles of radar interferometry are discussed, and an overview of the processing techniques used here is given. During this study, an extension to InSAR timeseries processing was developed. The motivation for this extension, as well as an in-depth overview of its implementation is presented in Chapter 4. The extension had to be validated and tested during this study, which is addressed in Chapter 5. Two cases are used for the testing of the extension, a simulated set of interferograms, and a set of interferograms covering the 2010 Eyjafjallajökull eruption. The processing and results of the InSAR timeseries covering Katla is discussed in Chapter 6. This chapter will cover the data selection, creation of the InSAR timeseries, removal of contaminating signals, and interpretation of the results. Finally, Chapter 7 will provide some concluding remarks and future outlook of the study.

4 CHAPTER TWO

STUDY AREA

Humans settling around volcanoes inevitably results in a hazardous situation. Volcanoes can lie dormant for hundreds or thousands of years, but when an eruption occurs, the surrounding area has to be evacuated due to lava-flows, pyroclastic clouds, poisonous fumes or floods. As demonstrated by the Eyjafjallajökull eruption in spring 2010 [Sigmundsson et al., 2010b], volcanic eruptions can also have more widespread consequences. These consequences include disruption of air traffic and climatological effects. To effectively al- leviate and mitigate these hazards, the ability to forecast an impending eruption is essential. In this study, surface deformations around Katla volcano in Iceland are monitored. This chapter will introduce some background on the study areas, volcanoes in Iceland. In Section 2.1, Iceland and its geodynamical properties will be discussed. Sections 2.2 will describe the volcano studied during this research, Katla.

2.1 Iceland

Iceland is one of the few places in the world where a subaerial spreading zone can be found. It houses around thirty active volcanoes, some of Europe’s largest icecaps, geysers and vast geothermally active areas. All this is located in an area roughly three times the size of the Netherlands. It makes Iceland a country with beautiful landscapes, but also makes it prone to natural hazards like volcanic eruptions, earthquakes, outburst ﬂoods and landslides. Although ever increasing, our geophysical understanding of the processes causing

5 2. Study area

these hazards remains too limited to forecast them. The only way to increase our compre- hension is to study these phenomena, and Iceland represents a prime study area to do just this.

2.1.1 Tectonic setting and volcanic zones

Iceland is located on the Mid-Atlantic Ridge (MAR), a spreading zone separating the North-American and the Eurasian tectonic plates. The MAR enters Iceland on the Reyk- janes peninsula, the south-western tip of the country, and leaves at the Tjörnes fracture zone in the north of Iceland. Within the land boundaries of the island, the MAR jumps eastward by about 150 km when going from south to north. The jump is caused by the interaction with the Iceland mantle plume, a thermal anomaly in the crust approximately located beneath Vatnajökull icecap in the east. The grey dashed line in Fig. 2.1 shows the location of the spreading axis throughout Iceland. The jump of the MAR makes for a complex tectonic setting, as well as creating several zones of active volcanism. Two distinct types of volcanic zones can be identified in Iceland [Sigmundsson, 2006]; Volcanic zones where little to no spreading occurs are classified as volcanic flank zones, as opposed to volcanic rift zones, where extensive spreading occurs. There are three volcanic flank zones in Iceland, namely the Snæfellsness Volcanic Zone in the west, the South Ice- land Flank Zone and the Öræfajökull-Snæfell Flank Zone in the east. Furthermore, there are four volcanic rift zones. The volcanic rift zone in the west of Iceland can be divided in two parts, based on their obliquity with respect to the MAR. The rift zone in the south west is named after the Reykjanes peninsula, the Reykjanes Peninsula (RP) oblique rift. The less oblique Western Volcanic Zone (WVZ) is located between Hengill volcano and Langjökull icecap. The two remaining rift zones are the Eastern Volcanic Rift Zone (EVRZ), located between Torfajökull and Vatnajökull icecaps and the Northern Volcanic Zone (NVZ), north of Vatnajökull. Fig. 2.1 shows the distribution of the volcanic zones in Iceland. In total, over thirty active volcanoes can be defined within these volcanic zones.

2.1.2 Volcanism

Volcanic eruptions occur in Iceland on average every few years. The majority of the volcanoes are located on volcanic rift zones. The approximately thirty active volcanic systems

6 2. Study area

Figure 2.1: The spreading axes and volcanic zones in Iceland. The grey dashed line shows the main spreading axes running through Iceland. The Reykjanes Peninsula oblique rift (RP) runs from the south-western tip of Iceland to Hengill volcano, where it transitions into the Western Volcanic Zone (WVZ), which terminates at the Langjökull icecap (L). The main spreading axis jumps to the east, starting at Torfajökull (T), where the Eastern Volcanic Rift Zone (EVRZ) begins. To the south of Torfajökull is the South Iceland Flank Zone, containing amongst others Katla (K) and Eyjafjallajökull (E) volcanoes. At Vatna- jökull icecap, the EVRZ transitions into the Northern Volcanic Zone (NVZ), which exits the country in the north. The Öræfajökull-Snæfell Flank Zone (OSFZ) is located below the eastern part of Vatnajökull. The South Iceland Seismic Zone (SISZ) and the Tjörnes Frac- ture Zone (TFZ) are two transform zones that accommodate the offsets in the spreading axis throughout Iceland. Adapted from [Albino et al., 2010]

7 2. Study area

in the country that have been identified typically consist of a central volcano and a fissure swarm (zone of extensive normal faulting and fissuring) that crosses it [Sigmundsson, 2006]. Many of Iceland’s volcanoes are sub-glacial, which results in jökulhlaups (glacial outburst floods) being one of the main hazards of volcanic eruptions in Iceland. Other hazards include pyroclastic clouds, ash fall and lava flows. Section 2.2 discusses in more detail the main volcano studied during this project, Katla.

2.1.3 Glacio-Isostatic Adjustment

Isostasy is a term used to describe the gravitational equilibrium between the rigid litho- sphere and the ductile, relatively low-viscosity asthenosphere [Fowler, 2005]. It describes how e.g. a mountain at the surface has to be compensated by a mass deficiency below it. When the surplus mass is caused by an ice-sheet, the term Glacio-Isostasy is used. Ice accumulating on the Earth’s surface represents a load bearing down on it, causing a mass adjustment below, resulting in the the crust being forced down. Conversely, melting ice results in an uplift. This phenomenon is referred to as Glacio-Isostatic Adjustment (GIA). While GIA describes the viscous response of the asthenosphere, which can take hundreds to tens of thousands of years, there is also an near-instantaneous, elastic effect. Many of Iceland’s volcanoes are covered by large icecaps, which are gradually melting. The removal of mass from these volcanoes increases the amount of magma generated in the mantle. Furthermore it changes the stress fields below them, which could influence the amount of eruptions and the severity of eruptions Albino et al. [2010]. For this reason, GIA research and volcanic research in Iceland are closely related. However, as GIA signals and the elastic response of ice mass unloading can obscure magma deformation signals, they can also be a nuisance term in deformation studies of volcanoes.

2.2 Katla

Katla is one of the most active volcanoes in Iceland, with 20 eruptions since settlement in the 9th century [Sturkell et al., 2008]. It is located on the South-Iceland ﬂank zone, and is thus away from extensive rifting areas, see Fig. 2.1. Katla is therefore classiﬁed as an intra-plate volcano, and plate spreading velocities at Katla are nearly identical to the

8 2. Study area

Figure 2.2: Surface elevation map of Mýrdalsjökull/Katla, with the caldera indicated by the black line. The red circles indicate surface depressions in the ice formed by sub-glacial magmatic activity. The three main outlet glaciers, Kötlujökull, Entujökull and Sólheima- jökull, are indicated on the map. Adapted from [Björnsson et al., 2000].

Eurasian tectonic plate velocity. Interaction with the Eastern Volcanic Zone to the north does however occur, due to the proximity of Katla to it [Sturkell et al., 2009]. The volcano is partly covered by Mýrdalsjökull icecap, which has a mean diameter of thirty kilometers and is up to 750 m thick [Björnsson et al., 2000]. Katla’s eruptions are therefore generally phreato-magmatic (explosive water-magma interaction) and tend to be accompanied by jökulhlaups. Katla’s caldera has an elliptical shape, with a 13 km major axis and a 9 km minor axis, which can be seen in Fig. 2.2 as the black line. Its rim is breached in 3 places, where ﬂood water from sub-glacial eruptions can discharge towards the main outlet glaciers Kötlujökull (south-east), Entujökull (north-west) and Sólheima- jökull (south). Fig. 2.2 shows a surface elevation map of Mýrdalsjökull. Seismic studies detected the presence of a low velocity P-wave and S-wave shadow zone below the Katla caldera, which indicates a magma chamber located below the volcano [Gudmundsson et al., 1994].

9 2. Study area

The last major eruption of Katla was in 1918, which was accompanied by a massive jökulhlaup draining from Kötlujökull, ﬂooding the Mýrdalssandur plains south of Kötlu- jökull and subsequently draining into the ocean [Tómasson, 1996]. In 1955 a small jökulh- laup drained from the eastern side. No eruption breached the icecap during this time, however two ice cauldrons were formed. This event is interpreted as a small eruption below the icecap [Sturkell et al., 2006]. The most recent activity at Katla stems from July 1999, when a jökulhlaup came down the Sólheimajökull outlet glacier. The 1999 jökulhlaup was preceded by seismic tremor and relatively small earthquakes below the icecap, and again a depression was formed in the icecap’s surface [Sturkell et al., 2006].

10 CHAPTER

THREE

RADAR INTERFEROMETRY

The chief geodetic technique used in this study is interferometric synthetic aperture radar (InSAR), otherwise known as radar interferometry. Using radar images obtained with satellites, surface deformation can be detected with centimeter precision. In the course of this study, InSAR techniques are applied over two volcanoes, allowing their activity to be monitored and explained.

In terms of spatial distribution of measurements, InSAR combines large coverage with dense sampling. The radar images used typically have resolutions of several tens of meters, and cover up to hundreds of kilometers in the horizontal directions. Furthermore, InSAR does not require ﬁeldwork, reducing labour intensity and costs. The main shortcomings of InSAR are that deformations can only be resolved in the radar Line-Of-Sight (LOS) and that the temporal coverage is limited by the satellite revisit time, which are weeks in between. InSAR has become an important tool in measuring surface deformations, and has proven itself to be a valuable addition to other geodetic techniques like GPS and levelling.

In the course of this chapter, the reader will be given an overview of the basics of InSAR. Section 3.1 explains the difference between real and synthetic aperture radar. In Section 3.2, the radar interferometry principle will be introduced and the processing techniques relevant to this study will be discussed.

11 3. Radar interferometry

3.1 Real and Synthetic Aperture Radar

Radio detection and ranging (Radar) works by emitting electromagnetic radiation in the microwave range to an object and measuring the (two-way) travel time and the intensity of the signal. From the travel time, the range to a target can be determined, while the intensity of the signal allows information about the target’s shape and surface properties. Typically satellite-mounted radars use wavelengths in the X-band ( 3 cm), C-band ( 6 cm), S-band ( 9 cm) or L-band ( 24 cm). The direction in which the radar emits its radar signal is commonly referred to as the range direction. The resolution in range direction is deﬁned as the minimum distance between two targets such that the signals can still be separable in the return signal. This distance is determined by the pulse length τ. Two targets can be separated if the distance between them is more than the distance the signal travels within its pulse length, i.e. [Cur- lander and McDonough, 1991]: 1 ∆ = cτ, (3.1) r 2 where c is the propagation velocity and τ represents the pulse length. For a nominal pulse length of 30 ms, this results in a resolution of 4.5 km. This resolution can naturally be improved by using a shorter pulse. The pulse length however also determines the signal- to-noise ratio (SNR), which prevents the pulse length from being too short. The solution to the range resolution problem is to introduce a so-called chirp. A chirp is a linear signal

which is modulated on the frequency of the radar signal. The bandwidth of the chirp Bc is deﬁned as the difference between the maximum and the minimum frequency of the chirp. By using the chirp compression technique during processing, the effective pulse length is greatly reduced [Hanssen, 2001]: 1 τeff = . (3.2) Bc A bandwidth of 10 MHz for example leads to an effective pulse length of 100 ns, resulting in a range resolution of 15 m. This is a large improvement over the 4.5 km obtained without using a chirp. The other direction of interest for resolution is the ﬂight direction of the platform, commonly referred to as the azimuth direction. The resolution in azimuth direction for a real aperture radar is determined by the diffraction limit. A well known approximation for this

12 3. Radar interferometry

Figure 3.1: SAR imaging geometry. Frequently used terms are ‘along-track’ or ‘azimuth’ for x, ‘ground range’ for y, and ‘slant range’ for the distance of a particular point from the SAR sensor. [Bamler and Hartl, 1998] limit is given by [Hanssen, 2001]:

0.886λ βa ≈ , (3.3) LA where βa is the angular resolution, λ is the wavelength of the signal and LA is the antenna length. A real aperture radar with a wavelength of 5 cm and an antenna length of 10 m, flying 800 km away from its target would have an azimuth resolution of 3.5 km. Fig. 3.1 shows the typical sidelooking viewing geometry of the type of radar satellite used during this study, including the range (y) and azimuth (x) directions. Synthetic Aperture Radar (SAR) is a technique that allows significant improvement of the azimuth resolution. It utilizes the movement of the radar platform to create an artifi- cially large aperture, resulting in a far superior azimuth resolution. As a satellite moves, the radar instrument sends out radar pulses towards the Earth’s surface. The frequency at

13 3. Radar interferometry

which pulses are sent is known as the pulse repetition frequency (PRF). Arbitrary targets on the Earth’s surface are thus illuminated by multiple pulses. Using a SAR algorithm to process all these pulses, a high resolution SAR image can be generated. This process is known as focussing the data. The azimuth resolution obtained using SAR is given by [Hanssen, 2001]: L ∆ = A . (3.4) a 2

3.2 InSAR

InSAR is a term used to describe all techniques that infer information from the difference in phase between two or more SAR images. The result of InSAR processing is an interferogram, the visualization of the phase difference between corresponding pixels in a SAR image pair. As the phase is only known modulo-2π, the interferometric phase before further processing is modulo-2π as well. This is commonly referred to as the data being wrapped, which results in the interferograms being made up of color cycles, known as fringes. For every pixel in a SAR image, two properties of the radar reflection are recorded by the satellite. The first is the amplitude, which contains information on the reflective properties of the surface, like shape, orientation and reflectivity. The second is the phase of the signal. As a measure of distance, the phase cannot be used, due to interaction of the phase with the many scatterers within the target area. As the interaction with the scatterers is consistent however, the difference in phase between two acquisitions does provide valuable information. Consider two images of the same area, taken from the same point in orbit, where the surface moves in between the two acquisitions. The difference in phase between the two images will then, ceteris paribus, represent the surface movement. Nat- urally, conditions in practise will change between acquisitions. The effects resulting from these changes can however be removed or mitigated during processing. It is at this point important to note that radar measures in line-of-sight (LOS) only, and surface movements extracted from interferograms therefore represent the projection of the movement onto the LOS vector. This means that surface deformations in azimuth directions can thus not be resolved using InSAR. Before the phase difference between two images can be determined, some preprocess- ing is required. Firstly, one image has to be co-registered with respect to the other image.

