Multi-image InSAR Analysis over the Three Gorges Region:

Techniques and Applications  

Teng Wang

Supervisors: Fabio Rocca and Mingsheng Liao

Politecnico di Milano,

Dipartimento di Elettronica ed Informazione

Piazza L. da Vinci 32, 20133, Milano, Italy

and

Wuhan University

State Key Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing

Luoyu Road 129, 430079, Wuhan, China

Tel. +39 02 2399 3040; Fax +39 02 2399 3413

Email: wang.teng@gmail.com

September, 2009

 

 

曾经沧海难为水, 除却巫山不是云. 

‐唐，元稹 

It is difficult to be water for one who has seen the great seas ,

and difficult to be clouds for one who has seen the Yangtze Gorges.

-Yuan Zhen, Tang Dynasty, translated by Lin Yutang

Contents

Introduction ...................................................................................................................................... 5 

Chapter 1.  Background and Datasets ........................................................................................ 10 

1.1. Three Gorges Project Background ...................................................................................... 10 

1.2. Test sites Description .......................................................................................................... 12 

1.2.1.  Badong county ......................................................................................................... 12 

1.2.2.  Three Gorges Dam .................................................................................................. 13 

1.3. Datasets ............................................................................................................................... 14 

Chapter 2.  Reconstruction of DEMs from Tandem Data in Mountainous Area Facilitated by

SRTM Data .............................................................................................................................. 16 

2.1. Introduction ......................................................................................................................... 16 

2.2. Linear Model of Phase Errors in Interferogram .................................................................. 18 

2.3. Methodology ....................................................................................................................... 21 

2.3.1.  Correspondence Determination Between Interferogram and SRTM DEM ............. 22 

2.3.2.  Linear Regression Analysis ..................................................................................... 23 

2.3.3.  Filtering Of Unreliable Height Points ..................................................................... 24 

2.4. Experimental Results ........................................................................................................... 26 

2.4.1.  Zhangbei Test Site ................................................................................................... 27 

2.4.2.  Three Gorges Test Site ............................................................................................ 32 

2.5. Conclusions ......................................................................................................................... 37 

Chapter 3.  Coherence Decomposition Analysis in Badong ..................................................... 38 

3.1. Introduction ......................................................................................................................... 38 

3.2. Coherence Decomposition ................................................................................................... 40 

3.2.1.  Geometric Coherence Estimation ............................................................................ 40 

3.2.2.  Temporal Coherence Estimation ............................................................................. 42 

3.3. Results ................................................................................................................................. 43 

3.4. Conclusions ......................................................................................................................... 50 

Chapter 4.  Time Series InSAR Image Analysis Methods ......................................................... 51 

4.1. Introduction ......................................................................................................................... 51 

4.2. Original Permanent Scatterer Technique ............................................................................. 52 

4.3. Stanford Method for Persistent Scatterer (StaMPS) ............................................................ 54 

4.4. Quasi- Permanent Scatterer Technique ............................................................................... 56 

4.5. Comparison and Discussions ............................................................................................... 57 

Chapter 5.  Slow Landslides Monitoring in Badong ................................................................. 59 

5.1. Instruction ............................................................................................................................ 59 

5.2. Test Site and Data Sets ........................................................................................................ 60 

5.3. Data Processing ................................................................................................................... 62 

5.3.1.  QPS Data Processing ............................................................................................... 62 

5.3.2.  StaMPS Data Processing ......................................................................................... 63 

5.4. Results and Discussion ........................................................................................................ 63 

5.5. Conclusions ......................................................................................................................... 66 

Chapter 6.  Three Gorges Dam Stability Monitoring ................................................................. 67 

Conclusions and Future Work ....................................................................................................... 68 

Bibliography .................................................................................................................................. 71 

Introduction Nowadays, China is in an era of rapid urbanization and infrastructure construction. Three

Gorges Project (TGP), the largest hydroelectric project in the world, is one of the most

significant constructions in China. The three main functions of TGP, namely, flood control,

power generation and navigation capability enhancement have been bringing about

remarkable economic, social and environmental benefits.

As a huge man-made project, TGP greatly changed the natural terrain of the upriver gorges.

During the 17-year construction, the water level of Yangtze River was risen more than 100

meters in Three Gorges region. A reservoir that is about 660 kilometers in length and

1.12 kilometers in width on average has been formed when the construction of the dam was

finished in 2006. More than 600 km2 land was flooded by the rising water.

Due to the high pressure of the reservoir on the riverbed and the water infiltration affection,

there exist potential crust instability along the river. The earth crust structure and the dynamic

variations of the gravity field in this area has been studied after the river was blocked [1, 2].

On the other hand, since the basement of the steep mountains was permanently flooded,

landslides caused by loosing mountain bodies endanger the residences near the river and the

navigating ships. Although high spatial density deformation monitoring in this area is highly

needed, the expenses of building more monitoring stations or carrying out more traditional

level survey are not feasible in such a huge scale. Using optical satellite images is able to

detect different kinds of rocks, and assess the regional landslides impact [3], however, the

Three Gorges area is often covered by dense clouds, optical images are not capable enough

for landslide monitoring. Moreover, it is impossible to measure quantitative deformation from

optical images.

Besides the upriver region, the stability of Three Gorges Dam has to be considered as well.

Indeed, deformation is unavoidable for each dam. Although small deformation is acceptable,

when the deformation overtakes certain extent, it could be very risky for a dam and obviously

the down river areas. Since the safety of Three Gorges Dam relates to millions of people

living in the downriver plain, the stability monitoring is extremely important. If we consider

that the dam deformation happens with millimeter level, high precision deformation

measurement methods are needed. Actually, a deformation monitoring network has been

designed and built around the dam [4], nevertheless, as we have mentioned, it is very difficult

to improve the spatial density of the measurement points.

Since radar was widely used in the Second World War, the resolution and capability of

imaging radar such as Synthetic Aperture Radar (SAR) was developing rapidly[5, 6].

Different from optical sensors, SAR offers us a capable tool to observe the earth in the

microwave frequency. Different from optical remote sensing, SAR actively transmits

electromagnetic wave to the earth, and receives, records the echo in a synthetic way.

Therefore SAR image is not affected by sun illustration or clouds. Along with the

development of space-borne SAR instruments, SAR interferometry (InSAR) that measures

coherent phase difference between SAR images were widely researched [7-13].

Two of the most important applications of InSAR technique are Digital Elevation Models

(DEM) generation and surface deformation monitoring [14-18]. The DEM generation is based

on the measurement of phase difference between two complex radar signals, i.e. the range

difference between the sensor and targets. Using the range difference and sensor orbital

parameters, one can derive the elevation of the illuminated surface. If the phase derived from

terrain can be subtracted from the interferogram, the movement of the ground in the light of

sight (LOS) direction can be measured by the interferometric phases.

The main limitations of repeat-pass mode InSAR technique are the geometric and temporal

de-correlations [19, 20]. Even though the coherence of two radar signals is high enough, the

atmospheric phase screen (APS) difference between master and slave images still reduces the

accuracy of the final results [21].

Aiming at the above restrictions of InSAR, Ferretti et al. proposed a framework to generalized

DEM from multi-interferogram with a wavelet approach [22] and then presented the

Permanent Scatterers InSAR (PS-InSAR) technique [23-25] in POLIMI. Instead of extracting

information from each pixel of an interferogram, PS InSAR firstly identify certain artificial or

natural point-like stable reflectors i.e. PS from long time series interferometric SAR images.

The coherence on PS is good enough to obtain sub-meter accuracy DEM and millimetric

terrain motion [26, 27]. The applications of PS-InSAR technique have been successfully

achieved especially in urban areas [28, 29]. Different implementations of PS technique have

also been developed by many research groups [30-36].

The main drawback of PS technique is the low spatial density of the detectable permanent

targets, particularly in extra-urban areas. Indeed, the lack of measured points can prevent

from monitoring an area of interest affected by deformation with space-borne SAR

techniques. In order to extract information from the distributed targets, small baselines

(SBAS) technique has been proposed in [37]. The main concept is the analysis of

interferograms with small normal baselines to reduce the geometrical decorrelation. On the

other hand, A. Hooper et al. developed the Stanford Method for Persistent Scatterer (StaMPS)

for exploiting the earth deformation without a priori deformation model [38, 39]. StaMPS

filters the phase in spatial and temporal dimensions separately to divide the interferometric

phase into height and ground deformation dependent, APS differential, and noisy parts. After

that, the time series phases are unwrapped in a three-dimensional (3-D) way. Besides SBAS

and StaMPS, new hints were also presented for multi-temporal analysis of SAR images that

allow to extract information also from partially coherent targets, namely, Quasi-PS (QPS)

technique [40].

With regular revisiting cycle and high precision deformation measurement capability, time

series InSAR images offer a very effective earth observation data to monitor the deformation

of Three Gorges Dam and its upriver region. The benefits that can be obtained are in three

aspects:

With time series InSAR image analysis techniques, it is not necessary to build

monitoring stations or carry out field work.

Since each SAR image can cover an area about 100kmx100km, the whole reservoir

can be observed with 7-8 tracks SAR images. In such a scale, we can measure not

only the deformation of the dam but also the slow landslides in the upriver area.

Many more deformation measurements can be extracted from the data sets. In some

area, even hundreds measurement points per km2 can be detected.

Since 2004, within the framework of China-EU cooperation Dragon Project, we began to

collect SAR images over Three Gorges region with mid-resolution ESA satellites, namely,

ERS and Envisat. However, at beginning of this work, the number of images was not enough

to carry out a reliable time series analysis. Therefore, we began this dissertation with some

results coming from single interferometric image pairs (chapter 2 and 3). From the end of

2007, as soon as we collected enough SAR images, different time series analysis methods

were applied over two test sites in Three Gorges region and the obtained results are shown in

chapter 5 and 6. The contributions of this dissertation are listed as follows:

1, A new approach is presented to produce DEM in mountainous areas with steep slopes

using ERS-1/2 tandem data.

2, Coherence decomposition analysis is proposed to extract temporal coherence and detect

point-like target from only one interferogram.

3, Three different kinds of time series InSAR analysis methods are described and compared.

4, Several subsidence areas are identified by StaMPS and QPS techniques in Badong. The

results are compared and cross validated.

5, For the first time, the deformation of Three Gorges Dam is measured and analyzed with 40

SAR images acquired from 2003 to 2008.

Chapters 2, 3 and 5, 6 of this work are written as independent studies based on manuscripts.

Chapter 2 has been published in a journal, Chapter 3 has been accepted in a journal, Chapter 5

has been presented in an international conference, Chapter 6 has been submitted to a journal.

For each associated manuscript there are multiple authors, the author of this dissertation is the

primary researcher for all of the four Chapters. Part of Chapter 4 is based on a manuscript

that is going to be submitted in a journal, the author of this dissertation is the second author,

and the material presented here is with permission of the first author.

Chapter 1 In this chapter, we provide a brief overview of TGP background. Badong county

and the dam area are selected as our test sites. Details of the processed ERS and Envisat SAR

image series are shown.

Chapter 2 In this chapter, a novel approach is proposed in order to reduce the impact of

phase errors on the InSAR-generated DEM. An external DEM such as that from Shuttle

Radar Topography Mission (SRTM) is utilized in the conventional InSAR procedures. The

proposed algorithm includes two steps: the first step is to model and remove phase trends with

a linear regression analysis before converting phase to height; the second step is to filter

unreliable height points before interpolating the DEM from the InSAR height map. The

method is tested in Badong to generalize a DEM in this vegetated area with steep terrain. this

chapter is based on the material that is published in Geoscience and Remote Sensing, IEEE

Transactions on [41].

Chapter 3 this chapter proposes an approach that allows in mountain areas 1) a simple and

very fast rough estimation of the temporal coherence 2) the identification of point-like targets

using just two images. The method has been applied and tested in Badong site using ERS

tandem data. This chapter is based on the material that is going to be published in Geoscience

and Remote Sensing Letters, IEEE [42].

Chapter 4 In this chapter, we briefly recall the original PS, StaMPS and QPS techniques. The

comparison among these three kinds of time series SAR image analysis methods is described

in a methodology point of view. The QPS technique is going to be submitted to Geoscience

and Remote Sensing, IEEE Transactions on [43].

Chapter 5 In this chapter we applied two time series InSAR techniques, namely QPS and

StaMPS, to measure the deformation trends around Badong with the same focused and co-

registered data set. The results are analyzed and compared. Two subsidence areas are

identified by both techniques. However, since the QPS is able to process partially coherent

targets, many more points are extracted than in StaMPS, and more information can be

retrieved. This chapter is based on the material presented in IGARSS08 with Travel Grant

Award [44].

Chapter 6 In this chapter, we carry out both PS and QPS analysis to extract geometric

information over the Three Gorges Dam and its surroundings. From our results, we find that

the temporal deformation of the left (north) part of the dam has stopped since 2003; the

deformation was influenced by the changing levels of Yangtze River. The seasonal

deformation caused by the temperature can be also observed. The results fit close to the

published Three Gorges Dam deformation trends measured by traditional survey methods.

We also find a potential landslide near Zigui county. This chapter is based on the material

submitted to Science in China, Series D: Earth Sciences [45].

Chapter 1.

Background and Datasets Since this work focuses on time series InSAR applications over Three Gorges region, at

beginning of this dissertation, we introduce some background knowledge about this

magnificent river-gorge area and TGP, the significant engineer project. Badong and the dam

are selected as our test sites for the following chapters. Thus, it is also necessary to give brief

introductions about the emigration history of new Badong city and some structure details

about the dam site. The time series InSAR images that we processed are also described.

1.1. Three Gorges Project Background

Three Gorges is an overall name given for a series gorges from Fengjie, Chongqing

Municipality to Yichang, Hubei Province along Yangtze River in China. The total length of

this region is about 200km. From west to east, the three most famous gorges are QuTang

Gorge(瞿塘峡), Wu Gorge (巫峡) and XiLing Gorge (西陵峡). Within this region, mountains

with steep terrain usually reach more than 1000m above the river. Yangtze that comes from

Tibetan Plateau passes these mountainous gorges and then reaches the most populated and

urbanized regions of China. Since Yangtze is a seasonal river, floods happen each raining

season (from May to October), the downriver plains, for example, Jianghan plain is

endangered almost each five years. Actually, the most important objective for constructing

TGP is to control the seasonal floods of Yangtze.

