InSAR Principles: [620612]

TM-19
February 2007
InSAR Principles:

Guidelines for SAR Interferometry
Processing and Interpretation

TM-19 _________________________________________________________________________ InSAR Principles
ii Acknowledgements
Authors:
Alessandro Ferretti, Andrea Monti-Guar nieri, Claudio Prati, Fabio Rocca
Dipartimento di Elettronica ed Informazione, Politecnico di Milano, Italy
Didier Massonnet
CNES, Toulouse, France
Technical coordination:
Juerg Lichtenegger
ESA/ESRIN (retired) , Frascati, Italy
Publication: InSAR Principles: Guidelines for SAR
Interferometry Processing and Interpretation
(TM-19, February 2007)
Editor: Karen Fletcher
Published and distributed by: ESA Publications ESTEC Postbus 299
2200 AG Noordwijk
The Netherlands
Tel: +31 71 565 3400 Fax: +31 71 565 5433
Printed in: The Netherlands
Price: €40
ISBN: 92-9092-233-8
ISSN: 1013-7076
Copyright: © 2007 European Space Agency

______________________________________________________________________________ Table of Contents
iii Table of Contents
Scope ………………………………………………………………………………… viii
Part A Interferometric SAR image processing and interpretation
1. Synthetic Aperture Radar basics………………………………………………… A-3
1.1 Introduction……………………………………………………………………… A-3
1.1.1 Introduction to ERS ………………………………………………. A-3
1.1.2 Introduction to Envisat…………………………………………… A-4
1.2 SAR images of the Earth’s surface ……………………………………… A-5
1.2.1 What is a strip-map SAR imaging system?……………….. A-5
1.2.2 What is a complex SAR image?………………………………. A-6
1.2.3 SAR resolution cell projection on the ground………….. A-11
2. SAR interferometry: a pplications and limits ……………………………… A-17
2.1 Introduction……………………………………………………………………. A-17
2.2 Terrain altitude measuremen t through the interferometric
phase …………………………………………………………………………….. A-18
2.2.1 Interferogram flattening ……………………………………….. A-19
2.2.2 Altitude of ambiguity …………………………………………… A-20
2.2.3 Phase unwrapping and DEM generation…………………. A-20
2.3 Terrain motion measurement: Differential Interferometry ……. A-23
2.4 The atmospheric contribution to the interferometric phase …… A-24 2.5 Other phase noi se sources………………………………………………… A-25
2.6 Coherence maps……………………………………………………………… A-26
3. SAR Differential Interferometry basics and examples ………………… A-31
3.1 Introduction……………………………………………………………………. A-31 3.2 Landers co-seismic deformation ……………………………………….. A-31
3.3 Small earthquake modelling …………………………………………….. A-33 3.4 The quiet but complicated deformation after an earthquake….. A-35 3.5 A case of coherence loss: India…………………………………………. A-37
3.6 A case of damaged raw data, studying a large earthquake in
Chile……………………………………………………………………………… A-38
Part B InSAR processing: a practical approach
1. Selecting ERS images for InSAR processing………………………………. B-3
1.1 Introduction……………………………………………………………………… B-3
1.2 Available information about ERS images…………………………….. B-3
1.2.1 The ESA on-line multi-mission catalogue ………………… B-3
1.2.2 DESCW……………………………………………………………….. B-4
1.2.3 Expected coherence (prototype)………………………………. B-6
1.3 Selecting images for InSAR DEM generation………………………. B-8
1.4 Selecting images for Differential InSAR applications……………. B-9
2. Interferogram generation ………………………………………………………… B-11

TM-19 _________________________________________________________________________ InSAR Principles
iv 2.1 Introduction……………………………………………………………………..B-11
2.2 Generation of synthetic fringes…………………………………………..B-12 2.3 Co-registering ………………………………………………………………….B-13
2.3.1 Co-registering coefficients……………………………………..B-14
2.3.2 Co-registering parameter estimation………………………..B-16
2.3.3 Implementation of resampling ………………………………..B-17
2.4 Master and slave oversampling…………………………………………..B-17
2.5 Range spectral shift & azimuth common bandwidth filtering …B-18
2.5.1 Range spectral shift filtering…………………………………..B-18
2.5.2 Azimuth common band filtering……………………………..B-20
2.6 Interferogram computation ………………………………………………..B-22
2.6.1 Complex multi-looking………………………………………….B-24 2.6.2 Generation of coherence maps………………………………..B-26
2.7 Applications of coherence ………………………………………………..B-27
2.8 Interferogram geocoding & mosaicking ………………………………B-29
3. InSAR DEM reconstruction …………………………………………………….B-31
3.1 Introduction……………………………………………………………………..B-31
3.2 Processing chain and data selection…………………………………….B-31
3.3 Phase unwrapping techniques for InSAR DEM reconstruction.B-33
3.3.1 What are we looking for?……………………………………….B-34
3.3.2 Case p=2, Unweighted Least Mean Squares method …B-37
3.3.3 Case p=2, Weighted Least Mean Squares method …….B-38
3.3.4 Case p=1, Minimum Cost Flow method…………………..B-38
3.3.5 Case p=0, Branch-Cut and other minimum L
0
methods……………………………………………………………….B-39
3.3.6 Outlook ……………………………………………………………….B-41
3.4 From phase to elevation…………………………………………………….B-42
3.4.1 Polynomial approximation of satellite orbits, point
localisation and data geocoding ………………………………B-42
3.4.2 Data resampling ……………………………………………………B-45
3.4.3 Impact of baseline errors on the estimated
topography …………………………………………………………..B-45
3.4.4 Precise orbit determination ……………………………………B-47
3.5 Error sources, multi-baseline strategies and data fusion…………B-48
3.5.1 Multi-interferogram InSAR DEM reconstruction………B-50
3.6 Combination of ascending and descending passes ………………..B-53
3.7 Conclusions……………………………………………………………………..B-55
4. Differential Inteferometry (DInSAR)…………………………………………B-57
4.1 Examples of differential interferometry on land……………………B-57
4.1.1 Physical changes …………………………………………………..B-57
4.1.2 Volcano: Okmok…………………………………………………..B-57
4.1.3 Surface rupture: Superstition Hill ……………………………B-58
4.1.4 Subsidence: East Mesa…………………………………………..B-60
4.2 Example of differential interferometry on ice ………………………B-62
4.3 Review of various criteria for data selection ………………………..B-63

______________________________________________________________________________ Table of Contents
v 4.4 Interferometric interpretation……………………………………………. B-63
4.4.1 Interferometry phase signal ruggedness………………….. B-64
4.4.2 Fictitious example interferograms for analysis ………… B-65
4.4.3 Analysis of fictitious situations……………………………… B-67
Part C InSAR processing : a mathematical approach
1. Statistics of SAR and InSAR images………………………………………….. C-3
1.1 The backscattering process ………………………………………………… C-3
1.1.1 Introduction………………………………………………………….. C-3 1.1.2 Artificial backscatterers …………………………………………. C-3
1.1.3 Natural backscatterers: the spectral shift principle …….. C-4
1.1.4 Statistics of the return ……………………………………………. C-7
1.2 Interferometric images: coherence………………………………………. C-8
1.2.1 Statistics of coherence estimators ……………………………. C-9 1.2.2 Impact of the baseline on coherence ………………………. C-12
1.3 Power spectrum of interferometric images …………………………. C-13
1.4 Causes of cohe rence loss …………………………………………………. C-13
1.4.1 Noise, temporal change………………………………………… C-13
1.4.2 Volumetric effects……………………………………………….. C-13
2. Focusing, interferometry and slope estimate ……………………………… C-15
2.1 SAR model: acquisition and focusing………………………………… C-15
2.1.1 Phase preserving focusing…………………………………….. C-15
2.1.2 CEOS offset processing test………………………………….. C-18
2.2 Interferometric SAR processing ……………………………………….. C-18
2.2.1 Spectral shift and common band filtering (revisited)… C-19
2.3 DEM generation: optimal slope estimate……………………………. C-21
2.4 Noise sources …………………………………………………………………. C-24
2.5 Processing decorrelation artefacts……………………………………… C-25
2.5.1 Examples of decorrelation sources…………………………. C-25
3. Advances in phase unwrapping ……………………………………………….. C-29
3.1 Introduction……………………………………………………………………. C-29
3.2 Residues and charges ………………………………………………………. C-31
3.2.1 Effects of noise: pairs of residues, undefined
positions of the ‘ghost lines’ …………………………………. C-33
3.2.2 Effects of alias: unknown position of the ghost lines… C-36
3.3 Optimal topographies under the L
p norm……………………………. C-37
3.3.1 L2, L1, L0 optimal topographies …………………………….. C-37
3.3.2 Slope estimates……………………………………………………. C-40
3.3.3 Removal of low resolution estimates of the
topography …………………………………………………………. C-41
3.3.4 Bias of the slope estimate……………………………………… C-41
3.4 Analysis in the wave-number domain………………………………… C-42
3.4.1 L2 optimisation in the wave-number domain…………… C-42
3.5 Weighting factors in the optimisation………………………………… C-43

