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					           A method for the automatic characterization of interferometric fringes free of
        atmospheric artifacts : application to the study of the subsidences on the city of Paris

                                         Bénédicte FRUNEAU 1, Francesco SARTI2

                          1
                           Laboratoire des Géomatériaux, Institut Francilien des Géosciences (IFG)
                              Université de Marne-la-Vallée 5 Bd Descartes, Champs-sur-Marne
                                            77454 Marne-la-Vallée cedex 2, France
                        Tel : 33.1.49.32.90.61 / Fax : 33.1.49.32.91.37 / e-mail: fruneau@univ-mlv.fr
                                                       ² CNES, QTIS/SR,
                                 18 avenue Edouard Belin, Bpi 811, 31401 Toulouse, France
                              Tel : 33.5.61.28.21.33 / Fax : 33.5 / e-mail: francesco.sarti@cnes.fr


ABSTRACT
                                                               INTRODUCTION
Differential SAR interferometry allows for the detection
and mapping of ground subsidences, usually attributable           The use of SAR interferometry has now become
to human activities, associated with the extraction of         essential for the detection of ground deformations
fluids beneath the surface, or underground mining…             caused by earthquakes, volcano activity, and ice motion,
Limiting factors for monitoring slow subsidences are           which are usually phenomena of large spatial extension.
mainly temporal coherence loss and varying                     It has also proven to be a feasible tool for the detection
atmospheric conditions between the acquisitions of             and mapping of ground subsidences, associated with
images. Such variations induce a path difference               geothermal fields, oil fields, compaction of aquifer
generating InSAR artifacts that cannot be corrected if         system, underground mining…Most of these studied
only one interferogram is available. On urban areas, the       subsidences occur either in non urban context, and are
coherence remains often high over long time scales. The        of small spatial extension (Carnec et al., 1996), or
main problem then appears to be the atmospheric                concern urban areas, but are very large (Amelung, 1998;
heterogeneities. This kind of artifacts can be easily          Fielding et al., 1998; Wegmüller et al., 1999). Here we
detected on the different interferograms we generated          examine the feasibility of SAR interferometry for the
on the city of Paris. Significant phase variations are         detection of slow deformations on urban areas with
clearly visible, and can not be associated with                standard atmospheric conditions. We focus on the city
topographic fringes, nor with displacements.                   of Paris, where displacements of a few hundred meters
Several techniques exist in order to eliminate or reduce       in extension and a few centimeters in amplitude occur.
the effect of atmospheric artifacts: a solution consists in    They are mainly due to the water pumping of working
summing and averaging interferograms, but requires             sites, and also to underground quarry.
several interferograms over the same site. The
advantages of a novel approach based on complex
correlation of interferograms are presented here, in                            INTERFEROGRAMS
particular robustness when only a few interferograms
are available (two interferograms are enough, under               Ten interferograms of the city of Paris are derived
given hypotheses). These algorithms were tested in the         from tandem SAR images acquired during the period of
context of automatic detection of atmospheric artifacts        July 28 1993, August 10 1996 (Fig.1). Those
by means of correlation of interferometric triplets.           interferograms are generated with the Diapason
On the city of Paris, this method reveals 2 subsiding          software developed at CNES, and have time separation
zones. One zone has the same location as an important          ranging from 1 day to about 3 years (table 1).
underground working site, which took place from 1995
to 1997. The existence of subsidences in the area was             The contribution of the topography is removed using
known already from ground truth data. Their spatial            a Digital Elevation Model provided by the Institut
extent can now be mapped by interferometry, and the            Géographique National, with a 25 m horizontal
temporal evolution of the subsidences is also examined         resolution. With an altitude of ambiguity larger than 400
here.                                                          m and a good quality DEM, we can affirm that coherent
                                                               interferometric changes can only be due to surface
                                                               deformations and/or changes in radar propagation
  through the atmosphere between the acquisition of the 2                 Significant phase variations as high as one fringe can
  images.                                                               be easily detected on all interferograms. Large scale
                                                                        bubbles (20 km diameter) are observed, as well as small
                                                                        ones (1 to 5 km diameter) (Fig. 2a and 2b).