14 3. Radar interferometry

The co-registered image subsequently has to be re-sampled, such that the pixel locations of both images match. Generally, spectral ﬁltering is applied to both images before calculat- ing the interferometric phase, in order to remove non-overlapping parts of the Doppler and range bandwidths. The range bandwidth is determined by the chirp, see Section 3.1. The Doppler bandwidth is caused by the radar pulses moving over a scatterer. As each pulse illuminates scatterers from a slightly different angle, the relative velocity of the scatterer with respect to the radar instrument changes. This causes a shift in the frequency, known as the Doppler effect. The range of frequencies resulting from this effect is the Doppler spectrum. The non-overlapping Doppler and range bandwidths are caused by changes in squint and look angle between acquisitions, respectively. A change in squint angle will change the center frequency of the Doppler spectrum, thus creating a non-overlapping parts of the master and slave Doppler bandwidth. A change in look angle results in a similar shift in the center frequency of the chirp spectrum. The non-overlapping parts of the bandwidths do not carry information, and can thus be removed.

After the interferometric phase has been determined, two of the main nuisance terms in the resulting interferogram are the reference phase and the topographic phase. Both contributions are part of the same phenomenon, caused by the difference in position of the satellite at the two acquisition times. This difference in position causes a stereoscopic effect, similar to the way in which the distance between the two human eyes allows us to perceive depth. A convenient way to remove this effect is to split it into two; The reference phase (or flat-earth phase) is the phase difference present if the surface was the reference ellipsoid, while the topographic phase is the result of the topography that is present in re- ality on this ellipsoid. Both are estimated separately, and removed from the interferogram. After removal of these two terms, the interferogram is referred to as being flattened and topographically corrected. Fig. 3.3 shows a flow diagram of the most general interferometry processing steps. A detailed overview on radar interferometry can be found in e.g. [Hanssen, 2001].

Interferograms have two separation parameters that, to a large extent, determine their quality: the perpendicular baseline and the temporal baseline. Where the spatial baseline represents the total distance between the satellite positions at the time of the two acquisitions, the perpendicular baseline represents the projection of the spatial baseline onto the direction perpendicular to the LOS. Fig. 3.2 shows the difference between the absolute

15 3. Radar interferometry

Figure 3.2: Schematic representation of the difference in position of the SAR satellite at two acquisition times. The absolute distance between the satellite at time 1 (S1) and time 2 (S2) is given by the baseline, B. The parameter commonly used for InSAR is the perpendicular baseline, Bperp. baseline and the perpendicular baseline. For deformation applications, it is always preferable to minimize the perpendicular baseline. The temporal baseline is the separation in time between the two acquisitions. While for the quality of the interferogram it is preferable to minimize this baseline as well, the temporal baseline is limited by the deformation process. For slow deformation processes, one might be forced to use longer baseline interferograms. Too high values for either baseline will however result in decorrelation. Decorrelation (or a loss of coherence) occurs when the interaction of the radar signal with a set of scatterers changes between acquisitions. Decorrelation results in noise in the interferometric phase. A measure for the amount of decorrelation is coherence, where good coherence means little decorrelation. Typically, decorrelation sources can be identiﬁed as being one of two categories [Zebker and Villasenor, 1992]. The ﬁrst type, geometric decorrelation, results from a change in viewing geometry between acquisitions. The second type is temporal decorrelation, which is caused by a change of the scattering surface over time. It can therefore be concluded that geometric decorrelation is dependent on the perpendicular

16 3. Radar interferometry

baseline and temporal decorrelation is related to the temporal baseline. The Stanford Method for Persistent Scatterers (StaMPS) is an InSAR processing technique that allows selection of stable scattering pixels, Persistent Scatterers (PS), out of a stack of interferograms [Hooper et al., 2007]. The technique reduces the problem of decorrelation between interferograms over long timespans and large perpendicular baselines. This allows long time series to be generated, utilizing all images available. StaMPS accomplishes this by extracting pixels that have a dominant scatterer, and therefore decorrelate slower. The interferometric phase of every pixel in an interferogram is the coherent sum of the many individual scatterers present in the resolution cell. When the position of the SAR instrument changes too much between two acquisitions, or too many of the individual scatterers change, pixels become increasingly decorrelated. The phase in a resolution cell can however also be dominated by a single scatterer. When a dominant scatterer is present, the pixel is far less sensitive to decorrelation, as this pixel will dominate the coherent summation. Identifying and extracting these pixels allows interferograms with longer perpendicular and temporal baselines to be used. The interferometric processing done during this study was performed using the Delft Object-oriented Radar Interferometric Software (DORIS) [Kampes, 1999]. Section 3.2.1 describes in what way DORIS was used during this study. Section 3.2.2 explains in more detail the StaMPS processing technique. Focusing of raw SAR data was achieved using scripts from the Repeat Orbit Interferometry PACkage (ROI_PAC) by the Jet Propulsion Laboratory (JPL) [Rosen et al., 2004].

3.2.1 DORIS processing

There are several differences between conventional InSAR and StaMPS interferogram gen- eration, see Fig. 3.3. As StaMPS uses a single-master stack, a master has to be chosen initially. The master is chosen by maximizing the expected stack coherence, based on three baselines; the perpendicular, the temporal and the Doppler baseline [Hooper et al., 2007]:

N 1 X γm = g(Bk,m,B ) · g(T k,m,T ) · g(f k,m, f ), (3.5) N ⊥ ⊥,crit crit dc dc,crit n=0

17 3. Radar interferometry

Figure 3.3: Flow diagram of basic DORIS interferometric processing. Green steps are unchanged for StaMPS processing, red steps are omitted, and orange steps are changed. Adapted from [Kampes, 1999].

k,m where N is the number of images, B⊥ is the perpendicular baseline between images m k,m k,m and k, T is the temporal baseline, fdc is the Doppler baseline and the subscript crit represents the critical value for the sensor used. The function g is given by:

 1 − |x|/c if |x| < c, g(x, c) = (3.6) 0 otherwise.

Interferograms are formed between the selected master and every slave image.

During the co-registration step, every slave is co-registered with respect to the master. Sub-pixel accuracy can be obtained here by oversampling, and the result is a two- dimensional polynomial describing the translation of the slave with respect to the master. PS processing allows much larger perpendicular baselines to be used than traditional In- SAR. These large baselines however hinder the co-registration. It is therefore preferable to not co-register the slaves with large perpendicular baselines directly to the master. Instead, the large baseline slaves are co-registered to assisting slaves, which have more suitable

18 3. Radar interferometry

perpendicular baselines to both the master and the slave in question. Spectral filtering in both azimuth and range directions is not applied during StaMPS interferometry. Spectral filtering reduces the bandwidth, i.e. increases the size of resolution cells. Larger resolution cells will increase the number of individual scatterers in a cell, reducing the likelihood of a scatterer being dominant. As persistent scatterers should not be significantly influenced by the noise introduced due to non-overlapping bandwidths, spectral filtering is omitted. Finally it must be noted that unwrapping of the interferograms is performed after the PS selection is completed, not before.

3.2.2 StaMPS processing

Besides the interferogram formation described in the previous section, StaMPS processing consists of three additional steps, namely:

• Phase stability analysis,

• PS selection, and

• Deformation estimation.

These three steps will be explained in this section.

Phase stability analysis

The phase stability analysis is performed on an initial subset of all the pixels in the interferograms, the PS candidates (PSc). This subset contains the pixels most likely to be PS, based on the amplitude dispersion index. The amplitude dispersion index DA is deﬁned as:

σ D = A , (3.7) A A¯ ¯ where σA is the standard deviation of a pixel’s amplitude over all interferograms, and A is the mean amplitude of the pixel. There exists a statistical relationship between the amplitude dispersion index and phase stability, which says that phase stable pixels are expected to have low amplitude dispersion indices [Ferretti et al., 2001]. This relation is exploited to reduce the amount of points that have to be analysed. By setting the amplitude dispersion

19 3. Radar interferometry

index threshold relatively high, one can ensure that nearly all PS are in the selected PSc. Still, most of the PSc will not be PS.

The ﬂattened and topographically corrected interferometric phase at pixel x in interferogram i can be described as [Hooper et al., 2007]:

ψx,i = W (φD,x,i + φA,x,i + φS,x,i + φθ,x,i + φN,x,i) (3.8)

where φD,x,i is the phase due to the displacement of the point, φA,x,i is the phase due

to atmospheric delays, φS,x,i is the residual phase due to orbit inaccuracies, φθ,x,i is the

look angle error, and φN,x,i holds all remaining noise terms. W represents the wrapping operator. The look angle error (also commonly referred to as DEM error), can be caused by DEM inaccuracies and phase center position uncertainties. The atmospheric phase and orbit inaccuracies are spatially correlated, and usually so is the deformation signal. The look angle error is partly spatially correlated. So by estimating the spatially correlated

part of ψx,i, an estimate for the ﬁrst three and part of the fourth term in Eq. (3.8) can be obtained. StaMPS uses a band-pass ﬁltering method that adapts to phase gradients in the data, as described in [Goldstein and Werner, 1998]. The resulting estimate for the spatially sc correlated interferometric phase ψx,i is subtracted from the original phase and the result re-wrapped: sc u W (ψx,i − ψx,i) = W (φθ,x,i + φN,x,i + δx,i), (3.9)

u where φθ,x,i represents the spatially uncorrelated part of the look angle error and δx,i contains the spatially uncorrelated parts of the displacement, orbit error and atmospheric signal. This process is illustrated by Fig. 3.4. The spatially correlated phase (middle) is estimated by band-pass ﬁltering the interferometric phase (left). Subtracting the spatially correlated phase from the original phase values leaves the spatially uncorrelated phase (right).

u The spatially uncorrelated part of the look angle error φθ,x,i is linearly related to the perpendicular baseline [Hooper et al., 2007]. This relation can be used to obtain an estimate for the remaining look angle error. After removal of this estimate, the phase noise and the residuals of the estimates remain:

sc ˆu 0 W (ψx,i − ψx,i − φθ,x,i) = W (φN,x,i + δx,i), (3.10)

20 3. Radar interferometry

(a) Interferometric phase, ψi (b) Estimated spatially correlated (c) Spatially uncorrelated phase, sc sc phase, ψi W (ψi − ψi )

Figure 3.4: Estimating and removing the spatially correlated phase from the original interferometric phase. The spatially correlated phase is estimated by band-pass ﬁltering the original phase values. Removing the estimate from the original phase results in the spatially uncorrelated part of the interferometric phase. W () represents the wrapping operator.

ˆu 0 where φθ,x,i is the estimate for the spatially uncorrelated look angle error, and δx,i holds the remainders for all estimated phase constituents. Fig. 3.5 visualizes the estimation process of the spatially uncorrelated look angle error. By taking the spatially uncorrelated phase values of a PSc point in all interferograms, a linear relation between the phase values and the perpendicular baseline can be estimated (black line).

The estimated spatially uncorrelated look angle error is now removed from the spatially 0 uncorrelated phase. If we neglect the remainders of the estimates (δx,i), which are expected to be small, all that is left on the right side of eq. (3.10) is the phase noise. By deﬁnition, PS points are the pixels that have little phase noise. The estimated phase noise thus represents the quality of a point x in interferogram i. A measure for the magnitude of the phase noise is deﬁned as [Hooper et al., 2007]:

N 1 X γ = W ψ − ψsc − φˆu , (3.11) x N x,i x,i θ,x,i 1 where N is the number of interferograms.

21 3. Radar interferometry

Figure 3.5: Spatially uncorrelated phase values of PSc point x in all interferograms, plotted as a function of their perpendicular baseline. Due to the linear relation between the look angle error and the perpendicular baseline, the spatially uncorrelated look angle error can easily be estimated. The estimate here is given by the black line. The vertical distance between a point and the black line represents the phase noise of PSc point x in interferogram i.

The estimation of the phase noise is done iteratively. During successive iterations, the

γx of the previous iteration is used to weight the contribution of each pixel to the estimation of the spatially correlated phase for the next iteration. To asses the convergence of the estimation process, the iterations continue until the difference between two successive γx estimations is below a threshold value set by the user. During the PS selection step, the

ﬁnal values for γx obtained here are used as a measure for the probability of a PSc being a PS.

PS selection

The selection of PS is performed by setting a threshold on the γx value. The threshold value depends on the allowable percentage of false positives, as given by the user. The set of PSc is the union of two subsets, one containing PS points and one containing non-PS points. In the previous section, γx was deﬁned as a measure for the probability of a pixel being a PS. The probability density function (PDF) of the PSc as a function of γx, p(γx), is thus the sum of the PDF of PS pixels, pps(γx), and the PDF of non-PS pixels, prand(γx), see Fig. 3.6. A set of pixels with random phase is generated to determine the shape of prand(γx). For low values of γx, γx < 0.3, p(γx) is expected to be identical to prand(γx),

22 3. Radar interferometry

Figure 3.6: An example of a probability density function of γx. The PDF of the PSc (blue) is the weighted sum of the PDF of non-PS points (green) and the PDF of PS points (red). α is determined in StaMPS by exploiting the fact that the PDF of non-PS is identical to the total PDF for low values of γx. Adapted from [Hooper, 2006]. that is [Hooper et al., 2007]:

Z 0.3 Z 0.3 p(γx)dγx = (1 − α) prand(γx)dγx, (3.12) 0 0 where the term (1 − α) is the weight factor of prand(γx) compared to pps(γx), and

0 < α < 1 . The shape of p(γx) and prand(γx) are known, which allows an estimate for α to be obtained. The PDFs are now fully known, and a threshold for γx can be set based on the percentage of random pixels allowed. However, if the PSc pixels are binned based on their amplitude dispersion index, a more accurate threshold for γx can be estimated, depending on DA. In practice it turns out that the threshold for γx varies linearly with DA. The final threshold for γx is thus set as a function of the amplitude dispersion of that pixel, DA,x. Additionally, the PS selected using the above method are put through a weeding step. Pixels with a strong reflection will dominate the signal for their neighbouring pixels. Adja- cent selected PS are therefore weeded out, only the one with the highest γx is kept. Further- more, the selected PS can optionally be re-evaluated during this step, and the phase noise re-estimated. Instead of band-pass filtering the phase, the spatially correlated phase constituents are now removed by taking the difference in phase between neighbouring pixels.

23 3. Radar interferometry

Figure 3.7: Flow diagram showing the three-dimensional unwrapping routine used in StaMPS.

The arcs connecting the neighbouring pixels are found using a Delaunay triangulation. The estimate for the spatially uncorrelated part of the look angle error from the initial selection step is re-used. What remains after removal of the spatially correlated phase and the spatially uncorrelated look angle error once again represents the phase noise. For every pixel, several estimates for the phase noise are obtained in every interferogram, one for every natural neighbour (i.e. arc). The lowest mean phase noise for a pixel over all interferograms is used to weed the PS points, based on a threshold value set by the user. By setting the frac- tion of random points relatively high in the ﬁrst selection step, and afterwards re-evaluating the selected phases using arc phases, one expects to ﬁnd more PS points.

