Generation of deformation maps at low resolution using differential interferometric SAR data O. Mora, J. J. Mallorquí, J. Duro Universitat Politècnica de Catalunya (UPC) Signal Theory and Communication Dept. (TSC) C\ Jordi Girona, 1-3, D3-212, 08034 Barcelona (Spain) Phone: +34 93 401 73 61, Fax: +34 93 401 72 32, E-mail:
[email protected] Abstract - In this paper, an advanced technique for the generation of deformation maps using SAR data is presented. The input data is a set of low resolution Differential Interferograms (multi-looked data) and their associated coherence images. An important advantage of this algorithm is that it can work with a reduced number of SAR images with a diversity of spatial baselines. The algorithm takes advantage of those pixels presenting a good coherence level in the whole set of interferograms, avoiding the rest affected by temporal decorrelation. All pixels accomplishing the selection criteria are related using a Delaunay triangulation. The subsidence velocity map over the scene is obtained adjusting an interferometric phase model, which also considers the error on the DEM used to remove the topography from the interferogram set, to the pixel phase increments. If the density of quality pixels is high enough over the scene, an interpolation of the areas with no information can be performed to obtain a complete deformation map of the zone. Otherwise, the information can be presented only on those zones with enough pixel density. This algorithm has been tested with ERS data from an area of Catalonia (Spain) and validated with precise levelling measurements.
I. INTRODUCTION The detection of Earth surface movements using remote sensing techniques is a great deal that has shown excellent results in the last years of research. The first steps in this context were made by simply using a pair of short-baseline SAR images enough separated in time, and generating the associated interferogram. If the topographic phase is not significant, due to the short spatial baseline, in front of the one caused by deformation, the wrapped interferometric phase shows the spatial distribution and magnitude of the displacement. This technique was successfully used to monitor deformations caused by earthquakes, due to the short time gap necessary between both SAR acquisitions, which reduces the temporal decorrelation. Nevertheless, when studying low velocity deformations, the differential interferograms are forced to have a large time baseline, and the temporal decorrelation largely affects the interfrometric phase making almost impossible the extraction of useful information. In order to overcome the inherent limitations caused by temporal decorrelation the new techniques are focused on the usage of a large set of SAR images distributed along time, in order to have redundant data, and working at pixel level. Examples of these advanced techniques can be
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found in [1] and [2]. The main differences between algorithms relay in data requirements: like the minimum number of SAR images, the limitations on baseline length or the need of multi-looked data. The presented algorithm is based on the idea of Permanent Scatterers (PS) published in [2], but extended to more flexible data requirements. The selection of pixels in [2] was performed studying the amplitude stability in the set of SAR images. This procedure introduces an important limitation in the minimum number of images, typically thirty [2], and requires and excellent radiometric calibration of the images. Nevertheless, these requirements can be relaxed by using coherence as selection criteria. Once those pixels have been selected, the estimation of mean deformation velocity is calculated carrying out a temporal-spatial study of the phases. Another parameter that can be obtained is the topography error generated when subtracting the DEM information to interferograms. Results obtained with ERS data from a zone of Catalonia (Spain) are presented. II. THE ALGORITHM From the initial set of SAR images, all the possible interferograms are generated and the topographic phase component removed using a DEM. For each interfrogram the coherence is calculated. One important step is the image coregistration, more critical than with the traditional topographic applications, because the presence of noisy areas can introduce mis-registration problems. On the other hand, the algorithm has not limitations with the combinations to generate the interferograms, being possible to perform multiple pairs. The goal is to calculate the constant deformation velocity in the period of time of observation and the error of the DEM. These are the basic components of the differential phase, without taking into account atmospheric artifacts, orbital errors, mis-registration and thermal noise. To correctly compute the velocity vector of deformation it is very important an homogeneous distribution of time baselines. The larger the spatial baseline the larger the impact of DEM errors on the interferometric phase, then, better results can be achieved using the shortest spatial baselines available. The algorithm calculates the DEM error, but its precision will depend on the spatial baselines used.