TGP locates in Sandouping (三斗坪), the east exit of Three Gorges region. Figure 1-1 shows

the geographic location of TGP in China. With the formed huge reservoir, TGP can release or

store the water by considering different flow runoffs. In the mean while, clean electricity

power can be generalized by the different water levels between up- and down-river of the

dam.

However, the benefits are not gained without paying for. By the numbers from TGP official

website, 13 cities (or towns), 116 villages have to be totally or partially flooded. 1.1 million

people have to be emigrated. Many ancient towns and buildings have to be moved and rebuilt

in higher locations. Badong, one of the typical emigrated towns is selected as one of the test

sites in this dissertation.

Figure 1-1 location of TGP in China. Map of China comes from Chinese State Bureau of Surveying and Mapping, The map of TGP comes from wikipedia.

The construction of TGP consists of three phases in 17 years:

1, the preparatory and first-phase projects spanned five years from 1992-1997, its completion

was signaled by blocking Yangtze River on November 8; 1997

2, the second phase ran from 1998 to 2003. This phase was completed when the first

generator unit in the left-bank hydropower station went on line and the permanent ship lock

began operation. In 2002, the construction of the dam (left part and mid part) finished.

3, the third phase was planned for 2004-2009. This final phase includes the completion of all

32 electricity-producing turbo generators, in which, 26 units are in left and right hydropower

plants, 4 units are underground power plants and 2 units are built for power needed by the

project itself.

The timeline of this 17-year construction is indicated in Figure 1-2 with changing water levels

of Yangtze River.

Figure 1-2 Timeline of the 17-year TGP construction. The blue line represents the water level of upriver part of Yangtze River.

1.2. Test sites Description

Except for the dam site and some towns, most of Three Gorges region is vegetated terrain

with extremely steep mountains. Therefore, the test site should be carefully selected

considering both processing time and application paybacks. In other words, for DEM

generation and land use monitoring, large area should be included with different types of

terrain. For deformation monitoring, small areas with residences and the dam itself should be

considered. Following this strategy, Badong and the dam are selected as our test sites.

1.2.1. Badong county

Badong County is settled on riversides of the Yangtze River, in Hubei province. It is located

just between Wu Gorge and Xiling Gorge in the Three Gorges region. The old town of

Badong has a history of more than 1500 years. Due to the construction of TGP, this town was

going to be under the rising water. Therefore, the emigration of the whole town was organized

in the summer of 1997. Almost all the buildings of the old town were demolished.

Meanwhile, a new town was under construction about 5 km away toward the west. After 5-

year construction, in 2002, the new town which covers about 7.3 km², with more than 50,000

residences began to form. A bridge over the Yangtze River was also built to connect the south

and north parts of the new town.

Figure 1-3 shows the old and new Badong from Google Earth. It also shows steep mountains

and complicated land use types around this area. Moreover since the town was built along the

steep river banks, slow landslides monitoring is very important for all the residences in new

Badong. Actually, many consolidation works were settled for landslide protection in Badong.

In the following chapters of this dissertation, the results presented in Chapter 2, 3 are in a

50km x 50km area centered with new Badong county. The results presented in Chapter 5 will

focus on a smaller area around the new-built town.

Figure 1-3 Badong old and new county from Google Earth.

1.2.2. Three Gorges Dam

Naturally, besides Badong, Three Gorges Dam is considered as another test site for this work.

Three Gorges Dam locates in Sandouping, where 40km away from Yichang, Hubei province.

The terrain around the dam site is quite open and a small island located in the middle of the

river before TGP was constructed. The geological conditions are very suitable for concrete

gravity dam [46].

Three Gorges Dam is a huge man-made target, the concrete gravity dam wall is about 2,335

meters long and 185 meters high above the sea level. The body of the dam is 115 meters wide

on the bottom and 40 meters wide on top. The project used 28,000,000 m³ of concrete,

463,000 tons of steel, and moved about 134,000,000 m³ of earth. The sketch map of the dam

area from Google Earth is shown in Figure 1-4. Different letters are used to indicate the

complicated targets in this test sites. The structural details of hydropower stations, spillway

etc. that reflect the electromagnetic signal can be seen by the SAR satellites. This allows

monitoring it from the time series InSAR images.

Figure 1-4 Sketch map of Three Gorges project. The background image comes from Google Earth software.

1.3. Datasets

Since 1992, European Spatial Agency (ESA) European Resource Satellite-1 (ERS-1) began to

acquire SAR images over Three Gorges area. ERS-2 and Envisat satellites joined in from

1996 and 2003 respectively. Two tracks of time series images are collected for obtaining the

results shown in this dissertation, namely Track 347 and Track 75. Both these two tracks data

are in the same Frame, 2979.

The coverage and topography of the images are shown in Figure 1-5. The elevation data are

from 3-arc SRTM DEM. Badong and Three Gorges Dam test sites are indicated with red

rectangle. Black holes in the background are void data in SRTM DEM. Figure 1-6 shows all

the available images in these two tracks. The acquisition time was indicated with different

Yangtze River level. In the following chapters, we begin our results obtained from two

tandem image pairs and then move to the Envisat time series images.

Figure 1-5 Coverage and topography of ESA satellites, Track 347 and Track 75. The elevation data are from 90m resolution SRTM DEM. Badong and Three Gorges Dam test sites are indicated with red frame. Black holes in the background are void data in SRTM DEM.

Figure 1-6 data set of Track 347 and Track 75. Images are shown with different Yangtze River levels.

Chapter 2. Reconstruction of DEMs

from Tandem Data in Mountainous

Area Facilitated by SRTM Data

In this chapter, a new approach is presented in this paper to produce Digital Elevation Model

(DEM) in mountainous areas with steep slopes using ERS-1/2 tandem data. In order to reduce

the impact of phase errors on the InSAR-generated DEM, an external DEM such as that from

SRTM is utilized in this approach. The proposed algorithm includes two steps: the first step is

to model and remove phase trends with a linear regression analysis before converting phase to

height; the second step is to filter unreliable height points before interpolating the DEM from

the InSAR height map. The critical points are: 1) determining the one-to-one correspondence

between the interferogram and the SRTM DEM before knowing the InSAR derived elevation

values; 2) estimating the elevation range of every pixel from SRTM DEM. To solve the first

problem, an iteratively geocoding algorithm is performed. A DEM interpolation error model

solves the second one. For InSAR data processing the SRTM DEM is not only usable for

modeling systematic phase errors but also for filtering gross height errors. The experiments in

Zhangbei and Three Gorges areas in China show that our approach improved the accuracy of

the resulting DEMs significantly without any ground control points.

2.1. Introduction

One of the most important applications of nSAR technology is the generation of Digital

Elevation Models (DEM). The DEM generation is based on the measurement of phase

difference between two complex radar signals, i.e., the range difference between the sensor

and the targets. Using the range difference and sensor orbital parameters, one can derive the

elevation of the illuminated surface [47].

It is well considered that phase error is one of the main error sources of InSAR-generated

DEM with repeat-pass satellite mode [7]. The phase error consists of three parts. 1) phase

trends caused by orbital errors in the flattened interferogram; 2) errors caused by de-

correlation, thermal noise; 3) Atmospheric Phase Screen (APS) difference between master

and slave images.

When a DEM is constructed from interferogram, the phase trends will convert to systematic

elevation error, which can be reduced or removed using ground control points (GCPs) in data

processing [14]. However, it is not always easy to identify GCPs in some wild areas from

SAR images.

For the phase errors caused by geometrical and temporal de-correlation, the accuracy of the

elevation is affected by these accidental and/or gross errors especially for the repeat-pass

satellite mode [19]. Although the accidental phase errors can be reduced by filtering or

averaging the interferogram, the gross errors are difficult to remove.

The model of atmospheric affect errors in interferogram is very complex. It can be divided

into topographic dependent and independent parts [13, 48]. Without knowledge of terrain

information before DEM generation, the topographic dependent atmospheric errors are very

difficult to remove. Ferretti et al. averaged multi-baseline InSAR DEMs using wavelet

approach for weighting to remove atmospheric effect in DEMs [22]. Although the accuracy of

the resulted DEM can be very good, the requirement of multiple data sets is hardly to meet in

most cases of topographic mapping.

From geometry formulation of InSAR, the impact of all these phase errors is in inverse

proportion to the length of normal baseline. The height errors from interferometric phase

errors are reduced when the normal baseline is long, but the signal-to-noise ratio (SNR) of

interferogram decreases with the baseline increasing [47]. Moreover, the height change that

leads to a change in interferometric phase (height ambiguity) is also inversely proportional to

the length of normal baseline. Therefore, in mountainous areas, steep terrain often causes

phase aliasing in interferogram with long baselines, which make it difficult to unwrap the

phase.

On the other hand, in the case of short normal baseline, though the interferogram may be

unwrapped easily with high coherence and low local phase frequency, the errors mentioned

above will make the resulted DEM far from application. Additional, errors from de-

correlation and thermal noise may convert to gross height errors which destroy the

interpolated DEM. Therefore, to get good result from short baseline data set, the restrain of

phase error is strongly required.

As a consequence of the analysis above, the selection between long and short baseline data

sets for mountainous area DEM generation is in a dilemma. However, when certain prior

knowledge about terrain of the interested area is obtained, most of the difficulties could be

overcome.

Seymour and Cumming presented an approach to use coarse low-quality DEMs reducing

local phase bandwidth of interferograms. Lower local fringe frequency makes the probability

of residues lower and the procedure of phase unwrapping easier [49]. Eineder and Adam used

external DEMs to reduce the search range of elevation when using a maximum likelihood

estimator to simultaneously unwrap, geocode, and fuse SAR Interferograms from different

viewing geometries into one DEM [50]. Y. Sang-Ho et al. presented an approach to merge the

high and low resolution InSAR derived DEMs in the frame of a prediction-error filter [51].

All the works above offered clues of making use of existed low resolution DEMs in

procedures of InSAR DEM generation.

In this study, the usage of external low resolution DEMs, such as Shuttle Radar Topography

Mission (SRTM) DEM data is concerned from a novel aspect. As an external DEM data set

here, the SRTM DEM is used with the following two purposes: One is to model the linear

part of phase errors (trends) that are relative to azimuth, range and height in radar’s slant

range space by linear regression analysis; another is to remove the unreliable height points

before DEM reconstruction.

Facilitated by SRTM DEM, the systematic errors in interferogram can be removed. Although

the accuracy of SRTM DEM is not as high as GCPs, depending on the amount and

distribution of the elevation grids, our work shows that the estimation of phase trends

coefficients is reliable from statistic perspective. Besides the systematic error, the pixels with

gross errors can be filtered as well depending on the estimated elevation range.

2.2. Linear Model of Phase Errors in Interferogram

InSAR geometry and error model of DEM generation have been discussed in many

publications . In this section we review the interferometric phase errors from the view of a

linear model. The variable in this model are coordinates in azimuth, range directions and

phase calculated from SRTM DEM.

The interferometric phase of a pixel is caused by:

1, sensor-target range difference between sensors;

2, possible physical and geometric character changes of ground scatters;

3, changes of atmosphere between two data acquire times;

4, thermal noise etc.

As shown as (3.1), the interferometric phase consists of above four terms, which are written

as , , , r t a nφ φ φ φ respectively.

r t a nφ φ φ φ φ= + + + (3.1)

Because we focus on InSAR DEM generation in this paper, tφ is neglected by using ERS-

1/2 tandem data sets due to their one day interval.

rφ can be divided into two parts. Figure 2-1 (a) shows the phase difference resulting from the

height difference with an identical slant range and Figure 2-1 (b) shows that resulting from

the slant range difference with an identical height. In Figure 2-1 (a) and (b), A1 and A2

represent two SAR sensors, B is the baseline, R is the range in the line of sight (LOS) from

ground target to the SAR sensor, θ is the incidence angle, and α is the angle of baseline with

respect to the horizontal plane.

Figure 2-1 phase difference geometry. (a) geometry of phase difference from the height difference with an identical slant range. (b) geometry of phase difference from the slant range difference with an identical height.

From Figure 2-1 (a) and (b), the phase difference, i.e. zφ and fltφ , can be written as (3.2) and

(3.3), respectively:

cos( )4

sinzB z

R

θ απφ

λ θ− ∆

= − (3.2)

cos( )4

tanfltB R

R

θ απφ

λ θ− ∆

= − (3.3)

Here, z∆ is the height difference of target on ground with an identical slant range, and R∆ is

the slant range difference of target on ground with an identical height. Equation (3.3) means

that flatten earth can also cause phase changes. In InSAR processing, this part of phase

differences can be modeled and removed as reference phase in the “flatten earth” step using

orbital information.

However, errors in orbital parameters may cause additive phase trends in the flattened

interferogram. Because most of orbital errors are systematic and relative to SAR coordinates

in azimuth and range directions, we can model the phase trends as:

1 2trd c l i l jφ = + + (3.4)

In (3.4), c is a constant, i and j mean SAR image coordinates in azimuth and range

directions respectively, 1l and 2l are linear coefficients of phase trends.

Using the model shown as (3.4), the mean value of atmospheric effect can be estimated as

well. However, as mentioned in Section 2.1, in mountainous areas, except from azimuth and

range directions, the APS difference between master and slave images is also partly relative to

terrain. So we modify the model described in (3.4) as:

1 2 3trd zc l i l j lφ φ= + + + (3.5)

Now we can rewrite (3.1) as:

z flt trd n rsdφ φ φ φ φ φ= + + + + (3.6)

In this phase model, fltφ was removed in the generation of interferogram and zφ can be

obtained from SRTM DEM. Additionally, nφ is the phase noise and rsdφ is the APS difference

residue phase.