Displacement estimation

The displacement estimation step consists of unwrapping the selected PS, and estimating nuisance terms. Conventional phase unwrapping works on single interferograms, that is, in two (spatial) dimensions. Since a third dimension (time) is available during PS processing, the extra information in this dimension can be used to aid the unwrapping. Fig. 3.7 shows a flow diagram of the 3D unwrapping routine used by StaMPS. The original wrapped interferometric phase of every interferogram is first re-sampled to a grid, allowing efficient Fast Fourier Transform (FFT) techniques to be used. The gridded phase is filtered using an adaptive Goldstein filter [Goldstein and Werner, 1998]. Empty grid cells are filled using nearest-neighbour interpolation. An example of the result after each of the first three steps can be seen in Fig. 3.8. The atmospheric nuisance term in the interferometric phase can be larger than π, making direct unwrapping of the gridded phase values in time impossible. The solution to this is to unwrap over arcs connecting neighbouring grid cells. As the atmospheric signal is spatially correlated, it is largely cancelled out by taking the difference in phase between neighbouring pixels. This makes it possible to unwrap the phase differences in time, assuming that all phase differences lie between −π and π. The unwrapped time series is low-pass

24 3. Radar interferometry

filtered to smooth the result. The results from the unwrapping and smoothing in time are used to obtain a-priori PDFs, describing the (unwrapped) phase difference between neighbouring grid cells. The mean value of the PDF is the smoothed unwrapped phase value, and the variance is the variance over time of the difference between the smoothed and original unwrapped phase values, see Fig. 3.9. The wrapped phase value should be preserved, meaning that only full phase cycles can be added or subtracted from the wrapped phase values. This is known as congruence, and can be seen as the red lines in Fig. 3.9. The PDFs derived from the unwrapping in time are used to create cost functions for the spatial unwrapping. The optimisation routine described in [Chen and Zebker, 2001], the statistical network cost flow routine, is used to do the spatial unwrapping. This results in a grid of unwrapped phase values. The original points are unwrapped from the grid by taking the unwrapped value of the nearest grid cell, and adding the difference between the wrapped grid cell value and the wrapped point value. A more detailed description of the quasi-3D unwrapping algorithm can be found in [Hooper, 2009]. The unwrapped phase still contains the atmospheric, look angle and orbit inaccuracy nuisance terms. The look angle error can be estimated from the unwrapped phase values by estimating the phase component linearly related to the perpendicular baseline. Orbit inaccuracies, visible as linear ramps in the interferograms, can be estimated using this linear relation in space. However, since for most satellites, the ramps are randomly oriented, they will cancel out over time. It is therefore also common practise to neglect the orbital ramp removal. All nuisance terms have a contribution from the master acquisition, which will therefore be present in all interferograms. This contribution is obtained by low-pass filtering arcs in time, and retrieving the offset of the arc phases at the master time, at

(a) Gridded phase values (b) Filtered phase values (c) Region growing

Figure 3.8: Example of the result after each of the initial three unwrapping steps.

25 3. Radar interferometry

Figure 3.9: Unwrapped phase PDF. The green line describes the PDF derived from estimates for the expected value of displacement, µ, and the standard deviation of the phase noise, σ. The red lines give the PDF after enforcing congruence (not scaled). [Hooper, 2009] which time the deformation contribution is zero. The only nuisance term remaining are the slave contributions of the atmospheric signal to each interferogram. The atmospheric slave contributions are expected to be correlated in space, but uncorrelated in time. A reasonable estimate can be obtained by high-pass ﬁltering unwrapped phase values in time, and low- pass ﬁltering the resulting phase values in space. The estimation of slave contribution is however commonly skipped, especially when the deformation is expected to be correlated in time. The slave contributions to the atmospheric signal can then be treated as noise in the timeseries during modelling or interpretation of the results.

26 CHAPTER FOUR

PARTIAL PERSISTENT SCATTERER PROCESSING METHODOLOGY

Radar interferometry is a convenient technique to monitor large scale deformation processes. It is however plagued by decorrelation problems. The decorrelation problems is what lead to the development of persistent scatterer techniques. StaMPS in particular has been successfully applied to monitor volcanic, tectonic and other geodynamic processes, see for example [Hooper et al., 2009; Decriem et al., 2010]. Although these techniques allow for improved analysis of the radar data, problems do remain. One of these problems is the difference in coherence between images, after PS analysis. During the InSAR processing of data over Katla volcano, Iceland, the inﬂuence of snowcover and large baselines led to a handful of interferograms with inferior coherence compared to the rest of the stack. This resulted in pixels which were coherent in most interferograms to be removed because of the few low coherence interferograms. Further- more, the large amounts of decorrelation noise led to questionable unwrapping reliability of the affected interferograms. Although the source of decorrelation may be different, the same problem with decorrelated images appears in many datasets, covering different parts of the Earth. The routine described in this chapter is an extension on conventional StaMPS processing, aimed at mitigating the detrimental effects that low coherence images have on the PS processing results. The extension allows the usage of images that previously would have to be dropped from processing, and will increase the amount of information that can

27 4. Partial persistent scatterer processing methodology

be obtained from the interferogram stack. This chapter is composed of four sections. Section 4.1 elaborates on the motivation behind the routine. Section 4.2 describes the relation between the different sets of PS points that will be selected. In section 4.3, the method to select PS points from the low coherence images will be discussed. Section 4.4 deals with the unwrapping and nuisance term estimation of the partial PS points.

4.1 Motivation

The idea to look for pixels that were persistent in most, but not necessarily all interferograms was inspired by problems with snow cover in wintertime around Iceland’s volcanoes. Snow covering the Earth’s surface will decorrelate pixels, making them useless for extracting a deformation signal. However, these pixels might be very coherent whenever the ground is clear of snow. Very coherent pixels in the majority of the interferograms have to be sacriﬁced to reduce decorrelation noise in the near-winter acquisitions. Fig. 4.1 illustrates this issue nicely. It shows two interferograms from data in the Katla volcano area. One is a low coherence winter acquisition, the other is a good coherence summer acquisition. Both interferograms have similar baselines, and the results shown are after PS selection. The coherent summer interferogram shows spatially correlated signal, with relatively low noise levels. The less coherent winter acquisition shows much more spatially uncorrelated, noisy signal. I sought out to solve two problems resulting from these low coherence images in a relatively high coherence stack:

• Removal of stable points in the high coherence images because of decorrelation in the few low coherence images, and

• The large difference in noise levels of PS results after selection.

Both problems are related. On the one hand, coherent pixels get removed from the high quality interferograms. Conversely, low coherence pixels also get accepted in the low quality interferograms due to their low phase noise in the other interferograms. After PS selection, this results in a loss of signal in the high coherence images, and relatively high noise levels in the low coherence images.

28 4. Partial persistent scatterer processing methodology

(a) Near-winter acquisition (b) Summer acquisition

Figure 4.1: Comparison between a near-winter and a summer interferogram after PS selection, covering Katla and Eyjafjallajökull volcanoes. The interferogram on the left has a perpendicular baseline of 271 m, the one on the right has a perpendicular baseline of -254 m. The master is on 22 July 2007. Although there is some difference in the temporal baseline, the considerable difference in coherence is mostly caused by snow cover. Radar images were acquired with the Envisat satellite.

4.2 Interferogram selection

I address the problems caused by heavily decorrelated interferograms by splitting the total set of interferograms into two subsets:

• One where coherence is expected to be best. This set needs to contain enough interferograms to do the PS processing. It will be referred to as the coherent interferograms in the remainder of this document.

• One where some pixels are expected to decorrelate. This set will be referred to as the semi-coherent interferograms from now on.

The coherent set of interferograms is used to perform the conventional StaMPS analysis, whereby I obtain a set of phase stable points in these interferograms. For the semi- coherent interferograms, I use the selected set in the coherent interferograms as a starting point. I evaluate these in each of the semi-coherent interferograms, and select those points that remain phase stable even in these interferograms. For every semi-coherent interferogram, this results in a subset of the coherent PS points. I thus obtain one set of coherent

29 4. Partial persistent scatterer processing methodology

Figure 4.2: Venn diagram showing the relation between pixels, coherent PS points and semi-coherent PS points. The set of coherent selection PS points is the subset of the full set of pixels, representing points with consistently low phase noise in the coherent interferograms. From the coherent selection PS points, N sets of semi-coherent selection PS points are selected, where N is the number of semi-coherent interferograms. selection PS points, and N sets of semi-coherent PS selection points, where N is the number of interferograms. Fig. 4.2 illustrates the relation between the different sets of selected PS points. Treating the semi-coherent interferograms separately results in more ﬂexibil- ity in the PS analysis, allowing selected points to be only partially persistent. Selected points are persistent in the coherent set, but do not have to be persistent in some or all semi-coherent interferograms. In distinguishing between the set of PS points selected in the coherent interferograms and the subsets of those PS points in the semi-coherent interferograms, I will refer to the coherent interferogram set as the coherent PS points and the semi-coherent interferogram PS points as semi-coherent PS points. Strictly speaking this naming is not correct, since the semi-coherent points are actually the points that remain coherent in that interferogram. However, as the naming convention is in line with the two sets of interferograms, it is a practical one. Before the selection of points can be treated, the division of coherent and semi-coherent interferograms has to be dealt with. As discussed above, the full stack of interferograms has to be split into coherent and semi-coherent interferograms. There are multiple ways in

30 4. Partial persistent scatterer processing methodology

which this could be done. When a speciﬁc decorrelation source is known, semi-coherent interferograms can be selected based on this. For snow cover, this would result in all (near) winter acquisitions to be selected as semi-coherent. Alternatively, they can be selected based on the average phase noise per interferogram. The downside of this is that part of the processing has to be run before (and rerun after) the semi-coherent interferograms can be identiﬁed. The advantage however is that this method will minimize the overall phase noise. During this study, I opted to use the latter method, to maximize the effectiveness of the technique, and not be limited by concentrating on one decorrelation source.

4.3 Partial PS selection

With the sets of coherent and semi-coherent interferograms deﬁned, the selection of PS points can be performed. The coherent PS point selection runs parallel to the semi-coherent PS point selection. Both selection procedures will therefore be discussed, allowing their interrelations to be illustrated. The emphasize will however be on semi-coherent interferogram PS selection.

4.3.1 Gamma estimation

The initial phase stability analysis, as described in Section 3.2.2, is performed only on the coherent interferograms. In other words, the selection of the initial set of PSc using the amplitude dispersion index, as well as the iterations to determine γx (Eq. (3.11)) and the estimation of the spatially uncorrelated look angle error are performed using the coherent interferograms only. sc For every coherent interferogram, the spatially correlated phase constituents (ψx,i in Eq. (3.9)) are estimated by applying a band-pass ﬁlter. The estimated spatially correlated phase is then subtracted from the interferometric phase. Per pixel, the spatially uncorrelated ˆu look angle error (φθ,x,i in Eq. (3.10)) is now estimated by using its linear relation to the perpendicular baseline over all interferograms, see Fig. 4.3. The phase that remains after subtracting both the spatially correlated and uncorrelated terms represents the phase noise. In Fig. 4.3, the phase noise per interferogram of the pixel in question is represented by the difference between the estimated line and the spatially uncorrelated part of the phase.

31 4. Partial persistent scatterer processing methodology

The average phase noise per pixel over all (coherent) interferograms is used as a measure for the coherence of that pixel. Note that the processing steps described above form the conventional StaMPS routine, applied only on the coherent interferograms. The result of this step is two-fold:

• An estimate for the spatially uncorrelated look angle error as a function of the perpendicular baseline, and

• An estimate for the coherence of each pixel (γx) in the coherent interferograms.

4.3.2 Selection

Using the phase stability results from the previous section, PS points in the coherent interferograms are selected in the conventional StaMPS way, as described in Section 3.2.2. A threshold value for γx is set as a function of the amplitude dispersion index DA, using the

PDF of the randomly generated set of points (prand(γx) in Fig. 3.6) and the PDF of the full

set of coherent interferogram PSc (p(γx) in Fig. 3.6). After the set of coherent PS points is selected, I evaluate the same set of points in each of the semi-coherent interferograms for phase stability. I estimate and remove the spatially correlated phase for the selected points in each semi-coherent interferogram, leaving the spatially uncorrelated look angle error and the phase noise. For every point, I obtained an estimate for the spatially uncorrelated look angle error during the selection of coherent PS points. This estimate allows me to calculate the spatially uncorrelated look angle error for each point in the semi-coherent interferogram, using the known perpendicular baseline. I use this property to remove the remaining, spatially uncorrelated look angle error from the signal, which leaves only phase noise and estimation residuals. The issue that remains is the method of selecting the semi-coherent PS points. The normal way of using a threshold on γx will not work, as the initial goal was to treat the semi- coherent interferograms separately from the coherent ones. Using γx will once again allow the coherent interferograms to compensate for the semi-coherent interferograms. There- fore, the selection must be done based directly on the phase noise of the semi-coherent PS candidates. I therefore set the threshold for the phase noise of the semi-coherent interferograms based on the phase noise of the accepted coherent PS points, such that the standard deviation of the phase noise of each semi-coherent interferogram is the same as the mean

32 4. Partial persistent scatterer processing methodology

Figure 4.3: Spatially uncorrelated PS point phase values as a function of perpendicular baseline. The blue points are the coherent PS points, the green point is an accepted semi- coherent PS point and the red point is a rejected semi-coherent PS point. The black line is the estimated spatially uncorrelated look angle error phase component as a function of perpendicular baseline. The vertical distance between a point and the black line represents the phase noise of that point.

33 4. Partial persistent scatterer processing methodology

standard deviation of the phase noise over the coherent interferograms. In other words, the points with the highest phase noise are removed, such that the standard deviation of the phase noise for the remaining points is equal to the mean standard deviation of the coherent interferograms. Fig. 4.3 shows the estimation of the spatially uncorrelated look angle error and the selection of the semi-coherent PS points. In this ﬁgure, the green point is accepted, since it is close to the line and has therefore little estimated phase noise. The red point is not close and is therefore rejected.

4.3.3 Random point reduction

One of the main problems resulting from the method above is the number of random points that it selects. Decorrelated points have a random phase value, which results in some decorrelated points falling within the phase noise threshold range, and thus falsely get accepted. As long as the spatially correlated phase represents actual signal present in the interferograms, this does not cause any significant problems. Problems do occur when the estimated spatially correlated phase does not represent any physical signal. The band-pass adaptive filter will always give an output. In the case of fully decorrelated areas, this results in patches of nearly identical phase values, as can be seen in Fig. 4.4(a). The selected points, see Fig. 4.4(b), show the same pattern as the band-pass filter results, which in this case are meaningless. Under the assumption that the phase values in a fully decorrelated area are uniformly distributed within the range -π to π, the number of random points selected in a fully decorrelated area should equal: r n = thres · n , (4.1) rand 2π coh

where nrand is the number of random points in the area which are selected in the semi-

coherent interferogram, rthres is the range of phase values covered by the phase noise

threshold, and ncoh is the number of coherent PS points that were selected in the same area. In the case that the area is not fully decorrelated, the number of random points predicted above will be selected, in addition to the phase stable points in the area. In other words, the partial PS routine will always select more points in a coherent area than in a decorrelated area.

