ANALYSIS OF LAND SURFACE DEFORMATION GRADIENT BY DINSAR

Dhinaharan Nagamalai et al. (Eds) : ACSIT, ICITE, SIPM - 2018
pp. 127–136, 2018. © CS & IT-CSCP 2018 DOI : 10.5121/csit.2018.80810
ANALYSIS OF LAND SURFACE
DEFORMATION GRADIENT BY DINSAR
Karima Hadj-Rabah1
, Faiza Hocine2
,SawsenBelhadj-Aissa3
and
Aichouche Belhadj-Aissa4
1,2,3,4
Department of Telecommunications,University of Sciences and
Technology Houari Boumediene (USTHB), Algiers, Algeria
ABSTRACT
The progressive development of Synthetic Aperture Radar (SAR) systems diversify the
exploitation of the generated images by these systems in different applications of geoscience.
Detection and monitoring surface deformations, procreated by various phenomena had
benefited from this evolution and had been realized by interferometry (InSAR) and differential
interferometry (DInSAR) techniques. Nevertheless, spatial and temporal decorrelations of the
interferometric couples used, limit strongly the precision of analysis results by these techniques.
In this context, we propose, in this work, a methodological approach of surface deformation
detection and analysis by differential interferograms to show the limits of this technique
according to noise quality and level. The detectability model is generated from the deformation
signatures, by simulating a linear fault merged to the images couples of ERS1 / ERS2 sensors
acquired in a region of the Algerian south.
KEYWORDS
Radar Interferometry (InSAR & DInSAR), Surface Deformation Gradient (SDG), Coherence,
Resolution, Filtering
1. INTRODUCTION
The interferometry (InSAR) is a technique allowing the generation of altimetric information and
its variations from couples of SAR radar images. Although, interferometric techniques had known
an important development in terms of correction treatments and telemetric phase analysis
approaches and methods, their evaluation in comparison with the required precision by geodesy,
showed limitations as for their use in cartography deformation and sources characterization
causing these last. The quality of interferometric products depends, from one side, on the
acquisition geometry and periodicity of radar systems, and from the other side on, the
atmospheric conditions, the scene degradations and the surface state observed at a moment ‘t’. As
a result, differential interferometry (DInSAR) processes do not allow in all cases the deformations
detection. However, it is essential to know the deformations that can be detected by the
differential interferometry, thus making it possible to decide on the best solution to opt for
measuring and monitoring a surface displacement phenomenon [1][2].
Massonnet and Feigl [3] had shown that the necessary condition for the detection of a
deformation is that the maximum surface deformation gradient (SDG) equals a fringe by the pixel
resolution. Indeed, a fringe of deformation equals half a wavelength. This definition depends on
two parameters: the wavelength and the resolution, these last are fixed and specified for each

128 Computer Science & Information Technology (CS & IT)
sensor. However, in reference to this relation, SAR radars can detect several types of variable
intensity deformations. Unfortunately, in practice, the interferometric measurements are too
noisy. These phenomena of noise and phase discontinuity are essentially due to: spatial and
temporal decorrelation, atmospheric heterogeneity and others [4][5]. Therefore, the small and the
large deformations become undetectable when the level of noise is high.
Otherwise, the estimation of the maximum surface deformation gradient (SDG) does not take into
account the noise factor [6] where the first indicator is the interferometric coherence. In practice,
the lower the coherence is, the more the maximum SDG decreases [7]. In this context, the work
that we are about to present is a contribution to the modelling of the surface deformation gradient
from the differentials interferograms. To show the effectiveness of this modelling, we proceeded
at first by simulating a brittle deformation (linear fault) which we had integrated in pairs of the
ERS1/ERS2 sensor images. The remainder of the paper is organized as follows: a synthesis on the
deformation detectability models by DInSAR will be presented in section 2, section 3 will include
a description of the methodological approach that we propose. Section 4 will be devoted to the
deformation gradient modeling as well as the obtained results. To finish, we generalize in section
5 our modelling for a case of a real deformation. The paper will end with a general conclusion
and perspectives in order to enrich this work.
2. RELATED WORK
The first formula based on the consideration of Massonet and Feigl [3] defines the maximum
deformation gradient as:
= ∗
1
(1)
Where: is the differential phase of one fringe (a turn of 2π) which corresponds to half the
wavelength λ and the pixel resolution .
In order to introduce the coherence which best describes the noise effect, Baran et al. [6] have
proposed a functional model to determine the minimum and the maximum surface deformation
gradient for different values of the coherence, by using real images with a simulated deformation
(surface subsidence) for a number of looks L equals 5. Subsequently, Jiang and Li [8] have
extended this model in order to adapt it for different number of looks (L= 1, 5, and 20). In the
same context, Wang and Li [9] had resumed the same work for the acquired data by the PALSAR
sensor. Recently, Hadj-rabah and Hocine [10] had proposed an automatic approach for surface
deformation detection based on a multi-scales analysis that can be adapted and implemented to
determine the minimum and the maximum surface deformation gradient instead of the subjective
approach implemented in the works mentioned above. These works are focused on a single type
of deformation (mining subsidence) and do not include a spatial filtering step in advance. For our
part, we proposed a methodological approach (see Fig. 1) for surface deformation gradient
detection and analysis for different resolutions and noise levels. In addition, we have analyzed the
deformation detectability for a linear fault.
3. METHODOLOGICAL APPROACH
In order to achieve our goal,A linear fault of the surface is modeled by simulating deformation
images with different parameters representing its temporal evolution (see Fig. 2). These
deformations are then wrapped (converted) into phase images. They have been merged with
Single Look Complex (SLC) images considered as the ‘master’ images giving birth to the
modified SLC images containing the deformation signature. The generating process of
differential interferograms is, then applied. In the course of this procedure, a step of spatial