TM-19 _________________________________________________________________________ InSAR Principles
vi 4. Multiple image combination for DEM generation and ground
motion estimation ……………………………………………………………………C-45
4.1 Multi-baseline phase unwrapping for InSAR topography
estimation………………………………………………………………………..C-45
4.2 Applications to repeat-pass interferometry…………………………..C-48
4.2.1 Example 1: the Vesuvius data set ……………………………C-50
4.2.2 Example 2: The Etna data set………………………………….C-53
4.3 The ‘Permanent Scatterers’ technique …………………………………C-56
4.3.1 Space-time estimation……………………………………………C-58 4.3.2 Subsidence in Pomona ………………………………………….C-59
4.3.3 Ground slip along the Hayward fault……………………….C-62
4.3.4 Seasonal deformation in the Santa Clara Valley………..C-63
5. Applications based on spectral shift ………………………………………….C-65
5.1 Introduction to spectral shift ………………………………………………C-65
5.2 Interferometric quick look (IQL)………………………………………..C-67 5.3 Super-resolution……………………………………………………………….C-69
6. Differential interferometry ……………………………………………………….C-71
6.1 Introduction……………………………………………………………………..C-71 6.2 Differential interferometry using an available DEM ……………..C-72 6.3 Differential interferometry with three or more combined
images …………………………………………………………………………….C-77
6.4 Techniques to avoid phase unwrapping……………………………….C-79
6.4.1 Integer combination ………………………………………………C-79
6.4.2 Interferogram stacking …………………………………………..C-82
6.5 Information contained in in terferometric measurements………..C-83
6.5.1 Residual orbital fringes ………………………………………….C-83
6.5.2 Uncorrected topography…………………………………………C-86
6.5.3 Heterogeneous troposphere…………………………………….C-86
6.5.4 Heterogeneous ionosphere ……………………………………..C-87
6.5.5 Static atmosphere ………………………………………………….C-88
6.5.6 Radar clock drift …………………………………………………..C-88
7. Envisat-ASAR interferometric techniques and applications ………….C-91
7.1 Introduction……………………………………………………………………..C-91
7.2 ScanSAR: an introduction …………………………………………………C-92
7.2.1 Acquisition…………………………………………………………..C-93
7.2.2 Focusing………………………………………………………………C-94
7.3 ScanSAR inte rferometry……………………………………………………C-96
7.3.1 Common band (CB) filtering ………………………………….C-97
7.4 Multi-mode SAR interferometry…………………………………………C-98
7.4.1 Multi-mode interferometric combination………………….C-98
7.5 Applications…………………………………………………………………..C-101
7.5.1 AP/AP/IM interferometry …………………………………….C-101
7.5.2 WSM/WSM and WSM/IM interferometry ……………..C-102
8. ERS-Envisat interferometry ……………………………………………………C-107
8.1 Introduction……………………………………………………………………C-107

______________________________________________________________________________ Table of Contents
vii 8.2 ERS-Envisat interferometric combination………………………… C-107
8.3 Frequency gap compensation………………………………………….. C-108 8.4 Vertical accuracy ………………………………………………………….. C-108
8.5 Altitude of ambiguity…………………………………………………….. C-109
8.6 Effect of volume scattering…………………………………………….. C-110
8.7 Experimental results………………………………………………………. C-110
References ………………………………………………………………………………..I

TM-19 _________________________________________________________________________ InSAR Principles
viii Scope
This manual has been produced as a text book to introduce radar
interferometry to remote sensing specia lists. It consists of three parts.
Part A is meant for readers who already have a good knowledge of optical
and microwave remote sensing, to acq uaint them with interferometric SAR
image processing and interpretation.
Part B provides a practical approach and the technical background for
people who are starting up with InSAR processing.
In Part C a more mathematical approach can be found, for a deeper
understanding of the interferometric process. There, the manual also
includes an appreciation of themes such as super resolution and ERS/Envisat interferometry.

Part A

Interferometric SAR image
processing and interpretation

___________________________________________________________________Synthetic Apertu re Radar basics
A-3 1. Synthetic Aperture Radar basics
1.1 Introduction
Synthetic Aperture Radar (SAR) is a microwave imaging system. It has
cloud-penetrating capabilities because it uses microwaves. It has day and
night operational capabilities because it is an active system. Finally, its
‘interferometric configuration’, Interferometric SAR or InSAR, allows
accurate measurements of the radiatio n travel path because it is coherent.
Measurements of travel path variations as a function of the satellite position and time of acquisition allow generation of Digital Elevation Models
(DEM) and measurement of centimetric surface deformations of the terrain.
This part of the InSAR Principles manua l is dedicated to beginners who wish
to gain a basic understanding of what SAR interferometry is. Real examples derived from ESA satellites, ERS-1, ERS- 2 and Envisat, will be exploited to
give a first intuitive idea of the information that can be extracted from InSAR images, as well as an idea of the limits of the technique.
1.1.1 Introduction to ERS
The European Remote Sensing sate llite, ERS-1, was ESA’s first Earth
Observation satellite; it carried a co mprehensive payl oad including an
imaging Synthetic Aperture Radar (SAR). With this launch in July 1991 and
the validation of its interferometric cap ability in September of the same year,
an ever-growing set of interferometr ic data became available to many
research groups. ERS-2, which was identical to ERS-1 apart from having an extra instrument, was launched in 1995.

