Long-term subsidence monitoring of urban areas using ... - IEEE Xplore

Long-term subsidence monitoring of urban areas using differential interferometric SAR techniques O. Mora, J. J. Mallorquí, J. Duro, A. Broquetas Universitat Politècnica de Catalunya (UPC) C/ Jordi Girona 1-3, D3-212, Campus Nord-UPC Barcelona, 08034. Spain

Abstract- Subsidence monitoring of areas affected by low velocity displacements is an extremely useful application of SAR (Synthetic Aperture Radar) techniques. However, the required long time-baselines reduce the quality of the information stored in differential interferograms, adding difficulties to their processing. Typical characteristics of these interferograms are the presence of coherent areas that correspond to urban zones and totally incoherent areas of vegetation. A partial reconstruction of the subsidence map can be achieved by means of DInSAR (Differential Interferometric SAR) techniques based on the processing of coherent patches. On the other hand, PS (Permanent Scatterers) techniques can deal with incoherent areas, generating subsidence information of the whole image. A comparison of both techniques using ERS data is presented in this paper.

I. INTRODUCTION Images that include small towns or cities surrounded by vegetation are the most difficult ones to obtain their subsidence map using DInSAR processing [1][2]. If low velocity subsidence is supposed in these areas, the problem is worse due to the necessity of long time-baselines to monitor the displacement. To study subsidence there are two options, DInSAR and PS [3]. DInSAR is based on the generation of short baseline interferograms, minimizing the decorrelation produced by long time-baselines. Nevertheless, only small areas of urban and non-vegetated zones will preserve enough coherence to process their phase later. This is the main limitation of this technique. On the other hand, theoretically, only a pair of SAR images will be necessary to generate a subsidence map, but the presence of atmospheric artifacts could require the usage of more interferograms to reduce this error. PS is a different approach to the problem that consists on the selection of stable punctual scatterers that are spread over the image. In this case, several interferograms are required to monitor the phase evolution of each PS during the desired time period. These punctual scatterers can be natural or nonnatural structures, and they are found either in coherent and non-coherent areas. Finally, the displacement map can be reconstructed after solving the system that relates PS phases with their subsidence velocity.

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Fig. 1. Ortophoto of the zone of interest. In this paper, the application and comparison of both techniques are presented. The processed data are from ERS1/2 satellites of the area shown in the ortophoto of Fig.1. This area covers a Spanish small town, surrounded by vegetation, where subsidence problems in buildings have been reported. In addition, some DGPS (Differential Global Positioning System) measurements of the same area are available to compare with the results obtained by means of differential SAR interferometric techniques. The maximum reported subsidence was 2 centimeters per year. II. DInSAR PROCESSING The first step was the selection of a suitable pair of SAR images to generate the interferogram. SAR images acquired on June 13th 1995 and February 18th 1998 with a spatial baseline of 36 meters were selected. Therefore, the observed time period was about 980 days. Weather conditions were also tested to avoid the influence of atmospheric artifacts. Once the interferogram was generated, the topographic component was subtracted using a high quality DEM (Digital Elevation Model) with an rms error of 2 meters and a pixel size of 2.5 meters. Obviously, the differential interferogram presented two different characteristics. On one hand, the urban patches with good phase quality, and on the other hand, the vegetated areas that are totally noisy.

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Fig. 2. Subsidence map derived from DInSAR technique (in centimeters per year). Finally, a growing algorithm was applied to isolate and unwrap the information from coherent areas. The result is shown in Fig. 2. It is clearly observed how the zone with useful phase corresponds to the town of Fig. 1. The maximum subsidence in the south is 2 centimeters per year, as it was reported by the authorities. III. PS PROCESSING Seven SAR images were used to perform PS processing. The first image was dated on June 13th 1995, and the last one on July 27th 1999. A PS selection method based on the coherence of all combinations between the available SAR images (21 interferograms) was carried out. Imposing a restrictive criteria, 25 permanent scatterers were found. The location of the PS’s found in the subsidence reported area is shown in Fig. 3. The differential phase, after topographic removing, of each PS can be expressed as follows:

φi = K ⋅ Bi ⋅ ξ h + C ⋅ Ti ⋅ v + µ i

(1)

where φi is the phase associated with differential interferogram i, K and C are constants, Bi the spatial baseline, Ti the temporal baseline, ξh the DEM error, v the subsidence velocity, and µi non-linear terms related with atmospheric artifacts and non-linear velocity components. The procedure to calculate the displacement velocity is based on the minimization of the following function: f min = 1 −

