A FUNCTION MODEL FOR PREDICTING THE DETECTABLE DEFORMATION
GRADIENT BY D-INSAR
M. Jiang (1), X. L. Ding (1), Z. W. Li (2), L. Zhang (1)
(1)
Dept. of Land Surveying & Geo-Informatics, the Hong Kong Polytechnic University, Hong Kong, Email:
09901979r@polyu.edu.hk
(2)
School of Info-Physics and Geomatics Engineering, Central South University, Changsha 410083, Hunan, China,
Email: zwli@mail.csu.edu.cn
ABSTRACT
In this paper, a new function model for determining the
minimum and maximum detectable deformation
gradient in synthetic aperture radar interferometry
(InSAR) with Envisat ASAR images is developed. The
model incorporates the parameters of both
interferometric coherence and multilook operator for 1,
5 and 20, rather than the interferometric coherence only
in previous studies. Experimental results with real data
sets show that the new model performs very well for
interferograms with different look numbers and
interferometric coherences. The model is thus an
essential extension of the previous model constructed.
Nevertheless the simplicity of the modeling processes
involved, the model can serve as a preliminary tool to
judge whether the InSAR technology can be used to
monitor a given ground deformation. In addition, it can
possibly reveal which look number will result in better
monitoring of a ground deformation in the InSAR data
processing.
1.
INTRODUCTION
Interferometric synthetic aperture radar (InSAR) has
been used widely for topographic mapping and for
ground deformation monitoring [1-3]. However, due to
the effects of interferometric noise and the intrinsic
limitations of the existing synthetic aperture radar (SAR)
systems, not all ground deformations can be detected
with InSAR [4]. It is therefore very important to know
what deformation phenomena can be effectively
detected with a particular InSAR sensor. Such
knowledge is essential in deciding whether or not to
apply an InSAR system to a given deformation
monitoring problem and more importantly in preventing
mis-interpreting InSAR measurement results. One of the
most important factors to examine in this process is the
minimum and maximum detectable deformation
gradients (DDG) of a SAR sensor.
Massonnet and Feigl [3] considered that the maximum
DDG of InSAR is one fringe per pixel, and based on
this consideration defined a dimensionless ratio, i.e.,
half the wavelength λ / 2 to the pixel size μ , as the
maximum DDG:
_____________________________________________________
Proc. ‘Fringe 2009 Workshop’, Frascati, Italy,
30 November – 4 December 2009 (ESA SP-677, March 2010)
D =
λ
2μ
(1)
For example, for the Envisat ASAR the maximum DDG
is 1.4 ×10-3 (28 mm divided by 20 m) when the pixel
size is 20 m × 20 m, where a look number of L = 5 is
used in multi-looking operation.
The definition in Eq. (1) is only valid under an ideal
condition that there is no noise in the radar observations.
However, InSAR phase measurements are always noisy
due to such factors as temporal and geometrical
decorrelation, thermal noise, Doppler centroid
decorrelation, and atmospheric water vapor [5][6]. The
phase noise can significantly affect the deformation
gradients detectable with InSAR. Baran et al. proposed
a new functional model for the minimum and maximum
DDG [7]:
Dmin = −0.00007(γ − 1)
Dmax = 0.0014 + 0.002(γ − 1)
(2)
(3)
where Dmin and Dmax are the minimum and maximum
DDG, respectively, and γ is the interferometric
coherence.
Eqs. (2) and (3) relate the minimum and maximum
DDG to the interferometric coherence that is a measure
of interferometric phase noise, and therefore make the
models more realistic. However, the phase noise in an
interferogram is a function of both the interferometric
coherence and the look number used in multi-looking
operation [8]. The phase standard deviation varies
apparently with both parameters. In addition, multilooking operation in interferometric processing
increases the size of the pixel, and also gives rise to
phase aliasing due to steep phase slopes, both which
significantly alters the minimum and maximum DDG.
We will in this paper investigates the relationship
among the maximum/minimum detectable deformation
gradient, the multilook number and the coherence, and
establishes the empirical function models of the
maximum/minimum detectable deformation gradients
for look number 1, 5 and 20. The developed models
will be validated with some SAR data sets.
2.