Figure 1-1: An artist’s impression of ERS-2

TM-19 _________________________________________________________________________ InSAR Principles
A-4 Shortly after the launch of ERS-2, ESA decided to link the two spacecraft in
the first ever ‘tandem’ mission, which lasted for nine months, from
16 August 1995 until mid-May 1996. During this time the orbits of the two
spacecraft were phased to orbit the Eart h only 24 hours apart, thus providing
a 24-hour revisit interval.
The huge collection of image pairs from the ERS tandem mission remains
uniquely useful even today, because the brief 24-hour revisit time between
acquisitions results in much greater interferogram coherence. The increased
frequency and level of data availa ble to scientists offered a unique
opportunity to generate detailed elev ation maps (DEMs) and to observe
changes over a very short space of time. Even after the tandem mission ended, the high orbital stability and careful operational control allowed
acquisition of more SAR pairs for the remainder of the time that both
spacecraft were in orbit, although without the same stringent mission constraints.
The near-polar orbit of ERS in combination with the Earth’s rotation (E-W)
enables two acquisitions of the same area to be made from two different look
angles on each satellite cycle. If just one acquisition geometry is used, the
accuracy of the final DEM in geographic coordinates strongly depends on
the local terrain slope, and this may not be acceptable for the final user. Combining DEMs obtained from ascending (S-N) and descending (N-S) orbits can mitigate the problems due to the acquisition geometry and the uneven sampling of the area of interest, especially on areas of hilly terrain
(this is illustrated in Figure 1-14 on pa ge A-15). The ERS antenna looks to
the right, so for example a slope that is mainly oriented to the West would be
foreshortened on an ascending orbit, he nce a descending orbit should be
used instead.
In March 2000 the ERS-1 satellite fina lly ended its operations. ERS-2 is
expected to continue operating for some time, although with a lower
accuracy of attitude control since a gy ro failure that occurred in January
2001.
1.1.2 Introduction to Envisat
Launched in 2002, Envisat is the larges t Earth Observation spacecraft ever
built. It carries ten sophisticated optical and radar instruments to provide
continuous observation and monitoring of the Earth’s land, atmosphere,
oceans and ice caps. Envisat data collectively provide a wealth of information on the workings of the Earth system, including insights into
factors contributing to climate change.

___________________________________________________________________Synthetic Apertu re Radar basics
A-5

Figure 1-2: Artist’s impression of Envisat
Furthermore, the data returned by its suite of instruments are also facilitating
the development of a number of opera tional and commercial applications.
Envisat’s largest single instrument is the Advanced Synthetic Aperture
Radar (ASAR), operating at C-band. This ensures continuity of data after
ERS-2, despite a small (31 MHz) central frequency shift. It features
enhanced capability in terms of c overage, range of incidence angles,
polarisation, and modes of operation. The improvements allow radar beam
elevation steerage and the selection of different swaths, 100 or 400 km wide.
Envisat is in a 98.54 ° sun-synchronous circular orbit at 800 km altitude, with
a 35-day repeat and the same ground track as ERS-2.
Its primary objectives are:
• to provide continuity of the observations started with the ERS satellites,
including those obtained from radar-based observations;
• to enhance the ERS mission, notably the ocean and ice mission;
• to extend the range of parameters observed, to meet the need for
increasing knowledge of the factors affecting the environment;
• to make a significant contribution to environmental studies, notably in the
area of atmospheric chemistry and ocean studies (including marine
biology).
1.2 SAR images of the Earth’s surface
1.2.1 What is a strip-map SAR imaging system?
A SAR imaging system [Curlander91] from a satellite (such as ERS or
Envisat) is sketched in Figure 1-3. A satellite carries a radar with the antenna
pointed to the Earth’s surface in the plane perpendicular to the orbit (in
practice this is not strictly true, becau se it is necessary to compensate for the
Earth’s rotation). The inclination of the antenna with respect to the nadir is
called the off-nadir angle and in contemporary systems is usually in the

TM-19 _________________________________________________________________________ InSAR Principles
A-6 range between 20° and 50° (it is 21° for ERS). Due to the curvature of the
Earth’s surface, the incidence angle of the radiation on a flat horizontal
terrain is larger than the off-nadir (t ypically 23° for ERS). However, for the
sake of simplicity we assume here that the Earth is flat, and hence that the
incidence angle is equal to the off-n adir angle, as shown in the figure.

Figure 1-3: A SAR system from a satellite
Currently, operational satellite SAR syst ems work in one of the following
microwave bands:
• C band – 5.3 GHz (ESA’s ERS and Envisat, the Canadian Radarsat,
and the US shuttle missions)
• L band – 1.2 GHz (the Japanese J-ERS and ALOS)
• X band – 10 GHz (the German-Italian X-SAR on the shuttle missions)
In the case of ERS, the illuminated area on the ground (the antenna
footprint ) is about 5 km in the along-track direction (also called the
azimuth direction ) and about 100 km in the across-track direction (also
called the ground range direction ).
The direction along the Line of Sight (LOS) is usually called the
slant-range direction.
The antenna footprint moves at the satellite speed along its orbit. For ERS,
the satellite speed is about 7430 m/s in a quasi-polar orbit that crosses the
equator at an angle of 9° and an el evation of about 800 km. The footprint
traces a swath 100 km wide in ground range on the Earth’s surface, with the
capability of imaging a strip 445 km long every minute (strip map mode).
1.2.2 What is a complex SAR image?
A digital SAR image can be seen as a mosaic (i.e. a two-dimensional array
formed by columns and rows) of small picture elements (pixels). Each pixel is associated with a small area of the Earth’s surface (called a resolution
cell). Each pixel gives a complex number that carries amplitude and phase
information about the microwave field backscattered by all the scatterers
(rocks, vegetation, buildings etc.) within the corresponding resolution cell

___________________________________________________________________Synthetic Apertu re Radar basics
A-7 projected on the ground (see section 1.2.3). Different rows of the image are
associated with different azimuth locations, whereas different columns
indicate different slant range locations.
The location and dimension of the resolution cell in azimuth and slant-range
coordinates depend only on the SAR system characteristics.
In the ERS case, the SAR resolution cell dimension is about 5 metres in
azimuth and about 9.5 metres in slant-range. The distance between adjacent
cells is about 4 metres in azimuth and about 8 metres in slant range. The
SAR resolution cells are thus slightly overlapped both in azimuth and in
slant-range.
1.2.2.1 The detected SAR image
The detected SAR image contains a measurement of the amplitude of the
radiation backscattered toward the radar by the objects ( scatterers )
contained in each SAR resolution cell. This amplitude depends more on the
roughness than on the chemical composition of the scatterers on the terrain. Typically, exposed rocks and urban areas show strong amplitudes, whereas
smooth flat surfaces (like quiet water basins) show low amplitudes, since the radiation is mainly mirrored away from the radar.
The detected SAR image is generally visualised by means of grey scale
levels as shown in the example of Figure 1-4 . Bright pixels correspond to
areas of strong backscattered radiation (e.g. urban areas), whereas dark
pixels correspond to low backscattered ra diation (e.g. a quiet water basin).

Figure 1-4: ERS SAR detected image of Milan (Italy). The image size is about 25 km
in ground range (vertical) and 25 km in azimuth (horizontal).

TM-19 _________________________________________________________________________ InSAR Principles
A-8 1.2.2.2 The phase SAR image
The radiation transmitted from the radar has to reach the scatterers on the
ground and then come back to the radar in order to form the SAR image
(two-way travel). Scatterers at different distances from the radar (different slant ranges) introduce different delays between transmission and reception of the radiation.
Due to the almost purely sinusoidal nature of the transmitted signal, this
delay
τ is equivalent to a phase change φ between transmitted and received
signals. The phase change is thus proporti onal to the two-way travel distance
2R of the radiation divided by the transmitted wavelength λ. This concept is
illustrated in Figure 1-5.

Figure 1-5: A sinusoidal function sin φ is periodic with a 2 π radian period. In the
case of a relative narrow-band SAR (i.e. ERS and Envisat), the transmitted signal
can be assimilated, as a first approximation, to a pure sinusoid whose angle or
phase φ has the following linear dependence on the slant range coordinate r:
φ = 2πr/λ (where λ is the SAR wavelength). Thus, assuming that the phase of the
transmitted signal is zero, the received si gnal that covers the distance 2R travelling
from the satellite to the target and back, shows a phase φ = 4πR/λ radians.
However, due to the periodic nature of the signal, travel distances that differ
by an integer multiple of the wavele ngth introduce exactly the same phase
change. In other words the phase of the SAR signal is a measure of just the
last fraction of the two-way travel distance that is smaller than the
transmitted wavelength.
In practice, due to the huge ratio between the resolution cell dimension (of
the order of a few metres) and wavelength (~5.6 cm for ERS), the phase
change passing from one pixel to another within a single SAR image looks random and is of no practical utility.