∑ exp( j ⋅ ∆φ ) ⋅ exp(− j ⋅ (K ⋅ B ⋅ ε i

i

h

+ C ⋅ Ti ⋅ v )) (2)

Fig. 3. Permanent scatterers over the neighbourhood affected by subsidence. In (2), ∆φi is the increment of differential phase between neighbor PS. After solving this minimization, DEM error and velocity for each PS are obtained. Note that the used model only considers linear subsidence velocity. Once all PS were processed, a subsidence map of the whole area was generated by interpolation, as shown in Fig. 4. In order to illustrate better the mechanisms of subsidence another image was created wrapping the obtained subsidence map to cycles of 1 centimeter per year, shown in Fig. 5. The most active subsidence area is placed approximately where it was supposed to be, in the south part of the town. However, the subsidence map obtained is not very detailed due to the low number of PS used in the processing. Obviously, more details would be obtained with a less restrictive criteria selection of PS. These results show that the subsidence focus is placed in the south outskirts of the populated area, making possible a further study to determine which is the real cause of this problem. Consequently, these data should be very useful to decide, considering the characteristics of the terrain, if the problems are due to water pumping, mine exploitations, or other mechanisms.

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Fig. 4. Subsidence map using PS (in centimeters per year).

Fig. 5. Wrapped subsidence map (each color cycle corresponds to a subsidence increment of 1 centimeter per year).

IV. RESULTS

ACKNOWLEDGMENT

A qualitative analysis of the results have been done in the previous sections. Nevertheless, a quantitative one is necessary to evaluate the potentials of these techniques. The available DGPS measurements are restricted to a neighbourhood located in the south of the town. These measurements were made between November 1998 and January 2000. A comparison table taking into account three PS placed in the area of interest is shown in Table 1. These values are expressed in centimeters per year for each type of measurement, DInSAR, PS, DGPS.

The authors would like to thank the ICC (Cartographic Institute of Catalonia) for providing the placement and data used for this study. They also acknowledge the CICYT (Spanish Commission for Science and Technology), project TIC99-1050-C03-01, and REPSOL-YPF and the CIRIT (Catalan Commission for Research) for their financial support of this work.

DInSAR and PS measurements coincide with DGPS measurements. Nevertheless, each velocity result corresponds to a different period of time. If subsidence didn’t have a constant velocity [4], results would be slightly different, because DInSAR observation is from June 13th 1995 to February 18th 1998, and PS study goes from June 13th 1995 to July 27th 1999. DInSAR and PS measurements are extremely coincidental, but DGPS results are slightly different, what could imply that from 1999 to 2000 the subsidence velocity was lower than the one from 1995 to 1999. In conclusion, the implementation of non-linear components of velocity in the model would be a highly interesting advance in the future.

PS number 16 17 18

TABLE 1 SUBSIDENCE RESULT COMPARISON DinSAR PS -1.1 cm/year -1.1 cm/year -1.5 cm/year -1.6 cm/year -1.7 cm/year -1.6 cm/year

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DGPS -1.1 cm/year -1.4 cm/year -1.4 cm/year

REFERENCES [1] P. Berardino, G. Fornaro, G. Franceschetti, R. Lanari, E. Sansosti, and M. Tesauro, “Subsidence Effects Inside the City of Napoli (Italy) Revealed by Differential SAR Interferometry”, IGARSS 2000, Honolulu, Hawaii, 24-28 July 2000. [2] P. Berardino, A. Borgia, G. Fornaro, R. Lanari, E. Sansosti, M. Tesauro, “Anticline growing beneath the urban area of Catania (Italy) measured by SAR Interferometry”, IGARSS 2000, Honolulu, Hawaii, 24-28 July 2000. [3] A. Ferretti, C. Prati, and F. Rocca, “Permanent Scatterers in SAR Interferometry”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 39, No. 1, January 2001. [4] A. Ferretti, C. Prati, and F. Rocca, “Nonlinear subsidence rate estimation using Permanent Scatterers in Differential SAR Interferometry”, IEEE Transactions on Geoscience and Remote Sensing, Vol. 38, No. 5, September 2000.

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