Ground subsidence in a local area often has a “bowl”
shape and can be approximated with a two-dimensional
(2D) elliptical Gaussian function [7],
METHODOLOGY
The flowchart in Fig. 1 outlines the methodology
deployed for the study. First, representative surface
deformations with varying magnitudes and spatial scales
are simulated and converted into phases. The phases are
then introduced into the slave SAR image which had
been resampled into the space of the master Envisat
ASAR image beforehand. Second, the modified Envisat
ASAR interferometric pair is processed to generate
differential interferograms. In this process, look
numbers L = 1,5 and 20 are used respectively. Third,
for each of the look numbers, the detectability of the
simulated deformation/phase fringes in areas with
different coherences is examined. Fourth, the above
three steps are repeated until the whole set of the
simulated deformations (and their modified slave
images) are used. Finally, a new empirical functional
model is constructed based on the results derived from
the analysis.
2
f ( x, y ) =
1
2πσ xσ y
e
1 ( x − μ x )2 ( y − μ y )
− [
+
]
2
σ x2
σ y2
(4)
where x and y represent coordinates in the range and
azimuth directions, respectively in the range-Doppler
coordinate system; f ( x, y ) is the simulated deformation
along the radar line of sight; ( μ x , μ y ) are the
coordinates of the center of the deformation bowl; and
σ x and σ y are the standard deviations of the simulated
deformation. For simplicity, we set μ x = 0 and μ x = 0 .
By altering the values of σ x and σ y , deformations with
different spatial variations can be obtained. The final
simulated deformations with different amplitudes are
calculated by scaling f ( x, y ) . All the deformations thus
simulated are resampled into the space of the master
Envisat ASAR image.
Figure 2 Simulated ground deformations along the sight
line of radar and their corresponding wrapped phases.
h is the magnitude of the maximum deformation.
Figure 1 Flowchart showing the procedure of the
proposed study
3.
DEFORMATION SIMULATION AND TEST
SITE SELECTION
3.1. Deformation simulation
Fig. 2 shows the simulated deformations and their
corresponding wrapped phases. Two groups of ground
subsidence surfaces are simulated as denoted by Group I
and Group II, respectively (see Tab. 1). Group I
includes 7 ground subsidence surfaces (each being
distinguished by a model code), each with a spatial
extent of 960 m × 480 m, or 240 × 24 pixels in the
azimuth and range directions respectively. Group II
includes 6 ground subsidence surfaces, but each with a
spatial extent of 480 m ×320 m, or 120 × 16 pixels. The
size of region is chosen to allow for an accurate
estimation of mean sample coherence under the
assumption of locally stationary, and at the mean while
remaining small enough to avoid excessive inclusion of
image texture.
Table 1 Parameters for ground deformation simulation
Group I
Group II
Model A1 B1 C1 D1 E1 F1 G1 A2 B2 C2 D2 E2 F2
h (mm) 3.5 7 14 28 56 84 112 3.5 7 14 28 56 84
Fringes 1/8 1/4 1/2 1 2 3
A/R*(m)
960×480
4
1/8 1/4 1/2 1 2 3
480×320
* A and R represents azimuth direction and range direction respectively.
3.2. Selection of test site
Since interferometric coherence is an important
parameter to consider in constructing minimum and
maximum DDG models, the selected experimental
interferometric pair would be better if it satisfies the
following conditions. Firstly, the imaging region has a
local homogeneous surface feature, ensuring stable
mean coherence value with relative low standard
deviation in each patch. Secondly, the interferometric
pair includes different effects of decorrelation [5]. An
image pair will satisfy the requirement with appropriate
temporal and spatial baseline, e.g., specific spatial
separation not larger than critical baseline (about 2 km
for C-band SAR system), but not less than ~10 m that
will lead to serious geometry decorrelation lost. Thirdly,
the image patches over large rugged terrain and small
scale local topography should be excluded to avoid the
influence of steep topographic phase on coherence
estimation [9]. Finally, a wide variety of coherence
values throughout the whole image should exist so that
model mis-fitting can be alleviated. As implied from the
pervious study, the coherence extent between 0.20 and
0.65 will be more essential to model the SAR
deformation gradients detection.
Therefore, in this paper, the Envisat ASAR image pair
covering the city of shanghai is chosen as test site to
establish observations. The two images were acquired
on February 22, 2005 and March 29, 2005, respectively.
The perpendicular baseline spanned between 222 and
209 meters from near to far range. Tab. 2 lists the
acquisition date, spatial B perp and temporal baseline
Btemp , and coherence range for the image pairs. Fig. 3(a)
shows the optical image of the area from Google Earth
and the spatial extent of descending ASAR data used for
study.