___________________________________________________________________Synthetic Apertu re Radar basics
A-9 1.2.2.3 Speckle
The presence of several scatterers w ithin each SAR resolution cell generates
the so-called ‘speckle’ effect that is common to all coherent imaging
systems. Speckle is present in SAR, but not in optical images.
Homogeneous areas of terrain that extend across many SAR resolution cells
(imagine, for example, a large agricultural field covered by one type of
cultivation) are imaged with different amplitudes in different resolution
cells. The visual effect is a sort of ‘salt and pepper’ screen superimposed on
a uniform amplitude image.
This speckle effect is a direct consequence of the superposition of the signals
reflected by many small elementary scatterers (those with a dimension
comparable to the radar wavelength) within the resolution cell. These
signals, which have random phase becau se of multiple reflections between
scatterers, add to the directly reflected radiation. From an intuitive point of
view, the resulting amplitude will depe nd on the imbalance between signals
with positive and negative sign.
An example of speckle is shown in Fi gure 1-6. Here the ‘salt and pepper’
effect is clearly visible on the homogenous fields that surround the Linate
Airport as seen by ERS-2.
The same area as seen from the SPOT optical system is shown in Figure 1-7 .
Here no speckle is present and the fields that surround the Linate Airport
appear homogeneous.

Figure 1-6: ERS-2 SAR detected image of the Linate Airport in the eastern part of Milan (Italy): the speckle effect
on the homogeneous fields surrounding the airport is clearly visible.

TM-19 _________________________________________________________________________ InSAR Principles
A-10

Figure 1-7: Optical image of Linate Airport taken from the SPOT satellite. No speckle is
visible and the fields that surround the airport look homogeneous.
Speckle has an impact on the quality and usefulness of detected SAR
images. Typically, image segmentation suffers severely from speckle.
However, by taking more images of the same area at different times or from
slightly different look angles, speck le can be greatly reduced: averaging
several images tends to cancel out the random amplitude variability and
leave the uniform amplitude level unchanged.
An example of speckle reduction is shown in Figure 1-8 . Here the average of
60 separate ERS-1 and ERS-2 SAR images of the area surrounding the
Linate airport in Milan is shown. A comparison between this image and the
single SAR image shown in Figure 1-6 gives an idea of the speckle reduction achieved and of the improved visibility of detail.

Figure 1-8: Average of multiple ERS SAR images of Linate airport: the speckle effect on the
homogeneous fields around the airport has disappeared.

___________________________________________________________________Synthetic Apertu re Radar basics
A-11 1.2.3 SAR resolution cell projection on the ground
The terrain area imaged in each SAR resolution cell (called the ground
resolution cell ) depends on the local topography. It strongly depends on the
terrain slope in the plane perpendicula r to the orbit (ground range direction),
and on the terrain slope in the azimuth direction.
The dimension of the ground resolution cell in azimuth is related to that of
the SAR resolution cell by the usual pers pective deformation we experience
every day looking at surfaces from different angles (e.g. a postcard seen at
90 degrees is a line).
The dimension of the ground resolution cell in range is related to that of the
SAR resolution cell by an unusual perspective deformation. Figure 1-9
shows how slant-range is projected onto the ground.
Here five identical slant-range resolution
cells are shown. The first two cells
correspond to flat terrain and they contain
three triangles each. The third cell contains
seven of these triangles due to the positive
slope of the terrain. Finally the fourth and
fifth cells contain less than three triangles
due to the negative slope of the terrain.
Figure 1-9: Effect of terrain on the SAR image. For SAR resolution cells in the
plane perpendicular to the orbit, the part of the terrain imaged in each resolution
cell clearly depends on the topography.
As the terrain slope increases with respect to a flat horizontal surface (i.e. as
the normal to the terrain moves toward the line of sight (LOS) ), the ground
resolution cell dimension in range increases. This effect is called
foreshortening. When the terrain slope is close to the radar off-nadir angle,
the cell dimension becomes very large and all the details are lost. Moreover,
when the terrain slope exceeds the rada r off-nadir angle the scatterers are
imaged in reverse order and superimposed on the contribution coming from
other areas. This effect is called layover , and is sketched in Figure 1-10.

TM-19 _________________________________________________________________________ InSAR Principles
A-12

Figure 1-10: Layover and shadow effects. Depending on the terrain slope,
scatterers that are located at increasing ground range positions can be imaged in
reverse order by the SAR system (points D, E, F and G). Moreover they are imaged
in the same SAR resolution cells as scatterers B and C, which belong to a different
area on the ground (layover). On the other side of the elevation profile, scatterers
located between points G and H cannot be illuminated by the radar since they are in
shadow. As a consequence, SAR resolution cells from 5 to 8 do not contain any
signal from the ground and they generate a dark gap on the detected image.
On the other hand, when the terrain slop e decreases with respect to the flat
horizontal reference surface, the resolution cell dimension decreases. The
minimum resolution cell dimension (i.e. equal to the slant range resolution) is reached when the terrain is parallel to the LOS. This is also the lower
slope limit that can be imaged at all by a SAR system, since beyond this
angle the terrain is in shadow.
As an example, in the case of ERS syst ems, the resolution cell dimension as
a function of the terrain slope is shown in Figure 1-11 .

Figure 1-11: ERS resolution cell dimension in ground range as a function of the
terrain slope. The vertical dotted line indicates the incidence angle relative to a flat
horizontal terrain (23°).

___________________________________________________________________Synthetic Apertu re Radar basics
A-13 It should be pointed out that foreshortening has a strong impact on the
amplitude of the detected SAR image. Foreshortened areas are brighter on
the image because the resolution cell is larger (hence more power is backscattered towards the satellite) and the incidence angle is steeper. An
example that illustrates this effect is shown in Figure 1-12 with reference to
the area of Mount Vesuvius (Italy) as seen by ERS-1.

Figure 1-12: ERS-2 SAR image of Mount Vesuvius (Italy), as detected. The slant range direction is vertical
on the image (near range is in the upper part of th e image). Brighter levels correspond to stronger
backscattered radiation. The coastline along the Tyrrenian Sea is clearly visible (the sea is dark due to the
almost specular reflection of electromagnetic waves). Urban areas can be identified as bright spots on the
image (strong backscattering from buildings), as can the main crater of the volcano. It should be noted that
positive slopes of the volcano (in the upper flanks on the image) are shortened with respect to the flanks
descending to the sea. At the same time, the shortened flanks appear brighter on the image.

___________________________________________________________________Synthetic Apertu re Radar basics
A-13 It should be pointed out that foreshortening has a strong impact on the
amplitude of the detected SAR image. Foreshortened areas are brighter on
the image because the resolution cell is larger (hence more power is backscattered towards the satellite) and the incidence angle is steeper. An
example that illustrates this effect is shown in Figure 1-12 with reference to
the area of Mount Vesuvius (Italy) as seen by ERS-1.

Figure 1-12: ERS-2 SAR image of Mount Vesuvius (Italy), as detected. The slant range direction is vertical on the
image (near range is in the upper pa rt of the image). Brighter levels correspond to stronger backscattered
radiation. The coastline along the Tyrrenian Sea is clearly visible (the sea is dark due to the almost specular
reflection of electromagnetic waves). Urban areas can be identified as bright spots on the image (strong
backscattering from buildings), as can the main crater of the volcano. It should be noted that positive slopes of the
volcano (in the upper flanks on the image) are shortened with respect to the flanks descending to the sea. At the
same time, the shortened flanks appear brighter on the image.

TM-19 _________________________________________________________________________ InSAR Principles
A-14 Referring to the same area, Figure 1-13 shows how the regular resolution
grid in SAR coordinates (azimuth and slant-range) is deformed by the
topography when projected on the ground.