34 4. Partial persistent scatterer processing methodology

(a) Estimated spatially correlated phase (b) Selected semi-coherent PS points

Figure 4.4: Estimated spatially correlated phase and selected semi-coherent PS points for a simulated interferogram containing random phase values exclusively. The selected phase values converge to the estimated spatially correlated phase, which has no physical meaning.

The ratio of selected semi-coherent PS points in an area with respect to the number of coherent PS points selected in that area thus forms an indicator if the area is decorrelated or not. I exploit this property to reduce the effect of random point selection by the partial PS routine. After partial PS processing selection, I compare for every point in every semi- coherent interferogram the ratio of selected semi-coherent and coherent PS points in a predefined area around this point to the ratio between the threshold range and the full phase range. The predefined area is set based on the spatial density of the coherent PS selection results. As random point values are never completely uniformly distributed, an additional margin is used to counter this. Testing on simulated data showed that increasing the ratio by 15% maximized the removal of random points, without affecting the coherent areas significantly.

4.3.4 Weeding

During weeding, adjacent points are removed from the set of selected coherent PS points.

Only the point with the highest γx is kept. If a point is removed from the coherent set, I have to remove it from all semi-coherent sets as well, to ensure that all semi-coherent PS points are in fact part of the coherent set. This means that even when a semi-coherent PS

35 4. Partial persistent scatterer processing methodology

point does not have any points directly abutting it (because that point was removed due to excessive phase noise), it will still be removed if it is adjacent to another point in the coherent set. The weeding based on arc phases over time is skipped during partial PS processing. For the initial selection to be successful, the amount of random points allowed must be set low, below 5 points per km2. This is much lower than the default 20 points per km2 for conventional StaMPS processing, which eliminates the need for additional weeding. Furthermore, during the evaluation of arc phases in time, a smoothing is performed on these arc phases, weighted by the time difference between them. This causes problems when introducing the semi-coherent PS points. Adding these additional points in time for some, but not all, points in the coherent set will inﬂuence the smoothing signiﬁcantly, making the phase noise estimation results impossible to compare. Initial attempts to perform partial PS processing selection during the weeding step instead of during the selection step failed, partly due to this problem with the smoothing. The weeding step concludes the selection step of the partial PS routine. I obtain a set of coherent PS points using the conventional StaMPS routine on the coherent interferograms, as well as N sets of semi-coherent PS points, where N represents the number of semi- coherent interferograms. The selected points are used during the displacement estimation, which will be discussed in section 4.4.

4.4 Displacement estimation

As described in Section 3.2.2, the displacement estimation is the ﬁnal step in StaMPS processing, and consists of phase unwrapping and nuisance term estimation. StaMPS’ three-dimensional unwrapping is however designed to have a constant set of points in time. Clearly, the combined sets of coherent and semi-coherent PS points do not have a constant set of points, as the semi-coherent sets are all different. This section will describe how I adapted the three-dimensional unwrapping algorithm to unwrap the semi-coherent interferograms. Also, the nuisance term estimation is presented, which concludes the displacement estimation.

36 4. Partial persistent scatterer processing methodology

Figure 4.5: Flow diagram showing the three-dimensional unwrapping routine used here. The light blue part displays the conventional StaMPS unwrapping routine. The red branch shows the deviation from the conventional routine taken by the partial PS routine.

4.4.1 Phase unwrapping

The procedure used by the three-dimensional unwrapping routine in StaMPS, previously discussed in Section 3.2.2, is shown in Fig. 4.5 as the blue part. The wrapped phase is re-sampled to a grid using nearest neighbour interpolation. The gridded phase values are then filtered using an adaptive low-pass filter. After the filtering, holes in the grid are filled using region growing. These steps are performed separately for each interferogram, and can therefore be applied to the semi-coherent interferograms without much difficulty. The only difference is that the regions for all coherent interferograms are the same, while the regions for the semi-coherent interferograms might be completely different from each other. I thus obtain a separate re-sampling grid for every semi-coherent interferogram. Firstly, the coherent interferograms are unwrapped following the blue part of the flow diagram of Fig. 4.5. The semi-coherent interferograms are not used during this process. Arcs are formed between connecting regions. The arc phases can now be (locally) smoothed and unwrapped in time, and the results are used to form a-priori PDFs of the unwrapped phase difference between regions. These PDFs are used to obtain the cost functions used by the minimum cost network flow optimisation routine. The optimisation routine unwraps the phase spatially for each grid, which is then used to unwrap the phase at each PS point. I unwrap the semi-coherent interferograms in a very similar fashion, depicted by the red part of the flow-diagram. The process described below is valid for one semi-coherent interferogram, and is done separately for every semi-coherent interferogram. In the initial steps, I grid the phase, filter it, and perform the region growing. As the selected points

37 4. Partial persistent scatterer processing methodology

in each semi-coherent interferogram are different, I generate a different set of regions for every semi-coherent grid. I use the ﬁltered coherent grids to resample every coherent grid to the semi-coherent regions. In other words, the points present in the semi-coherent grid are taken from the coherent grids. I use these points to obtain regions matching the semi- coherent grid for every coherent interferogram. This gives a timeseries of grids with regions matching the semi-coherent points, which can be used for the 3D unwrapping. I form arcs between the semi-coherent regions, and obtain cost-functions for every arc by unwrapping the arc phases in time. The cost functions are naturally only used to unwrap the semi-coherent grid, as the coherent interferograms have already been unwrapped. All the semi-coherent interferograms can now be unwrapped, aided by information from the time dimension.

4.4.2 Nuisance term estimation

The four main nuisance terms still present in the unwrapped interferograms are:

• Master atmosphere,

• Slave atmosphere,

• Orbital errors, and

• Look angle error.

Three of these errors get reduced during the partial persistent scatterer processing. The fourth one, slave atmosphere, will be treated as noise during the post-processing. It must also be noted that although the three before-mentioned nuisance terms are estimated, the actual removal of them is a choice left up to the user, as is done by conventional StaMPS. Orbit inaccuracies introduce orbital ramps, a linear plane in the interferogram. Due to their linear nature, these planes are easily estimated. Furthermore, since the estimation is done separately for each interferogram, the fact that the partial interferograms contain less points is irrelevant. Orbital ramps are therefore estimated in the conventional way. The fact that the look angle error is linearly proportional to the perpendicular baseline of the interferometric pair is exploited during the selection step of StaMPS. During the processing however, I obtained an estimate for the spatially uncorrelated part of the look

38 4. Partial persistent scatterer processing methodology

angle error. Now that the unwrapped phase is known, a line can be ﬁtted through the phase values per pixel as a function of the perpendicular baseline. Incidentally, the offset of the line at zero baseline gives an estimate for the combined master atmosphere and master look angle error nuisance terms. The estimation and removal of the nuisance terms described here is identical to the conventional StaMPS method. The only extension I implemented here was to allow the semi-coherent PS points to be used whenever they were available (i.e. whenever they have not been removed by the partial PS selection routine).

39 4. Partial persistent scatterer processing methodology

40 CHAPTER

FIVE

PARTIAL PERSISTENT SCATTERER TESTCASES

In the course of the previous chapter, the theory behind the partial PS processing extension to StaMPS, developed during this study, was explained. Partial PS processing was developed to mitigate the detrimental effects low coherence images have on an otherwise higher coherence stack of images, by analysing these images separately from the rest of the stack.

Following the development of the technique, I tested it on two testcases, allowing me to asses the technique’s effectiveness, speciﬁcally compared to conventional StaMPS processing. Initially, I processed a set of simulated interferograms. Furthermore, I also applied the partial PS processing routine on a set of 28 TerraSAR-X interferograms covering the 2010 Eyjafjallajökull eruption. Where the simulated data allowed me to test the routine in a con- trolled environment, the Eyjafjallajökull data provides a real example of the improvements that can be made using the newly developed extension to StaMPS processing.

This chapter provides an overview of the results obtained during the processing of the two testcases. Section 5.1 presents the results for the simulated data. In Section 5.2, the results for the TerraSAR-X interferograms covering the Eyjafjallajökull eruption are described.

41 5. Partial Persistent Scatterer testcases

5.1 Simulated data

Simulated data allows for processing results to be compared to a ground truth, the original simulated phase values. The main purpose of this section is to demonstrate how low coherence images inﬂuence the selection process of conventional StaMPS, while, at the same time, showing the improvements made when using partial PS processing.

5.1.1 Simulated dataset

I generated a set of 19 interferograms containing approximately 100,000 simulated phase values each, showing the signal of an inﬂating and deﬂating Mogi point source at 2 km depth. The radar incidence angle was set to 19◦, and the radar wavelength at 5.6 cm (C- band). A different atmospheric phase screen was added to each interferogram. A perpendicular baseline dependant DEM error was added, based on a critical baseline of 1100 m. Phase noise with a normal distribution was added, having a standard deviation of 50 degrees. To simulate the data, I used a script kindly provided by Dr. Andy Hooper. Since StaMPS needs random points to set its selection threshold, I replaced 50,000 points by uniformly distributed random phase value between −π and π, the same points in all interferograms. Finally, to demonstrate the problems caused by low coherence images, I replaced additional points by random phase values in four interferograms, 20 October 2000, 11 March 2003, 10 April 2005 and 29 December 2005. These images will represent the semi-coherent interferograms, and their dates were chosen arbitrarily. For the 20 Octo- ber 2000, 11 March 2003 and 10 April 2005 interferograms, I replaced 20,000 additional points, while for the 29 December 2005 interferogram I replaced all points with random phase values. Figure 5.1 shows the wrapped simulated data, including all the noise terms and random phase value points. The semi-coherent interferograms are shown with a red box surrounding them.

5.1.2 Processing

I processed the simulated dataset using both conventional StaMPS and the partial PS routine. The partial PS processing was performed with an allowable random point density of 3 per km2, and besides removal of adjacent points, no additional weeding. A problem arose

42 5. Partial Persistent Scatterer testcases

Figure 5.1: Simulated wrapped phase values including random phase points. The signal contains deformation, atmosphere, DEM error and noise. The semi-coherent interferograms, indicated by the red boxes, have additional random points.

43 5. Partial Persistent Scatterer testcases

here; The threshold set by StaMPS does not depend solely on the parameters set by the user, but also on the dataset. In other words, two different datasets processed with identical processing parameters can yield different quality results. It is for this reason that in practise user intervention is required after selection, to tweak parameters and ensure a reliable result.

The need for user intervention in tweaking the selection parameters is an inherent short- coming of StaMPS. It is up to the user to determine which noise levels are acceptable in the worst interferograms, so as not to remove too many good points from the best interferograms. Although this is a valid criticism on the method, StaMPS has proven its worth in recent years, and further discussion of this issue is not within the scope of this research. The difference in noise levels of different datasets processed with identical parameters did present an issue for this simulation: How to set the parameters such that the results are comparable? I could have set the parameters such that the amount of points selected using conventional StaMPS matches the amount of points selected in the coherent interferograms using the partial PS routine. This however proved not to be a valid option, since the conventional StaMPS results are inﬂuenced by the partly decorrelated semi-coherent interferograms, which the partial PS results are not. This makes the selected points different, and results in an overall far noisier result for the conventional StaMPS processing. This method would thus not have demonstrated the shortcomings of the StaMPS selection routine, but instead would have demonstrated the ability of StaMPS’ unwrapping routine in dealing with noisy data.

An alternative to the amount of selected points is the measure for the quality of selected points in each interferogram, provided by StaMPS. This measure is the standard deviation of the phase noise over all points in an interferogram, after selection and weeding. It gives an objective estimate of the quality of selected points. For conventional StaMPS processing, I initially set the allowable random point density to 5 per km2, and subsequently adjusted the selection parameter during the weeding phase such that the mean estimated noise standard deviations over the coherent interferograms matches that of the coherent interferograms in the partial PS results. This resulted in a weeding parameter of 0.91 for the conventional StaMPS processing. Table 5.1 shows the standard deviations of the phase noise after selection and weeding in the interferograms for both selection routines. The red dates indicate the semi-coherent interferograms.

44 5. Partial Persistent Scatterer testcases

StaMPS Partial PS Slave date Noise std [deg] Noise std [deg] 01-Jan-2000 42.51 40.85 17-Apr-2000 40.64 40.41 20-Oct-2000 49.95 46.41 07-Apr-2001 40.13 40.48 08-Dec-2001 41.19 42.68 12-Jul-2002 39.49 40.16 11-Mar-2003 51.22 46.33 17-Apr-2003 39.72 40.34 01-Jul-2003 39.97 40.59 10-Dec-2003 54.85 54.79 30-Apr-2004 39.48 40.76 03-Oct-2004 46.62 44.85 16-Feb-2005 40.38 41.48 10-Apr-2005 49.92 46.39 18-Jul-2005 39.90 40.89 30-Oct-2005 48.69 45.85 29-Dec-2005 66.70 45.13 31-Mar-2006 40.56 40.73 05-Nov-2006 41.32 40.65 29-Dec-2006 41.41 40.64 Mean 42.3 42.3 Table 5.1: Estimated phase noise standard deviations per interferogram for both the conventional StaMPS and the partial PS selection results on the simulated data. The black dates are those of the coherent interferograms, while the red ones represent the semi-coherent interferograms. The mean value displayed at the bottom represents the mean value over the coherent interferograms.

45 5. Partial Persistent Scatterer testcases

Slave date Points selected 20-Oct-2000 23673 11-Mar-2003 23541 10-Apr-2005 23815 29-Dec-2005 458 Table 5.2: Selected number of points in the semi-coherent interferograms, using the partial PS processing routine. The ﬁrst three interferograms each had 20,000 additional random points. The 29th of December 2005 interferogram had no signal, only random points.

After selection and weeding, 16,669 points are selected by conventional StaMPS for all interferograms. Partial PS processing selects 34,561 points in the coherent interferograms, and the amount of points selected for the semi-coherent interferograms is given by Table 5.2. Fig. 5.2 shows the wrapped selection results using conventional StaMPS, and Fig. 5.3 shows the same for partial PS processing.

5.1.3 Selection comparison

Just the amount of selected points, together with the phase noise standard deviations of those points, already tell quite a story. By treating the four low coherence images separately, double the amount of points were selected in the coherent interferograms, at no extra cost in overall noise levels. This conﬁrms that a few low coherence images can cause conventional StaMPS to remove a signiﬁcant amount of phase stable points from the high coherence images. This effect is also clearly visible in the plots of the wrapped results, see Fig. 5.2 and Fig. 5.3. The deformation fringes are much more pronounced in the partial PS results compared to the conventional StaMPS results. Fig. 5.4 shows a more detailed view of the wrapped result for the 29 December 2006 interferogram, one of the coherent interferograms, using both selection routines. In the area around the edges of the image, where no deformation is present, the signal is similar in the two results. In the deforming area, the additionally selected points in the partial PS results show the signal much more clearly than the conventional StaMPS results. The additional points selected in the coherent interferograms add to the signal, but do not increase the noise levels. With conventional StaMPS, the most commonly used solution to mitigate the effect of the low coherence images is to remove these low coherence images from the time series

46 5. Partial Persistent Scatterer testcases

Figure 5.2: Wrapped phase values of selected points in the simulated interferograms using conventional StaMPS. The interferograms with additional random points added to them are indicated with a red box.