Computer Science & Information Technology (CS & IT) 129
filtering is performed and the resolution is gradually changed in order to observe the effect of
noise as well as the level of detail on the deformations detectability. the coherence γ and the
deformation gradient are calculated for each generated differential interferogram.
Finally, the modeling is carried out basically, on a step of decision. This last consists in deciding
if the deformation is detectable or not, interactively.
Figure 1. Proposed approach
3.1. Deformation Simulation
The simulated deformation according to a direction, supposed to be the acquisition one, is
gendered by a linear fault. The spatial two-dimensional function f (following azimuth and
distance directions) has been adopted to model such a deformation with a scaling obtained by
varying the parameter 'h', also called the deformation temporal amplitude. Its expression is as
follows:
( , , ℎ) = ℎ ∗ ∗ cos + ∗ sin (2)
With: R and A, the coordinates of the deformation image following the range and the azimuthal
directions respectively. The value of the angle θ representing the fracture line orientation is
considered constant, assuming that the deformation coincides with the radar sight angle, thus we
obtain a series of simulated images, which their 3D representation shows the deformation
evolution as a function of time (see Fig. 2).

Figure 2.
The deformation parameters in the simulated images are represented in the following table:
Table 1. Parameters of simulateddeformation
Name Simulated Surface Deformation
SD1
θ 35°
h(m) 0.014
3.2. Deformation Signature Integration
The variation of the parameter ‘h: fault depth’ makes it possible to generate three deformation
forms at surface, noted SD1, SD2 and SD3. Surface fault signatures are then generated by
merging the deformation to one of the two SLC im
interferograms are generated from the modified images. The selected SLC images have different
coherences and resolutions values (8 m, 20 m and 40 m respectively). A filtering step is applied
on the complex interferograms consisting to attenuate the noise effect mainly due to spatial
decorrelation, geometry effects of acquisition and observed field. Interferometric pretreatments
are applied, namely: orbital fringes removal, topographic pair generation from a digital ele
model (DEM) of the region by bringing it back to interferometric pairs geometry.
3.3. Detectability Analysis
The deformation fringes in the differential interferograms are analyzed by an interactive method
based on rows and columns profile plots.
figures 3 to 6, in order to illustrate the necessary fringes analysis for detectability decision, for
different coherences γ, and resolutions values as well as filtering level.
SD1
Figure 3. Interferometric phase of the simulated deformations
Fig. 3 and Fig. 4 show the interferometric phase of the simulated deformations (SD1 to SD3) and
its corresponding differentials interferograms, with different coherence values for a 20 m
resolution.
Computer Science & Information Technology (CS & IT)
Figure 2. Simulated deformation in 3D
Table 1. Parameters of simulateddeformation.
Simulated Surface Deformation
SD2 SD3
0.084 0.14
Signature Integration
merging the deformation to one of the two SLC images of the interferometric pairs. The
ams consisting to attenuate the noise effect mainly due to spatial
are applied, namely: orbital fringes removal, topographic pair generation from a digital ele
model (DEM) of the region by bringing it back to interferometric pairs geometry.
based on rows and columns profile plots. Three groups of interferograms are represented in
, and resolutions values as well as filtering level.
SD2 SD3
Interferometric phase of the simulated deformations
ages of the interferometric pairs. The
ams consisting to attenuate the noise effect mainly due to spatial
are applied, namely: orbital fringes removal, topographic pair generation from a digital elevation
Three groups of interferograms are represented in