After fltφ and zφ are subtracted from the interferogram, the phase difference can be written as:

trd err n rsdφ φ φ φ φ∆ = + + + (3.7)

Here, errφ is the SRTM DEM elevation error in phase. Because SRTM was a single-pass

mission, the influence of uncertainty of baseline and APS difference has been highly reduced.

The assumption that the errors of SRTM DEM fit a normal distribution of zero mean and

constant standard deviation in the range of test area is performed. Also, the impact of nφ and

rsdφ is neglected in the linear regression analysis due to the large number of regression

samples and selective strategy described in the next section.

Except the modeled phase trends errors, the gross errors in some pixels due to phase noise,

phase unwrapping and/or radar shadow in InSAR-derived height map may exist, which will

reduce the accuracy of DEM product. This part of errors can be handled by estimating

reasonable elevation range from SRTM DEM.

From the above analysis, the motive of our algorithm is obvious. Firstly the coefficients

, ( 1,2, 3)nc l n = are regressed, and then the threshold to filter gross errors from unwrapped

interferogram and SRTM DEM is estimated. These estimations are performed on radar’s slant

range space and object space i.e. map geometry space respectively.

2.3. Methodology

Figure 2-2 Flow of our approach

As described in the previous sections, the working flow of our approach is shown in Figure

2-2. Phase difference between interferogram and the SRTM DEM are calculated. Then linear

regression analysis is performed to model the systematic errors before the phase to height

conversion. Finally, on the height map, a certain threshold is estimated from the SRTM DEM

to remove pixels with gross errors.

Although the data processing looks straightforward, still some technical details need to be

well considered. The most important two problems are how to get the one-to-one

correspondence between interferogram and the SRTM DEM before knowing the elevation

values derived from InSAR and how to estimate the elevation range of every pixel from the

SRTM DEM. The solutions are shown as follows.

2.3.1. Correspondence Determination Between Interferogram and SRTM DEM

In order to model the systematic errors of the InSAR DEM, the difference between InSAR

and SRTM data should be calculated. This difference can be described in two spaces, the

object space showing the height difference and the radar’s slant range space representing the

phase difference.

If the height difference is measured, the unwrapped interferogram should be converted to a

height map and geo-referenced into the object space. However, precise geocoding requires

every pixel’s elevation [8]. The height calculated from interferogram is far off from true value

before removing the phase trends and obtaining the absolute phase. Thus, the horizontal errors

caused by geocoding make the measurement of the height difference be very inaccurate.

Although from the SRTM DEM, we can obtain every grid point’s coordinates in the SAR

image, the phase still need be resampled from the interferogram. So, the problem is that we

cannot directly get a one-to-one correspondence between interferogram and SRTM DEM in a

forward way that is from azimuth and range direction to geographic coordinates or the

backward way either.

In our algorithm, the solution is using the SRTM DEM elevation to modify the ellipsoid

parameters i.e., the semimajor and semiminor axes and iteratively approach each pixel’s

SRTM DEM elevation. After the procedure converging, the SRTM elevation can be

converted to the interferometric phase.

Delft Object-oriented Radar Interferometric Software (Doris)’s phase to height ambiguity

algorithm [52] is adopted to compute the corresponding SRTM DEM elevation of every

image pixel and other parameters. This procedure is iteratively performed for each pixel as

the following steps:

1. Use the azimuth coordinates and orbital parameters to locate the SAR positions of the

master and slave images.

2. Set current height to be zero as an initialized value.

3. Modify ellipse parameters using the current height.

4. Compute the latitude and longitude for each pixel using Doppler equation, slant range

equation, and earth ellipse equation.

5. Calculate the parameters in (3.2) such as the incidence angle, the sensor-to-target

range and the normal baseline corresponding to the current height.

6. Interpolate bilinearly the current height from SRTM DEM grid. If the elevation value

is void, neglect this pixel and go to next pixel of the interferogram.

7. If the difference between current and previous heights is less than a threshold initially

set, the procedure halts. Otherwise, go back to steps 3 to 6.

Since the SRTM DEMs are generated with radar interferometric technique, missing elevation

values i.e. voids exist in the data sets. In this algorithm, the voids were discarded due to the

large number of regression samples.

Because some targets on ground have the same ranges to the sensor, mapping from radar

coordinate system to earth is not a unique transformation especially in mountainous areas. If

the number of the iterations reaches a pre-setting value, and the height has not converged yet,

this pixel will be discarded as the relationship between its SAR coordinate and the SRTM

elevation cannot be reconstructed in object space. Thus, only the pixels with stable and valid

SRTM elevation values are selected for linear regression analysis.

2.3.2. Linear Regression Analysis

Considering that the phase difference for pixels with low coherence may be far off from our

model, a certain coherence threshold should be set to discard these pixels. A trial-and-error

method is used in this paper.

Excluding the residue of atmospheric effects, the power of phase noise nφ can be estimated

from the absolute value of the coherence γ̂ [53]:

2

20 2

ˆ1[( ) ]

ˆ2 l

En

γφ φ

γ

−− = (3.8)

Here ln is the multi-look number, 0φ is the noise-free phase value and 20[( ) ]E φ φ− is a kind

of absolute coherence estimation value. In order to reduce the phase noise by averaging the

interferogram, ln is set to 20 (10 in azimuth and 2 in range) in this paper. ln is depends on the

quality of the data. The coherence threshold was set as 0.2 experientially in this study to

discard low coherence pixels and offer enough regression samples.

Once the pixels of the multi-looked interferogram as well as their phase difference φ∆ are

determined, the linear regression equations can be written as:

1 11 1 1

2 2

3

1

... ... ... ......

1

z

n n znn

li j

l

li j

c

φφ

φ

φφ

⎡ ⎤ ⎡ ⎤∆⎡ ⎤ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥∆⎢ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ∆⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

(3.9)

n means the number of phase difference samples. Then, the coefficients 1 2 3, , ,c l l l are derived

by a least-square estimation as shown as (3.9).

For avoiding the affect of phase unwrapping errors, the regression procedure is also

performed iteratively. When the phase trends are estimated, the statistics of residue phase are

considered. The pixels with residue phase values larger than 2 times of standard deviation are

removed and the phase trends are estimated again until the number of the pixels with larger

phase residue is less than a certain value, for example, 1% of the total interferogram pixels.

Then the phase trends can be modeled as described as (3.5). Using this model, the phase

trends are removed pixel by pixel across the whole interferogram before the phase to height

conversion.

2.3.3. Filtering Of Unreliable Height Points

After removing the phase trends, the unwrapped interferogram can be converted to a height

map by using the iterative procedure described above, except for step 6. Here, the height

should be calculated from (3.10), which can be inferred from (3.2):

sin

4 cos( )z RzB

φ λ θπ θ α

= −−

(3.10)

Since geocoding can be done in this procedure, the longitude, latitude, and height referenced

to WGS84 are obtained for each pixel. Then the threshold to remove pixels with gross height

errors is determined depending on the location in the SRTM DEM elevation grid.

Based on Chebyshev theorem, no matter what distribution of the errors fits, the probability

that any error is within the interval of 4µ δ± is at least 94%. (µ and δ are mean and standard

deviation here) [54]. Therefore, we set 4 times of the SRTM elevation error as the criteria to

remove unreliable pixels. The absolute height difference between InSAR-resulted height

points and corresponding SRTM elevation is considered. Only the points with smaller height

difference than the threshold are used to reconstruct DEM. The difficulty here is how to

estimate error standard deviation of SRTM DEM in the location of each interferogram pixel.

The SRTM height values are interpolated using a bilinear interpolation as shown in the

following equation, which is based on the location of pixels in interferogram as shown in

Figure 2-3:

1 2 3 4(1 ) (1 ) (1 ) (1 )ih dx dy h dx dy h dx dy h dx dy h= − ⋅ − ⋅ + ⋅ − ⋅ + − ⋅ ⋅ + ⋅ ⋅ (3.11)

Figure 2-3 Sketch of SRTM elevation interpolation.

Here 1h to 4h are height values of grid nodes 1 to 4. ih is the interpolated height value. dx

and dy are the distances from the interpolated height point to the upper left grid node in x and

y axes which are normalized to 1. The error deviation of the interpolated height can be

expressed from the deviation of the grid node and dx , dy as:

2 2 2

2 2

2 2(1 ) (1 ) (1 )

2 2(1 )

i nod nod

nod nod

dx dy dx dy

dx dy dx dy

δ δ δ

δ δ

⎡ ⎤ ⎡ ⎤= − ⋅ − ⋅ + ⋅ − ⋅⎣ ⎦ ⎣ ⎦⎡ ⎤ ⎡ ⎤+ − ⋅ ⋅ + ⋅ ⋅⎣ ⎦ ⎣ ⎦

(3.12)

2iδ is the deviation of interpolated height, and 2

nodδ is the deviation of grid nodes of the SRTM

DEM. To estimate 2iδ , 2

nodδ should firstly obtained. The experiential model (3.13) from [54] is

adapted to get 2nodδ in (3.12):

2 2 24 5

9 3Surf nod Tδ δ δ= + (3.13)

Here 2Surfδ is the mean value of elevation deviation on the bilinear surface, and 2

Tδ is the

reduced accuracy due to the linear model to express the real surface. The estimation of 2Tδ is

very complicated, which depends on the mean slope of terrain. If the values of 2Surfδ and 2

Tδ

are obtained, the interpolated SRTM elevation error iδ can be estimated from (3.12) and

(3.13). The detail of getting 2Surfδ and 2

Tδ , which depend on the test sites, will be presented in

the next section.

Because the height threshold for each pixel of interferogram needs to be estimated from the

SRTM DEM grid, the voids of SRTM DEM should be removed before this procedure by a

3 3× moving window using the following equation, which was applied to the entire study

area.

1( 1,2,... )ih i n

n=∑ (3.14)

Where, n means number of valid height points in the window.

Then, the elevation difference between the interferogram and the SRTM DEM is obtained,

and the pixel with this difference over the estimated threshold is removed. Finally, the

resulted DEM is interpolated from the filtered height map.

2.4. Experimental Results

Two pairs of ERS-1/2 tandem images in different areas are chosen as our test data sets. The

basic information of these data sets is summarized in Table 2-1.

The interferograms are averaged with the factor of 10 in azimuth and 2 in range. Flynn’s

minimum discontinuity method was used for phase unwrapping because of its global

minimum L-1 normal solution [55, 56].

Table 2-1 BASIC INFORMATION OF DATA SETS

Zhangbei Data Set. TRACK: 32 FRAME: 2781

ERS1 Orbit ERS2 Orbit ERS1-2 Date |Bn|

32585 12912 08-09/10/97 287 Three Gorges Data Set. TRACK: 32 FRAME:2979

ERS1 Orbit ERS2 Orbit ERS1-2 Date |Bn|

23610 03937 20-21/01/96 16

The threshold to filter unreliable height points was estimated depending on accuracy

assessment of SRTM DEM and terrain undulation of the test sites.

The expected vertical accuracy is about 16 m (at 90% confidence) for the 1 arc-second SRTM

DEM released for the U.S. territories [57, 58]. For the areas out of the U. S., the resolution of

the SRTM DEM is reduced to 3 arc-seconds and the accuracy should be lower than 16 m.

Considering the steep slopes in our test sites, we assume the standard deviation of SRTM

DEM error 2Surfδ as 50m and 2

Tδ as 10 m. 2nodδ was obtained from (3.13). Then the threshold

of every InSAR height points was determined by 4 times of the standard deviation. The

results in these two test sites are shown as following.

2.4.1. Zhangbei Test Site

Zhangbei area locates in north-west of Hebei province, China. Figure 2-4 is the sketch of the

50 50× km wide test site acquired from Google Earth. The grassland in Zhangbei is well

known as “hometown of clouds” in China. It means that this area is often covered by clouds

as shown on the Google Earth image of Figure 2-4. So the advantages of InSAR DEM

generation technology are obvious in this area.

Figure 2-4 Sketch of our test site from Google Earth.

The test site is a part of Ba Shang grassland. The meaning of the Chinese word Ba Shang is

“above a dam”. In this area, the terrain rises from 1000m to near 2000m rapidly. The black

line in the middle of Figure 2-4 flags the step-shape topography. Figure 2-5 and Figure 2-6

show the unwrapped interferogram and coherence map.

Figure 2-5 Unwrapped interferogram of Zhangbei data set.

Figure 2-6 Coherence map of Zhangbei data set

The estimated phase trends are shown in Figure 2-7. Because the absolute phase of

interferogram is also determined in the procedure, range of the phase trends is from 200 to

320 radians. The local APS difference, which is relative to terrain, can be seen from this

figure.

Figure 2-7 The estimated phase trends of Zhangbei data set

Figure 2-8 presents height maps and their histograms before and after removing phase trends.

From the histogram of height map, the step-shape terrain can be clearly identified after the

phase trends are removed.

Figure 2-8 Height maps and their histograms before and after removing phase trends of Zhangbei data set. (a) Height map before phase trends removal. (b) Histogram of (a). (c) Height map after phase trends removal. (d) Histogram of (c).

Because of the satisfied baseline for DEM generation of this data set, the number of filtered

pixels with gross height errors is not so large (only 40739 of 1416064 pixels).

Figure 2-9 Resulted DEM of Zhangbei data set with 2692 vector check points from aerial-photogrammetry.

Figure 2-10 The comparison of errors on check points between traditional InSAR technology, SRTM DEM and our approach.

The resultant DEM is show in Figure 2-9. The left rectangle is selected for quality evaluation.

In this patch, dense elevation data are collected from aerial-photogrammetry as check points.

Total 2692 vector height points are shown in the right rectangle. The elevation data are

measured for generating 1/10000 topographic map and the accuracy is better than 2m. The

elevation values on this check points are interpolated from the resultant DEM to compare

these data sets. The errors of the traditional InSAR technology, SRTM DEM and our

approach are plotted in Figure 2-10. The standard deviation of elevation errors of SRTM

DEM on these check points is about 11.4m. After phase trends removal and height map

filtering, the standard deviation of elevation errors improved from 57.9m to 9.2m and was

better than SRTM DEM.