Fig. 3(b) illustrates the geocoded coherence map with
multilook factor 5. The overall coherence in the map is
not very high, but it is still enough to setting up the
minimum and maximum DDG model, as its range is
well between 0.20 and 0.65. It should be noted that, for
most of the land region, the distribution of coherence
are highly related to the land cover type. Compared with
Fig. 3(a), the vegetated areas show lower coherence in
the right bottom corner of fig. 3(b), while higher
coherence can be found in the center of urban areas. The
obvious correlation between land cover types and
observed coherences implies that land cover properties
could help for pre-determining the coherence magnitude
before interferometric measurement [10].
Table 2 SAR interferometric pair selected for the study
Image
Date
Master
200502-22
Slave
200503-29
Area
B perp
Btemp
Coherence
value
Shanghai
215
m
35
days
0.20- 0.65
Figure 3 (a) Optical image from Google Earth over
shanghai region. The red frame shows the coverage of
the descending Envisat ASAR image used for the study.
(b) Geocoded coherence map with multilook operation
of 5 pixels in the azimuth and 1 pixel in the range
direction.
In summary, the aim of test site selection is to find
different coherence levels accompanying with stationary
noise in interferogram patches, and to reduce the effect
of real deformation on modeled subsidence. Both
factors will benefit for fringe interpretation and model
construction that will be described in the following
context.
4.
INTERFEROMETRIC PROCESSING AND
DEFORMATION DETECTABILITY
ANALYSIS
4.1. Interferometric processing
As noted earlier, we have simulated 13 different ground
subsidence surfaces, which are grouped into two
categories according to their spatial extents. Each of the
ground subsidence surfaces has a unique deformation
gradient. We then choose 20 small patches in the
resampled slave SAR image. The spatial extents of
small patches are the same as those of the simulated
ground subsidence surfaces (i.e., 240×24 pixels for
Group I and 120×16 pixels for Group II). The patches
have very different interferometric coherence values as
estimated from the original interferogram (see Tab. 2).
For the two SLC images, the per-processing includes
orbital state vectors manipulation with DELFT precision
orbital data, initial offset estimation and precise
estimation of offset polynomials based on the
maximization of intensity correlation. Once coregistration at subpixel level has been completed, the
slave image will be resampled to the reference geometry
of master image. Then one of the 13 ground subsidences
will be inserted into all the 20 selected small patches of
the resampled slave image in each slave image
modification. The total number of modified slave
images is up to 13.
Of all the 13 slave images, each time the master image
together with one of the slave images are processed with
the standard Two-pass differential InSAR approach,
where the topographic phases are removed with the 90m SRTM DEM. Look numbers of L = 1, 5 and 20
respectively are used in turn in processing the data to
generate different differential interferograms. We then
analyze the detectability of the simulated ground
subsidence within each of the patches based on the
differential interferograms and the results will be used
as observational samples later for model construction.
For each look number, we can get around 260 such
observational samples, i.e., 20 patches (per ground
subsidence surface) times 13 ground subsidences.
In differential interferometric processing, the coherence
within each of the patches is estimated. As coherence
estimation is contaminated by biases when the
coherence is low [9] and the observational samples at
low coherence levels play a crucial role in such model
construction [7], a good coherence estimator must be
adopted. In this study, the maximum likelihood (ML)
coherence estimation algorithm, including correction for
local topographic phase, is used [9]. To limit biased
estimation on sample correlation and reduce the
uncertainty of coherence observation, we remove all
bias by inverting the Eq. 6 in [9] prior to establish
functional model.
4.2. Detectability analysis
After differential interferometric processing, the ground
subsidence within each patch is converted into
deformation fringes. The analysis of the detectability of
the ground subsidences, i.e., the detectability of the
corresponding deformation fringes can then be carried
out. There have not been any well-developed numerical
methods for this purpose so that the visual inspection
method will be adopted for this study [7]. In each
observation, the number of clear fringes rather than the
contour of the fringes is the key criterion to identify the
subsidence model. Here, we select two groups of
representative interferogram patches in Fig. 4 and 5 to
illustrate the detectability of the deformation fringes
under different interferometric coherences and look
numbers.