Figure 1-13: Deformation of the regular resolution grid on the ground when
projected in SAR coordinates. The deformation is due to topography.
1.2.3.1 Geometric deformation from ascending and descending
ERS passes
With ERS there is the possibility to ob serve the same scene with incidence
angles of both plus and minus 23 degrees. Observation of the whole of the
Earth’s surface is achieved by combination of the orbital satellite motion
along the meridians (almost polar orbits) and the Earth’s rotation in the
equatorial plane. This possibility comes from the fact that during orbits that
go from South to North ( ascending passes ) and from North to South
(descending passes ), the SAR antenna pointing is usually fixed to the same
side of the orbital plane with respect to the velocity vector (e.g. the radar
antenna is always pointed to the right side of the track for ERS and Envisat),
as shown in Figure 1-14.
Thus, the same scene on the ground is observed by the SAR antenna from
the east during the descending passes and from the west during the ascending passes.

TM-19 _________________________________________________________________________ InSAR Principles
A-16 Here two detected ERS images of Mount Etna (Italy) taken from ascending
and descending passes are shown together with an elevation model of the
imaged area. A comparison of these two images clearly shows the effect of the different perspective: the summit is shifted away from the coastline in
the ascending (left) ERS SAR image and towards it in the descending (right) image. From these images it is also evid ent that high resolution details of the
western flank of the volcano are obtained from ERS ascending passes,
whereas the eastern flank is ‘squeezed’ into a few pixels of the SAR image;
the opposite happens with descending ERS passes. Thus, both ascending and
descending passes should be exploited to get a high resolution SAR image of the whole area. It is necessary, however, to resample both images on a common reference grid in order to be able to make such a combination.

__________________________________________________________SAR interferom etry: applications and limits
A-17 2. SAR interferometry: applications and
limits
This section gives a brief overview of the subject. Details of the method may
be found in parts B and C of this document.
2.1 Introduction
A satellite SAR can observe the same area from slightly different look
angles. This can be done either simu ltaneously (with two radars mounted on
the same platform) or at different times by exploiting repeated orbits of the
same satellite. The latter is the case fo r ERS-1, ERS-2 and Envisat. For these
satellites, time intervals between observations of 1, 35, or a multiple of 35
days are available.
The distance between the two satellites (o r orbits) in the plane perpendicular
to the orbit is called the interferometer baseline (see Figure 2-1) and its
projection perpendicular to the slant range is the perpendicular baseline .

Figure 2-1: Geometry of a satellite interferometric SAR system. The orbit
separation is called the interferometer baseline, and its projection perpendicular to
the slant range direction is one of th e key parameters of SAR interferometry.
The SAR interferogram is generated by cross-multiplying, pixel by pixel, the
first SAR image with the complex conjugate of the second [Bamler98A,
Massonnet98, Franceschetti99, Rosen00]. Thus, the interferogram amplitude
is the amplitude of the first image multiplied by that of the second one, whereas its phase (the interferometric phase ) is the phase difference
between the images.

TM-19 _________________________________________________________________________ InSAR Principles
A-18 2.2 Terrain altitude measurement through the
interferometric phase
Let us suppose we have only one domin ant point scatterer in each ground
resolution cell that does not change over time. These point scatterers are
observed by two SARs from slightly different look angles as shown in
Figure 2-1. In this case the interferometric phase of each SAR image pixel would depend only on the difference in the travel paths from each of the two
SARs to the considered resolution cell. Any possible phase contribution
introduced by the point scatterers does not affect the interferometric phase
since it is cancelled out by the difference.
Once a ground reference point has been identified, the variation of the travel
path difference Δr that results in passing from the reference resolution cell to
another can be given by a simple expr ession (an approximation that holds for
small baselines and resolution cells that ar e not too far apart) that depends on
a few geometric parameters shown in Figure 2-2.

Figure 2-2: Geometric parameters of a satellite interferometric SAR system
The parameters are:
1. The perpendicular baseline Bn
2. The radar-target distance R
3. The displacement between the reso lution cells along the perpendicular to
the slant range, qs
The following approximated expression of Δr holds:
RqBrsn2−=Δ Equation 2.1

__________________________________________________________SAR interferom etry: applications and limits
A-19 The interferometric phase variation Δφ is then proportional to Δr divided by
the transmitted wavelength λ:
RqB rsn
λπ
λπφ4 2=Δ=Δ Equation 2.2
2.2.1 Interferogram flattening
The interferometric phase variation can be split into two contributions:
1. A phase variation proportional to the altitude difference q between the
point targets, referred to a horizontal reference plane
2. A phase variation proportional to the slant range displacement s of the
point targets
θ λπ
θ λπφtan4
sin4
RsB
RqBn n− −=Δ Equation 2.3
where θ is the radiation incidence angle with respect to the reference
It should be noted that the perpendicular baseline is known from precise
orbital data, and the second phase term can be computed and subtracted from
the interferometric phase. This operation is called interferogram flattening
and, as a result, it generates a phase ma p proportional to the relative terrain
altitude.
An example of interferogram flatte ning is shown in Figure 2-3. An
interferogram of a portion of the Italian Alps and the Pianura Padana that has
been obtained from ERS-1 and ERS-2 data (taken one day apart with a
normal baseline of about 30 metres) is shown on the left. The flattened
interferogram is shown on the right side. Here the phase discontinuities
resemble the contour lines. The altit ude between two adjacent discontinuities
is called the altitude of ambiguity (symbol ha) and can be computed from
the interferometer paramete rs (see section 2.2.2).

Figure 2-3: Left : interferogram of a portion of the Italian Alps and the Pianura
Padana that has been obtained from ERS data. Right: flattened interferogram. Here
the phase discontinuities rese mble the contour lines.

TM-19 _________________________________________________________________________ InSAR Principles
A-20 2.2.2 Altitude of ambiguity
The altitude of ambiguity ha is defined as the altitude difference that
generates an interferometric phase change of 2π after interferogram
flattening. The altitude of ambiguity is inversely proportional to the
perpendicular baseline:

naBRh2sinθ λ= Equation 2.4
In the ERS case with λ = 5.6 cm, θ = 23ș, and R = 850 km, the following
expression holds (in metres):
naBh9300≈ Equation 2.5
As an example, if a 100 metre perpendicular baseline is used, a 2π change of
the interferometric phase corresponds to an altitude difference of about
93 metres. In principle, the higher the baseline the more ac curate the altitude
measurement, since the phase noise (see next section) is equivalent to a
smaller altitude noise. However, it will be shown later that there is an upper
limit to the perpendicular baseline, over which the interferometric signals
decorrelate and no fringes can be gene rated. In conclusion there is an
optimum perpendicular baseline that maximises the signal to noise power
ratio (where the signal is terrain altit ude). In the ERS case, such an optimum
baseline is about 300–400 metres.
2.2.3 Phase unwrapping and DEM generation
The flattened interferogram provid es an ambiguous measurement of the
relative terrain altitude due to the 2π cyclic nature of the interferometric
phase. The phase variation between two points on the flattened interferogram
provides a measurement of the actual a ltitude variation, after deleting any
integer number of altitudes of ambiguity (equivalent to an integer number of
2π phase cycles). The process of adding the correct integer multiple of 2π to
the interferometric fringes is called phase unwrapping .
An example of phase unwrapping is shown in the following figure, in which
the SAR interferometric phase, its unw rapped version and a map with the
correct integer multiple of 2π added to the original phase are shown together.