Although the accuracy of our method is nearly the same as the SRTM DEM, the elevation

data density of these two data sets should be considered. The SRTM DEM has about 90-m

node distance, which is near three times of the multilooked interferogram in our experiment.

In this sense, more details of surface will be reflected when the terrain is difficult to be

interpolated from low-density elevation data. Therefore, the advantage of our method will be

more obvious when the terrain is more complex.

2.4.2. Three Gorges Test Site

The Three Gorges region of Yangtze River in China was chosen as another test site due to its

mountains with steep slopes and complex water vapor distribution. In this test site, the

geometry de-correlation strongly reduces the coherence of interferogram with long baseline.

Figure 2-11 shows interferograms and their coherence maps with different baseline in this

area. From this figure, the interferogram with 200m baseline is impossible to be unwrapped

successfully due to the phase aliasing, and the coherence value is much lower than the

interferogram with 16m baseline.

However, with short baselines, the phase and baseline errors would lead to large uncertainty

when a DEM is constructed. The distribution of phase errors are influenced by the uncertainty

of orbital parameters and APS difference of the master and slave images as mentioned in

section 2.1. In the case of short baselines, the height trends caused by systematic errors of the

interferogram will be up to useless values. These shortcomings make interferogram with high

coherence but short baseline be scarcely used for DEM generation. Facilitated by the SRTM

DEM, the disadvantages of short baseline interferogram can be partly overcome. The

following results show that the quality is improved by using the presented approach.

The procedures for data processing are the same as the ones in Zhangbei data set. The

estimated phase trends in Three Gorges data set are shown in Figure 2-12. Considering the

baseline of this data set, if not being removed, the phase trends will cause height errors even

up to thousands of meters. Therefore, the DEM from the interferogram with phase trends is

not considered in the quality assessment.

Figure 2-11 Interferograms and their coherence maps with different baseline in Three Gorges area. (a) Interferogram with 200m baseline. (b) Interferogram with 16m baseline. (c) Coherence map of (a). (d) Coherence map of (b)

The procedure for height map filtering is very important due to the short baseline. It showed

that 907 711 height points among 1 725 635 pixels of the interferogram were observed with

the height difference between InSAR and SRTM height values less than the estimated

threshold. Although the number of points for DEM reconstruction is only about half of the

whole interferogram, the terrain details are more clearly portrayed, as shown in Figure 2-13.

Figure 2-12 The estimated phase trends of Three Gorges data set

In order to assess the quality of the DEM derived from our approach, a 1 : 50 000 DEM over

the Three Gorges was used for intercomparison. This DEM was created by digitizing maps in

the National Center for Geomatics of China, and the accuracy of grid nodes is claimed to be

11 m in mountainous region.

Due to the lack of high-accuracy DEMs or check points in this test site, the comparison

among the DEMs is performed on two profile lines. Fig. 14 plots the profile analysis among

1:50 000 DEM, and the InSAR DEM before filtering gross errors and after filtering gross

errors of the Three Gorges area. From this figure, the high frequency errors caused by gross

height errors are strongly reduced. Because of the steep terrain, some radar shadow areas

strongly affect the error standard deviation (about 50 m), which is calculated from the

elevation difference between the resulted DEM and 1:50 000 DEM. Also, the horizontal

errors while converting the InSAR-derived DEM into map project (Xi’an geodetic coordinate

system 1980 of China) carry certain elevation errors caused by the horizontal errors as well.

However, as shown in Figure 2-13 and Figure 2-14, the quality improvement using our

approach is obvious.

Figure 2-13 Comparison of DEMs before and after filtering gross errors of Three Gorges data set. The white rectangle indicates the profile analysis area. (a) DEM before filtering gross errors. (b) DEM after filtering gross errors.

Figure 2-14 Profile analysis among 1:50,000DEM, InSAR DEM before filtering gross errors and after filtering gross errors of Three Gorges area. (a) Sketch map of two profile lines. (b) Profile line A. (c) Profile line B.

2.5. Conclusions

In this paper, an approach for DEM construction from ERS Tandem data is presented. The

SRTM DEM is used as external DEM data to model and remove symmetrical phase errors

and APS difference. Another advantage of the presented approach is that, before interpolating

the resulting DEM from the InSAR height map, pixels with gross height errors can be

removed by the threshold derived from the SRTM DEM. Experimental results in two test sites

proved the potential of our approach in reducing phase errors and APS difference. Taking into

account the steep slopes, the improvement of standard deviation of elevation errors is

remarkable. Since the SRTM has opened the world wide 3 arc-seconds resolution DEMs and

made them downloadable from Internet, this new approach provides an effective tool to make

use of existing low-resolution DEMs in interested cloud-covered and rainy areas, which are

hardly observed by optic technology. Also, one can obtain high resolution and quality DEMs

from InSAR data sets and other external DEM such as 1 : 100 000 scale DEMs or even DEMs

with lower resolution by our approach.

Chapter 3.

Coherence Decomposition Analysis

in Badong The phase coherence in InSAR is often used in classification algorithms to detect possible

temporal changes of the imaged terrain. However, in mountain areas the interferometric

coherence is also sensitive to the slight variations of the acquisition geometry. In this letter we

propose a very simple but effective method to separate the temporal de-correlation from the

geometrical one. Assuming the imaged terrain can be modeled as a distributed target, the

geometrical coherence can be estimated by exploiting a topographic model and the sensor

acquisition parameters. The discrepancy between the geometrical coherence and the observed

one can then be ascribed to temporal changes. Moreover, in presence of point-like targets, the

hypothesis of distributed target is not valid anymore and higher values of the observed

coherence with respect to the synthetic geometrical one can be used to detect such targets.

The proposed approach allows then in mountain areas 1) a simple and very fast rough

estimation of the temporal coherence 2) the identification of point-like targets using just two

images. The method has been applied and tested in the Badong site using ERS tandem data.

3.1. Introduction

Coherence is a measure of similarity of InSAR echoes [59]. The magnitude of coherence is

often used to describe different degrees of terrain changes. For example, bodies of water

always show very low coherence; distributed targets such as agricultural fields show

moderate coherence after one day, and low coherence after one month; rocks and artificial

buildings in urban areas show high coherence even after years. Therefore, coherence plays an

important role in certain InSAR applications, such as classification, change detection etc. [14,

60-63].

Coherence between two complex signal 1s and 2s is defined as their correlation coefficient

[59]:

*

1 2

2 21 2

{ }

{ }

E s s

E s sγ

⋅=

⋅ (3.1)

where 1s and 2s are complex signals from co-registered interferometric SAR images, * is

complex conjugate operator, { }E i means mathematical expectation.

Since mathematical expectation of radar signals is not attainable in practice, under the

assumption of distributed targets, coherence is usually estimated by spatially averaging the

radar echoes in a moving window [64]:

* ( )1 2

1

2 2

1 21 1

ˆ

Lj i

i in

L L

i in n

s s e

s s

φ

γ

−

=

= =

⋅

=∑

∑ ∑ (3.2)

where i denotes i-th pixel in a Coherence Estimate Window (CEW). For each CEW, L

pixels are used to obtain a coherence estimate.

As stated with more details in [65], there exist both under- and overestimate in the observed

coherence map. The coherence estimates will bias to lower values because the correlated part

of the signals contains interferometric fringes. Therefore, ( )iϕ that represent the topographic

phase of i-th pixel has to be compensated by means of DEM. Nevertheless, there also exist an

overestimate bias that is due to the limited number of pixels in a CEW [64]. This bias

becomes remarkable in low coherence areas. As a consequence, even incoherent signals

rarely show zero coherence.

Moreover, coherence estimation is under the assumption of distributed targets. For a point-

like target that dominates the reflected signal in a resolution cell, this assumption cannot be

valid. In order to correctly interpret the observed coherence map, different de-correlation

sources and the extensions of targets have to be considered.

The observed coherence depends not only on target properties but also on geometric relations

between the two acquisitions. Zebker and Villasenor [19] modeled different de-correlation

sources as:

total temporal geometric thermal= γ γ γ γ⋅ ⋅ (3.3)

where thermalγ depends on radar thermal noise, temporalγ measures the degree of physical

changes of the illuminated surface over the period between acquisitions, geometricγ depends on

the geometric relations between the two acquisitions.

For distributed targets, geometricγ can be measured from the ratio between overlapping and total

spectra widths in the two dimensions of SAR image. In azimuth dimension, non-overlapping

spectrum is caused by squint angle variation between the two images; in range dimension, it

depends on normal baseline of the two acquisitions and terrain local slope [66].

For point-like targets, the relations between geometricγ and the physical extension of targets are

described in [29]. In synthesis, higher coherence can be observed when the target extension is

smaller than the SAR resolution cell. This phenomenon offers a clue for locating point-like

targets from only one interferogram.

Usually, azimuth and range spectral shift filtering are used to reduce the degree of

interferogram noise by filtering out the non-overlapping part of spectra [66]. However,

obtaining a better interferogram is not essential for applications such as change detection

and/or classification. In this letter, instead of filtering, a simple but effective approach is

proposed to decompose the observed coherence map. Firstly, geometricγ is estimated from

geometric relations between the two acquisitions and an external DEM under distributed

target assumption. Then the observed coherence is decomposed according to model (3.3).

Since the thermal contributions caused by radar system noise are usually negligible [19], an

appropriate temporal coherence map can be extracted. Moreover, given a stable point-like

target, according to the relations between the target extension and the observed coherence,

geometricγ estimated with distributed targets statistic will be lower than the observed value . If

we consider the multiplicative model (3.3), possible point-like targets can be identified from

the larger-than-one values in the extracted temporal coherence map.

3.2. Coherence Decomposition

3.2.1. Geometric Coherence Estimation

As presented in [66], for distributed targets, the geometric coherence between two SAR

images can be estimated from the ratio between the overlapping spectra and bandwidths. In

azimuth dimension, the non-overlapping spectrum can be obtained by calculating the Doppler

frequency difference fα∆ . In range dimension, it can be obtained from the wavenumber shift

rf∆ that has been described as [66]:

tan( )

nr

Bcf

rλ θ α∆ = −

− (3.4)

where c is light velocity, λ is the wavelength of SAR signal, nB is normal baseline, r is

sensor-target distance, θ is incidence angle and α is local terrain slope. All the parameters in

(3.4) can be obtained directly except α .

Figure 3-1 Local slope geometry of SAR image. s and 's are two adjacent pixels in slant range axis. R∆ is their slant range difference, h∆ is their elevation difference, θ is local incidence angle, α is the local slope of terrain.

Let us assume a piece of distributed scattering terrain lying on a slope α with respect to the

ground as described in Figure 3-1. Two adjacent pixels s and 's in slant range axis are

considered. They are collecting the contributions coming from the terrain around P and

'P with height difference h∆ . The length 'PP can be written as:

'sin( )

RPP

θ α∆

=−

(3.5)

where θ and α have the same meaning as in (3.4), R∆ is the slant range difference. Since

the elevation for each pixel can be obtained from the external DEM, h∆ in Figure 3-1 is

known. Then, local slope α can be expressed as:

sin( )'

h

PPα

∆= (3.6)

Then α can be written as:

sin( )arctan( )

/ cos( )R h

θα

θ=

∆ ∆ + (3.7)

With known α in (3.4), geometricγ can be derived from the ratio between the overlapping

spectra and the bandwidths in range rB and in azimuth aB dimensions:

geometr

ricr

r

B f B f

B Bα α

α

γ− ∆ − ∆

= ⋅ (3.8)

In order to guarantee the validation of the geometricγ estimation, the accuracy of the external

DEM has to be considered. From (3.4)-(3.8), the differential coefficients that represent the

relations between h∆ error and the consequently geometricγ error can be obtained as follows:

2sin ( )

geometri n

r

cd B f cB

d B B r

α α

α α

γ

α λ θ

− ∆= ⋅

− (3.9)

2 2

sin( )

2 cos( )

Rd

d h R h R h

θα

θ

∆=

∆ ∆ + ∆ ∆ + ∆ (3.10)

where h∆ can be also derived from α with (3.7). Therefore, for an interferometric system,

given a tolerable geometricdγ , the acceptable d h∆ is a function of the local slope α . A

quantitative analysis that depends on the SAR system and the external DEM will be given in

the next section.

3.2.2. Temporal Coherence Estimation

After estimating geometricγ , temporalγ can be obtained by simply dividing the observed coherence

map by geometricγ . However, three particular points have to be considered: 1) overestimating

bias; 2) point-like targets; and 3) volumetric de-correlation.

As previous analysis, depending on the local slope, the geometric coherence can even become

close to zero. However, such values cannot be obtained from the observed coherence

estimation because of the overestimating biases. This phenomenon has to be taken into

account in order to avoid meaningless outcomes when dividing the observed coherence by the

geometric one. Thus, we flag the areas where the geometric coherence is less than a certain

threshold. This allows also highlighting where low observed coherence is due to geometric

de-correlation and not for other reasons.

In high coherence areas, since geometric coherence is related to the extension of the targets,

when a point-like scatterer dominates the reflected radar signal, the estimated geometric

coherence geometricγ may be smaller than the observed value [29]. If so, the extracted temporal

coherence will be larger than 1. Obviously, the temporal coherence should also be high

enough to get such result; however, point-like targets usually have stable physical

characteristic, which makes our assumption feasible.

It has to be mentioned that, in order to keep the procedures of our approach as simple as

possible, volumetric coherence is ignored in the decomposition model. Nevertheless, since no

volumetric de-correlation can be expected from the point-like targets, this ignorance do not

influence our target detection result. On the other hand, because the value of volumetric

coherence represents the elevation variance within a resolution cell [66], different densities of

vegetation can be observed from the decomposed coherence map. As future work, if multi

coherence maps are available, volumetric coherence can be considered in the coherence

decomposition model. Then, it is also possible to quantitatively analyze the different densities

of vegetations from the extracted volumetric coherence map.