47 5. Partial Persistent Scatterer testcases

Figure 5.3: Wrapped phase values of selected points in the simulated interferograms using partial PS processing. The semi-coherent interferograms are indicated with a red box.

48 5. Partial Persistent Scatterer testcases

(a) Conventional StaMPS (b) Partial PS

Figure 5.4: Comparison of selected points in the December 29 2006, coherent interferogram, using both selection routine. The conventional StaMPS result contains 16,669, and the partial PS result contains 34,561 points analysis. Indeed, removing the images would yield the same results for the coherent interferograms. However, the removed images might still, and often will, contain valuable signal, and removing them means this information is lost. Also, the question which interferograms to select as semi-coherent carries much less weight during partial PS processing, compared to the question of which interferograms to remove during conventional StaMPS. Partial PS processing provides a way to extract as much signal as possible from the good coherence images, while preserving, and in some cases improving, the information contained in the partial interferograms. Fig. 5.5 to 5.7 show the wrapped results using both selection method, for the three semi-coherent interferograms which have some pixels with coherent phase. The partial PS results show signiﬁcantly more signal. Although the noise is somewhat less in the partial PS results, see Table 5.1, the increased signal must mainly be attributed to the larger amount of selected points. This can in part be explained by the fact that the random points in the fourth, completely decorrelated interferogram are not affecting the selection of the points in each of the other three partial interferograms. Another signiﬁcant contributor to the larger amount of selected semi-coherent PS points are spatially correlated random points, random phase points which happen to have a phase that matches the long wavelength signal.

49 5. Partial Persistent Scatterer testcases

Assuming the same points are random in at least several other interferograms, these points would get removed using conventional StaMPS, as the chance of them matching the long wavelength signal in multiple interferograms is greatly reduced. Although technically these points should be considered noise, they do not add to the noise levels of the selection results, as long as the estimated spatially correlated phase represents actual signal in the interferograms. The fully decorrelated interferogram of 29 December 2005 represents an interesting test subject. From the above results it has already become clear that a heavily decorrelated image can have an effect not only on the coherent, but also on the other semi-coherent interferograms. Fig. 5.8 shows the wrapped phase values of the selection results for the interferogram. The conventional StaMPS result shows, as expected, spatially uncorrelated noise. Very few points get selected by the partial PS routine, less than 500. This is mostly due to the removal of points with insufﬁcient accepted point density, see Eq. (4.1). Before the evaluation of accepted semi-coherent point density, almost 16,000 points were accepted in the December 29 interferogram. Fig. 5.9 compares the wrapped phase values of accepted points using partial PS processing with and without the point density evaluation. When the point density is not considered, the partial PS routine accepts many random points, those that are close in phase value to the estimated spatially correlated phase. By removing points that have too many rejected semi-coherent points surrounding them, the majority of these false positives are removed. At the same time, for the three semi-coherent interferograms with signal left in them, only 4, 32 and 0 additional points get removed, a negligible amount. This shows that the point density algorithm removes points in fully decorrelated areas, but leaves them when there is coherence.

50 5. Partial Persistent Scatterer testcases

(a) Conventional StaMPS, 16,669 (b) Partial PS, 23,673 points points

Figure 5.5: Wrapped phase values of selected points in the 20 Oct 2000 interferogram.

(a) Conventional StaMPS, 16,669 (b) Partial PS, 23,541 points points

Figure 5.6: Wrapped phase values of selected points in the 11 Mar 2003 interferogram.

(a) Conventional StaMPS, 16,669 (b) Partial PS, 23,815 points points

Figure 5.7: Wrapped phase values of selected points in the 10 Apr 2005 interferogram.

51 5. Partial Persistent Scatterer testcases

(a) Conventional StaMPS, 16,669 points (b) Partial PS, 458 points

Figure 5.8: Wrapped phase values of selected points in the 29 December 2005 interferogram.

(a) Partial PS, no additional removal of points (b) Partial PS

Figure 5.9: Wrapped phase values of selected points using partial PS routine, with and without the removal of points based on the density of accepted points, in the 29 December 2005 interferogram.

52 5. Partial Persistent Scatterer testcases

5.1.4 Phase unwrapping

The unwrapped phase values of the selected PS points are given in Fig. 5.10 for conventional StaMPS and in Fig. 5.11 for partial PS processing. The additional points selected using the partial PS routine results in more deformation signal being extracted after unwrapping, especially in the later interferograms. In the conventional StaMPS results, the 3D unwrapping algorithm still manages to extract an impressive amount of signal from the limited amount of points selected. The unwrapped phase values are compared to the original simulated phase values. Fig. 5.12 shows the difference between the original simulated phase values, including nuisance terms, and the unwrapped phase values. In both selection results, scattered unwrapping errors can be seen. The residual plot also conﬁrms that the additional deformation signal extracted by partial PS is in fact real signal, which is in some cases not extracted by conventional StaMPS. This section has demonstrated the problems StaMPS can have during selection in dealing with several low coherence images in a higher coherence stack. It was shown that partial PS processing successfully mitigates the detrimental effects that the low coherence images have on the points selected in the high coherence images. At the same time, partial PS still extracts signal from the low coherence images, making it preferable to removing the low coherence images altogether. Problems that occurred for partial PS processing when areas within semi-coherent interferograms decorrelate too heavily, have been resolved by evaluating the point density of accepted points compared to the coherent set.

53 5. Partial Persistent Scatterer testcases

Figure 5.10: Unwrapped phase values of selected points in the simulated interferograms using conventional StaMPS. The interferograms with additional random points added to them are indicated with a red box.

54 5. Partial Persistent Scatterer testcases

Figure 5.11: Unwrapped phase values of selected points in the simulated interferograms using partial PS processing. The semi-coherent interferograms are indicated with a red box.

55 5. Partial Persistent Scatterer testcases

(a) Conventional StaMPS

(b) Partial PS

Figure 5.12: Residual between original simulated phase values (before addition of random points) and unwrapped phase values for the selected points.

56 5. Partial Persistent Scatterer testcases

5.2 Eyjafjallajökull eruption

After a decade of little activity, the Eyjafjallajökull volcano erupted in the spring of 2010. The first phase of the eruption started on March 20th 2010 [Sigmundsson et al., 2010b], when a fissure opened on Fimmvörðuháls, the ridge connecting Eyjafjallajökull to Katla. Effusive activity continued until April 11th. A second phase initiated on April 14th 2010, when an explosive eruption started from within the caldera. Continuous activity would persist at this location until May 23rd. The first eruptive phase was harmless, whereas the second phreato-magmatic eruption had widespread consequences. A jökulhlaup, draining from Gígjökull outlet glacier on the north side of the caldera, forced the authorities to destroy part of the highway in order to save a bridge over Markarfljót, the glacial river flowing north of Eyjafjallajökull into the ocean. The ash cloud produced by the eruption forced hundreds of farmers around Eyjafjallajökull and Katla out of their houses, as well as disrupting air traffic over large parts of Europe for days on end. The German Aerospace Center (DLR) was asked to program their SAR satellite, Terra- SAR-X, to acquire radar images covering the volcano. The short eleven day revisit time of TerraSAR-X means that the eruption could be monitored using InSAR with unprece- dented temporal sampling, resulting in a very detailed overview of magmatic movements prior, during and following the eruptive activity. Besides the usual seasonal coherence problems (mainly snowcover in Iceland), the second phase of the 2010 Eyjafjallajökull eruption resulted in a thick tephra layer in the area around the volcano, easily exceeding ten centimeters at times. This tephra layer decorrelates interferograms. These interferograms thus represent a convenient testcase for the partial persistent scatterer routine. This section gives an overview of the data used and provides a comparison between conventional StaMPS processing and partial PS processing of the data.

5.2.1 TerraSAR-X satellite and data

The TerraSAR-X satellite is an X-band SAR satellite operated by DLR, launched in 2007 and operational since January 2008. The top part of Table 5.3 gives an overview of the main orbit and system parameters for the TerraSAR-X instrument. The eleven day repeat cycle is a considerable improvement compared to most previous SAR missions, e.g. the Envisat satellite with its 35 day repeat cycle. The requested SAR data over the volcano

57 5. Partial Persistent Scatterer testcases

System parameters Mean orbital height 514 km Orbit repeat cycle 11 days Orbit inclination 97.44◦ Radar frequency 9.65 GHz (X-band) Radar wavelength 31 mm Look direction Right (Left possible) Incidence angle 20◦-45◦ Operation modes - Stripmap - ScanSAR - Spotlight - High resolution spotlight

Image parameters Swath width 30 km Azimuth resolution 3 m Ground range resolution 1.7 m (far range) 3.5 m (near range) Table 5.3: Orbit and system parameters of the TerraSAR-X instrument, as well as image characteristics for the Stripmap mode [Eineder and Fritz, 2010].

during the eruption was acquired in the Stripmap mode, the basic SAR mode. The bottom part of Table 5.3 describes the main characteristics of the Stripmap mode. It shows that TerraSAR-X images have high resolution, but have a limited swath width. The swath width barely sufﬁces to cover the relatively small Eyjafjallajökull volcano. If the volcano were any larger, data from another satellite or imagemode (ScanSAR) would have had to be used. What makes TerraSAR-X data preferable from other satellite data is its short revisit time, as discussed previously.

Out of the many tracks in which data was acquired during the Eyjafjallajökull eruption, one contained by far the most images, track 132. Between June 2009 and September 2010, 29 images were acquired, which is nearly twice as much as the next highest number of images. Table 5.4 provides the acquisition dates and the perpendicular baselines with respect to the selected master of the 29 images. The master image, September 3rd 2009, was chosen using Eq. (3.5). Additional constraints were used to ensure the master image is coherent. The master image was therefore not allowed to be a (near-)winter acquisition,

58 5. Partial Persistent Scatterer testcases

Date Baseline [m] Date Baseline [m] 18-Jun-2009 27 20-Mar-2010 -168 29-Jun-2009 -5 31-Mar-2010 17 10-Jul-2009 69 11-Apr-2010 17 21-Jul-2009 82 22-Apr-2010 -70 01-Aug-2009 -88 03-May-2010 108 12-Aug-2009 -94 14-May-2010 174 03-Sep-2009 0 25-May-2010 208 14-Sep-2009 -141 05-Jun-2010 53 25-Sep-2009 -239 16-Jun-2010 121 06-Oct-2009 -75 08-Jul-2010 46 17-Oct-2009 46 19-Jul-2010 -42 28-Oct-2009 -103 30-Jul-2010 -24 08-Nov-2009 -27 10-Aug-2010 153 19-Nov-2009 134 01-Sep-2010 -103 04-Feb-2010 -64 Table 5.4: Image acquisition dates and perpendicular baseline with respect to the selected master. excluding all options between October and March, and the master could not be after the explosive eruptive phase. The chosen master resulted in maxima of one year for the temporal baseline and 239 m for the perpendicular baseline.

5.2.2 Processing

Using the data described above, I formed 28 topographically corrected and flattened interferograms with respect to the master image, using the processing steps described in Section 3.2.1. The topographic phase removal was performed using a 25 meter posted DEM. I chose five interferograms as semi-coherent interferograms, which were the five interferograms with the highest phase noise standard deviation from earlier processing results. These interferograms are the 4th of February, the 20th of March, the 31st of March, the 25th of May and the 5th of June. The first three dates are most likely decorrelated by snow cover, where ash fallout most likely decorrelated the latter two. With the exception of the February interferogram, all of the semi-coherent interferograms cover at least part of the eruption deformation signal.

59 5. Partial Persistent Scatterer testcases

I applied both conventional StaMPS and the partial PS routine on the set of interferograms. The partial PS processing was done using a random point threshold of 0.5 per km2, with no additional noise removal during weeding. The conventional StaMPS processing was performed using a random point threshold of 5 per km2, and I subsequently changed the weeding threshold until the mean phase noise standard deviation of the coherent interferograms matched the one obtained by the partial PS processing. The phase noise standard deviation per interferogram using both processing routines can be seen in Table 5.5. The red dates indicate the ﬁve selected semi-coherent interferograms. It must be noted that the displayed phase noise standard deviation is that obtained after weeding. The results obtained during the conventional StaMPS processing here are very close to what was obtained during analysis of the data for modelling purposes, and therefore form a good benchmark to compare with the partial PS results. After processing, I obtain several sets of selected points. For the StaMPS results, 605,218 points are selected as being stable in all 28 interferograms. The partial PS processing yields 1,216,502 stable points in the 23 coherent interferograms. As for the semi- coherent interferograms, the number of points selected is shown in Table 5.6. Fig. 5.13 shows the points selected using conventional StaMPS and Fig. 5.14 those selected using partial PS processing. Eyjafjallajökull icecap is visible as the centered region where no points are selected. The western part of Mýrdalsjökull icecap can be seen in the east.

5.2.3 Selection comparison

From the results presented in the previous section, two things can already be concluded. Firstly, as expected, the partial PS processing routine extracts more phase stable points from the coherent interferograms than conventional StaMPS does from the full set. In fact, double the points are extracted by the partial PS routine, at the same noise standard deviation. In other words, more points get extracted at no extra cost in noise levels. Secondly, from the semi-coherent interferograms, a signiﬁcant number of points are extracted by the partial PS routine, with a lower phase noise standard deviation compared to those points selected by conventional StaMPS. Similar to what was seen in the simulated data results, more points get selected in many of the semi-coherent interferograms using partial PS processing than the number of points extracted using conventional StaMPS.

60 5. Partial Persistent Scatterer testcases

StaMPS Partial PS Slave date Noise std [deg] Noise std [deg] 18-Jun-2009 36.72 33.63 29-Jun-2009 34.99 31.75 10-Jul-2009 38.73 34.69 21-Jul-2009 38.81 34.26 01-Aug-2009 31.38 28.81 12-Aug-2009 33.33 31.23 03-Sep-2009 37.39 35.72 14-Sep-2009 32.94 30.20 25-Sep-2009 42.37 37.57 06-Oct-2009 42.74 47.64 17-Oct-2009 41.04 40.88 28-Oct-2009 33.07 33.50 08-Nov-2009 35.24 36.84 19-Nov-2009 48.26 48.62 04-Feb-2010 66.83 39.67 20-Mar-2010 52.21 39.66 31-Mar-2010 53.07 40.12 11-Apr-2010 43.80 54.97 22-Apr-2010 51.07 58.47 03-May-2010 40.28 47.55 14-May-2010 49.63 51.54 25-May-2010 69.10 39.46 05-Jun-2010 53.43 40.23 16-Jun-2010 46.42 49.17 08-Jul-2010 41.06 40.17 19-Jul-2010 42.39 39.56 30-Jul-2010 42.08 39.10 10-Aug-2010 40.53 38.49 01-Sep-2010 47.42 44.26 Mean 40.48 40.36 Table 5.5: Estimated phase noise standard deviations per interferogram for both the conventional StaMPS and the partial PS selection results.