         20 Km

                                                                          061093-100896
   Fig.1: SAR amplitude image of Paris and surroundings                     1037 days

                                                                            Figure 2a: 1037 days differential interferogram
280793     061093                    210795 220795             100896
10631      11633                     20995 1322                 6833

   71 d, h = 257 m
              723 d, h = - 964 m
                724 d, h = 405 m

                      1108 d, h = 348 m
                      652 d, h = -203 m
                       653 d, h = -705 m
                            1037 d, h = -985 m
                                          1 d, h = 285 m

                                                385 d, h = 256 m
                                                   384 d, h = 2474 m



                      Table 1: Data selection
                                                                          210795-220795
     Data selection offers the opportunity to study the
                                                                              1 day
  evolution of the coherence on a time scale of 3 years.
  Low values of baselines ensure there is no geometric
  decorrelation. As we expected, the coherence is shown                       Figure 2b: 1 day differential interferogram
  to remain high over more than 3 years, thus indicating
  that the detection of very low subsidence rates over a
  long time span on urban areas is not limited by the                   Most fringes can neither be associated with topography,
  coherence loss on the time scale required.                            nor with displacements, each fringe corresponding in
                                                                        this case to a half wavelength displacement. This
                                                                        phenomenon is even visible on the 1-day interferogram
and excludes the hypothesis of such displacements,
distributed everywhere in Paris and surroundings
(Fig.2b). Most of these bubbles are furthermore
absolutely not stationary, their location changing from a
day to another, and they do not have the size we
expected for the deformations. Most of the signal may
be attributed to tropospheric effects.
   Using the logic of pair wise, we found that
interferograms generated with the 06/10/93 image or
with the 21/07/95 one show phase shifts similar in their
geometry. Interferograms having the 21/07/95 image in
common show little bubbles of small scale, everywhere
in the image. This indicates the presence of convective                    Figure 3: 21 July NOAA images
cells. Interferograms containing the other one display an
almost South-Northern fringe. This may be related to a        We also have 2 NOAA images for the August
frontal zone.                                                 acquisition, but not at the time of SAR acquisition.
                                                              Here, clouds are of stratocumulus type. Those kind of
          INFLUENCE OF TROPOSPHERIC                           clouds are observed in frontal zones, which would be
               HETEROGENEITIES                                responsible of the parallel fringe.

   Atmospheric effects, as coherence preserving phase
phenomenon, may be misinterpreted as subsidence on
interferograms. Those effects are related to the variation
of the refractive index distribution of the propagating
medium. Homogeneous variations are highly correlated
with altitude (Delacourt et al., 1997) and can be
neglected in our case (almost flat terrain). We are then
only disturbed by the heterogeneous atmospheric
component.
   Those kind of artifacts are impossible to correct, since
we need index profiles for almost each pixel of the
images, that is for the 2 acquisition dates.
   We tried to compare our interferograms with NOAA                      Figure 4 : 10 August NOAA images
images (with a 1 km x 1 km resolution) in order to
identify meteorological artifacts, and discriminate them         DISPLACEMENTS DETECTED OVER PARIS
from the signature of displacements. We intend to find
common structures, and see if the spatial signature of          An usual solution to reduce the effect of the artifacts
the atmospheric effects in the interferograms could be        caused by atmospheric fluctuations consists in summing
correlated with the signal observed on NOAA images.           and averaging interferograms.
The problem is that it is very difficult to have                Here, we consider only a few interferograms:
simultaneous acquisitions with SAR images, since they
are acquired every 6 hours.