__________________________________________________________SAR interferom etry: applications and limits
A-21

Figure 2-4: Left: SAR interferometric phase generated by means of two ERS
images. The 2π phase discontinuities are clearly visible as black/white transitions.
Right: Unwrapped phase. Below: The 2π phase discontinuities have been
eliminated by adding or subtracting an integer multiple of 2π to each pixel of the
original interferometric phase image.
There are several well-known phase unwrapping techniques that will be
described in the advanced section of this manual. However it should be noted here that usually phase unwrappi ng does not have a unique solution,
and a priori information should be exploited to get the right solution.
Once the interferometric phases are unwrapped, an elevation map in SAR
coordinates is obtained. This is the first step towards getting a DEM. The
SAR elevation map should then be referr ed to a conventional ellipsoid (e.g.
WGS84) and re-sampled on a different grid (for example UTM).
As an example, the flattened interfe rogram and the relative DEM of Mount
Etna obtained through phase unwrappi ng and re-sampling are shown in
Figure 2-5, Figure 2-6 and Figure 2-7.

TM-19 _________________________________________________________________________ InSAR Principles
A-22

Figure 2-5: Flattened interferogram of Mount Etna generated from ERS tandem
pairs. The perpendicular baseline of 115 metres generates an altitude of ambiguity
of about 82 metres.

Figure 2-6: Perspective view of Mount Etna as seen from the Northeast . The DEM of Mount Etna has
been generated by unwrapping and re-sampling the flattened interferogram of Figure 2-5: The
estimated vertical accuracy is better than 10 me tres. Contour lines are shown below the DEM.

__________________________________________________________SAR interferom etry: applications and limits
A-23

Figure 2-7: Perspective view of Mount Etna as seen from the Northeast. The average of many
detected ERS SAR images has been draped on the DEM.
2.3 Terrain motion measurement: Differential
Interferometry
Suppose that some of the point scatterers on the ground slightly change their
relative position in the time interval between two SAR observations (as, for example, in the event of subsidence, landslide, earthquake, etc.). In such
cases the following additive phase term, i ndependent of the baseline, appears
in the interferometric phase:

ddλπφ4=Δ Equation 2.6
where d is the relative scatterer displacement projected on the slant
range direction.
This means that after interferogram flattening, the interferometric phase
contains both altitude and motion contributions:
dRqBn
λπ
θ λπφ4
sin4+ −=Δ Equation 2.7
Moreover, if a digital elevation mode l (DEM) is available, the altitude
contribution can be subtracted from the interferometric phase (generating the
so-called differential interferogram ) and the terrain motion component can
be measured. In the ERS case with λ = 5.6 cm and assuming a perpendicular
baseline of 150 m (a rather common value), the following expression holds:
dq22510+ Δ −=φ Equation 2.8
From this example it can be seen that the sensitivity of SAR interferometry
to terrain motion is much larger than th at to the altitude difference. A 2.8 cm
motion component in the slant range direction would generate a 2π
interferometric phase variation. As an example, the differential

TM-19 _________________________________________________________________________ InSAR Principles
A-24 interferogram showing the surface de formation that occurred during the
Mount Etna eruption of July 2001 is shown in Figure 2-8.

Figure 2-8: The differential interferogram of the Mt Etna eruption that occurred in
July 2001. The interferogram has been generated by means of two ERS images
taken before (11 July 2001) and after (15 August 2001) the eruption. The
topography has been removed by means of an available DEM. Contour lines of the
DEM are shown in black.
2.4 The atmospheric contribution to the
interferometric phase
When two interferometric SAR images are not simultaneous, the radiation
travel path for each can be affected differently by the atmosphere. In
particular, different atmospheric humidity, temperature and pressure between
the two takes will have a visible cons equence on the interferometric phase.
This effect is usually confined within a 2π peak-to-peak interferometric

__________________________________________________________SAR interferom etry: applications and limits
A-25 phase change along the image with a smooth spatial variability (from a few
hundred metres to a few kilometres). The effect of such a contribution
impacts on both altitude (especially in the case of small baselines) and terrain deformation measurements.
As an example, the atmospheric phase contribution to the ERS interferogram
generated on the Pianura Padana valley (N orth Italy) is shown in Figure 2-9.
Here the perpendicular baseline is quite small (30 metres) and the
differential turbulence effect is clearly visible on the interferogram where an
almost flat phase contribution is expected from the known topography.

Figure 2-9: An example of atmospheric phase contribution to the ERS interferogram
generated on the Pianura Padana. The perpendicular baseline is about 30 metres and the
altitude of ambiguity (from black to white in the grey scale used) is about 300 metres.
2.5 Other phase noise sources
In the previous sections it has be en hypothesised that only one dominant
stable scatterer was present in each resolution cell. This is seldom the case in
reality. We should analyse the situation where many elementary scatterers are present in each resolution cell (distributed scatterers), each of which may
change in the time interval between two SAR acquisitions. The main effect
of the presence of many scatterers per resolution cell and their changes in
time is the introduction of phase noise.

TM-19 _________________________________________________________________________ InSAR Principles
A-26 Three main contributions to the phase noise should be taken into
consideration:
1. Phase noise due to temporal change of the scatterers
In the case of a water basin or densely vegetated areas, the scatterers
change totally after a few millis econds, whereas exposed rocks or
urban areas remain stable even after years. Of course, there are also the intermediate situations wher e the interferometric phase is still
useful even if corrupted by change noise.
2. Phase noise due to different look angle
Speckle will change due to the different combination of elementary echoes even if the scatterers do not change in time. The most important consequence of this effect is that there exists a critical
baseline over which the interferometric phase is pure noise. The
critical baseline depends on the dimension of the ground range
resolution cell (and thus also on the terrain slope), on the radar
frequency, and on the sensor-target distance. In the ERS case, the
critical baseline for horizontal terrain is about 1150 metres. It
decreases for positive terrain slop es and increases for negative ones.
This phase noise term, however, can be removed from the
interferogram by means of a pre-processing step of the two SAR
images known as spectral shift or common band filtering. This will
be described in detail in the advan ced sections of this manual (part B
section 2.5 and part C section 2.2.1).
3. Phase noise due to volume scattering
The critical baseline reduces in the case of volume scattering when the
elementary scatterers are not disposed on a plane surface but occupy a
volume (e.g. the branches of a tree) . In this case the speckle change
depends also on the depth of the volume occupied by the elementary
scatterers.
2.6 Coherence maps
The phase noise can be estimated from the interferometric SAR pair by
means of the local coherence γ. The local coherence is the cross-correlation
coefficient of the SAR image pair estimated over a sm all window (a few
pixels in range and azimuth), once all the deterministic phase components
(mainly due to the terrain elev ation) are compensated for.
The deterministic phase components in such a small window are, as a first
approximation, linear both in azimuth and slant-range. Thus, they can be estimated from the interferogram itsel f by means of well-known methods of
frequency detection of complex sinusoids in noise (e.g. 2-D Fast Fourier
Transform (FFT) ).
The coherence map of the scene is then formed by computing the absolute
value of
γ on a moving window that covers the whole SAR image.

__________________________________________________________SAR interferom etry: applications and limits
A-27 The coherence value ranges from 0 (the interferometric phase is just noise)
to 1 (complete absence of phase noise).
As an example, a coherence map of the North East part of Sicily is shown in
Figure 2-10. Here the exposed lava on Mount Etna shows a very high
coherence value, whereas vegetated areas appear dark, showing lower
coherence values. Note the very low co herence value of the sea (dark in the
image), which changes completely in the one day interval between the two
ERS observations.

Figure 2-10: Coherence map of the North East part of Sicily
The exact relation between the interferometric phase dispersion and coherence can be found through comp licated mathematical computation
[Lee94]. However, if the number of looks ( NL) is greater than four, then
independent pixels with the same c oherence are averaged after topography
compensation (multi-look interferogram) and the following simple
approximation holds [Rosen00]:

γγσφ21
21 −=
NL Equation 2.9

TM-19 _________________________________________________________________________ InSAR Principles
A-28 From a mathematical point of view, this formula is a good approximation of
the exact phase dispersion shown in Figure 2-11 when σφ < 12° That is,
when NL is large and γ close to one. However, for most practical
applications of SAR interferometry, the approximated formula can be
suitably exploited for coherence values higher than 0.2 and NL > 4.