Figure 4. Differentials interferograms and their profiles (red lines), corresponding to simulated
deformations SD1 to SD3 with different coherence values (a)γA= 0.582355, (b)γB = 0.679226 and (c)γC=
0.778999, for a resolution of 20 m
These results show that the more the coherence is, the best the deformation fringes are
distinguished and detected. For low coherence values, no deformation can be detected properly,
(e.g., image A). On the other hand, for a same coherence value, the more the deformation gradient
is, the more the deformation fringes are distinguished and detected.
Fig. 5 shows the differentials interferograms corresponding to deformations SD1 to SD3 with and
without filtering for a 20 m resolution. These results show that the noise spatial filtering makes
the fringes contours more readable, thus facilitating the detectability analysis.
Without
filtering
With
filtering
Figure 5. Differentials interferograms corresponding to simulated deformation SD1 to SD3 with a
coherence equals to γD= 0.697129, for a resolution of 20 m with and without filtering
Regarding the resolution, we have noticed from the results shown in Fig. 6, that the differentials
interferograms using a 40 m resolution are more smoothed than those using an 8 m resolution.
However, if the deformation is very deep, the number of fringes increases and their width
decreases, decreasing the resolution leads to a fringes elimination and an erroneous estimation of
the deformation. In the same analysis sense, we have noticed that the simulated images for which
the deformation fringes are more tighter and the deformation gradient is big (e.g., SD3), are better
observed in the case of interferograms using a 20 m resolution. This result presents a better
compromise between the use of a 40 m and 8 m resolutions.

(a)
(b)
(c)
Figure 6. Differentials interferograms corresponding to simulated deformation SD1 to SD3 and a
coherence equals to γC= 0.778999, with different resolutions:
4. SURFACE DEFORMATION
The objective of DInSAR deformation detectability analysis is establishing two deformation
gradient equations in function of the coherence (see Fig. 7). The linear curves,
two equations, allow the delimitation of detectability surface in function of the DInSAR quality
product. The intersection, the slopes and the offset of the two curves define the deformation
detectability model with respect to types of SA
and mapping applications of land surfaces and/or Over
Figure 7. Observations and linear models
m, (1)
Differentials interferograms corresponding to simulated deformation SD1 to SD3 and a
= 0.778999, with different resolutions: (a) 8 m, (b) 20 m and (c)
EFORMATION GRADIENT MODELLING BY DINSAR
gradient equations in function of the coherence (see Fig. 7). The linear curves, obtained from the
detectability model with respect to types of SAR radar images set to be explored in monitoring
and mapping applications of land surfaces and/or Over-surfaces movements.
Figure 7. Observations and linear models dmin (γ) and dmax (γ), for a resolution (a) 8 m, (b) 20 m and (c) 40
(1) without and (2) with spatial filtering
Differentials interferograms corresponding to simulated deformation SD1 to SD3 and a
(c) 40 m
obtained from the
R radar images set to be explored in monitoring
20 m and (c) 40

4.1. Model Parameters
This model is defined by two parameters: the coherence and the deformation gradient [6]. The
coherence describes the correlation degree between the two SLC images, the modified master
image MS and slave image S; it is given by:
=
!∑ #$ .&
'( $ ∗
!
)∑ |#$ | ∑ |$ |&
'(
&
'(
(3)
Where: L is the number of looks corresponding to its appropriate resolution value.
The deformation gradient d is defined as:
, = (4)
Where: DA is the deformation amplitude and ris the images resolution according to the range
direction.
4.2. Interactive Model Analysis
Each differential interferogram, obtained for a given coherence threshold and a given resolution,
associated with the 2D profiles plots are visually analyzed, the decision making on the
detectability is related to the fringes limits perception: discernable fringes. On a d = f (γ) graph,
we attribute a value ‘1’ if it is discernible, otherwise the value is equal to zero. Fig. 7 represents
the deformation gradients (d) plots as a function of the coherence (γ), for the different resolution
values (8 m, 20 m and 40 m), with and without the spatial filtering application. By observing the
six graphs, the clouds of points forming the decision that equals 1, represented by the red stars
can be delimited by two linear curves (one upper bound and another lower one) [6][8]. The
minimum and the maximum SDG differ from one resolution to another, and for the same
resolution, the spatial filtering makes it different. As the resolution decreases, the SDG upper
bound becomes lower; the same happens for the minimum SDG, this means that the Max(SDG)
and the Min(SDG) vary in the same direction as the resolution.
Linear plots are proposed to approximate the SDG lower and upper boundaries. For this purpose,
we obtained a deformation gradient modelling with a resolution of 8 m, 20 m and 40 m
respectively, which their equations are the following (with a normalization factor of (10-4
)):
• Without spatial filtering
.
,/01 = (9,7504 − 11,4 )
,/78 = (−97,241 + 127,2 )
(5. 7)9
.
,/01 = (3,3064 − 3,89 )
,/78 = (−9,625 + 17,5 )
(6. 7)9
.
,/01 = (3,085 − 3,6496 )
,/78 = (−4,954 + 10,989 )
(7. 7)9
• With spatial filtering
.
,/01 = (3,427 − 3,919 )
,/78 = (−21,35 + 35 )
(5. <)9