3.3. Results

The Results presented in this letter are obtained with ERS-1/2 Tandem data acquired in

January, 1996. The normal baseline is 199m. The test site is around Badong county, Three

Gorges area, China. The CEW used here is 15 pixels in azimuth and 3 pixels in range.

Figure 3-2 shows the observed coherence map of our test site, in Figure 3-2 (b), the

topographic phase has been removed by means of SRTM DEM. The resolution of SRTM

DEM is 90m , lower than the one of ERS SAR image (about 5m in azimuth and 25m in

range). A simulated SAR image was generated from the SRTM DEM and then co-registered

to the master image to obtain an elevation map in SAR coordinates. Although the resolution

and accuracy of SRTM DEM are not high, they are sufficient for compensating the

interferometric fringes during coherence estimation [63]. From Figure 3-2, the Yangtze River

can be recognized in the middle. However, the river boundaries are not so clear, especially in

the right part. Below Yangtze River, many areas with low coherence can be seen. Without a

priori information, it is difficult to detect different temporal coherence levels.

Figure 3-2 Observed coherence map of Badong test site, (a) before removing topographic phase, (b) the topographic phase has been removed with SRTM DEM.

Different from observedγ estimation, the accuracy of SRTM DEM has to be evaluated for

estimating geometricγ . Given the parameters of the ERS data set: 16rB MHz= , 5.66cmλ = ,

847r km= , 23θ = , 199nB m= and ( / 0.8)a a aB f B− ∆ = , and given maximum

tolerable error 0.1geometricdγ = , the acceptable d h∆ values can be obtained from (3.9) - (3.10)

and shown as a function of the local slope α in Figure 3-3.

Figure 3-3 Given 0.1geometricdγ = , acceptable d h∆ from the external DEM is plotted as a function of the local slope α .

From Figure 3-3, the highest requested h∆ accuracy (about 5m) is needed only when the

local slope is near 90° (in radar shadow areas, i.e. 67α < − ° , high accuracy DEM is also

needed, however no coherent information could be expected from such areas). For most

terrain slopes, say from -10° to 10° , 10m h∆ accuracy is enough for obtaining a geometric

coherence estimate with 0.1geometricdγ < . Moreover, since the simulated SAR elevation map

has to be interpolated from sparser SRTM DEM grids, SRTM DEM error can be strongly

reduced by calculating the height difference h∆ between two adjacent pixels in SAR

coordinates. In other words, because of the differential operation, both low and high pass

SRTM DEM errors are partially cancelled out. As a consequence, a higher accuracy can be

expected from h∆ estimate. To sum up, in our approach, 90-m resolution SRTM DEM is

usually enough for obtaining a geometricγ estimate whose error is less than 0.1. The resultant

geometric coherence map is shown in Fig. <ref>scoh</ref>. It is easy to realize that the

geometric coherence is strongly related to the terrain in this test site. In some areas, very low

coherence can be observed.

Figure 3-4 Estimated geometric coherence map of Badong test site.

After coherence decomposition analysis, the extracted temporal coherence map is shown in

Figure 3-5. The areas with geometric coherence lower than 0.2 are flagged as zero in order to

distinguish them from low temporal coherence areas. In Figure 3-6. the histograms of

geometricγ , observedγ and temporalγ are plotted together, from which the proposed approach shows

the capability of temporal coherence extraction. Because of the one-day temporal baseline,

most of the pixels show high temporal coherence after the coherence decomposition.

Compared with Figure 3-2, the vegetated areas show moderate coherence in Figure 3-5

instead of low values. Even different densities of vegetation can be recognized without the

affection of topography. The resultant temporal coherence map is helpful for correctly

interpreting different types of surfaces. For qualitatively assessing our result, the observed

and extracted temporal coherence along the Yangtze River are geocoded and shown with the

optical image from Google Earth in Figure 3-7. It has to be noticed that the river is narrower

in the coherence maps than in the optical image because the SAR images were acquired

before the construction of the Three Gorges Dam. A significant example to be shown is

pointed out with arrows in Figure 3-7, it is easy to distinguish the radar shadow and

vegetation areas from our result.

Figure 3-5 Extracted temporal coherence map from coherence decomposition analysis.

Figure 3-6 Histogram of the observed coherence and the estimated geometric and temporal coherence.

Figure 3-7 One part of our test site that is along Yangtze River. (a): geocoded observed coherence map, (b): geocoded extracted temporal coherence map, (c): optical image from Google Earth. The arrows in (a) and (b) point at an area with steep terrain and vegetation. The black rectangle in (b) indicates a typical area with possible point-like targets, where the details are shown in Figure 3-8.

The east part of the riverbank shows high coherence in both Figure 3-7 (a) and (b). As

discussed in Section 3.1, larger-than-one "coherence" can be obtained when the distributed

target hypothesis is not valid. A typical area with this kind of targets is indicated within the

black rectangle in Figure 3-7 (b) and the details are shown in Figure 3-8. For better

understanding the locations of point-like scatterers, larger-than-one pixels are plotted with the

values scaled from 1 to 1.2. For evaluating the locations of the detected stable point-like

targets, PS InSAR analysis was carried out in this test site with 12 ERS SAR images. The PSs

with temporal coherence higher than 0.95 are shown in red cross in Figure 3-8.

Figure 3-8 Details in the area indicated within the black rectangle in Figure 3-7(b). Point-like targets show larger-than-one values after the coherence decomposition. The pixels with resultant "coherence" from 1 to 1.2 are shown with the point-like scatterers detected by Permanent Scatterer InSAR analysis (red cross).

Because of the short spatial and temporal baselines of our tandem images, the number of

possible point-like scatterers detected from our approach is obviously more than the number

of PSs. Moreover, since observed coherence is estimated from moving CEWs, locally

maximum coherence surrounded by reducing values can be observed from the enlarged view

in Figure 3-8. It could be difficult to precisely locate the position of point-like targets from the

low resolution coherence map. Nevertheless, from Figure 3-8 most of the possible PSs were

identified from the coherence decomposition analysis (6 misdetections in 93 PSs). The 6.5%

misdetection rate can be explained by the geometricγ estimation errors. We could set the

threshold slightly less than 1, say 0.98, then all PSs can be detected by our approach. In the

worst case, the result can be used as point-like scatterer candidates in many target detection

algorithms. Our future work is going to be estimating the locations and extensions of point-

like scatterers from multi coherence maps.

3.4. Conclusions

In this chapter, a simple approach to decompose observed InSAR coherence map was

presented. Instead of filtering, we separated the estimated geometric coherence from the

observed one for obtaining an approximately temporal coherence map. The geometric

coherence was estimated from sensor parameters and SRTM DEM. Since the geometric

coherence estimation is performed with distributed-target statistic, for stable pointlike targets,

the estimated coherence is lower than the observed values. As a consequence, larger-than-one

values can be used to identify the possible stable pointlike target from only one interferogram.

The results in the Three Gorges area qualitatively demonstrated the improvement of the

extracted temporal coherence and the locations of pointlike targets. Although the temporal

coherence map and pointlike targets locations are estimated in an approximate way, the

simple and fast procedures make the approach useful for many coherence based applications.

Chapter 4.

Time Series InSAR Image Analysis

Methods In the previous 2 chapters, we proposed several improved conventional InSAR methods and

presented their applications in Three Gorges region. Since the unavoidable shortcomings of

InSAR technique, the precision of the results are limited. Nevertheless, for the cases that only

few SAR images are available, our approaches showed the capabilities of DEM generation

and temporal coherence map extraction. From the end of 2007, a reasonable number of

Envisat SAR images have been acquired and time series analysis became feasible. In this

chapter, we briefly recall the original PS, StaMPS, and QPS techniques, which are the main

analysis tools for obtaining the results showing in Chapter 5 and Chapter 6.

4.1. Introduction

By means of the PS technique [24], repeated space-borne SAR images with mid resolution

(about 25m x 5m for ESA ERS and Envisat) can be used to estimate displacement (1mm

precision) and 3D location (1m precision) of targets that show an unchanged electromagnetic

signature [26, 27].

However, as a differential system in both spatial and temporal dimensions, successfully

carrying out a PS analysis is restricted by some limitations. In spatial dimension, the density

of PS has to be high enough to correctly interpolate APS. In temporal dimension, the main

part of target deformation has to be linearly changing with time or at least the deformation

model has to be known[25].

In order to expand the PS applications to geological applications with complicated

deformation patterns, A. Hooper et al used spatial-temporal filtering and 3-D phase

unwrapping techniques, namely StaMPS, to solve the mentioned limitations of PS. StaMPS

was successfully applied in several crustal and volcanic deformation monitoring

applications[38].

Nevertheless, because of the single-master interferometric system, only point-like targets can

keep coherent due to the long-spatial-baseline interferograms [29]. As a consequence, the

main drawback of PS and StaMPS technique is the limited spatial density detected PS

(hundreds of PS per km2 in urban site, up to few points in vegetated areas).

In this chapter, we briefly recall the core ideas of PS and StaMPS techniques and describe

new hints for multi-temporal analysis of SAR images that allow to extract information also

from partially coherent targets, i.e. QPS technique.

4.2. Original Permanent Scatterer Technique

In this section, we recall briefly some concepts that underlie PS technique, but neglect what is

not needed for the comprehension of this chapter. The interested reader can refer [24, 25] for

detail.

Let us denote with is the i-th complex SAR image (with 1,...i N= ). The interferogram

between the images i and k can thus be expressed as , *i ki kI s s= ⋅ , Taking target p₀ as

reference point, the interferometric phase 0

,,, 0 ,

i ki kp p p p

Iφ = ∠∆ of target p depends on its

geometrical location as well as on its displacement, atmospheric disturbances and noise. In

particular the terms that depend on the target height difference 0,p ph∆ and linear deformation

trend difference 0,p pv∆ are expressed respectively as:

00

, ,,, ,

4 1

sini k i k

p p nH p ph B

R

πφ

λ θ∆ = ∆ (4.1)

and

00

, ,,, ,

4i k i kp p tD p pv B

πφ

λ∆ = ∆ (4.2)

where ,i knB is the interferometric normal baseline, ,i k

tB is the temporal baseline, λ is the radar

wavelength, θ and R are the looking angle and sensor-target distance of target p .

Within original PS technique, the target height and deformation velocity are estimated by

maximizing pξ (we omit index 0p to lighten the notation):

ˆ ˆ( , ) arg{max( )}p p ph v ξ∆ ∆ = (4.3)

where

, ,,, ,( )

,

1 i k i ki kp H p D pj

pi k

eM

φ φ φξ ∆ −∆ −∆= ∑ (4.4)

In (4.4), (M is the number of image pairs , i k ) the following terms can be highlighted as:

,i kpφ∆ is the acquired interferometric phase (compensated for the terms that can be

otherwise estimated, such as flat terrain and external DEM);

,,i kH pφ∆ is the elevation-dependent term given by (4.1);

,,i kD pφ∆ is the deformation trend-dependent term given by (4.2).

The maximum of the absolute value of (4.4) max(| |ˆ )p pξ ξ= is called temporal coherence

and it can be approximately expressed as a function of the dispersion 2φδ of the phase

residuals 2 /2ˆ

p e φδξ − [25]. The variance of the estimates of height and deformation trend

(respectively 2hδ∆ and 2

vδ∆ ) depend on the phase dispersion, the number of interferograms M

and the lever arms i.e. normal and temporal baselines. More precisely, as derived in [25], we

can approximate them with the following relations:

2

2 22

sin( )

4n

h

B

R

M

φδλ θδ

π δ∆ (4.5)

and

2

2 22

( )4v

BtM

φδλδ

π δ∆ (4.6)

Usually, considering the orbital tubes of the ESA satellites ERS and Envisat, the minimum

number of images to successfully carry out a PS analysis is about 20. The minimum temporal

coherence to consider a target as a PS with such number of images is 0.9, and it decreases to

0.7 or 0.6 when many images (more than 60) are available. Under these conditions, the

accuracy of the estimate reaches 1m for the height and 1mm/year for the deformation trends.

Since in (4.3), p̂v∆ is estimated to maximize pξ , the deformation between target p and the

reference point 0p has to be linearly changing with time. Moreover, PS technique implies that

after removing ,,i kH pφ∆ , the phase difference between nearby PS is small enough to avoid a real

phase unwrapping procedure. These assumptions may not be true in extra-urban area with

complicated deformation patterns. Therefore, StaMPS was developed in Stanford and tried to

solve the restrictions.

4.3. Stanford Method for Persistent Scatterer

(StaMPS)

In this section, we try to describe the primary algorithms of StaMPS, the interested readers

can refer [38] for more detail. The core idea of StaMPS is that on certain target (Persistent

Scatterer), the signal is distinguishable from the noise. This principle implies that

interferometric phases can be filtered due to their different spatial and temporal characteristics.

Since no a priori deformation model is assumed, phases has to be unwrapped to represent

physical meanings of the illuminated ground.

StaMPS uses the same interferometric configuration as PS technique, i.e. all the

interferograms are obtained with the same master image. The interferometric phase is divided

into spatial correlated, normal baseline correlated and temporal correlated parts:

, , ,, ,i k i k i ki k i kp S B T Nφ φ φ φ φ= + + + (4.7)

where:

,i kφ is the interferometric phase of target p between SAR image i and k (after

flattening and extern DEM removing).

,i kSφ is the spatial correlated phase caused by APS, orbital errors and, spatial correlated

external DEM errors and deformation fields.

,i kBφ is the normal baseline correlated phase caused mainly by the incidence angle

errors, i.e. external DEM errors and signal reflecting center shift.

,i kTφ is the temporal correlated phase caused by target deformation and seasonal APS

difference.

,i kNφ is noise part.

It is has to be noticed that different from PS technique, StaMPS is not a spatial differential

system at beginning, thus no reference point 0p is needed to model the interferometric phase.

Furthermore, all the phases in (4.7) are wrapped modulo 2π.

The first step of StaMPS is to filter out ,i kSφ from all the interferograms. All the PS candidates

(PSC) are geocoded and the complex phase is transformed to a grid with spacing over which

little variation in phase is expected (40-100m). by a designed bandwidth-pass filtering, ,i kSφ can be estimated as ,i k

Sφ and removed from all the interferograms.