Figure 2-11: Interferometric phase dispersion (degrees) as a function of the
coherence for varying numbers of looks (NL)
A comparison between the exact and approximated curves is shown in
Figure 2-12.

Figure 2-12: Interferometric phase dispe rsion exact values (blue curves) and
approximated ones (red curves)

__________________________________________________________SAR interferom etry: applications and limits
A-29 The phase dispersion can be exploited to estimate the theoretical elevation
dispersion (limited to the high spatial frequencies) of a DEM generated from
SAR interferometry:
BR
hπθ λσ σφ4sin= Equation 2.10
On the other hand, low spatial frequencies of the DEM error cannot be
predicted from the coherence map since the coherence estimation is carried
out on small windows. The information ca rried by the coherence map can be
usefully exploited to help image segm entation, as will be seen in part B.

__________________________________________________ SAR D ifferential Interferometry basics and examples
A-31 3. SAR Differential Interferometry basics
and examples
3.1 Introduction
‘Differential interferometry’ is the commonly used term for the production
of interferograms from which the topographic contribution has been
removed. However, the term may occasionally be misleading, because on the one hand interferometry is a differentia l technique right from the beginning,
and on the other hand, the subtraction process can be pushed further as well
as in other directions (e.g. subtr action of an expected geophysical
contribution through earthquake or volcano dynamic modelling).
3.2 Landers co-seismic deformation
On 18 June 1992, a very large earthquake occurred in the desert northeast of
the city of Los Angeles. It was named after the small city of Landers, which
is nearby this largely unpopulated area. Its magnitude of 7.3 on the Richter
scale made it one of the largest of th e century in California. The earthquake
was strongly felt in the w1hole area, including Los Angeles, but it caused
few casualties and little damage because of its remote location. To
geophysicists, the Landers Earthquake w as an excellent opportunity to study
the mechanisms of a large earthquake using the most recent geodetic and
seismological instrumentation, which had previously been put in the field in
the area, making it (along with Japan) one of the most densely instrumented
areas in the world.
In a much less publicised way, the ra dar imaging community was eager to
demonstrate the power of radar inte rferometry applied to displacement
mapping. The Landers Earthquake was also an excellent opportunity for
radar scientists. It took place after ERS-1 had been placed on its 35-day
orbit, which was to be maintained for most of the useful life of the satellite
and which guaranteed a regular flow of high quality data. The desert
environment raised some hopes that the interferometric comparison of radar
images acquired a long time apart could work, since the degradation of the soil during the time elapsed might be minimal, despite some previous
pessimistic estimations that predicted a decay in a matter of days. Another positive was the availability of a topographic model of the area, of reasonable accuracy. Such a model would allow removal of the effect of
topography in the interferograms (section C6.2), so that just two radar
images would suffice to catch the displ acements. Finally, that the area was
so heavily instrumented and being studi ed was a great benefit, because other
geodetic measurements could at th e same time confirm the radar
measurement and provide the highest le vel of ‘geodetic competition’ against
interferometry.
The study of the Landers Earthquake ac tually exceeded all expectations. In
the first study [Massonnet93] two im ages acquired before the earthquake

TM-19 _________________________________________________________________________ InSAR Principles
A-32 (24 April 1992) and after it (7 August 1992) combined into a nice
interferogram despite the 105 days elapsed. A third image (3 July 1992) was
used in combination with the 7 Augu st image. This combination did not
include the earthquake. It demonstrated the quality of the topographic model
used in conjunction with the first in terferogram and produced the error bars.
The result of the study went beyond the mere demonstration of
interferometry. It was a big surprise for geophysicists, who did not expect
such a revolutionary way of looking at the Earth, but it also sets a new aesthetic standard in the geosciences. The cover of the magazine Nature
popularised the ‘fringes’ as a new way to look at ground deformation with coloured, and sometimes shaky, contour lines, each amounting to 3 cm or so of additional deformation.
The interferometric image of Figure 3-1 provides a striking collision of
scales: it shows the central part of the 100 km by 300 km area under study, where displacements are recorded with millimetre accuracy from 800 km
away in space. The ratio of the widt h of the scene and the potential accuracy
is 10
8. The ratio of the distance of ob servation and the maximum amplitude
of the displacement in the image is 106.

Figure 3-1: The Landers Earthquake of 18 June 1992

__________________________________________________ SAR D ifferential Interferometry basics and examples
A-33 One year later, another study [Mass onnet94] demonstrated that the fringes
were even more robust than anticipated. The interferogram in Figure 3-1 was
actually part of this second study, and was made from two images separated
by 18 months. Landers was also a good test site for demonstrating the method using three radar images (section C.6.3), which does not need a
topographic model [Zebker94B] and for testing various mixes of geodetic
and seismological data [Hernandez96] to refine earthquake modelling.
Because it created a large surface rupture, the Landers Earthquake could be modelled rather accurately by elastic modelling (see an example of the latter in Figure 3-2) based on the rupture parameters, which are easier to determine when they are evidenced by fault shifts that reach the surface. The striking
resemblance between the artificial fringes inferred from the geophysical
elastic modelling and the actual interfe rogram was crucial to making people
simply believe the result. The Big Bear Earthquake that took place three
hours after Landers did not create a surface rupture and was much more difficult to model. On the interferogram, it is the set of six or seven large,
circular fringes south of Landers. The same interferogram thus proved both
the validity of the method (with Landers) and its unique capabilities (with
Big Bear).
3.3 Small earthquake modelling
Unlike Landers, the earthquake that st ruck the northern side of the San
Bernardino mountain range had nothing sp ectacular to draw attention. It had
a small magnitude of 5.1 and was located far from populated centres. It took
place on 4 December 1992, more than five months after the Landers Earthquake. It was, however, well recorded as a small concentric
deformation in the southwest part of the previous illustration, which is
considerably zoomed on the left pa nel of Figure 3-2. We dubbed this
nameless small earthquake ‘Fawnskin’, after the name of the corresponding
USGS topographic map.

TM-19 _________________________________________________________________________ InSAR Principles
A-34

Figure 3-2: Fawnskin earthquake and its modelling
In interferometry, all the deformations occurring in the time elapsed between
the images are stacked together, rega rdless of their date. The event is
therefore superposed on a network of fringes created by the other, more
powerful, earthquake in the area. We can see two of the fringes that cross
our zoom obliquely. The smaller earthqu ake created four fringes of its own.
The sign of these fringes, which is so mewhat obscured because they are
represented by an arbitrary colour table, indicates that the deformation
brought the terrain closer to th e radar during the second pass.
An anticipated limitation of interferometr ic geodesy that was expected to be
serious before actual experiments took place, is that only the line-of-sight displacement is measured. Therefore, de formations that are basically 3-D are
projected on 1-D. This limitation was not such a nuisance in practice because, for most events , geophysicists can recognise the nature of the
displacement and propose a likely model. The radar data is then used to find
the few free parameters of the model. The model starts from hypotheses of
what the fault rupture mechanism at depth might be. This is well illustrated
by the specific study of Fawnskin ear thquake [Feigl95]. Using an approach
which has become routine since then, ten parameters are required to characterise a rupture on a single planar patch:
• the position of the lower corner of the patch (3 coordinates)
• the two angles for the orientation of the plane (2 coordinates)
• the size of the ruptured rectangle (2)
• the vector indicating the amount of slip in direction and amplitude (3)

