Lateral Ground Movement Estimation from Space borne Radar by Differential Interferometry.

Transcription

1 Lateral Ground Movement Estimation from Space borne Radar by Differential Interferometry. Abstract S.Sircar 1, 2, C.Randell 1, D.Power 1, J.Youden 1, E.Gill 2 and P.Han 1 Remote Sensing Group C-CORE 1 / Faculty of Engineering and Applied Science 2 Memorial University St. Johns NF Canada. - sircar@engr.mun.ca Synthetic Aperture Radar (SAR) Interferometry (InSAR) is a powerful and exciting technique that has gained eminence in the last 10 years after the advances in Satellite imaging systems. Interferometry is a phase-based technique which uses a coherent imaging system to extract topographical information from image pairs. This paper will demonstrate the possibility of extracting lateral ground displacement with InSAR. Movement derived from one look direction (subsidence only) will contain errors, if it is incorrectly assumed that the other two components (East-West and North-South) are zero. The suggested technique can be used to improve the accuracy of single-pair subsidence estimates by fusing two non-parallel pass images and measuring the lateral movement. 1. Introduction SAR (Synthetic Aperture Radar) interferometry is a relatively new technique for remote sensing applications. InSAR (interferometric SAR) was first introduced for topographic mapping by researchers Zebker and Goldstein in 1986 and its usefulness for precise terrain mapping has been validated [1]. Interferometry, by definition, is a technique that utilizes interference of waves for precise determination of distance. In SAR interferometry, the phase of the received backscattered signal from two images of the same scene are used to measure path length differences with millimeter accuracies [1]. These path length differences can be related to parameters such as terrain height and deformation of the earth s surface. What distinguishes SAR from other typical radar is that it is a coherent imaging system which records and processes both amplitude and phase information of the radar echo. The phase recordings can be used to measure differential range change in two or more SAR images of the same scene. A single SAR image does not contain enough information to say anything about the movement or relative height change of the imaged scene [2]. InSAR combines two complex and co-registered images of the same scene from almost identical perspectives into a so-called interferogram. The phase difference for each picture element (pixel) in the interferogram is a measure of relative change in distance between the ground (scatterer) and the SAR antenna as shown in Figure 1. A Digital Elevation Model (DEM) can be obtained from this if there is no large-scale ground deformation between image acquisition times. φ 2 φ1 λ D = x After Movement α + SAR Beam Width j β Before Movement Figure 1. Image acquisition geometry of SAR. ϕ 1 and ϕ 2 are the phase differences obtained from the two image scenes related to slant range change D and λ is the wavelength. α+jβ is the Cartesian representation of amplitude and phase recorded by the SAR. In general, the phases corresponding to differential range change in the interferogram will contain topographical information as well as movement information. Thus, there is a need for two interferometric pairs (4 images), so that the first two images can be used to generate an accurate topographical model and then this model can be used to remove the topographical phases from the subsequent pair to obtain movement information. In principle, phase relating to range change can be written as 1

2 ϕ = ( ϕtopography) + ( ϕdisplacement) + ( ϕerror) The two interferometric pairs (4 images) are required to generate the movement-only interferogram, assuming there is no other way to get the topographical information of the scene [3]. 2. Experimental Methodology A test site was selected in the southern California San Joaquin Valley where ground movement is of considerable magnitude due to oil extraction. In that area there are buried high-pressure gas pipelines, which might undergo damage due to ground movement. Global Positioning System (GPS) ground movement measurements require GPS transponders to be placed in the ground. This can be tedious and only discrete points of ground movement can be measured. So, there is a need of a technique for remote detection and measurement of ground movement (vertical and lateral). For this experiment two images from the two European Remote-Sensing Satellites (ERS-1/2) were used for developing the DEM (Digital Elevation Model), and two images from RADARSAT-1 (each ascending and descending pass images), separated over 4 months, were used to estimate the lateral and subsidence components of ground displacement. These remote-sensing satellites are in the sun synchronous orbit, which means their travel path is over the poles. Ascending pass refers to the satellite flight path from South to North and descending pass vice versa. In order to validate the results from InSAR-measured ground movement, GPS measurements over the same interval were obtained. 2.1 Processing Steps The ERS-1/2 and RADARSAT-1 SAR processing used is detailed in [4,5]. An output product of the SAR processing is called the Single Look Complex (SLC) (see Figure 2a), which is required for interferometric processing. A SLC image forms the basis for interferometry, and contains both magnitude and phase of the radar echoes. InSAR processing includes coregistration of SLC images and generation of a coherence image (Figure 2b), interferogram generation (Figure 3), flat earth phase removal, elevation phase removal, differential interferogram generation, phase unwrapping and conversion from phase to range change maps. When the phase is converted to a change map, the output is change in slant range. Figure 2a Image Scene Figure 2b Coherence Figure 3. Interferogram or fringe image. Every cycle from red to red is (half wavelength) shift of the propagation path. Figure 2b is a coherence map of the interferometric pair. Coherence measures correlation of the two image pairs and varies in the range of 0 to 1. The degree of coherence can be used as a quality measure because it significantly influences the accuracy of phase differences and hence height measurements [4]. Bright areas in Figure 2b indicate regions of high coherence, whereas dark areas represent low coherence. Some of the factors that influence loss in coherence are steep slopes (surface slope > SAR incidence angles), major ground movement, extended period between the two passes (e.g. temporal decorrelation due to vegetation growth) and long baseline [3]. Baseline is the separation of satellite orbits for the two image acquisition times [4]. Figure 4. (Digital Elevation Model) 2