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The interferograms must be multi-looked, reducing the spatial resolution, and their coherence computed. The degree of resolution depends on the deformation scale to be computed. With high resolution interferograms, the deformation map will include small structures, but with a lower phase quality. With low resolution interferograms, the obtained deformation map will be at large scale, but with a higher phase quality. Obviously, at low resolution, coherent isolated structures will be omitted. The first step consists on a selection of pixels based on the time evolution of their spatial coherence. All those pixels having a coherence higher than a determined threshold in a minimum number of images are selected. With this criteria, the nosiy pixels are rejected and only the ones containing useful information pass to the next step of the algorithm. But the phase of individual pixels is not of practical utility due to the presence of different phase offsets among differential interferograms. These offsets could be calculated over high coherence stable areas not affected by subsidence and atmospheric artifacts, but in this case, additional input information will be required. Relating two neighboring pixels, (xm,ym) and (xn,yn), by means of Delaunay triangulation, the differential phase increment can be expressed as:
φ (x m , y m , x n , y n , Ti ) = +
4π
⋅
4π
λ
⋅ Ti ⋅ [v( x m , y m ) − v (x n , y n )] +
b(Ti ) ⋅ [ε ( x m , y m ) − ε ( x n , y n )] + r (Ti ) ⋅ sin (θ )
λ + [β ( x m , y m , Ti ) − β ( x n , y n , Ti )] + + [α ( x m , y m , Ti ) − α ( x n , y n , Ti )] +
(1)
φ model (x m , y m , x n , y n , Ti ) = 4π = ⋅ T ⋅ [v (x , y ) − vmodel (xn , yn )] + (2) λ i model m m b(Ti ) 4π + ⋅ ⋅ [ε (x , y ) − ε model (xn , yn )] λ r (Ti ) ⋅ sin(θ ) model m m A solution of velocity and topographic error increments can be obtained matching the data with the model. Taking into account that the atmospheric artifact component is very similar between neighboring pixels, its contribution will be negligible. The matching can be performed by a simple maximization process of the following function:
γ (xm , y m , xn , y n ) =
1 N ⋅ ∑ exp[ j ⋅ (φ ( x m , y m , x n , y n , Ti ) − (3) N i=0
− φ model ( x m , y m , x n , y n , Ti ))]
where N is the number of interferograms. This function gets value one when the matching is perfect and zero when decorrelation is total. Once this maximization process has been done for every relationship, the result is a set of velocity and topographic error increments on the pixel connections. Evidently, these increments are not the desired values, and an unwrapping process is necessary to obtain absolute values for each isolated pixel. A RG (Region Growing) based algorithm can perform this unwrapping successfully. The residues of the unwrapping process can be calculated by subtracting the increment values with the absolute ones. Finally, these residues can be used to reject the points not adjusting the model. If the spatial density of points is high enough, the information can be interpolated for visualization purposes.
+ [n( x m , y m , Ti ) − n( x n , y n , Ti )]
III. DATA
where x and y are the pixel position within the image, Ti is the time baseline of i-th interferogram, λ is the wavelength, v is the constant velocity of the linear model of subsidence, b the spatial baseline of i-th interferogram, r the range distance, θ the incidence angle, ε the topographic error, β the non linear component of the velocity, α the atmospheric phase component, and n the thermal noise. Therefore, the algorithm deals with phase increments and not with the isolated pixels. Obviously, the resulting values of velocity and topographic error will be expressed as increments between neighbor pixels. The result is a matrix where every relationship has associated its phase increment for every differential interferogram. The expression of phase increment has a high number of unknowns, but basically we are interested in the determination of velocity and topographic error. A model based on known variables can be constructed as follows:
The method can work with a reduced set of SAR images, and preliminary results were obtained with a set of seven SAR images. For this paper, a set of twenty ERS SAR images has been used. With these images, twenty-two interferograms with short spatial baseline, between 2 and 24 meters, have been generated. A patch of 10 km x 16 km from the whole frame, containing two interesting towns, has been selected. The small town of the upper part of the SAR image shown in Figure 1 has reported problems of subsidence, and the bigger bright zone of the lower part can be considered an stable area. The images have been multi-looked with a pixel dimension of 100 meters x 100 meters. A commercial DEM of the zone has been used to remove the topographic component. The images range from 1992 to 2000. Figure 1 shows the interferogram phase and coherence that corresponds to the pair of 23th July 1997 and 12th August 1998.
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Fig. 3. Detailed deformation maps of both towns, left and right. The maximum deformation (yellow) corresponds to a velocity of 1.8 centimeters per year.
Fig. 1. SAR amplitude image (left). Interferogram phase (center) and coherence (right).
Considering the low resolution of 100 x 100 meters per pixel and the reduced spatial dimensions of the studied deformation, these results can be considered excellent. It is also remarkable that results with seven SAR images were quite similar. V. CONCLUSIONS A new method for detection of surface displacement with a reduced set of SAR data has been presented in this paper. The main advantage of this algorithm is the flexibility related with data requirements. Results obtained with ERS data from an area of Catalonia (Spain) show an excellent agreement with field measurements. ACKNOWLEDGMENT
Fig. 2. Deformation map of the area under study. It is remarkable that the large coherent areas correspond to urban zones, where coherence preserves better along time.
The authors would like to thank the European Space Agency (ESA) for providing the ERS images used in this work under the EO Projects of category 1 (A03.421) and the CICYT TIC 1999-1050-C03-01 for the economical support to the project. The authors also would like to thank the Cartographical Institute of Catalonia (ICC) for providing a DEM of the studied area and measures of terrain deformation used for validating the algorithm.
IV. RESULTS
REFERENCES
The retrieved deformation map of the area is shown in Fig. 2. As it can be observed, only two small areas located in the upper part of the image present a displacement larger than 1 centimeter per year. These areas are located in the surroundings of the town on the north, where problems of subsidence are reported. It is also remarkable that the results over the bigger town in the south evidence no subsidence problems as it has been also reported. The details of deformation maps over these areas are shown in Fig. 3. The validation of these results has been carried out with precise levelling measurements provided by the Cartographical Institute of Catalonia (ICC). These measurements showed a maximum of subsidence of about 2 centimeters per year in the same geographical position where we detected the maximum of 1.8 centimeters per year.
[1] P. Berardino, G. Fornaro, A. Fusco, D. Galluzzo, R. Lanari, E. Sansosti, S. Usai: “A new approach for analyzing the temporal evolution of Earth surface deformations based on the combination of DIFSAR interferograms”, IGARSS 2001, Sydney (Australia). July 9-13, 2001. [2] A. Ferretti, C. Prati, 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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