__________________________________________________ SAR D ifferential Interferometry basics and examples
A-35 In the case of this study, Kurt Feigl and co-workers found that the patch was
2.9 by 3.1 km with an average 2.6 km depth. To infer this information from
the radar data, which deals only with the surface deformation, geophysicists
consider the Earth as being made of an elastic material like rubber. The
rupture at depth, or ‘focal mechanism’ as it is called, is then equivalent to a
cut in the rubber, followed by a relativ e displacement of the two lips of the
cut. Mechanical equations are then used to convert the at-depth displacement
into a 3-D surface displacement, using an assumption about the elastic
modulus of the crust material. This di splacement is itself converted to a
line-of-sight displacement and scaled as fringes. The process lasts until the
agreement between the model and the result is satisfactory. The best fit obtained by Feigl et al. is represented on the right of Figure 3-2.
Amusingly, when these elastic models were refined during the eighties, some approximations were made. The general feeling was that elastic
modelling might have some flaws but that no geodetic method would ever
provide measurements with sufficient density to reveal these flaws. This
opinion was doubly pessimistic, as radar interferometry provided the
required 100 or more measurements per square kilometre, and… proved that
this modelling is basically sound and flawless!
3.4 The quiet but complicated deformation after
an earthquake
The excitement over Landers as an ideal test site did not fade after the initial
studies. Crucial questions were still una nswered. Is such a large earthquake
preceded by geodetic precursors? What precisely happens to the ground in
the months or years following the earthquake? For these studies a wealth of
data became available as time went by after the earthquake and as ERS-1
and then ERS-2 continued to gather compatible data over the site.
Unfortunately the amount of radar data before the event remained small, and
the first of these questions, perhaps the most important in terms of hazard
mitigation, remains unanswered.
During the course of these experiments, significant new facts concerning the
interferometric technique were uncovere d. In particular, the importance of
atmospheric artefacts was suspected [Massonnet94] and fully characterised
[Feigl95] mainly on the Landers site. Two studies [Massonnet96 and Peltzer96] aimed to model the post-seism ic displacement that continued to
take place on the site after the earthquake. Different mechanisms of
post-seismic fault slip were proposed. Ra dar interferometry is all the more
important in this activity since most of these displacements were aseismic,
and therefore went unnoticed by conventional seismological records.
The scale on the post-seismic interferogram, Figure 3-3, speaks for itself. It
is clear that, to catch the smallest structures of displacement with ground instrumentation such as GPS receivers, it would be necessary to literally cover the ground with instruments. Such a density is not realistic. On
adequate surfaces, such as those that can be found in Iceland, the western
United States, Chile and many more places, having a radar archive suffices
for study of any upcoming event in the most remote regions. In this regard,

TM-19 _________________________________________________________________________ InSAR Principles
A-36 an archive such as the global coverage of the land surface gathered by ERS-1
and ERS-2 is a genuine ‘memory of the Earth’ that can be compared with
new acquisitions taking place years late r, possibly by another satellite. In a
sense, radar interferometry can turn every pebble into a GPS receiver.

Figure 3-3: Illustration of post-seismic displacement

__________________________________________________ SAR D ifferential Interferometry basics and examples
A-37 3.5 A case of coherence loss: India
One of the drawbacks of the academic way of communicating is that failures
are never published. Here we describe one of these failures.
After the disastrous earthquake of Latu r, in India, ESA made some ERS-1
images available. Unfortunately, the im ages show a mostly incoherent result.
Figure 3-4a shows the typical landscape: a
mostly agricultural landscape with many
small cities and villages scattered from place
to place. Some mild topography is
detectable in the south of this amplitude
image.
Figure 3-4b shows a co-seismic
interferogram created from ERS-1 orbits
8409 and 11916, i.e. between 23 February
1993 and 26 October 1993. The quality of
the interferogram, which includes a
negligible topographic component because of a very small orbital separation, does not
allow a clear recognition of any ground
displacement. The task is further aggravated because no reliable modelling of the expected displacement exists.

TM-19 _________________________________________________________________________ InSAR Principles
A-38 Figure 3-4c shows another interferogram
created from orbits 8409 and 5403, i.e.
between 23 February 1993 and 28 July
1992. The quality of the interferogram is
similar to the previous one, and includes a
topographic signature especially visible in
the south of the image.
Figure 3-4: Failed example due to coherence loss: the Latu r earthquake in India. The dr amatic event of Latur, on
30 September 1993, was an opportunity to expand the demonstration of interferometry for the mapping of
co-seismic deformation. Although some previous images from the site existed, and despite a systematic acquisition
by ESA after the event, difficulties ar ose because it was monsoon time, whic h drastically changes the surface
conditions. In addition, the region is used for agriculture.
The area is used mainly for agriculture and located in a monsoon region with
heavy rainfalls. Surprisingly, the only areas that retained coherence are the
cities and villages, despite the large-scal e destruction they experienced. This
is not a unique case; often cities heavily damaged by earthquake remain
quite coherent. This might be an indica tion that the main contributors in the
radar signal of a city are not much damaged by earthquakes. In any case, one
should not restrict interferometric studies of damaged cities for this reason.
3.6 A case of damaged raw data, studying a large
earthquake in Chile
Very large events emphasise the useful ness of the wide-area surveying that
is possible with radar interferometry. Sometimes, however, the deformation
field is so wide that even the wide 100 km swath of ERS cannot catch it
entirely. A large earthquake took place in Chile in July 1995, and was
studied, among others, by the IPGP (Figure 3-5). This example illustrates an
unusual error in data management.

__________________________________________________ SAR D ifferential Interferometry basics and examples
A-39

Figure 3-5: Large deformation field with errors: Chile earthquake
The large earthquake that struck the Atacama region in Chile on 30 July
1995 was an opportunity for interferome try very similar to the Landers
example: a large earthquake in a mostly desert environment. We see in
Figure 3-5 the typical behaviour of an interferometric signal (left is
amplitude, right is co-seismic phase). The area covered by ocean, around the
Mejillones peninsula, is not coherent. The rest of the landscape is
exceptionally coherent (except for the in terruption of fringe continuity which
is explained below). This example illustrates how very big events can actually outspan the size of ERS images, in spite of their being the widest radar images available in standard mode (i.e. not SCANSAR). Another
striking aspect of this example is the very smooth deformation pattern, without any visible surface rupture (again discounting the processing artefacts mentioned above). The data from this site that were processed,

TM-19 _________________________________________________________________________ InSAR Principles
A-40 analysed in cooperation with the IPG of Paris, were generally made of strips
of four or five ERS images in length.
The interruption in the fringe continuity is due to missing lines in the raw
data. The interferometric techni que relies heavily on the strong
self-consistency of the geometry of radar images. Missing lines can break
this consistency. There are ways, however, to detect missing lines in raw
data. Denoting the complex samples of a data take as A(i,j), where i
represents the range pixels (from 1 to N) and j represents the pulse lines, we
can form the complex number:

∑∑∑
=
==
==
=
++
=
Ni
iNi
iNi
i
jiA jiAjiAjiA
j
12
121*
)1,( ),()1,(),(
)(ρ Equation 3.1
This quantity is similar to the one fo rmed on interferograms to compute the
coherence. Here the result is a complex number. The phase φ(ρ(j)) of this
complex number is an estimator for the mean Doppler of the scene D, once
it has been multiplied by the pulse repetition frequency PRF :
PRFj fjD *2))(()(πρ= Equation 3.2
The amplitude of ρ(j) is also very interesting because it gives the correlation
between adjacent lines of raw data. For ERS, this amplitude should be about
0.3, and if two lines exhibit a lower value (for instance 0.1 or less), it means that the two lines of raw data are not r eally adjacent, and so there must be at
least one missing line between them!
The test is really easy to implement and can be used to check the raw data.
Unfortunately, it cannot tell whether there is one or several missing lines between two lines which are found to be not adjacent.