61 5. Partial Persistent Scatterer testcases

Figure 5.13: Wrapped phase values of selected points using conventional StaMPS selection on the interferograms covering the Eyjafjallajökull eruption. Semi-coherent interferograms are indicated by the red boxes.

62 5. Partial Persistent Scatterer testcases

Figure 5.14: Wrapped phase values of selected points using partial PS selection on the interferograms covering the Eyjafjallajökull eruption. Semi-coherent interferograms are indicated by the red boxes.

63 5. Partial Persistent Scatterer testcases

Slave date Points selected 04-Feb-2010 572454 20-Mar-2010 712373 31-Mar-2010 763902 25-May-2010 390885 05-Jun-2010 897769 Table 5.6: Number of points selected in the ﬁve semi-coherent interferograms using the partial PS routine.

The influence that the low coherence images have on the high coherence images is illustrated by Fig. 5.15. It shows the conventional StaMPS and partial PS results for one of the coherent interferograms. As the phase noise standard deviation from Table 5.5 indicates, the noise levels are approximately even. The additionally selected points in the partial PS results clearly add to the signal, but not to the noise. Furthermore, in several areas there is signal present in the partial PS results, which cannot be found in the conventional StaMPS results. Especially in areas prone to snowcover, like the north and close to the icecap, partial PS finds many more points. In this case, the points close to the icecap are very valuable, since this is where the intrusion took place. Several extra fringes can be seen on the south side of the icecap as a results of the extra points. The difference in the number of points selected for the semi-coherent interferograms using the partial PS routine, see Table 5.6, indicates the difference in quality between the five semi-coherent interferograms. The selection results using both selection methods for the five interferograms are shown in Fig. 5.16 to 5.20. The selection results can be divided into three groups, based on the quality of their results. The three groups will be discussed in turn below. The results for the March 31st and June 5th 2010, given by Fig. 5.16 and 5.17 respectively, both show a decrease in noise in the partial PS results, compared to the conventional StaMPS results. Furthermore, more signal can be detected in the partial PS results, especially in the areas close to the Eyjafjallajökull icecap. The combined effects of the additional points selected by using just the highest coherence images, together with treating each low coherence image separately, yielded 50 % extra points in these interferograms. Another thing to note is that these two images most likely have different decorrelation sources. The March 31st interferogram is likely to be affected by snow cover, as the point

64 5. Partial Persistent Scatterer testcases

(a) Conventional StaMPS (b) Partial PS

Figure 5.15: Wrapped phase values of selected points in the July 8th 2010 coherent interferogram, using conventional StaMPS and partial PS processing. The StaMPS result contains 628,238 points and has a phase noise standard deviation of 41.33 degrees, while the partial PS result contains 1,216,502 points and has a phase noise standard deviation of 40.17 degrees. density is low in the north, and in the area just west of the Eyjafjallajökull icecap. The June 5th interferogram is likely to be affected by tephra fallout resulting from the explosive phase of the Eyjafjallajökull eruption. The fine ash particles distributed relatively evenly over the area under the influence of strong winds sweeping over the mountain, thus affecting the entire region instead of specific areas. The second group is formed by the February 4th and March 20th 2010 results, which can be seen in Fig. 5.18 and Fig. 5.19 respectively. These two interferograms form the group where there is still signal in large parts of the interferogram, but where snow has decorrelated several large areas as well. Around Eyjafjallajökull itself, the signal is generally good in these two interferograms, except for close to the icecap, where the altitude is higher. In both cases however, the area to the north-east of Eyjafjallajökull is affected by decorrelation. The removal of semi-coherent PS points based on the ratio of points rejected in the area clears up most of the artefacts introduced by the band-pass filter. Conventional StaMPS has relative few points selected in this area, and the points that are selected are of low quality, at least in these images. In the February 4th image, partial PS does a good job of separating noise from signal. The signal in the north east is interrupted, but is spatially

65 5. Partial Persistent Scatterer testcases

(a) Conventional StaMPS (b) Partial PS

Figure 5.16: Wrapped phase values of selected points in the March 31st 2010 semi- coherent interferogram, using conventional StaMPS and partial PS processing.

(a) Conventional StaMPS (b) Partial PS

Figure 5.17: Wrapped phase values of selected points in the June 5th 2010 semi-coherent interferogram, using conventional StaMPS and partial PS processing.

66 5. Partial Persistent Scatterer testcases

correlated over a longer area than expected from low-pass filter artefacts. A surprising amount of points get selected high up on the flanks of Eyjafjallajökull, but the selected points do appear coherent. The March 20th partial PS result has far less points on the flanks. Comparing the removed points to the conventional StaMPS result, it can be seen that the area where these points are absent is indeed highly decorrelated, indicating that the points are correctly removed by the partial PS routine. In the north east, some filter artefacts possibly remain. It is not possible to distinguish here if it is an unfortunate distribution of random points that causes this, or if there are a few coherent points in this area which are surrounded by many random points with similar phase values.

Interesting to note at this point is the fact that in the conventional StaMPS results, both the March 31st and the June 5th result seem to have nearly the same phase noise standard deviation, even slightly higher, than the March 20th interferogram, see Table 5.5. Indeed, comparing the conventional StaMPS result in Fig. 5.16 and 5.17 to Fig. 5.19, it is difficult to determine which has the lowest coherence. But after partial PS processing, the first two interferograms seem to have much more signal on the flank than the latter interferogram. This builds the case for partial PS processing; It is hard to determine which images to remove from the series to produce optimal results. With partial PS processing, a similar choice has to be made for which images to process as semi-coherent. However, the fact that the semi-coherent images are not completely removed, but instead analysed separately, makes the choice easier. The images with high phase noise standard deviation can be processed as semi-coherent interferograms. If they have signal, it will get extracted. So although with conventional StaMPS the same results can be obtained for the coherent interferograms by just removing the semi-coherent images from the time series, the advantage of partial PS processing lies in that any information in these semi-coherent interferograms is preserved.

The ﬁnal group is formed by the May 25th interferogram, which is shown in Fig. 5.20. This is the most decorrelated interferogram in the stack, which shows by the large amount of noise in the conventional StaMPS result, as well as relatively small amount of points selected in the partial PS result. The partial PS routine does extract what little signal there is, but overall the point density is quite low. It is unlikely that much information can be extracted from this interferogram, which suffers from heavy decorrelation, most likely due to a tephra layer covering the surface.

67 5. Partial Persistent Scatterer testcases

(a) Conventional StaMPS (b) Partial PS

Figure 5.18: Wrapped phase values of selected points in the February 4th 2010 semi- coherent interferogram, using conventional StaMPS and Partial PS processing.

(a) Conventional StaMPS (b) Partial PS

Figure 5.19: Wrapped phase values of selected points in the March 20th 2010 semi- coherent interferogram, using conventional StaMPS and Partial PS processing.

68 5. Partial Persistent Scatterer testcases

(a) Conventional StaMPS (b) Partial PS

Figure 5.20: Wrapped phase values of selected points in the May 25th 2010 semi-coherent interferogram, using conventional StaMPS and partial PS processing.

5.2.4 Phase unwrapping

The unwrapped phase values for all interferograms are shown in Fig. 5.21 for conventional StaMPS and in Fig. 5.22 for partial PS processing. Clearly, the additional signal extracted by partial PS processing around the icecap has its effect on the unwrapped phase as well. This not only holds for the coherent interferograms, but also for a large part of the semi-coherent interferograms. An unfortunate side-effect of the additional selected points in some of the partial PS results can be seen in the difference of unwrapped phase value between the areas furthest away from the icecap, in the north and south. As there is no deformation expected in these areas, they should have approximately the same phase value. In some interferograms, this is not the case. A particularly striking example of this is the September 1st 2010 interferogram. Although this difference between north and south is also visible in the conventional StaMPS result, in the partial PS results the effect clearly is larger. The likely culprits here are the extra points selected on Fimmvörðuháls, which allow the unwrapping algorithm to take this path more easily. Ambiguities caused by a lack of point density in this highly deforming area most likely caused the difference in phase between north and south. Although unfortunate, this unwrapping error is not caused

69 5. Partial Persistent Scatterer testcases

(directly) by the selection routine. If these results have to be used for modelling, the unwrapping errors would have to be ﬁxed, either by reducing the amount of points selected, or by preventing the unwrapping algorithm from taking the path over Fimmvörðuháls. For testing purposes of the selection routine, the errors are however acceptable. In the course of this section, a comparison was given between the conventional StaMPS and the partial PS point selection routines. I showed that partial PS processing successfully selects more points in the images with good coherence. In the selected semi-coherent interferograms, distinguishable signal in the images is preserved, and gets extracted with far less noise compared to conventional StaMPS.

70 5. Partial Persistent Scatterer testcases

Figure 5.21: Unwrapped phase values for selected points using conventional StaMPS for all epochs. The semi-coherent interferograms are indicated by a red box.

71 5. Partial Persistent Scatterer testcases

Figure 5.22: Unwrapped phase values for selected points using the partial PS routine for all epochs. The semi-coherent interferograms are indicated by a red box.

72 CHAPTER SIX

KATLA

In Chapter 1, the goal of this study was defined as extracting deformation signals around Katla that could explain the residual horizontal movement detected by GPS measurements, shown in Fig 1.2. This was to be achieved by using InSAR processing techniques. Every- thing described in the previous chapters was aimed at reaching these goals. This chapter describes the InSAR processing chain performed on data covering Katla, from data selection to interpretation of the results. The choice of data was constrained by data availability and the expected movement direction. Although data choice often seems a trivial step, the effects the choices can have on the final results are very large, and should thus be made consciously. After selection of the data, it was processed using the techniques described in previous chapters. The partial PS processing extension to StaMPS was developed specifically with problems in mind that were encountered during the initial analysis of the Katla data. It has proven its worth during the final processing of the data, almost doubling the amount of points extracted. During the analysis of the PS processing results, the contribution of several sources to the total signal had to be separated. As the interest of this study was mainly deformation around Katla, long wavelength signals were removed as much as possible, leaving only deformations with smaller spatial extent. This chapter will follow the general outline described above. Section 6.1 will give an overview of the data selection. The processing strategy and initial results are discussed in

73 6. Katla

Section 6.2. The removal of long wavelength signals is dealt with in Section 6.3. A comparison between the InSAR results and GPS data will be given in Section 6.4. Concluding this chapter is a discussion of the ﬁnal results, which is done in Section 6.5.

6.1 Data selection

The residual south-westward movement at the two continuous GPS stations SOHO and HVOL was detected after the 2000 unrest of Katla, and discussed in 2006 [Geirsson et al., 2006]. Between 2006 and 2009, the start of this project, the residual movement seemed still present. Within the period between 2000 and 2009, two ESA SAR satellites were operational, although neither of them covers the whole period. The European Remote-Sensing (ERS) satellite mission composes two largely identical satellites. The ﬁrst, ERS-1, was launched in July 1991, and failed in March 2000. By that time, its successor, ERS-2, was already in orbit for 5 years, having been launched in March 1995. ERS-2 remains in orbit to this day, still collecting data. However, a failure of the gyroscopes in 2001 has degraded the quality of SAR data for radar interferometry purposes signiﬁcantly after this time. The follow-up mission of the ERS programme is the Envisat satellite. It was launched in March 2002, and remains in orbit till present day. In October 2010 however, ESA changed the orbit of Envisat. Envisat data clearly covers a much larger part of the period of interest. Furthermore, data remained available until the start of this project, which would also provide information on how ground surface movements continued after previous studies. As the main system parameters for Envisat and ERS, like resolution, frequency and swath width, are nearly identical, the choice was made to use Envisat data. The Envisat satellite orbits in a sun-synchronous orbit, revisiting the same scene every 35 days. The Advanced SAR (ASAR) instrument on board operates in the C-band, at a wavelength of 5.6 cm. In this study, only the imaging mode was considered, which provides images with 100 km swath width and approximately 30 m resolution in both range and azimuth directions. Table 6.1 summarizes Envisat’s system and image characteristics. An InSAR study using descending data over the Katla area provided no explanation for the residual deformation detected by GPS [Hooper and Pedersen, 2007]. This moved the choice of which type of data to use away from descending and towards ascending data. The choice was also largely based on the expected direction of movement. InSAR

74 6. Katla

System parameters Mean orbital height 800 km Orbit repeat cycle 35 days Orbit inclination 98.55◦ Radar frequency C-band Radar wavelength 56 mm Look direction Right Incidence angle 15◦-45◦

Image parameters Swath width 100 km Azimuth resolution 30 m Ground range resolution 30 m Table 6.1: Orbit and system parameters of the Envisat instrument, as well as image characteristics.

deformation measurements are in radar LOS, and deformations in azimuth direction are therefore not observed. Azimuth direction for descending tracks would be approximately in south-west direction, resulting in very poor sensitivity of the interferometric measurements to the expected residual movement. The sensitivity of ascending tracks to the expected deformation would be superior, although the expected movements could still be around the noise levels. The choice for ascending data was made based on these two factors.

After looking at the data availability for ascending tracks over the area, I selected the only track that had sufﬁcient radar images and covered the entire area of Katla. Fig. 6.1 shows the selected scene superimposed on a satellite image of the area surrounding Katla. The scene covers all of Katla, as well as the majority of Eyjafjallajökull. The scene extends far to the east, reaching all the way to Vatnajökull. The acquisition dates of the available images in the selected track are listed in Table 6.2. The image acquired on the 22nd of July, 2007, was selected as the master image, based on maximizing the expected stack coherence. The perpendicular baseline with respect to this master is given as well in Table 6.2.

75 6. Katla

Figure 6.1: The selected track, displayed in light green, superimposed on a satellite image of the area surrounding Katla. For reference, Katla is shown inside the pink rectangle.

Date Baseline [m] Date Baseline [m] 13-Jul-2003 -383 19-Nov-2006 271 23-May-2004 -419 13-May-2007 -212 27-Jun-2004 156 22-Jul-2007 0 01-Aug-2004 31 26-Aug-2007 267 10-Oct-2004 -1014 30-Sep-2007 -254 12-Jun-2005 223 01-Jun-2008 -90 17-Jul-2005 -207 06-Jul-2008 -87 21-Aug-2005 585 10-Aug-2008 182 25-Sep-2005 -737 14-Sep-2008 -566 30-Oct-2005 -420 19-Oct-2008 52 15-Oct-2006 -501 30-Aug-2009 235 Table 6.2: Image acquisition dates and perpendicular baselines w.r.t. the selected master, the 22nd of July 2007. The red dates indicate the interferograms that were chosen as partial interferograms based on the phase noise standard deviation after initial processing results.