A1
B1
C1
D1
E1
F1
G1
L=1
L=5
L=20
−3
−2
−1
0
1
wrapped phase [rad]
2
3
Figure 4 Differential interferogram patches for
deformation models A1-G1 and look number L = 1, 5
and 20 respectively. The mean and STD of the
coherences for the region are equal to γ ≈ 0.56 and
σ γ ≈ 0.17 respectively. The spatial extent of each patch
is 960 m × 480 m, and the pixel resolution for look
number and are 4 m × 20 m, 20 m × 20 m and 40 m
× 40 m respectively.
The results in Fig. 4 indicate that most of the differential
interferogram patches for look numbers L = 5 and 20
are clearer than those for look number L = 1 . However
for models E1-G1 that have large spatial gradients,
phase aliasing can be observed in the interferogram
patches with look number L = 20 . On the other hand,
phase fringes in the interferogram patches with look
number L = 5 are clearer and considered more
detectable. Therefore appropriate multilook factor can
reduce interferometric phase noise while maintain the
deformation signals. For models B1-D1 that have small
peak subsidence values, all the deformation fringes for
look numbers L = 20 can be regarded as detectable.
For model A1, it is difficult to detect the deformation
fringes under all look numbers.
Fig. 5 shows the differential interferogram patches for
group Ⅱ . It is apparent that most of the fringes are
clearer than that of the models in Fig. 4, owning to
higher coherence. However, when comparing the
corresponding columns in Figs. 5 and 4, we found that
the center of phase fringes in F2 for look number
L = 5 become aliasing while that in F1 are relatively
more distinguishable. This is considered due to the very
different deformation gradients resulted from the
different spatial scales although both pairs have the
same number of fringes (i.e., three). And the excessively
small spatial extent coupled with high phase gradient
isn’t likely to be unwrapped correctly. In addition, all
models for the look number L = 1 are visible except A2
and B2. For the look number L = 5 , the models B2-E2
can be identified clearly. And models A2, E2 and F2
should be regarded as unobservable for the look number
L = 20 .
A2
B2
C2
D2
E2
F2
L=1
L=5
L=20
−3
−2
−1
0
1
wrapped phase [rad]
2
3
Figure 5 Differential interferogram patches for
deformation models A2-F2 and look numbers L = 1, 5
and 20. The mean and STD of the coherences for the
region are equal to γ ≈ 0.62 and σ γ ≈ 0.14 respectively.
The spatial extent of each patch is 480 m × 320 m, and
the pixel resolution for look number L = 1, 5 and 20
are 4 m × 20 m, 20 m × 20 m and 40 m × 40 m
respectively.
It is evident from the above analysis that the
detectability of deformation gradients in SAR
interferograms is related to both the look number and
the interferometric coherence. Large ground
deformations, especially those occurring in a small
spatial extent, pose severe challenges to the task of
detecting them with InSAR. Understandably, the higher
the coherence is, the easier can the ground deformations
be detected. An appropriate look number should be used
in multi-looking operation considering both the noise
and the detectability of the expected ground
deformations.
5.
CONSTRUCTION OF FUNCTIONAL
MODELS
As discussed in Section 4, 260 observational samples
have been obtained in the experiments for each look
number ( L = 1, 5 and 20). Each of the observational
samples includes the deformation gradient D , the
interferometric coherence γ , the associated look number
L and the results of the deformation detection.
Regression analysis will be carried out based on the
observational samples to determine the upper and lower
bounds of the DDG as a function of the coherence
values for look number L = 1, 5 and 20, respectively.
Observational samples with coherences down to 0.20
are included in the analysis as samples with low
coherence play an important role in determining the
model parameters [7]. Fig. 6 shows the observational
samples for look numbers L = 1, 5 and 20 respectively.
It is very clear from Fig. 6 that the minimum and
maximum DDG are significantly different for look
numbers L = 1, 5 and 20. The upper bound between the
detectable and undetectable deformation gradients is
lowered gradually with the increase of the look number,
indicating that the maximum detectable deformation
gradient decreases with the increase of the look number.
This is mainly due to the aliasing effect caused by the
multi-looking operation. The lower bound between the
detectable and undetectable deformation gradients is
also lowered with the increase of the look number. This
indicates that the extent of the minimum DDG is
increasing with the increase of the look number. This
phenomenon occurs as more phase noise is reduced with
a larger look number so that the sparse phase fringes
(small deformations) can be more visible.
