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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 : 220.127.116.11.90.61 / Fax : 18.104.22.168.91.37 / e-mail: firstname.lastname@example.org ² CNES, QTIS/SR, 18 avenue Edouard Belin, Bpi 811, 31401 Toulouse, France Tel : 22.214.171.124.21.33 / Fax : 33.5 / e-mail: email@example.com 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) REFERENCES Amelung, F., Galloway, D., Bell, J., Zebker, H., and Laczniak, R., A sense of Las Vegas’ ups and downs: New satellite maps reveal aquifer-system deformation and structural control of land subsidence, Science, unpublished. Carnec, C., Massonnet, D. and King, C., 1996, Two examples of the use of SAR interferometry on displacement fields of small spatial extension, Geophys. Res. Lett, vol. 23, pp3579-3582. Delacourt, C., Briole, P., and Achache, J., 1998, Tropospheric corrections of SAR interferograms, Geophysical Research Letters, vol 25, pp 2849- 2852. Fielding, E., Blom, R., Goldstein, R., 1998, Rapid subsidence over oil fields measured by SAR interferometry, Geophys. Res. Lett., vol. 25, pp3215-3218. 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