.
,/01 = (2,735 − 3,18 )
,/78 = (−5,293 + 12,17 )
(6. <)9
.
,/01 = (2,699 − 3,1731 )
,/78 = (−2,307 + 7,162 )
(7. <)9
On the other hand, each graph illustrates two areas “1” and “0”, which cover the surface where
the coherence and the SDG value designate the deformations that can or not be detected by
DInSAR. The equation below defines the condition of detectability:
.
,/01 ≤ , ≤ ,/78 => ?7 "1"
, ≤ ,/01 A , ≥ ,/78 => ?7 "0"
9 (8)
This study shows the usefulness of the approach that we propose during the choice of the
technique to be implemented for a good detection of the surface deformation. The establishment
of the equation (8) will make it possible to decide if a deformation (linear fault) is detectable or
not by differential interferometry, taking into account the noise level in the differential
interferogram and by calculating only two parameters: the coherence and the gradient, that
describe the noise level and the deformation depth respectively.
4.3. Discussion
The proposed methodological approach is based on both simulated and real data, the advantage of
using simulated images is to be able to control the dimensions of the deformation. On the other
hand, introducing the deformation signature into SLC phase images allows reducing the chances
of obtaining interferograms with hidden information of the deformation caused by noise. By
comparing the deformation image and the resulting differentials interferograms, with the profiles
plots, a set of observations has led us to the establishment of a deformation modelling. In practice,
this last is useful to evaluate the capacity of the differential interferometry to detect a surface
deformation and to monitor its evolution. However, this model has essentially two limitations. In
the first place, the detectability decision depends on an interactive method, which makes it very
subjective. In addition, the upper and lower boundaries of the model are not certain. Otherwise,
this model has been created based on the deformations modeled by simulation. Although the
surface deformations are simulated in the form of a brittle surface deformation designating a
linear fault, the methodological approach can be generalized to other kinds of deformations.
However, in other kind of deformations, it is not practical to calculate the deformation gradient
using equations (5) to (7). Therefore, it is more appropriate to adapt the same methodology in
order to simulate specific deformations.
5. GENERALIZATION
The objective of the generalization is to validate the results obtained in the previous section by
checking the reliability of the relationship established between the coherence and the deformation
gradient for real data. Since there are no other methods dealing with the same type of deformation
and having the same objective and in order to generalize our proposed approach, we used a
differential interferogram of the region of Ouargla (Algeria) containing a brittle surface
deformation (see Fig. 8).