76 6. Katla

6.2 InSAR processing

The selected dataset was focused using scripts from the ROI_PAC software package. Using the resulting SLCs, I created 21 topographically corrected and ﬂattened interferograms. A 1 arc-second resolution DEM, acquired by the ASTER satellite mission, was used to remove the topographic phase. The DEM data is owned by the Japanese Ministry of Economics, Trade and Industry (METI) and the United States National Aeronautics and Space Admin- istration (NASA), and is made available freely for scientiﬁc use. I analysed the 21 interferograms using the partial PS routine, selecting 7 interferograms as semi-coherent, based on the phase noise standard deviations of earlier processing attempts. The semi-coherent interferograms are indicated by the red dates in Table 6.2. The distribution of the semi-coherent interferograms shows one of the reasons for the development of the partial PS extension. Many of the low coherence images are concentrated in the period between Fall 2004 and Fall 2006, a period where data was already sparse. Removal of the worst images from the stack would have meant large gaps in the timeseries. By using the partial PS routine, I was able to extract as much information as possible in that time period. For the processing, I set the allowable number of random points to 2 per km2. This resulted in 540,013 points being selected in the coherent interferograms. The amount of points selected for the seven semi-coherent interferograms is shown in Table 6.3. A large difference in the amount of selected points can be observed in the results. The worst interferograms have less than 100,000 points per interferogram. In the case of the 10th of October 2004, this could be explained by the perpendicular baseline being very large. The 30th of October 2005 image however does not have an extremely large baseline, and is likely to be affected by snow cover. Interesting is also the 19th of October 2008 image, which has a very small baseline, but still was relatively noisy during conventional StaMPS processing, as it was selected as a semi-coherent interferogram. Likely there is snow cover present in this image, but partial PS still manages to extract a large amount of coherent pixels. The wrapped phase values of the selected points can be seen in Fig. 6.2. Coherent signal can be seen in all of the coherent interferograms. In some of the semi-coherent interferograms, indicated by a P behind the date, clear signal is also observable. In the

77 6. Katla

Slave date Points selected 10-Oct-2004 89215 21-Aug-2005 288531 25-Sep-2005 161356 30-Oct-2005 70727 19-Nov-2006 115419 14-Sep-2008 335039 19-Oct-2008 313933 Table 6.3: Number of points selected for the Katla Envisat data in the seven semi-coherent interferograms. two images with the least amount of points, the 10th of October 2004 and 30th of October 2005, little signal is detectable. This is partly due to the low point density in most places. Undersampling of the wrapped signal and other unwrapping errors could occur in these images during unwrapping, however the correlation of the deformation in time should have aided the three dimensional unwrapping routine to minimize these effects. The detrimental effect of these images on the stack was deemed minimal due to the combined efforts of partial PS processing and the three dimensional unwrapping routine, and I therefore opted to let these two images remain in the stack. I unwrapped these points using the three-dimensional unwrapping scheme adapted for partial PS and removed master atmosphere, master orbit errors and look angle error, as described in Section 4.4. The unwrapped phase values, with the nuisance terms removed, can be seen in Fig. 6.3. In this figure, positive phase difference represents movement away from the satellite. Note that slave atmosphere signals and orbit errors are still present in the data. A relatively strong signal, correlated in time, increases in magnitude from south west to north east, the direction of Vatnajökull. The signal has a negative phase difference, meaning the vertical component of this movement represents uplift. The unwrapped interferograms indicate that the deformation gradually increases in time. This is confirmed by the time series of unwrapped displacements shown in Fig. 6.4. The first three time series are at the three continuous GPS stations south of Katla, the fourth was taken close to Vatnajökull in the north east of the scene. Given the correlation in time of the deformation velocity, as well as the continuous velocity of the residual motion detected by GPS, the estimated LOS velocity from the timeseries is a more convenient vi- sualisation of the results for the purpose of this study. The velocity values are less affected

78 6. Katla

Figure 6.2: Wrapped phase values of selected points in the Envisat track 87 data. The semi-coherent interferograms are indicated by a P behind the date.

79 6. Katla

Figure 6.3: Unwrapped phase values of selected points in the Envisat track 87 data. The master contribution to the atmosphere and orbit error have been removed, as well as the look angle error. The semi-coherent interferograms are indicated with a P behind the date. The unwrapped phase values have been re-referenced from the master (22 July 2007) to the ﬁrst image (13 July 2003). Positive phase differences represents movement away from the satellite. The asterisk in the top left corner of every image represents the spatial reference area.

80 6. Katla

Figure 6.4: Time series of unwrapped displacements at four locations in the Katla scene. The center value is the mean value of the 50 closest points to the selected location, the error bar represents the standard deviation of these 50 points. The ﬁrst points have zero standard deviation, as this is the reference interferogram. Blue points are from coherent interferograms, the red points are taken from semi-coherent interferograms. Location I, II and III are THEY, SOHO and HVOL continuous GPS stations, respectively. Location IV is near Vatnajökull icecap. The locations are indicated by black dots in the velocity plot of Fig. 6.5.

by atmospheric signals, and thus give a smoother picture of the results. Fig. 6.5 shows the velocity plot, estimated using the unwrapped phase values, after removal of the look angle error. Points from the semi-coherent interferograms were used in the estimation of the velocity, whenever available. The locations from which the four time series of Fig. 6.4 were taken are indicated in the velocity plot as well. In the time series and velocity plot, relative positive displacements and velocities, respectively, are towards the satellite. The sign convention is thus reversed with respect to the unwrapped individual interferograms of Fig. 6.3. This was done to make uplift show as positive velocities, making it more intuitively interpretable.

The velocity plot shows again the strong signal towards the satellite coming from Vat- najökull. Besides this signal, also apparent is a signal at Torfajökull, a volcanic system to

81 6. Katla

Figure 6.5: Estimated velocity in mm/yr using the unwrapped phase values with the look angle error removed. Relative positive velocities are towards the satellite. The asterisk indicates the spatial reference area. Locations I, II and III are THEY, SOHO and HVOL continuous GPS stations, respectively. Location IV does not represent a GPS station, but was chosen as it is close to Vatnajökull, approximately 15km to the east.

82 6. Katla

the north of Katla, showing movement away from the satellite with respect to its surroundings. The last major signal in the velocities is the signal which seems to curve around Katla in the south and west of the plot. These signals will be interpreted and explained further on in this chapter.

6.3 Long wavelength signals

Considering the goal of this study, which was explaining the residual movement on Katla’s south flank, two signals present in the velocity plot could obscure any signal in this area. Firstly, it is known that Envisat data suffers from systematic orbital ramps, in the order of 15 mm/yr over 100 km [Ketelaar, 2009]. Secondly, there is a GIA uplift signal expected, largely coming from Vatnajökull, but also locally influenced by the smaller icecaps in the area, namely Mýrdalsjökull, Eyjafjallajökull, Torfajökull and Tindfjallajökull [Árnadóttir et al., 2009]. Orbital ramps are easily estimated due to their linear nature, as long as there is no deformation signal covering the entire interferogram as well. A very long wavelength deformation signal will bias the estimation of the ramp, which can therefore not be reliably estimated. Models of the GIA signal show that in the area covered by the interferograms, the vertical uplift velocities caused by GIA range from 6 mm/yr at the coast south of Katla to 13 mm/yr in the north east, close to Vatnajökull [Árnadóttir et al., 2009]. The maximum relative velocity that could result from this in the InSAR velocities is about 7 mm/year in LOS, if the relatively small influence of the horizontal components is ignored for now. The GIA signal alone can therefore not explain the 25 mm/yr relative deformation found in the Envisat results, see Fig. 6.5. Furthermore, the signal does not seem sufficiently linear in space to be fully caused by an orbital ramp. The most likely explanation thus is that the long wavelength signal is caused by a combination of the two phenomena. In order to reveal local deformations around Katla, I had to remove the orbital ramp from the InSAR measurements, or at least limit its effects. The orbital ramp could not be reliably estimated with the long wavelength GIA signal entangled in it. I therefore chose to estimate and remove both long wavelength signals from the InSAR results. This section will describe the way in which this was achieved.

83 6. Katla

Layer Thickness [km] Poisson’s Viscosity Young’s Density ratio [Pa s] modulus [GPa] [kg/m3] 1 10 0.25 ∞ 40 2800 2 30 0.25 1020 130 3200 3 ∞ 0.5 1019 130 3200

Table 6.4: Earth model properties used during the GIA modelling [Árnadóttir et al., 2009]. Layer 1 represents the top layer, layer 3 the bottom layer.

GIA signal

In order to estimate the orbital ramp without bias from the GIA deformation, I had to remove the long wavelength part of this signal. In recent years, the applications of modelling techniques in geodynamical processes has made great progression. Computers have become powerful enough to perform complex Finite Element Modelling (FEM) models on normal desktop processing units, which makes modelling surface deforming phenomena, like GIA, much more accessible. For Iceland, several recent studies have modelled GIA deformations using FEM, constrained by GPS measurements, see e.g. [Pagli et al., 2007; Árnadóttir et al., 2009; Albino et al., 2010; Sigmundsson et al., 2010a]. One of these studies attempted, quite successfully, to model the GIA signal throughout Iceland [Árnadóttir et al., 2009]. Fig. 6.6 shows one of their models for the approximate area covered by the InSAR scene. The model consists of a compressible elastic top layer, a visco-elastic compressible intermediate layer and a visco-elastic incompressible mantle. Table 6.4 gives the properties of the layers used in the model. The model velocities are shown in Fig. 6.6, together with the residuals compared to the vertical components of the GPS measurements data. To compare the model to the InSAR results, I projected the three components of the GIA signal (North, East and Up) to the radar LOS. The LOS unit vector for every point was computed using the method described in Appendix A. The GIA model velocities in radar LOS are shown in Fig. 6.7. From the range of velocities, a little over 5 mm/yr, it is conﬁrmed that GIA alone cannot explain the velocities in the InSAR results, see Fig. 6.5. The pattern of the GIA does however resemble the pattern of the estimated velocities, albeit that the InSAR results look somewhat more linear towards the east. The curving of the signal around Katla on the south and west sides appears in the model as well, which represents the effect of Mýrdalsjökull on the GIA signal.

84 6. Katla

Figure 6.6: GIA model in the Mýrdalsjökull area. The left image shows the modelled deformation signal. The colours represent vertical movement, the arrows show the horizontal movement. The model was obtained by using FEM, constrained by combined campaign and continuous GPS measurements between 1993 and 2004, as described in [Árnadóttir et al., 2009]. Residuals with respect to the GPS vertical deformations are shown on the right. Model data and image courtesy of Uppsala University.

Figure 6.7: Modelled GIA velocities projected onto the radar LOS. Note that the modelled velocities shown here represent absolute velocities, while the InSAR results from e.g. Fig. 6.5 represent relative velocities. Positive velocities are towards the satellite.

85 6. Katla

Figure 6.8: Residual velocity after removal of the modelled GIA signal from the InSAR results. Positive velocities are towards the satellite. The asterisk indicates the spatial reference area, and the three black dots indicate from left to right the locations of THEY, SOHO and HVOL continuous GPS stations.

I used the GIA model to subtract the expected deformation signal from the velocities obtained from the InSAR timeseries. Fig. 6.8 shows the remaining signal. In doing this, I disentangled the long wavelength GIA uplift signal from the orbital ramp. As expected, a considerable amount of long wavelength signal remains. Removing the expected GIA signal does make the signal more linear, especially in the east, away from the smaller icecaps. It is likely that some GIA signal remains in the residual velocity of Fig. 6.8, due to residual velocities in the model compared to the GPS results. These residual GIA signals should however not have a signiﬁcant linear component, thus allowing estimation and removal of the orbital ramp.

Orbital ramp

The removal of the GIA signal from the velocity plot allowed me to estimate a linear trend in the velocities, which represented the systematic orbital ramp. I used unweighted

86 6. Katla

Figure 6.9: Estimated systematic orbital ramp. The estimation was done on the InSAR velocities, after removal of the modelled GIA signal. least-squares estimation to estimate the linear trend in the signal. The estimated ramp is displayed in Fig. 6.9. I removed the estimated signal from the velocities. With both long wavelength signals removed, the velocities that remain represented any deformation not contained in the GIA model. The residual velocities are shown in Fig. 6.10. The large deformation signal at Torfajökull in the north persists, as expected, since this is a local effect. The signal coming from Vatnajökull in the north east is however mostly removed. Finally, some residual velocities around Eyjafjallajökull appeared, previously largely obscured by the long wavelength signals.

6.4 Comparison to GPS data

The GPS data from the three continuous stations in the area provides a very interesting opportunity for comparison with the InSAR results, as well as validation of those results. Fig. 6.11 shows the east, north and up components of the deformation measurements at

87 6. Katla

Figure 6.10: Residual velocities after removal of both long wavelength signals. Positive velocities are towards the satellite. The asterisk indicates the spatial reference area, and the three black dots indicate from left to right the locations of THEY, SOHO and HVOL continuous GPS stations.

88 6. Katla

THEY,SOHO and HVOL GPS stations. The displacements shown are relative to the REYK station in Reykjavík, which is on the North-American tectonic plate. As the three stations are on the Eurasian plate, the full plate spreading velocity between these two plates are present in the data. The processed data were obtained from the Icelandic Meteological Office (IMO). The final row in Fig. 6.11 shows the projection of the three deformation components on the radar LOS. The conversion was done using the method described in Appendix A. The LOS velocities are plotted such that movement towards the satellite is positive. The GPS LOS velocities confirm that SOHO and HVOL have a higher velocity towards the satellite than THEY. This comes mostly from the vertical component, although the north component has some influence as well. The estimated LOS velocities at THEY, SOHO and HVOL are 2.01, 8.02 and 5.78 mm/yr, respectively. It must be noted that this is including the GIA signal, while the final InSAR velocities do not include these terms. Furthermore, the LOS velocities for GPS are an absolute quantity, while the InSAR results should be interpreted in a relative sense. To allow for a comparison between GPS and InSAR measurements, the GIA model was subtracted from the GPS LOS velocities. Furthermore, to account for the plate spreading in the GPS velocities, the spreading rates of the Eurasian plate compared to the North Amer- ican plate were calculated using the Nuvel-1A model [DeMets et al., 1994]. According to the model, the Eurasian plate moves away from the North American plate with rates of -4.7 mm/yr in north direction and 18.3 mm/yr in east direction. I projected the spreading rates on the radar LOS, and removed them from the GPS velocities. This meant that the residual GPS velocities are the absolute LOS residual velocities compared to the GIA model, under the assumption the plate spreading rates are accurate. To reference the InSAR with the GPS observations, I estimated the offsets between the relative InSAR velocities and the absolute GPS velocities in a least-squares sense, using the offsets at the three GPS stations as observations. I added the estimated offset to the InSAR velocities, making them absolute residual velocities, with respect to the GIA model and the Eurasian plate. Fig. 6.12 shows a velocity profile, running from THEY, through SOHO, up to HVOL GPS station. The InSAR velocities are shown in blue, and the GPS velocities at the three GPS stations are plotted on top. The agreement between GPS and InSAR is good, indicating that the InSAR results are reliable. The reason for removing

89 6. Katla

Figure 6.11: GPS deformations at THEY, SOHO and HVOL stations, in the north, east, up direction, as well as the LOS projection of the deformations. The green lines in the LOS plots are the estimated GPS LOS velocities. Data courtesy of the IMO.