The second step is to estimate ,i kBφ by a linear inversion from the residual phases and normal

baselines. Since the phases are wrapped, a rough search is used to estimate the best fitted

model. Bξ is defined as the coherence-like value to represent the SNR of each PSC:

1

1exp{ ( )}

Mi i i

B p Sp Bpi

jM

ξ φ φ φ=

= − −∑ (4.8)

Here, M is still the number of interferograms. Bξ likes pξ in PS technique defined by (4.4),

the only difference is that some spatial uncorrelated deformation phases make the value of Bξ

lower than pξ . Nevertheless, different Bξ values still indicate partly the phase stability in time

series InSAR images.

After obtaining Bξ , PS can be selected by a statistical analysis considering both phase and

amplitude stabilities. All the non-PS pixels are discarded and the estimated ,i kBφ is removed

from the original wrapped interferometric phase.

Then, the third step of StaMPS, phase unwrapping, has to be carried out. In the last two

decades, 2-D phase unwrapping algorithms are widely researched by many groups [10, 55, 56,

67-73]. However, the time series data have three dimensions, two in space and one in time,

thus a theory framework for 3-D phase unwrapping problem was presented and implemented

by different algorithms with StaMPS [74]. The phases in time series are unwrapped in a 3-D

way to obtain M unwrapped interferograms. After phase unwrapping, APS can be filtered

out by a temporal high-pass filtering and the deformation phase can be obtained by a spatial

differential system like PS technique.

StaMPS tries to extract information from more complicated phenomena, and successfully

applied in many geological fields. However, in some areas where few point-like target exist

(no matter buildings or rocks), the main restriction of PS technique, low spatial density of

detected point-like targets, is still unsolved.

4.4. Quasi- Permanent Scatterer Technique

As we discussed in the previous sections, the main drawback of PS and StaMPS technique is

the low spatial density of the detectable permanent point-like targets, particularly in vegetated

extra-urban areas such as many areas in Three Gorges region. Indeed, the lack of measured

points can prevent from monitoring an area of interest affected by deformation with space-

borne SAR techniques. As the results shown in Chapter 2 and Chapter 3, besides point-like

targets, stable distributed targets still can be coherently observed by SAR image pairs with

small normal baselines. Moreover, de-correlating targets may keep coherence in the

interferograms with small temporal baselines.

If we use the concepts of vertex and edge from graph theory to represent time series SAR

images and interferometric connections, original PS and StaMPS technique generalize a star-

like graph, i.e. all the time series SAR images are co-registered with single master image. The

benefits come from this interferometric configuration are in two aspects: 1) it is possible to

carry out the phase unwrapping in temporal dimension; 2) it has a relative high values of 2hδ∆ and 2

vδ∆ , from which higher precision estimates can be expected. However, as we

discussed at beginning of this section, the information contained in the distributed and de-

correlating targets cannot be extracted from the single-master interferometric configuration.

If we continue to think about the vertex and edge in a graph, we could give certain value as

weight for each interferometric pairs and try to find the best interferograms in the time series

InSAR data set. Toward this aim, SBAS selects interferograms with short normal baselines to

extract information from distributed targets [37], however de-correlating targets has also to be

considered by short temporal baseline image pairs. As modeled in [20], instead of the length

of baselines (no matter spatial or temporal baselines), we choose the amplitude of coherence ,ˆi kγ as the index to weight different interferograms.

By calculating the average coherence on some selected PSCs of all the interferometric

connections among time series SAR images, we can give ,

ˆ1i k

γ− as the distance index for

each interferogram. Minimum Spanning Tree (MST) algorithm [75] can be used to obtain the

optimum subset of interferograms ,{ }i kI with highest coherence that forms a spanning tree:

, ,ˆ{ } min (1 )i k i kI γ= −∑ (4.9)

Based on MST generalized interferograms, QPS is different from original PS and StaMPS in

both temporal and spatial dimensions. In temporal dimension, since the interferograms in

QPS image configuration contain also partially coherent targets, ,ˆi kpγ is used as weight in (4.4)

and get the QPS temporal coherence definition:

, ,,, ,( ),

( , )

,

( , )

ˆ

ˆ

i k i ki kp H p D pji k

pi k

p i kp

i k

e φ φ φγ

ξγ

∆ −∆ −∆

=∑

∑ (4.10)

During the procedures of maximizing pξ , when a target shows low coherence in some

interferograms, the interferometric phase cannot influence other measurements. On the other

hand, in spatial dimension, considering the baseline de-correlation effects, spatial filtering

technique has to be applied on all the interferograms.

QPS technique maximizes the temporal coherence by estimating elevation and deformation

related phases from a selected subset of interferograms in time series SAR images. It modifies

the core processing step of the PS technique, nevertheless, it can be easily inserted in the

processing chain present in literature [24] without remarkable changes.

4.5. Comparison and Discussions

In this chapter, we briefly described three different kinds of time series InSAR analysis

techniques, namely PS, StaMPS and QPS. Within time series InSAR images, they focus on

different phenomena at hand. PS technique can get very precise results if there exist enough

permanent point-like targets, particularly in urban sites, StaMPS is usually used in geological

deformation monitoring applications. QPS is more flexible than the previous techniques and

can be used in most of sites with the trade back of less accuracy.

The most significant difference between PS and StaMPS is that StaMPS tries to unwrapped

the time series phase in a 3-D way before estimating the deformation dependent phases.

However, to the author’s knowledge and experience, so far, no remarkable improvement has

been shown yet by StaMPS compared with original PS technique.

On the other hand, the QPS is different from original PS, StaMPS techniques in three aspects:

1. the images of the data-set are no more required to interfere with a unique common Master

image;

2. the target height and displacement are only estimated from an appropriate target-

depending sub-set of interferograms;

3. a spatial filtering is applied to enhance the SNR of the interferometric phases for

distributed targets .

QPS can be considered complementary with the other two techniques and one will be

preferred to the other according to constraints and requests of the case study at hand.

In the following chapters, all of the three time series SAR image analysis methods are

implemented for different cases. In Chapter 4, QPS and StaMPS are used to monitor the

landslide area of Badong, in Chapter 5, PS and QPS are applied to analyze the deformation of

Three Gorges Dam.

Chapter 5.

Slow Landslides Monitoring

in Badong After Three Gorges Dam began to function in 2003, the water level of the Yangtze River in

Three Gorges area rose more than 100 meters. The impact of the man-made reservoir on the

surroundings became object of several studies. In this chapter we implement two time series

InSAR analysis techniques, namely, QPS and StaMPS, to measure the deformation trends in

Badong. The results obtained by the two processing tools with the same focused and co-

registered data sets are analyzed and compared. Two subsidence areas are identified by both

techniques. However, since the QPS analysis is able to process partially coherent targets,

many more points are extracted than in StaMPS, and more information can be retrieved.

5.1. Instruction

Three Gorges Dam, in Hubei province, China is the largest dam in the world. The dam began

to function in 2003; as a consequence, the water level of the Yangtze River in Three Gorges

area raised more than 100 meters. Then, the largest man-made reservoir (600 kilometers long)

was formed in the upriver part of the dam. Although lots of benefits come out from the power

generation and flood control functions of the project, the raising of the water changed the

natural terrain and flooded the basements of the mountains in this area. Moreover, due to the

weight of the reservoir on the riverbed, there is potential rock instability in the gorges along

the river. The regional assessment of landslide impact in the upriver areas of the dam has been

reported in [3].

In order to assess the impact of the project on the ground stability of upriver area, it’s

necessary to measure and analyze the deformation in this region. Temporal Differential

Interferometric Synthetic Aperture Radar (D-InSAR) technique is one of the most suitable

tools for getting measurements in such case [9, 13, 14].

The main limitations of D-InSAR technique are geometrical and temporal de-correlations

with repeat-pass satellite mode [4]. Even though the coherence of the two radar signals is high

enough, the atmospheric phase screen (APS) difference between master and slave images still

reduces the accuracy of the final results [5]. Aiming at the above restrictions, Ferretti et al.

presented the Permanent Scatterers Technique (PS) [6] in the late 1990s. Instead of extracting

information from the whole SAR image, PS InSAR technique identifies natural point-like

stable reflectors i.e. PSs from long temporal series of interferometric SAR images. The

coherence on PS is good enough to obtain sub-meter accuracy DEM and millimetric terrain

motion [7]. The applications of PS InSAR technology have been successfully achieved

especially in urban areas [8].

In order to take advantage of all the coherent targets, partially coherent analysis was also

developed in Politecnico di Milano (POLIMI), named Quasi-PS technique (QPS) [9].

Different from classical PS technique, QPS analyzes the multi-temporal SAR images that

allow to extract information also from partially coherent targets. The benefit of QPS is that

the density of points with measured deformation trends increases significantly in non-urban

areas. In the mean while, A. Hooper developed the Stanford Method for Persistent Scatterer

(StaMPS) [10]. Without knowing the deformation model, StaMPS filters the phase in spatial

and temporal dimensions separately to divide the correlated interferogram phase into

incidence angle error, APS difference, deformation trends and noisy parts. After that, the

deformation series are unwrapped, exploiting different algorithms according to the

complexity of the phenomena at hand.

The objective of this case study is to present the preliminary results of deformation

monitoring in Badong, Three Gorges area by two different kinds of long term D-InSAR

analysis i.e. Quasi-PS technique and StaMPS. The available data have been acquired from

ERS and Envisat satellites in the time span from 1992 to 2007. More than 70 scenes of SAR

images in two tracks of Badong test site have been processed. ERS and Envisat images have

been kept separate, due to the different carrier frequencies and the big temporal changes of

the analyzed area. Here we will report the most significant results we obtained, that refer to a

single Envisat track. The few available images and the low coherence prevented from

achieving more information from the other data-sets.

5.2. Test Site and Data Sets

Badong County is selected as our test site, which is a county settled on the banks of the

Yangtze River, in Hubei province, China. It is located just east of the Wuxia Gorge in the

Three Gorges region. The old town of Badong has a history of more than 1500 years. Due to

the construction of the Dam, this town was going to be under the flood water level. Therefore,

the emigration of the whole town was organized in the summer of 1997. Almost all the

buildings of the old town were demolished in order not to affect the channel. A totally new

city began to grow up at the same time more than 5 km west from the old one.

After several years of construction, in 2002, the new city which covers about 7.3 km2, with

more than 50,000 residences began to be formed. A bridge over the Yangtze River was also

built to connect the south and north parts of the city. Since the city is built along the steep

river bank, many consolidation works were settled for landslide protection. Therefore it’s

very important to identify the potential landslides areas near the city, especially after the

rising water of the Yangtze River.

Another reason for selecting Badong as our test site is that the new city of Badong is observed

by 2 tracks of data sets, i.e. track 75 and 347, so it’s possible to take advantage of more data

sets and/or cross validate the subsidence measurements from two tracks. The available data

information is listed in Table 5-1.

Table 5-1DATA SET INFORMATION

Since the ERS and Envisat data are acquired before and after the construction of the dam, the

changes of the river in this area can be observed from the reflectivity maps of the data sets

from two sensors. Figure 5-1 (a) and (b) shows the incoherent average reflectivity maps of

ERS (a) and Envisat (b) data, the Yangtze River is much wider in the Envisat image, and the

urban changes due to the population migration can be seen in Fig 1, where indicated in the red

rectangle.

Track/Frame: 75/2979

ERS May,1992 – Nov, 2000 11 scenes

Envisat Aug, 2003 – June, 2007 34 scenes

Track/Frame: 347/2979

ERS Mar, 1993 – Nov, 2000 15 scenes

Envisat Jan, 2004 – June, 2007 21 scenes

Figure 5-1 Reflectivity maps of Track 75 Frame 2979, from (a) ERS images and (b) Envisat images. The red rectangle indicates the new city of Badong, which is brighter in the Envisat image because of the urbanization.

5.3. Data Processing

Two processing tools are used to extract deformation trends information from the data set,

namely, QPS tool from POLIMI and StaMPS open source software. The raw data of the test

site are firstly focused and co-registered, and then processed by both processing tools.

5.3.1. QPS Data Processing

Figure 5-2 Images connections graph of the data set. Horizontal axis: image acquisition time. Vertical axis: spatial baseline. Each dot indicates one image; each line represents one interferogram between the two endpoints. The color bar indicates the spatial coherence of each interferogram.

QPS connects the images for the minimum best coherent graph, and then creates a set of

interferograms from a given data-set. Figure 5-2 shows the image connection graph of track

75 data set. Then the deformation trends, DEM errors and APS are estimated in this multi-

master system, the PSs are selected by setting the temporal coherence threshold as 0.8.

Finally, 74618 PSs are selected with the deformation trends shown in Fig 3(a).

5.3.2. StaMPS Data Processing

StaMPS uses amplitude dispersion (Da) [6] to select PS Candidates (PSCs). Since our test site

is not in urban area, the Da threshold is set higher than usual to get enough PSCs. Then

StaMPS filters PSCs in small patches to estimate the incidence angle errors, APS and

deformation trends. The thresholds for selecting PSs are determined by calculating the PS

probability of every PSCs, which considers both the temporal coherence [6] and Da value.

After that, the phase series of the PSs are unwrapped by a three-dimensional unwrapping

algorithm. Finally, 1618 PSs are selected from the data set with the deformation trends shown

in Figure 5-3 (b).

Figure 5-3 Deformation trends from (a) QPS and (b) StaMPS, the red rectangle indicates the city of Badong.

5.4. Results and Discussion

Two subsidence regions in the south river bank of Badong city are identified by both

techniques. One is in the west part of the city, which is about 400m above the Yangtze River.

Another region is in the east part of the city near the river. But with many more PSs, the

borders of residence areas are easier to be identified from the QPS result. Furthermore, in

non-urban areas, more subsidence regions can be seen, for instance the area in the south east

direction from the city. Because of too few points from the result of StaMPS, no reliable

deformation measurements can be obtained in non-urban areas.