To make the new model more reliable, it is considered
necessary to refine the definition of the maximum DDG
in Eq. 1 to,
0
Dmax,L
=
λ
4μmin, L
(5)
where μmin,L is the smaller dimension of a pixel when
the dimensions of the pixel are different in the azimuth
and the range directions. It should be note that, the
definition given in Eq. 5 is valid only when the
interferogram is free from noise, i.e., γ = 1 . When this
condition cannot be met, the DDG will be lower than
0
0
Dmax,L
. Therefore Dmax,L
is the upper limit of the
maximum DDG. Besides, from the viewpoint of phase
unwrapping and instantaneous frequency estimation
[11], the correct phase gradient under noise-free
condition should be less than 0.5 fringe per pixel. Thus
the Eq. 1 should be reduced by a factor of two.
On the other hand, according to [3], the minimum
detectable deformation is 1 cm over the width of a SAR
scene (100 km for ERS and Envisat data), i.e., 1× 10-7 .
Below this limit, the ground deformation in the
interferogram will be mixed with such errors as the
residual orbital contribution and atmospheric ramps and
−4
becomes undistinguishable. The detectable deformation
gradient 1× 10-7 is also for γ = 1 . The actual minimum
L=1
x 10
undetectable
detectable
DDG will therefore be larger than 1× 10-7 in practice.
deformation gradient (D)
5
Linear models are proposed to approximate the upper
and lower bounds of the detectable deformation
gradients shown in Fig. 6,
Kmax=0.0063
4
3
⎧⎪ Dmin, L (γ ) = 10−7 + K min, L × (γ − 1)
⎨
0
⎪⎩ Dmax, L (γ ) = Dmax, L + K max, L × (γ − 1)
Kmin=−0.000232
2
(6)
1
0
0.2
0.25
0.3
0.35
0.4
0.45
coherence (γ)
0.5
0.55
0.6
0.65
estimated for look numbers L = 1, 5 and 20 , respectively.
(a)
−4
L=5
x 10
0
Replacing K max, L , K min, L and Dmax,
in Eq. 6 with their
L
undetectable
detectable
values as estimated above, we can get the functional
models for the minimum and maximum DDG for look
numbers L = 1, 5 and 20 respectively,
deformation gradient (D)
5
4
Kmax=0.000753
⎧⎪ Dmin,1 (γ ) = −0.000232(γ − 1) + 10-7
⎨
⎪⎩ Dmax,1 (γ ) = 0.0063(γ − 1) + 0.00354
3
Kmin=−0.000181
2
1
0
0.2
0.25
0.3
0.35
0.4
0.45
coherence (γ)
0.5
0.55
0.6
0.65
(b)
−4
L=20
x 10
deformation gradient (D)
5
4
3
Kmax=0.000348
2
Kmin=−0.000096
1
0.25
0.3
0.35
⎧⎪ Dmin,5 (γ ) = −0.000181(γ − 1) + 10-7
⎨
⎪⎩ Dmax,5 (γ ) = 0.000753(γ − 1) + 0.00070
⎧⎪ Dmin,20 (γ ) = −0.000096(γ − 1) + 10-7
⎨
⎪⎩ Dmax,20 (γ ) = 0.000348(γ − 1) + 0.00035
(7)
(8)
(9)
It is clear from the results that the slope of the upper
bound decreases while that of the lower bound increases
with the increase of the look number. Letting
Dmax, L (γ )=Dmin, L (γ ) , we get the intersection points of
undetectable
detectable
0
0.2
When fitting the results in Fig. 6 to the proposed linear
models in Eq. 6, the slopes K max,L and K min,L are
0.4
0.45
coherence (γ)
0.5
0.55
0.6
0.65
(c)
Figure 6 Observational samples and linear models of
the minimum and maximum DDG for different look
numbers. (a) Observations under look number L = 1 .
(b) Observations under look number L = 5 . (c)
Observations under look number L = 20 . A red dot
indicates that the deformation gradient is detectable
while a blue one indicates otherwise.
the linear functional models for look numbers L = 1 , 5
and 20 respectively. The corresponding coherence
values are γ ≈ 0.46, 0.25, and 0.21 respectively. These
are the critical coherence values below which the
ground deformations cannot be detected for the given
look numbers. For example, if γ < 0.21 , no ground
deformation will be detectable with InSAR when the
look number varies from 1 to 20. For 0.21 ≤ γ < 0.46 ,
multi-looking operation can help to improve the chance
for the deformation to be detected. When γ ≥ 0.46 ,
there is a good chance for the deformation to be
detected even without multi-looking operation.