   The 21 July SAR image was acquired at about 11
o’clock, between the first and second acquisition of
NOAA. Therefore we can only derive qualitative
conclusion. The only thing we can observe is the
presence of many cumulus in the second NOAA image,
corresponding to convective clouds development, which
creates the most disturbing localized anomalies in the
interferometric phase (Hanssen, 1998; Zebker et al.,
1997). This is also confirmed by MeteoFrance, which
indicates a high humidity rate in the lower layers in the
morning, and a high increase of the temperature. This
led to convective developments.
Figure 5 shows an example of the addition of                     The second one, using the coherence norm, is:
interferograms a, b, c and d. It is possible to detect on
the resulting image two areas of subsidence. But this          ρ2 ( AB ,CD ) = corr( γ AB ⋅ e jϕ ,γ CD ⋅ e jϕ )
                                                                                                   AB           CD

method requires several interferograms over the same
site, and atmospheric artifacts are still partially present.
                                                               An important parameter is the correlation window size:
                                                               this should be adapted to the spatial scale of the
                                                               expected displacements. In practice, we tested two
                                                               different sizes (1500 m and 750m) (fig. 6 a and b) and
                                                               we computed a multi-scale correlation, defined as the
                                                               sum of the two correlation rates.




                                                                            a                            b

                                                                Figure 6: Correlation rates for different window sizes
                                                               for interferograms b and c . (a)1500 m - (b) 750 m.
  Figure 5: Sum of interferograms a, b, c and d, and
zoom on the 2 areas of subsidence which are revealed
by means of correlation                                           Figure 7 shows the multiscale correlation rate
                                                               between interferograms b and c, and a and d. These 2
We propose here a novel approach based on complex              correlations give consistent results. We obtain 2 areas,
correlation of interferograms. These algorithms were           at the same position.
tested in the context of automatic detection of
atmospheric artifacts by means of correlation of                  The first halo (from the left) is located south of the
interferometric triplets (Sarti et al., 1999).                 Saint-Lazare rail station. Its location is the same as that
   The interferograms contain fringes due to the               of the working site for the construction of an
atmospheric conditions of the 2 SAR acquisitions, and          underground station "St-Lazare-Condorcet" for the Eole
due to ground displacements. By means of correlation           subway. Those entirely underground works took place
between interferograms, we wish to isolate the                 from 1995 to 1997, and required to lower the
deformation, that is the common fringes in the 2               piezometric level by pumping the phreatic water.
interferograms.                                                Subsidences of the overlying ground surface, with an
Of course, we need to select for the correlation two           amplitude of the order of a few centimeters had been
interferometric pairs with no common dates (no                 revealed already by ground truth. According to IFG,
common atmospheric artifacts) and containing the same          both correlation halos might therefore be linked to the
subsidences (spanning a similar time period, except if         construction of the subway.
the phenomenon is stable) : then, only common fringes
(common displacements) will correlate.                            The correlation rate is then used as a mask: we
   From an interferogram AB, we construct a complex            compute interferogram (b + c), masked with correlation
                                                               (b,c), after application of an adequate threshold (fig. 8a),
image, having a phase equal to the interferogram (ϕ)
                                                               and interferogram (a + d), masked with correlation
and a modulus equal to the unity or to the coherence (γ).
                                                               (a,d) (fig. 8b).
   We then compute the correlation rate of pairs of
interferograms AB and CD. The first formulation is:
                                                               Despite the different time interval (2 years, 3 years), the
                                                               observed phenomenon look similar on those two
ρ1 ( AB ,CD ) = corr ( 1 ⋅ e jϕ ,1 ⋅ e jϕ )
                                  AB        CD
                                                               interferograms: it seems that no deformation occurred
                                                               from July 1995 to august 1996.
                                                             as a measure of              the    evolution/reversibility         of
                                                             phenomena (Fig.9).




                                                                                 a                     b

                                                             Figure 8:
                                                             (a) = Interferogram (b + c), masked with correlation (b,c) (zoom)
                                                             (b) = Interferogram (a + d), masked with correlation (a,d) (zoom)




              Figure 7a: Multi-scale correlation
              between interferograms b and c.