Since the two results are obtained from the same co-registered data set, common PSs are

easily selected by searching the nearest points in a small window, here we use the window

with 9 in azimuth and 3 in range. Figure 5-4 (a) and (b) show the distribution and the value of

deformation trends of common PSs. More than 500 points are selected to cross validate the

results. Because there is no ground truth or reference points in this test site, the deformation

trends we got have only a relative meaning. As shown in Figure 5-4 (a), most of the common

PSs are located in the west subsidence area. Their deformation trends values are shown in

Figure 5-4 (b). Further validations will be carried out as soon as ground truth in the test site

will be available.

Figure 5-4 Superposition of PSs from QPS (green) and StaMPS (blue). Red points: common PSs. (b) Deformation trends (vertical axis) on common PSs. Green: QPS. Blue: StaMPS.

For what about the APS estimation, the QPS technique interpolates a map in the whole image,

whereas StaMPS estimates the APS only on PSs. In our test site, the APS low frequency

feature is very difficult to be identified from StaMPS results. From the APS results of QPS,

we find that the atmosphere distribution relates to the topography, for instance the APS

difference between the data acquired on 4th March, 2007 and 23rd January, 2005 that is

shown in Figure 5-5. The APS difference along the Yangtze River can be distinguished from

which is on the mountainous areas. That is the particular feature of water vapor distribution in

such area. Also, in the south bank of the river, the APS difference changes with the increasing

of the elevation.

For comparing the APSs estimated by the two techniques, the different way to combine the

images has to be taken into account. In fact, StaMPS exploits a single-master configuration,

whereas the QPS technique processes a more complex set of interferograms. Moreover, the

comparison has to be carried out on a set of common points. Since QPS produces interpolated

APS maps, we sampled the APS values on the location of StaMPS points. Then, the APS

values are referred to the same master image (temporal dimension) and to the point with

highest coherence (spatial dimension). The phase series are wrapped and then plotted for each

image as in Figure 5-6 (QPS on the left and StaMPS on the right). One example of the APS

difference on PSs between the data acquired on 30th November, 2003 and 23rd January, 2005

is shown in Figure 5-6 (a) and (b). Only in the area corresponding to the city of Badong, the

APSs retrieved by the two techniques are comparable (bottom of Figure 5-6). In the rest of the

mountain areas, StaMPS points are not enough to allow a reliable comparison.

Figure 5-5 APS difference between the data acquired on 4th March, 2007 and 23rd Jan, 2005. The correlation between APS and topography can be clearly observed.

Figure 5-6 APS difference on PSs between the data acquired on 30th Nov, 2003 and 23rd Jan, 2005 derived by QPS (a) and StaMPS (b). On the bottom, the zoom-in views over the Badong area.

5.5. Conclusions

In this case study, the long term D-InSAR analysis in Badong, Three Gorges area, China is

carried out by implementing StaMPS and QPS techniques. The results, obtained by

processing the same focused and co-registered data set, have been jointly analyzed. QPS

algorithm takes advantage of partially coherent targets and elaborates the best coherent

interferograms, whereas StaMPS finds only targets that stay coherent in the whole time span.

Two subsidence regions are identified by both techniques in Badong city. However, the PS

density of QPS is much higher than StaMPS. The StaMPS three-dimensional phase

unwrapping method is not useful in this case since no complex motion is present. Future work

will be focused on the combination of the two parallel tracks data sets to get more information

about the ground deformation before and after the Three Gorges Dam construction.

Chapter 6. Three Gorges Dam

Stability Monitoring In this chapter, we carry out a combination of PS and QPS time series InSAR analysis

techniques to extract geometric information over Three Gorges Dam and its surroundings. For

the first time, we measure and analyze the deformation of Three Gorges Dam with 40 SAR

images acquired from 2003 to 2008. From our results, we find that the temporal deformation

of the left (north) part of the dam has stopped, the deformation of the dam was influence by

the changing levels of Yangtze River. The seasonal deformation caused by the temperature

can be also observed. The results we obtained fit close to the published measurements from

traditional survey methods. In the result we also find an abnormal subsidence area near Zigui

county. This paper highlights and demonstrates the potential capability of time series InSAR

image analysis in the dam stability and landslides monitoring.

Please see the attached file Cha6_DamDef_CS09.pdf

Conclusions and Future Work Time series InSAR analysis has proven to be a very capable and effective technique for

obtaining precise elevation and displacement measures of the detected targets. However,

without enough images, almost nothing can be done, particular for the extra-urban cases.

When we were at the starting point of this work, the most challenging difficulty we faced to

was the limited number of archived images over Three Gorges region. Nevertheless, by

exploiting single interferograms with the facilitations from SRTM data, we can still

generalize a reliable DEM from a tandem interferogram with short normal baseline. In a

vegetated and mountainous area such as Three Gorges region, the accuracy of the obtained

DEM is quite encouraging. Moreover, by the proposed coherence decomposition analysis, an

approximate temporal coherence map can be extracted with the detected point-like targets.

Again, the result was obtained from a pair of tandem images over Three Gorges region. All

the results we presented with InSAR technique imply that, besides stable point-like targets,

still a lot of information is hidden in the time series InSAR images.

Thanks to the diligent works from many research groups, when we collected a reasonable

number of images, we were at the stage that many time series InSAR analysis techniques

have been developed and implemented. We applied StaMPS in Badong test site, and found

two subsidence areas within the new built Badong town. However, the new problem arose,

namely, the low density of the detected targets in this area. With this limitation, it is difficult

to correctly identify the boundary of the potential slow landslide area. The same problem also

appeared in other cases[40].

In order to solve this restriction, by working within the POLIMI InSAR group, we presented

and applied QPS technique in Badong and successfully obtained much higher spatial density

measurements. As a consequence, we can easily identify the boundaries of the detected

subsidence areas and also other subsidence areas outside of Badong. Furthermore, in this

river-gorge area, we observed strongly topography-related APS from the QPS results,.

After waiting another half year for acquiring more images, finally, we focused our work on

Three Gorges Dam. In order to exploit different target life spans and physical characteristics

over different parts of the dam, we began this work by an amplitude analysis over the dam.

From the amplitude series, we found that, on the left (north) part of the dam, most of the

targets keep stable with time; on the middle part, the target can be observed by SAR only

when the spillway is closed, on the right (south) part, very few stable targets can be detected

due to the construction.

Considering the phenomenon at hand, we carried out both QPS and PS analysis over the dam

site. From the QPS results, we found that there exist no visible temporal subsidence of the

dam from 2003 to 2008. By analyzing the measured deformation trends, we presumed that the

dam declined slightly on account of the upriver water pressure over the riverbed crust. Then

from the PS results, we found that the time series deformation of the dam strongly related to

different water levels. A seasonal deformation can be observed as well.

We also expected a PS analysis with the combination of ERS and Envisat images. However,

we could not get any significant results. The reasons are different for the two test sites. In

Badong, since only extremely point-like targets can be coherently observed by both ERS and

Envisat satellites [29], very few targets can be detected in such a small town surrounded with

vegetated mountains. For the dam, although many more man-made features exist, however,

since the ERS image were acquired before the construction of the dam, naturally, very few

common PS can be found.

In the last decade, the time series InSAR analysis has almost reached its theoretical accuracy.

The density of measured points has also been improved significantly by different techniques

like QPS. However, thematic demands still strongly drive SAR research to many specific

applications, such as water defense structures monitoring [76], railway, highway deformation

monitoring [77], and impervious surface mapping [78], etc. Also, the presented results are

partially a consequence from this developing trends in InSAR society.

Three Gorges Project is going to be finished in the end of 2009, at the same time as this

doctoral research. Nevertheless, the potential applications from time series InSAR data over

the Three Gorges region is still far away from being finished. Generally speaking, they are in

three aspects:

1, Multi-track analysis. From C-band data, we expect that more information could be

extracted from multi-track analysis. Actually, we have also collected another two tracks of

images over Three Gorges Dam, one paralleled track (Track 304, 22 scenes) and one

ascending track (Track 68, 9 scenes). We have already obtained some preliminary results

from the multi-track QPS and PS analysis [79]. However, since very few images are available

in the other two tracks, the results are still too raw to be shown in this version of the

dissertation.

2, Integration with field work. So far as we know, a lot of field work has been carried out

not only around the dam but also along the reservoir area. Usually, field work measurements

are used to cross validate the time series InSAR results. However, because of the complicated

deformation patterns shown by the dam, we could use the field work results to elaborate more

precisely the deformation model and thus improve the phase measurements. Furthermore,

corner reflectors can be considered to be designed and mounted on the dam site, from which,

higher SNR can be expected [80].

3, New generation SAR satellites. Recently, new generation SAR satellites, such as

TerraSAR-X [81], COSMO-SkyMed [82], ALOS [83], have been launched, providing SAR

images with higher temporal and spatial resolutions in different electromagnetic wave bands.

These images are new information sources to measure small deformations of single buildings,

such as Three Gorges Dam. For X-band data, with higher resolution, more structure details of

the dam reflecting the radar signal can be observed and more stable targets, namely PS, can

be expected [84]. From ALOS PALSAR L-band data, because of the penetrability of L-band

microwave, benefits can be gained in vegetated extra-urban area. Stable distributed targets

covered with bushes can be detected. Therefore, more landslides area in Three Gorges Area

could be monitored by time series analysis. Now, we are at a new starting point but with the

same task as before, waiting for the images.

In the final part of this dissertation, we’d like to give a prospect forecast to the potential

InSAR applications in China. As stated in [85], more than 95 cities have been suffering

different kinds of land subsidence in China since the end of the last century. The subsidence

even will impact the stability of the constructing high-speed railway system. China also has

most of the hydrological dams in the world. Each dam and its surroundings need to be

monitored regularly. For all the tasks at hand, time series InSAR analysis is one of the best

suitable techniques to be a complement of conventional survey methods. In our opinion, a

splendid future for InSAR applications can be expected in China for the next decade.

Bibliography [1] 申重阳, 孙少安, 刘少明, 项爱民, 李辉, and 刘光亮, "长江三峡库首区近期重力场

动态变化," 大地测量与地球动力学, vol. 24, pp. 6-13, 2004.

[2] 李强, 赵旭, and 蔡晋安, "三峡水库坝址及邻区中上地壳 P 波速度结构," 中国科学 D 辑: 地球科学, vol. 39, pp. 427-436, 2009.

[3] I. G.Fourniadis, J. G.Liu, and P. J. Mason, "Regional Assessment of Landslide Impact in the Three Gorges Area, China, Using ASTER Data: Wushan-Zigui," Landslides, vol. 4, pp. 267-278, 2007.

[4] 严建国 and 李双平, "三峡大坝变形监测设计优化," 人民长江, vol. 33, pp. 36-38, 2002.

[5] 郭华东, 雷达对地观测理论与应用. 北京: 科学出版社, 2000.

[6] J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing. New York: John Wiley & Sons, 1991.

[7] H. A. Zebker, C. L. Werner, P. A. Rosen, and S. Hensley, "Accuracy of topographic maps derived from ERS-1 interferometric radar," Geoscience and Remote Sensing, IEEE Transactions on, vol. 32, pp. 823-836, 1994.

[8] G. Schreier, "SAR Geocoding: Data and Systems," Heidelberg, Germany: Herbert Wichmann Verlag, 1993.

[9] A. K. Gabriel, R. M. Goldstein, and H. A. Zebker, "Mapping small elevation changes over large areas: Differential radar interferometry," J. Geophys. Res., vol. 94, pp. 9183-9191, Jul. 10 1989.

[10] R. M. Goldstein and H. A. Zebker, "Satellite radar interferometry: two-dimensional phase unwrapping," Radio Science, vol. 23, pp. 713-720, 1988.

[11] H. A. Zebker and R. M. Goldstein, "Topographic mapping from interferometric synthetic aperture radar observations," Journal of Geophysical Research, vol. 91, pp. 4993-4999, 1986.

[12] L. C. Graham, "Synthetic interferometer radar for topographic mapping," Proceedings of the IEEE, vol. 62, pp. 763-768, 1974.

[13] R. F. Hanssen, Radar Interferometry Data Interpretation and Error Analysis. Dordrecht, Netherlands: Kluwer Academic Publishers, 2001.

[14] P. A. Rosen, S. Hensley, I. R. Joughin, F. K. Li, S. N. Madsen, E. Rodriguez, and R. M. Goldstein, "Synthetic aperture radar interferometry," Proceedings of the IEEE, vol. 88, pp. 333-382, 2000.

[15] R. Bamler and P. Hartl, "Synthetic aperture radar interferometry," Inv. Probl., vol. 14, pp. R1-R54, 1998.

[16] H. A. Zebker, "Studying the Earth with interferometric radar," Computing in Science & Engineering [see also IEEE Computational Science and Engineering], vol. 2, pp. 52-60, 2000.

[17] 王超, 张红, and 刘智, 星载合成孔径雷达干涉测量. 北京: 科学出版社, 2002.

[18] 廖明生 and 林珲, 雷达干涉测量——原理与信号处理基础. 北京: 测绘出版社, 2003.

[19] H. A. Zebker and J. Villasenor, "Decorrelation in interferometric radar echoes," Geoscience and Remote Sensing, IEEE Transactions on, vol. 30, pp. 950-959, 1992.

[20] F. Rocca, "Modeling Interferogram Stacks," Geoscience and Remote Sensing, IEEE Transactions on, vol. 45, pp. 3289-3299, 2007.

[21] H. A. Zebker, P. A. Rosen, and S. Hensley, "Atmospheric effects in interferometric synthetic aperture radar surface deformation and topographic maps," J. Geophys. Res., vol. 102, pp. 7547-7563, 1997.

[22] A. Ferretti, C. Prati, and F. Rocca, "Multibaseline InSAR DEM reconstruction: the wavelet approach," Geoscience and Remote Sensing, IEEE Transactions on, vol. 37, pp. 705-715, 1999.

[23] A. Ferretti, C. Prati, and F. Rocca, "Nonlinear subsidence rate estimation using permanent scatterers in differential SAR interferometry," Geoscience and Remote Sensing, IEEE Transactions on, vol. 38, pp. 2202-2212, 2000.