90 6. Katla

the plate spreading rates from the GPS now becomes clear: This made the zero velocity in the proﬁle plot represent the GIA model that was removed, and the residual LOS velocities here thus show the agreement of the GPS and InSAR measurements to the modelled values, in LOS direction.

6.5 Discussion

The large signal to the north that dominates the residual velocities of Fig. 6.10 is at Torfa- jökull icecap and volcanic system. It shows a negative LOS displacement of approximately 1.5 cm/yr with respect to its surroundings. Although there have been no eruptions of Tor- fajökull in the last 500 years, seismic observations have indicated the presence of a large, solidified and cooling magma chamber below the central volcano [Soosalu and Einarsson, 2004]. A cooling magma body contracts, resulting in subsidence at the surface, which explains the negative residual velocities detected. More subtle, but also more interesting for this study, is the signal at Eyjafjallajökull. Especially on the south flank, a decrease in velocity can be seen. This area extends all the way to the THEY GPS station, indicated by the most westerly black dot in Fig. 6.10. Furthermore, at SOHO and HVOL, the two GPS stations on Katla’s flank, no significant movement is detected with respect to its surroundings. The conclusion reached by [Sturkell et al., 2008], that the unexpected movement seen in the horizontal GPS measurements was caused by a local magma source, seems unlikely due to this lack of relative movement. This confirms the conclusion reached by the InSAR study using descending data [Hooper and Pedersen, 2007]. In fact, the residual velocities indicate that it is actually THEY station that is being influenced by a local source. The profile plot in Fig. 6.13 also implies that a local source under Mýrdalsjökull is unlikely to be the cause of the residual horizontal movement at SOHO. The profile runs from the coast through SOHO, and continues towards Vatnajökull. No significant relative deformation can be seen at SOHO compared to the coast, as well as compared to the oppo- site side of the icecap. It must be noted here that the residual horizontal motions detected by GPS at SOHO and HVOL are approximately 3 to 4 mm/yr in magnitude. Converting these to radar LOS would result in velocities around 1 mm/yr under the best conditions, which is around the noise level of the InSAR results. This means that if the movement

91 6. Katla

Figure 6.12: InSAR velocity profile referenced to the GPS LOS velocities. Displayed velocities represent the absolute residual velocities, with respect to the expected plate spreading velocities, predicted by the Nuvel1-A model, and the GIA model. Positive velocities are towards the satellite. The profile starts at THEY, goes in a straight line to SOHO, and changes direction slightly to end at HVOL. The profile path is shown on the original velocity plot, shown below the profile plot as the red line. The plotted velocity in the profile represents the mean value of all points within an area approximately 1.5 km in diamater, and the error bar represents the standard deviation of the values within this area. The estimated GPS velocities at THEY, SOHO and HVOL are shown by the magenta, red and green points, respectively.

92 6. Katla

Figure 6.13: Profile of the residual velocities referenced using GPS. Positive velocities are towards the satellite. The profile starts at the coast, passes through SOHO, and continues towards Vatnajökull. The profile path is shown on the original velocity plot on the right as the red line. The plotted velocity in the profile plot represents the mean value of all points within an area approximately 1.5 km in diamater, and the error bar represents the standard deviation of the velocities within this area. The profile point containing SOHO is shown in red. The grey area in the profile plot represents the area covered by Mýrdalsjökull icecap. would be a purely horizontal phenomenon, it would not be detectable in the InSAR results. However, surface movements caused by magma intrusions and ice load reduction are always accompanied by larger vertical movements. This can also be expected for landslides and gravitational spreading. The vertical movements would be well above the noise levels, due to their expected magnitudes and the LOS vector being closer to the vertical. My results thus show that the hypothesis of a local deformation source, like magma intrusion or landslides, at Katla is not plausible. Fig. 6.12, used in the referencing of the InSAR velocities to the GPS velocities, gives an overview of the relative deformation on Katla’s south flank. It shows a profile going from west to east between the three GPS stations. A relative deformation signal in the first 8 kilometers of the profile can be seen, which is on Eyjafjallajökull south flank. It has a magnitude of 4-5 mm/yr away from the satellite compared to the rest of the profile. Prior to the period 2003-2009 covered by the SAR data, Eyjafjallajökull last activity was in 1994 and 1999, when large inflations were detected on its south flank [Hooper et al., 2009]. I therefore conclude that the most likely explanation for the deflation signal detected here is cooling of a magma volume injected during those events. Yet to be explained is the residual horizontal movement detected by GPS, see Fig.

93 6. Katla

Figure 6.14: Map of the Mýrdalsjökull area, showing residual horizontal GPS velocities compared to the movement of the Eurasian plate, assuming a ﬁxed North-American plate. Plate velocities were calculated using the Revel model. Adapted from [Geirsson et al., 2006].

6.14, as local sources are not detected in these areas. Considering the direction of the residual movement detected by GPS, and comparing this to the direction of the horizontal components of the GIA model, see Fig 6.6, one can see a striking resemblance. It must be noted here that, since the model was constrained using exclusively the vertical GPS velocities, there is some uncertainty in the magnitude of the horizontal velocities. This explains the discrepancy in magnitude between the GPS horizontal residuals and the GIA model horizontals. I therefore conclude that the residual movement at SOHO and HVOL is likely to be the result of GIA signal, from Vatnajökull and, to a lesser extent, from Mýrdalsjökull. This conclusion however raises another question: Why is there no residual horizontal movement in the GPS results for THEY? This can, at least partly, be explained by the deformation signal at Eyjafjallajökull, which is also present at THEY. A cooling magma volume would also cause horizontal motion, although the vertical component is expected to be dominant. It remains uncertain at this point if a cooling magma volume at Eyjafjal- lajökull can cause sufﬁcient horizontal signal to fully obscure the horizontal component of the GIA signal at THEY. To test this hypothesis, the cooling effect inside Eyjafjallajökull would have to be modelled, and the magnitude of the horizontal GIA component from the

94 6. Katla

GIA model results would have to be better constrained. During the referencing of the relative InSAR velocities to the absolute GPS velocities, the plate spreading rates were removed. This meant that, assuming uncertainties in the plate spreading rates to be negligible, the zero level in the profile plots, shown in Fig. 6.12 and 6.13, represents the GIA model. Several things can be concluded from this. Firstly, it seems that the low residual at THEY, also seen in Fig. 6.6 is actually somewhat misleading. The InSAR results imply that the area around THEY is affected by a local deformation source, and that the larger residuals at SOHO and HVOL are representative for the entire south side of Katla and Eyjafjallajökull. From the profile in Fig. 6.13, it seems an overall positive offset of 1-2 mm/yr might be present in the LOS velocities. As the vertical fits quite well east of Mýrdalsjökull, see the right side of Fig. 6.6, this could indicate that the horizontal components of the GIA are underestimated. Also, it is possible that the orbital ramp was not estimated accurately enough, and that this causes a residual over long distances. In order for the InSAR velocities to be helpful in constraining the GIA model, additional GPS data from e.g. campaign measurements would be necessary to check the estimated orbital ramp and aid in the referencing of the InSAR velocities. In this chapter, I have discussed the processing strategy used on the Katla data. I have shown how the data was chosen based on the availability of images and the expected direction of the movements. The value of the partial PS extension to StaMPS was demonstrated on the data for which it was initially developed for. Using the processing routine, I was able to obtain 21 interferograms, showing deformation signals correlated in time. Two long wavelength signals had to be removed from these results, one caused by a physical phenomenon, GIA, and one caused by the measurement platform, orbital ramps. After removal of these signals, I was able to exclude a local magma source as being the cause for the horizontal residuals detected by GPS. I concluded that the residual movements were most likely caused by the horizontal components of the GIA signal. I also showed that the station with no residual movement compared to plate spreading, THEY, was under the influence of a local deformation source, most likely a cooling magma volume under Eyjafjallajökull.

95 6. Katla

96 CHAPTER SEVEN

CONCLUSIONS AND RECOMMENDATIONS

This study set out to extract deformation signals on around Katla, and explain the residual horizontal velocities detected by GPS. In doing this, I tried to increase the knowledge of processes going on around Katla speciﬁcally, but also volcanoes in general. To achieve this, the work done can be split up into two parts; The ﬁrst part was aimed at extracting as much signal as possible from the available data, and lead to the development of the partial PS processing extension to the StaMPS software. The second part was focussed on explaining the signal, and was composed of post-processing the InSAR results and extracting the signals that could help me explain the movements at Katla. Both parts led to a set of conclusions and recommendations, which will be discussed in this chapter.

Conclusions

I have shown how the partial PS processing routine mitigates the effects that low coherence images have on the rest of the interferogram stack. From the high coherence images that form the coherent set, I extract a signiﬁcantly larger amount of points, up to double the amount, compared to conventional StaMPS, without increasing noise levels. This is done by excluding the low coherence images from the phase stability analysis. For the low coherence images that make up the semi-coherent set, I reduce noise levels considerably, while conserving any signal that is present in these interferograms. In areas where no signal is present, very few points get selected, especially compared to conventional StaMPS. Tests performed during this study show that the combined effects described above generally lead

97 7. Conclusions and recommendations

to more deformation signal being extracted, after unwrapping.

I applied the partial PS processing technique on 21 interferograms from an ascending Envisat track covering Katla and the area east of it. The unwrapped data showed signal correlated in time. A signal increasing in magnitude towards Vatnajökull was most prominent in the results. Initially suspected to be uplift due to GIA, after reviewing several studies into this phenomenon, the signal proved too large to be explained by GIA alone. System- atic orbital ramps, which have been detected in Envisat data before, were expected to have contaminated the results. I estimated this signal using a GIA model to remove the linear trend in the InSAR results caused by the GIA uplift signal, and estimating the remaining linear trend in the residual signal. After removal of the orbital ramp and the GIA signal, no local movements were found around the two GPS stations where the residual horizontal movement was detected, SOHO and HVOL stations. However, a local deformation signal did appear at the third station, THEY, a signal that was previously largely obscured by the long wavelength signals. I conclude from these results that SOHO and HVOL are not significantly influenced by local sources, but that in fact it is THEY that is moving due to a local source. The directions of the residual horizontal movements at SOHO and HVOL indicate that they are likely to be the result of horizontal movements due to GIA, the combined effects from Vatnajökull and Mýrdalsjökull losing ice mass over the last century. The absence of any horizontal movement at THEY could be caused by the local deformation signal, which is interpreted as a cooling of the magma volumes intruded during two events at Eyjafjallajökull in 1994 and 1999. It however remains uncertain if a cooling magma volume alone can produce sufficient horizontal movements.

Recommendations

The partial PS processing can be improved in several areas. During this study, partial PS processing was applied to datasets which were already processed using conventional StaMPS. This allowed the choice of semi-coherent interferograms to be made based on the quality of selected points in each interferogram. Ideally, partial PS should be able to be run independently, and the choice for the semi-coherent interferograms should be made during the processing. Related to that is the next recommendation, which is to change the

98 7. Conclusions and recommendations

processing routine such that instead of choosing a set of coherent and semi-coherent interferograms, each point could be evaluated separately for the quality of that point in each interferogram. This would essentially mean that for every point, the coherent and semi- coherent interferograms could be different. The main limitation for not doing this at the moment is the way in which the three-dimensional unwrapping routine is set up. While it was relatively easy to set it up for a relatively small number of different point sets, setting it up for a different set of points in every interferogram is much more complex.

Although a satisfying explanation was provided for the horizontal movement at SOHO and HVOL, this research also raised new questions, providing incentive for additional research, and exposing other applications for the data. Very interesting would be to model the subsidence detected around Eyjafjallajökull. This could be further constrained by analysing descending Envisat data, which could also shed light on the amount of horizontal motion contained in the deﬂating signal. GPS measurements in the area covered by the SAR images could be used to estimate the orbital ramp more accurately. This would also validate the InSAR results, and make them valuable in improving GIA models in the area. Finally, the track 87 scene used in this study overlaps in the east with InSAR results around the entire Vatnajökull icecap. It would be very interesting to combine the two results, and obtain a more complete picture of the widespread effects of the GIA effect.

99 7. Conclusions and recommendations

100 APPENDIX A

LINE-OF-SIGHT CONVERSION

During the analysis of the timeseries results around Katla, GPS data and GIA models were compared to the InSAR results. Since both the GPS data and GIA model were in north, east, up format, they had to be converted to radar line-of-sight (LOS). This chapter will discuss how the radar LOS unit vector is calculated using satellite metadata.

A.1 Incidence angle

Figure A.1 shows a schematic overview of the viewing geometry of a SAR satellite. From this schematic it can be seen that for an arbitrary point on the Earth surface, the look angle at the satellite towards that point, θ, is extended by the angle ψ to form the incidence angle on the ground w.r.t. the local zenith. The only unknown in Fig. A.1 is the angle ψ. The angle is however easily calculated using the Law of Cosines:

(R + h)2 + R2 − ρ2 cos ψ = e e (A.1) 2 · (Re + h) · Re

A.2 Bearing

The angle that the LOS unit vector makes in the (local) horizontal plane can be derived from the satellite heading. However, while travelling from the satellite to the scattering

101 A. Line-of-sight conversion

Figure A.1: Schematic overview of the viewing geometry of a SAR satellite. The incidence angle is the sum of the look angle at the satellite θ and the angular distance travelled ψ. Re represents the local radius of the Earth, h the height of the satellite above the Earth’s surface and ρ the range from the satellite to the point on the ground.

102 A. Line-of-sight conversion

resolution cell, the signal travels over a great arc, which makes the bearing of the LOS vector different from the bearing of the pulse at the satellite. The bearing of the LOS vector at the resolution cell can thus not be directly derived from the satellite heading, a correction has to be applied. The angular distance traversed by the signal was given by Eq. ◦ (A.1). The initial bearing of the signal θi is obtained by adding 90 to the satellite heading.

Furthermore, the latitude φs and longitude λs of the satellite are known.

The latitude φr and longitude λr of the resolution cell can be computed using:

−1 φr = sin (sin φs cos ψ + cos φs sin ψ cos βi) (A.2) and

λr = λs + atan2(sin βi sin ψ, cos ψ − sin φs sin φr). (A.3)

The bearing of projection of the LOS θLOS in the horizontal plane at the resolution cell can be calculated with:

βLOS = atan2(sin ∆λ cos φs, cos φr sin φs − sin φr cos φs cos ∆λ), (A.4)

where ∆λ = λs − λr. All equations in this section were derived from a script written by Dr. A.J. Hooper in 2007, which was also used in the computation of the bearing of the LOS vector.

A.3 LOS unit vector

The unit LOS vector is obtained by combining the two computed angles:

    uN cos βLOS sin (θ + ψ)     uLOS =  uE  =  sin βLOS sin (θ + ψ)  (A.5)     uZ cos (θ + ψ)

103 A. Line-of-sight conversion

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