                                                             Figure 9: Difference of interferograms d-a , masked
                                                             with correlation (a,d) (zoom)

                                                             This difference is quite flat, as expected. It reveals no
                                                             further evolution of the ground subsidences during the
                                                             period July 1995 - August 1996
                                                             Furthermore, we know that the works started in 1995 in
                                                             this area of Paris: the observed displacements are
                                                             included in the time period October 1993 - July 1995.
                                                             On the (b+c) and (a+d) interferograms, we can
                                                             distinguish on the western area one fringe of
                                                             displacement, corresponding to ½ fringe of real
                                                             displacement. One fringe corresponds to 2.8 cm of
           Figure 7b: Multi-scale correlation                deformation along the line of sight, or 3.1 cm of vertical
            betweeninterferograms a and d                    deformation, so that displacements are of the order of
                                                             15,7 mm in 650 days.
In order to verify this conclusion, we used the difference
of interferograms d-a , masked with correlation (a,d)        We localized the two areas of deformation on the ERS
                                                             amplitude image, using a Hue Intensity Saturation
composition with the amplitude image, the sum of              CONCLUSION
interferograms, and the correlation (fig.10). We also
superimposed the map of displacement on an airborne           We were able to detect slow deformations on the city of
radar image (SETHI, C band, VV polarization,                  Paris, despite the atmospheric heterogeneities which
Onera/CNES), acquired the first December 1997                 introduce large artifacts in the interferograms, and
(fig.11). The leading localization error is estimated to be   constitute their principal limitation. The new method we
less than 50 m. It appears clearly that the western           presented allows to separate displacement fringes from
subsidence is centered on the Lycée Condorcet, whereas        (non-standard) atmospheric effects, using only two
the second one contains in its central part the Rue           interferograms, when several conditions are verified.
Papillon. A whole building had to be evacuated in this        This method is valid under the hypotheses that there are
street.                                                       no common standard atmospheric effects on the two
                                                              interferograms used for correlation. In our application,
                                                              this was certainly the case because of flat topography.
                                                              Moreover, the time interval spanned by both
                                                              interferograms should be the same, or the observed
                                                              displacements should be stable.

                                                              The method was validated by correlating four different
                                                              interferograms (a,d) and (b,c) without common
                                                              acquisition dates : a similar result is obtained in both
                                                              cases (two areas, same positions). A building located in
                                                              the area to the west was evacuated. Subsidences in the
                                                              area to the right were already known by ground truthing.
                                                              According to IFG, they might be related to water
                                                              pumping associated with the construction of an
                                                              underground station (St.Lazare-Condorcet) for the Eole
                                                              subway, started in 1995 and ended in 1997.
                                                                 More acquisitions are necessary in order to delimit in
                                                              time the beginning and the evolution of the ground
     2.5 Km                                                   displacements, notably after the end of the underground
                                                              station construction and the water level re-
                                                              establishment. We intend to find also, if any, other
                                                              surface displacements on the city. The problem we are
Figure 10 : HIS composition. Red rectangle corresponds        confronted with is that we are in the limits of ERS SAR
to the extracted area of fig.11.                              resolution, which prevents to detect smaller events.
                                                              We plan as well to test this method on different sites.



                                                              ACKNOWLEDGMENTS


                                                                We thank ESA for providing the images, obtained
                                                              within the framework of the tandem project AOT.F309,
                                                              and project AO3.350. We thank IGN for the DEM. We
                                                              are also grateful to the CNES, DGA and the GDR
                                                              INSAR for their support. Warm thanks to D. Raymond,
                                                              D. Aubert, H.Vadon and D.Massonnet.




Figure 11 : Displacement map superimposed on an
ONERA/CNES airborne radar image (SETHI)
(copyright ONERA 1997; filtering by R.Touzi CCRS)
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