[24] A. Ferretti, C. Prati, and F. Rocca, "Permanent scatterers in SAR interferometry," Geoscience and Remote Sensing, IEEE Transactions on, vol. 39, pp. 8-20, 2001.

[25] C. Colesanti, A. Ferretti, F. Novali, C. Prati, and F. Rocca, "SAR monitoring of progressive and seasonal ground deformation using the permanent scatterers technique," Geoscience and Remote Sensing, IEEE Transactions on, vol. 41, pp. 1685-1701, 2003.

[26] A. Ferretti, G. Savio, R. Barzaghi, A. Borghi, S. Musazzi, F. Novali, C. Prati, and F. Rocca, "Submillimeter Accuracy of InSAR Time Series: Experimental Validation," Geoscience and Remote Sensing, IEEE Transactions on, vol. 45, pp. 1142-1153, 2007.

[27] D. Perissin, "Validation of the Sub-metric Accuracy of Vertical Positioning of PS's in C Band," Geoscience and Remote Sensing Letters, IEEE, vol. 5, pp. 502-506, 2008.

[28] D. Perissin, "SAR super-resolution and characterization of urban targets," in Dipartimento di Elettronica e Informazione. vol. Ph. D Milan: Politecnico di Milano, 2006.

[29] D. Perissin, C. Prati, M. E. Engdahl, and Y. L. Desnos, "Validating the SAR Wavenumber Shift Principle With the ERS Envisat PS Coherent Combination," Geoscience and Remote Sensing, IEEE Transactions on, vol. 44, pp. 2343-2351, 2006.

[30] N. Adam, B. Kampes, M. Eineder, J.Worawattanamateekul, and M. Kircher, "The development of a scientific permanent scatterer system," in ISPRS Hannover Workshop, Inst. for Photogramm. And Geoinf. Hannover, Germany, 2003.

[31] J. Closa, N. Adam, A. Arnaud, J. Duro, and J. Inglada, "High Resolution Differential Interferometry using time series of ERS and ENVISAT SAR data," in FRINGE'03 Symposium ESA-ESRIN, 2003.

[32] M. V. d. Kooij, "Coherent target analysis," in FRINGE'03 Symposium ESA-ESRIN, 2003.

[33] C. Maire, M. Datcu, and P. Audenino, "SAR DEM filtering by mean of Bayesian and multi-scale, nonstationary methods," in IGARSS '03, 2003, pp. 3916-3918 vol.6.

[34] C. Werner, U. Wegmuller, T. Strozzi, and A. Wiesmann, "Interferometric Point Target Analysis for Deformation Mapping," in IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2003), Toulouse, France, 2003, pp. 4362--4364.

[35] F. v. Leijen, G. Ketelaar, P. Marinkovic, and R. Hanssen, "Persistent scatterer interferometry: Precision, reliability and integration," in ISPRS Workshop, High-Resolution Earth Imaging for Geospatial Information Hannover, Germany, 2005.

[36] B. M. Kampes, Radar Interferometry Persistent Scatterer Technique. Dordrecht, Netherlands: Springer, 2006.

[37] P. Berardino, G. Fornaro, R. Lanari, and E. Sansosti, "A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms," Geoscience and Remote Sensing, IEEE Transactions on, vol. 40, pp. 2375-2383, 2002.

[38] A. Hooper, "Persistent Scatterer Radar Interferometry for Crustal Deformation Studies and Modeling of Volcanic Deformation," in Department of Geophysics. vol. PhD San Francisco: Stanford University, 2006.

[39] A. Hooper, "A multi-temporal InSAR method incorporating both persistent scatterer and small baseline approaches," Geophys. Res. Letters, vol. 35, 2008 2008.

[40] D. Perissin, A. Ferretti, R. Piantanida, D. Piccagli, C. Prati, F. Rocca, and F. d. Z. A. Rucci, "Repeat-pass SAR Interferometry with Partially Coherent Targets," in Fringe07, Frascati, Italy, 2007.

[41] M. Liao, T. Wang, L. Lu, W. Zhou, and D. Li, "Reconstruction of DEMs From ERS-1/2 Tandem Data in Mountainous Area Facilitated by SRTM Data," Geoscience and Remote Sensing, IEEE Transactions on, vol. 45, pp. 2325-2335, 2007.

[42] T. Wang, M. Liao, and D. Perrisin, "Coherence Decomposition Analysis," Geoscience and Remote Sensing Letters, IEEE, 2009.

[43] D. Perissin and T. Wang, "Repeat-Pass SAR Interferometry with Partially Coherent Targets," Geoscience and Remote Sensing, IEEE Transactions on, 2009.

[44] T. Wang, D. Perissin, M. Liao, and F. Rocca, "Deformation Monitoring by Long Term D-InSAR Analysis in Three Gorges Area, China," in Geoscience and Remote Sensing Symposium, 2008. IGARSS 2008. IEEE International, 2008, pp. IV - 5-IV - 8.

[45] T. Wang, D. Perissin, F. Rocca, M. Liao, and D. Li, "Three Gorges Dam Stability Monitoring with Temporal Series SAR Image Analysis," Science in China Series D: Earth Sciences, 2009.

[46] 刘广润, "三峡工程地质概况," 水文地质工程地质, vol. 20, pp. 56-57, 1993.

[47] S. N. Madsen, H. A. Zebker, and J. Martin, "Topographic mapping using radar interferometry: processing techniques," Geoscience and Remote Sensing, IEEE Transactions on, vol. 31, pp. 246-256, 1993.

[48] R. Goldstein, "Atmospheric limitations to repeat-pass interferometry," Geophys. Res. Lett, vol. 22, pp. 2517-2520, 1995.

[49] M. S. Seymour and I. G. Cumming, "InSAR terrain height estimation using low-quality sparse DEM," in 3rd ERS Symp, Florence, Italy, 1997.

[50] M. Eineder and N. Adam, "A maximum-likelihood estimator to simultaneously unwrap, geocode, and fuse SAR interferograms from different viewing geometries into one digital elevation model," Geoscience and Remote Sensing, IEEE Transactions on, vol. 43, pp. 24-36, 2005.

[51] Y. Sang-Ho, J. Jun, H. Zebker, and P. Segall, "On merging high- and low-resolution DEMs from TOPSAR and SRTM using a prediction-error filter," Geoscience and Remote Sensing, IEEE Transactions on, vol. 43, pp. 1682-1690, 2005.

[52] B. Kampes and S. Usai, "Doris: The Delft object-oriented radar interferometric software," in Proc. ITC 2nd ORS Symp, 1999, pp. 241-244.

[53] M. S. Seymour and I. G. Cumming, "Maximum likelihood estimation for SAR interferometry," in IGARSS '94, Pasadena, CA, 1994, pp. 2282-2285.

[54] Z. Li, Q. Zhu, and G. Chris, Digital Terrain Modeling: Principles and Methodology: CRC Press, Taylor & Francis Group, 2004.

[55] T. J. Flynn, "Two-dimension phase unwrapping with minimum weighted discontinuity," Journal of the Optical Society of America A., vol. 14, pp. 2692-2701, October 1997 1997.

[56] D. C. Ghighlia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software. New York: Wiley, 1998.

[57] P. A. Rosen, S. Hensley, E. Gurrola, F. Rogez, S. Chan, J. Martin, and E. Rodriguez, "SRTM C-band topographic data: quality assessments and calibration activities," in IGARSS '01, 2001, pp. 739-741 vol.2.

[58] B. Smith and D. Sandwell, "Accuracy and resolution of shuttle radar topography mission data," Geophysical Research Letters, vol. 30, pp. 1467-1470, 2003.

[59] S. H. C. L. Werner, and P. Rosen, "Application of the interferometric correlation coefficient for measurement of surface change," in AGU Fall Meeting, San Francisco, CA, 1996.

[60] J. I. H. Askne, P. B. G. Dammert, L. M. H. Ulander, and G. Smith, "C-band repeat-pass interferometric SAR observations of the forest," Geoscience and Remote Sensing, IEEE Transactions on, vol. 35, pp. 25-35, 1997.

[61] G. A. Arciniegas, W. Bijker, N. Kerle, and V. A. Tolpekin, "Coherence- and Amplitude-Based Analysis of Seismogenic Damage in Bam, Iran, Using ENVISAT ASAR Data," Geoscience and Remote Sensing, IEEE Transactions on, vol. 45, pp. 1571-1581, 2007.

[62] S. R. Cloude, "Dual-Baseline Coherence Tomography," Geoscience and Remote Sensing Letters, IEEE, vol. 4, pp. 127-131, 2007.

[63] M. Santoro, J. I. H. Askne, U. Wegmuller, and C. L. Werner, "Observations, Modeling, and Applications of ERS-ENVISAT Coherence Over Land Surfaces," Geoscience and Remote Sensing, IEEE Transactions on, vol. 45, pp. 2600-2611, 2007.

[64] R. Touzi, A. Lopes, J. Bruniquel, and P. W. Vachon, "Coherence estimation for SAR imagery," Geoscience and Remote Sensing, IEEE Transactions on, vol. 37, pp. 135-149, 1999.

[65] H. A. Zebker and K. Chen, "Accurate estimation of correlation in InSAR observations," Geoscience and Remote Sensing Letters, IEEE, vol. 2, pp. 124-127, 2005.

[66] F. Gatelli, A. M. Guamieri, F. Parizzi, P. Pasquali, C. Prati, and F. Rocca, "The wavenumber shift in SAR inferometry," Geoscience and Remote Sensing, IEEE Transactions on, vol. 32, pp. 855-865, 1994.

[67] D. Ghighlia and L. Romero, "Robust two-dimensional weighted and unweighted phase unwrapping that use fast transforms and iterative methods," Journal of the Optical Society of America A., vol. 4, pp. 267-280, 1994.

[68] C. W. Chen, "Statistical-cost Network-flow Approaches to Two-dimensional Phase Unwrapping for Radar Interferometry," in Department of Electrical Engineering San Francisco: Stanford University, 2001.

[69] A. Pepe and R. Lanari, "On the Extension of the Minimum Cost Flow Algorithm for Phase Unwrapping of Multitemporal Differential SAR Interferograms," Geoscience and Remote Sensing, IEEE Transactions on, vol. 44, pp. 2374-2383, 2006.

[70] M. B.-D. Jos and V. Gonalo, "Phase Unwrapping via Graph Cuts," Image Processing, IEEE Transactions on, vol. 16, pp. 698-709, 2007.

[71] R. Yamaki and A. Hirose, "Singularity-Spreading Phase Unwrapping," Geoscience and Remote Sensing, IEEE Transactions on, vol. 45, pp. 3240-3251, 2007.

[72] O. Loffeld, H. Nies, S. Knedlik, and W. A. Y. W. Yu, "Phase Unwrapping for SAR Interferometry;A Data Fusion Approach by Kalman Filtering," Geoscience and Remote Sensing, IEEE Transactions on, vol. 46, pp. 47-58, 2008.

[73] R. Yamaki and A. Hirose, "Singular Unit Restoration in Interferograms Based on Complex-Valued Markov Random Field Model for Phase Unwrapping," Geoscience and Remote Sensing Letters, IEEE, vol. 6, pp. 18-22, 2009.

[74] A. Hooper and H. Zebker, "Phase Unwrapping in Three Dimensions with Application to InSAR Time Series," Journal of the Optical Society of America A., vol. 24, pp. 2737-2747, 2007.

[75] N.Biggs, Discrete Mathematics. Oxford: Claredon Press, 1985.

[76] R. F. Hanssen and F. J. van Leijen, "Monitoring water defense structures using radar interferometry," in Radar Conference, 2008. RADAR '08. IEEE, Rome, Italy, 2008, pp. 1-4.

[77] D. Ge, Y. Wang, Xiaofang.Guo, Yi.Wang, and Ye.Xia, "Land Subsidence Investigation Along Railway Using Permanent Scatterers SAR Interferometry," in Geoscience and Remote Sensing Symposium, 2008. IGARSS 2008. IEEE International, 2008, pp. II-1235-II-1238.

[78] L. Jiang, M. Liao, H. Lin, and L.Yang, "Synergistic use of optical and InSAR data for urban impervious surface mapping: a case study in Hong Kong," International Journal of Remote Sensing, vol. 30, pp. 2781-2796, 2009.

[79] D. Perissin, C. Prati, F. Rocca, and W. Teng, "PSInSAR Analysis over the Three Gorges Dam and urban areas in China," in Urban Remote Sensing Event, 2009 Joint, 2009, pp. 1-5.

[80] X. Ye, H. Kaufmann, and G. Xiaofang, "Differential SAR interferometry using corner reflectors," in Geoscience and Remote Sensing Symposium, 2002. IGARSS '02. 2002 IEEE International, 2002, pp. 1243-1246 vol.2.

[81] 廖明生, 田馨, and 赵卿, "TerraSAR_X/TanDEM_X 雷达遥感计划及其应用," 测绘信息与工程, vol. 32, pp. 44-46, 2007.

[82] F. Caltagirone, A. Capuzi, R. Leonardi, S. Fagioli, G. Angino, and F. Impagnatiello, "COSMO-SkyMed: The Earth Observation Italian Constellation for Risk Management and Security," in SpaceOps, Rome, Italy, 2006.

[83] R. Furuta, M., T. Shimada, M. Tadono, and Watanabe, "Interferometric Capabilities of ALOS PALSAR and Its Utilization," in Fringe05 Frascati, Italy, 2005.

[84] S. Auer, S. Gernhardt, S. Hinz, N. Adam, and R. Bamler, "Simulation of Radar Reflection at Man-Made Objects and its Benefits for Persistent Scatterer Interferometry," in EUSAR Conference, Friedrichshafen, 2008.

[85] D. Ge, Y. Wang, L. Zhang, Y. Wang, and Q. Hu, "Monitoring urban subsidence with coherent point target SAR interferometry," in Urban Remote Sensing Event, 2009 Joint, 2009, pp. 1-4.