Fig. 7 depicts the fitted linear functional models for look
numbers L = 1, 5 and 20 . The deformations are
detectable in the polygon areas and undetectable in the
blank area. The models for look numbers L = 1, 5 and
20 overlap in certain areas. Six sub-areas marked as A
to F correspond to different combinations of look
numbers (See Tab. 3). For example, in sub-area A, only
when L = 1 , the deformations can be detected; while in
sub-area C, the deformation can be detected with all the
three look numbers L = 1,5 and 20 . This provides a
very useful reference for choosing an appropriate look
number to use in interferometric processing.
Table 3 Sub-areas and their corresponding look
numbers
Sub area
A
B
C
D
E
F
Look number(L)
1
1, 5
1, 5, 20
5, 20
20
5
From the whole interferogram, we choose a
representative patch illustrated in Fig. 8 for validating
the general model. A profile along OC has been chosen
in each interferogram. The three chosen profiles are
corresponding to the same ground extent and coherence
but different look numbers. The aim of using this case is
to examine whether the new model is able to correctly
predict the detectability of the given deformation
gradients under certain coherence levels and look
numbers.
−3
1
x 10
L=1
L=5
L=20
0.9
0.8
deformation gradient (D)
A
0.7
Undetectable
0.6
0.5
Detectable
0.4
0.3
OC
0.2
F
B
C
D
0.1
0
E
0
0.1
0.2
0.3
0.4
0.5
0.6
coherence (γ)
0.7
0.8
0.9
1
Figure 7 Depiction of the fitted linear functional models
for look numbers L = 1,5 and 20. Six sub-areas marked
as A to F can be identified where the deformations are
detectable according to the models. Point OC is used to
validate developed model.
6.
MODEL VALIDATION
An Envisat ASAR pair (Track: 211; Frame: 0675)
acquired on 13 November 2007 and 01 April 2008
respectively over the city of Zhengzhou, Henan
Province, China, will be used to validate the general
model for minimum and maximum DDG. The
perpendicular baseline of the interferometric pair is
approximately 30 m. The main advantages of choosing
this area are its significant surface deformation as a
result of underground mining, and the likeness of the
shapes of these small-scale deformations to the
simulated subsidence model.
The Envisat ASAR pair is processed with the two-pass
plus DEM differential interferometry approach and
under three different look numbers, i.e., L = 1,5 and 20 ,
respectively. The 3 arc-second SRTM DEM is used to
remove topographic phases in the processing. Then the
differential interferograms are filtered with the
improved Goldstein filter to suppress the noise [12].
Figure 8 Differential interferograms ( L = 1,5 and 20)
and their coherence map. The distance between points
O and C is 320 m.
It can be seen that the deformation fringes in the
elliptical shaped deformation area are up to three.
However, the overall low coherence (Fig. 8(d)) makes
the outlines of the fringes very blurry, and the features
of fringes vary significantly among the interferograms
with different look numbers. When L = 1 , the fringes
along profile OC are so noise that the number of fringes
couldn’t be distinguished. When L = 5 , the noise along
the profile is significantly suppressed and the fringes are
very clear and can be easily identified. When L = 20 ,
the fringes along the profile become aliased and can
hardly be detected correctly. The visual inspection
indicates that the fringes along OC profile could only be
detected under the look number L = 5 .
To validate the results from visual analysis, the
deformation gradient and the coherence along profile
OC are calculated. They are D = 2.63 × 10−4 (i.e., 3
fringes over a 320 m distance) and γ = 0.45 ,
respectively. The point (γ , D) , plotted in Fig. 7, falls
into the triangular area F, where the deformation
gradient can only be detected under L = 5 (see also
Tab. 3). Therefore we can see that based on the model
the deformation along OC is detectable when L = 5 .
This agrees very well with the visual analysis.
7.
CONCLUSION AND DISCUSSION
It is vitally important to know what deformations can or
cannot be detected when applying the widely used
InSAR technology. A new functional model for
determining the minimum and maximum DDG has been
established. The model incorporates both the
interferometric coherence and the look number for 1, 5
and 20, representing an extension to previous models
that consider only the coherence. The new model has
become much more useful in practice in assessing the
ability of InSAR in detecting surface deformation. Test
results with Envisat SAR data have shown that the
model works well under for subsidence phenomenon.