Figure 8. (a) Real differential interferogram containing a brittle surface deformation and
This interferogram was generated for a 20 m resolution, we have calculated the deformation
gradient, as well as the coherence value.
robustness of this modelling, we assessed the found parameters values in order to determine if the
point generated belongs actually to the area “1”. The results obtained are shown in the following
table:
Gradient Coherence
0.000140 0.578806
From the equation (8), we have noticed that the deformation gradient value fills the following
condition:, C ≤ , ≤ , DE, this implies that this deformation is part of the area “1”, then it is
detectable by radar differential interferometry DInSAR.
6. CONCLUSIONS
The objective of this study is to show the contribution and the limits of the differential
interferometry in altimetric surfaces and sub
However, these variations altered by diverse degradation sources contributing to the limitations of
the DInSAR and which can be highlighted by an interferometric quality indicator which is
coherence. In this sense, we have analyzed and modeled the surface deformation gradient (SDG)
by establishing a relationship between the coherence and the deformation gradient for different
resolution values. However, an extension of this work will be
a visual detectability analysis for the decision in model construction. Other methods based on an
automatic analysis can be adopted. In addition, for a reason of simplicity, linear models were used
to separate the regions describing detectable and undetectable deformations. Non
can be envisaged.
REFERENCES
[1] S.N. Madsen, H. Zebker, & J. Martin, (1993) “Topographic mapping using radar interferometry:
processing techniques”, IEEE Transactions on Geoscience
pp246-256.
[2] X.L. Ding, G.X. Liu, Z.W. Li, Z.L. Li, & Y.U. Chen, (2004) “Ground subsidence monitoring Hong
Kong with satellite SAR interferometry”, Photogrammetric Engineering and Remote Sensing, Vol.
70, No. 10, pp1151-1156.
[3] D. Massonnet& K. L. Feigl, (1998) “Radar interferometry and its application to changes in the earth’s
surface”, Rev. Geophys., Vol. 36, No. 4, pp441
[4] H. A. Zebker& J. Villasenor, (1992) “Decorrelation in interferometric radar echoes
Transactions on Geoscience and Remote Sensing, Vol. 30, No. 5, pp 950
(a) (b)
Real differential interferogram containing a brittle surface deformation and (b)
image
gradient, as well as the coherence value. Visually, the deformation is detectable, to evaluate the
Table 2. Calculated parameters.
Coherence FGHI FGJK
0.578806 0.8944 x10-4
1.7511 x 10-4
implies that this deformation is part of the area “1”, then it is
detectable by radar differential interferometry DInSAR.
ric surfaces and sub-surfaces variations detection and estimation.
the DInSAR and which can be highlighted by an interferometric quality indicator which is
resolution values. However, an extension of this work will be possible. Indeed, we have only used
s describing detectable and undetectable deformations. Non-linear models
S.N. Madsen, H. Zebker, & J. Martin, (1993) “Topographic mapping using radar interferometry:
processing techniques”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 31, No. 1,
X.L. Ding, G.X. Liu, Z.W. Li, Z.L. Li, & Y.U. Chen, (2004) “Ground subsidence monitoring Hong
D. Massonnet& K. L. Feigl, (1998) “Radar interferometry and its application to changes in the earth’s
surface”, Rev. Geophys., Vol. 36, No. 4, pp441–500.
H. A. Zebker& J. Villasenor, (1992) “Decorrelation in interferometric radar echoes
Transactions on Geoscience and Remote Sensing, Vol. 30, No. 5, pp 950–959.
135
(b) its coherence
Visually, the deformation is detectable, to evaluate the
implies that this deformation is part of the area “1”, then it is
surfaces variations detection and estimation.
the DInSAR and which can be highlighted by an interferometric quality indicator which is the
possible. Indeed, we have only used
linear models
S.N. Madsen, H. Zebker, & J. Martin, (1993) “Topographic mapping using radar interferometry:
and Remote Sensing, Vol. 31, No. 1,
X.L. Ding, G.X. Liu, Z.W. Li, Z.L. Li, & Y.U. Chen, (2004) “Ground subsidence monitoring Hong
D. Massonnet& K. L. Feigl, (1998) “Radar interferometry and its application to changes in the earth’s
H. A. Zebker& J. Villasenor, (1992) “Decorrelation in interferometric radar echoes,” IEEE

[5] X. L. Ding, Z. W. Li, C. Huang & Z.R. Zou, (2007) “Atmospheric effects on repeat-pass InSAR
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AUTHORS
Karima Hadj-Rabah received the M.Sc. degree in Telecommunication, networks and
multimedia from University of Science and technology HouariBoumedienne(USTHB),
Algeria, in 2016.She is curently working toward the Ph.D.degree insynthetic aperture
radar (SAR)tomography reconstruction using Very High-resolutiondata, in laboratory
of image processing and radiation, USTHB, under the supervision of Professor
AichoucheBelhadj-Aissa.
Faiza Hocine Graduated from the University of Sciences and Technology Houari
Boumedienne (USTHB), Algeria. PhD in image processing and remote sensing of the
same university, in 2015. Currently, she is researcher in Electronics, image processing,
remote sensing at USTHB. Her research interests include satellite image processing,
SAR interferometry radar.
SawsenBelhadj-Aissa received the M.Sc. degree in Telecommunication, networks and
multimedia from University of Science and technology HouariBoumedienne
(USTHB), Algeria, in 2013. She is curently working toward the Ph.D. degree in SAR
Differential Interferometry: 2D / 3D applied to the detection of surface’sdeformations,
in laboratory of image processing and radiation, USTHB, under the supervision of
Professor Salah Boughacha.
AichoucheBelhadj-Aissa obtained her engineering degree in electronics from National
Polytechnic School, Algiers, the magister degree and the Doctorate in image
processing and remote sensing from the University of the Sciences and Technology
Houari Boumediene, Algiers. Currently, she is university Professor and head of the
research team “GIS and integration of geo-referenced data”. The main research themes
focus on modeling and analysis of textures and forms, fusion and classification of
objects, SAR interferometry-polarimetry and GIS.

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ANALYSIS OF LAND SURFACE DEFORMATION GRADIENT BY DINSAR