Further extension to the work is still possible. For
example, we only used visual analysis in deciding
whether or not interferometric fringes can be recovered
in constructing the model. More sophisticated methods
such as the frequency domain analysis methods, i.e.,
wavelet analysis, multiple signal classification (MUSIC)
and the maximum-likelihood (ML) local frequency
estimator [13][14] may be considered for this purpose.
Also, for simplicity, linear models have been used to
determine the boundaries of various coherence values,
look number and deformation gradient regions. More
complicated models may be considered.
8.
ACKNOWLEDGEMENTS
This work was supported by the National Natural
Science Foundation of China (Nos. 40974006 and
40774003), a High-Tech Research and Development
“863” Program of China (No. 2006AA12Z156), the
Research Grants Council of the Hong Kong Special
Administrative Region (Nos.: PolyU5161/06E and
PolyU5155/07E), and Key Laboratory of Geoinformatics of State Bureau of Surveying and Mapping.
The Envisat data used in this study were provided by the
European Space Agency under Category 1 projects
(AO-4458 and AO-4914).
9.
REFERENCES
1. Madsen, S.N., Zebker, H.A. & Martin, J. (1993).
Topographic mapping using radar interferometry:
processing techniques. IEEE Trans. Geosci.
Remote Sens. 31(1), 246-256.
2. Ding, X.L., Liu, G.X., Li, Z.W., Li, Z.L. & Chen,
Y.Q. (2004). Ground subsidence monitoring in
Hong Kong with satellite SAR interferometry.
Photogrammetric Engineering and Remote
Sensing 70(10), 1151-1156.
3. Massonnet, D. & Feigl, K. (1998). Radar
interferometry and its application to changes in the
Earth's surface. Review of Geophysics 36(4), 441500.
4. Yun, S. H., Zebker, H. A., Segall, P., Hooper, A. &
Poland, M. (2007). Interferogram formation in the
presence of complex and large deformation.
Geophys. Res. Lett. 34, L12305.
5. Zebker, H.A. & Villasenor, J. (1992). Decorrelation
in interferometric radar echoes. IEEE Trans.
Geosci. Remote Sens. 30(5), 950-959.
6. Li, Z.W., Ding, X.L., Huang, C. & Zou, Z.R. (2007).
Atmospheric effects on repeat-pass InSAR
measurements over Shanghai region. J. Atmos.
Sol-Terr Phy. 69(12), 1344-1356.
7. Baran, I., Stewart, M. & Claessens, S. (2005). A new
functional model for determining minimum and
maximum detectable deformation gradient
resolved by satellite radar interferometry. IEEE
Trans. Geosci. Remote Sens. 43(4), 675-682.
8. Lee, J.S., Pathanassiou, K.P., Ainsworth, T.L.,
Grunes, M.R. & Reigber, A. (1998). A new
technique for noise filtering of SAR
interferometric phase images. IEEE Trans. Geosci.
Remote Sens. 36(5), 1456-1465.
9. Touzi, R., Lopes, A., Bruniquel, J. & Vachon, P. W.
(1999). Coherence estimation for SAR imagery.
IEEE Trans. Geosci. Remote Sens. 37(1), 135-149.
10. Santoro, M., Askne, J. I. H., Wegmuller, U. &
Werner, C. L. (2007). Observations, modeling, and
applications of ERS-ENVISAT coherence over
land surfaces. IEEE Trans. Geosci. Remote Sens.
45(8), 2600-2611.
11. Spagnolini, U. (1995). 2-D phase unwrapping and
instantaneous frequency estimation. IEEE Trans.
Geosci. Remote Sens. 33(3), 579-589.
12. Li, Z.W., Ding, X.L., Huang, C, Zhu, J.J. & Chen,
Y.L. (2008). Improved Filtering Parameter
Determination
for
the
Goldstein
Radar
Interferogram Filter. ISPRS J. Photogrammetry
and Remote Sensing 63(6), 621-634.
13. Trouvé, E., Caramma, H. & Maitre, H. (1996).
Fringe detection in noisy complex interferograms.
Appl. Opt. 35(20), 3799-3806.
14. Wu, N., Feng, D.Z. & Li, J.X. (2006). A Locally
Adaptive Filter of Interferometric Phase Images.
IEEE Geosci. Remote Sens. Lett. 3(1), 73-77.