3 The variation from white to grey in the DEM Figure 4 shows the change in elevation as obtained from the interferogram. A LANDSAT optical image was over-laid on the DEM after resampling to the original map grid to generate a visual perspective of the terrain shown in Figure 5. 6a and 6b identify points chosen for validation against GPS measurements. Figure 6a. Ascending. Figure 6b. Descending. Fusion of the resultant interferograms from ascending and descending passes can be understood on the basis of how the geometry of these image acquisitions can be decomposed to infer the relation between differential range change with ground displacement vectors. Figure 5 (LANDSAT over DEM) 3. Conversion of raw data to movement vectors Until now the discussion was confined to how movement vectors can be obtained from InSAR. No consideration was given as to how these vectors can be used to measure lateral and subsidence movements. In principle, only one component of the displacement vector can be obtained from a single interferometric pair [3]. To measure three components of displacement, one must have three sets of interferometric pairs, each of which have different look directions, unless additional information (e.g., from ground observations) is available to determine the full three-dimensional displacement field [3]. However, with RADARSAT only two interferometric pairs with different look directions can be obtained. Each ascending and descending pair can be fused together to obtain 2-D ground movement Fusion of Ascending and Descending Passes Pairs of ascending and descending pass RADARSAT-1 images were processed as discussed in Section 2.1 over an interval of 4 months. In Figure 6a and 6b (ascending, descending) bright regions show residual phases after removal of topographical phases and will be referred as the resultant interferogram. These resultant interferograms are where movement is to be expected. The cross hairs shown in Figure D A S E -W B(x,y,z) Figure 7. Shows the corresponding vectors that can be used for developing the required equations. B is the actual movement vector, A is the measured component of B from ascending pass, D is the measured component of B from descending pass, S is subsidence and E W as lateral component. As shown in Figure 7, the vectors A and D are obtained from the resultant interferogram. These are the two measured components of the real movement vector B. The letters A, D, B are shown in bold to identify them as vectors. Consider the projection of a satellite trajectory onto the ground as shown in Figure 8. This is used to obtain the satellite orientation angle with respect to the true North-South. The angle between the satellite track and North-South can be found knowing the latitude/longitude of the entire image scene, and from this geometry angle ϕ can be obtained. For this experiment the angle ϕ is approximately 8 degrees for the descending pass. This means the satellite flight path projected on to the ground is 8 degrees from the North-South axis. 3

4 Figure 8. E, N, Z in Rectangular coordinate system for Earthbased geometry and satellite-based geometry (LOS - line of sight, satellite track) for descending pass; θ is the look angle of the radar, and ϕ is the angle between the satellite track and North-South. The required rotation matrix can now be derived as LOS Look Direction Sattelite Track E sinθcosϕ cosθcosϕ -sinϕ N sinθsinϕ cosθsinϕ cosϕ Z cosθ -sinθ 0 In order to formulate the equations consider Figure 9, which shows the geometry of a descending orbit pass. (x 1,y 1,z 1 ) z D θ d B Z B. Ă and B.Ď are the relative slant range change that is extracted from the change in phase. With these parameters it is now possible to solve equations 1 and 2. Since there are two equations and three unknowns, y is arbitrarily set to zero, which implies there is no North-South movement. This was done mainly because most of the GPS movements were located along an East-West line on which the North-South movement was known to be small. The solution is then lateral movement x that is East-West and vertical movement z that is subsidence. 4.Verification and Results GPS data collected over along with a series of satellite SAR data (both ascending and descending scenes) were available for testing the developed algorithms. The 3-dimensional GPS measurements of discrete ground points in the imaging area were processed and a trend pattern of the GPS measurements was taken to reduce the errors in GPS readings. In order to compare GPS displacement fields with the interferometric displacement fields, the GPS data had to be normalized on the same time scale as that of the interferometric measurements. The results of the estimated ground movement are then plotted against GPS reading for verification. Figure 10 shows the subsidence plot InSAR VS GPS. (x,y,z) Figure 9. Descending pass geometry. Vector D is the measured component of the actual movement B. The component of B in D s direction would be B.Ď = sin ( 180-θ d ) cos( ϕ d ) x + sin ( 180-θ d ) sin ( ϕ d ) y + cos (180- θ d ) z -(1), where ϕ d is the projection of the satellite trajectory on to the ground as explained in Figure 8 and θ d is the corresponding incidence angle of the descending pass. Similarly, we can formulate a second equation for ascending pass geometry as B.Ă = sin ( θ a ) cos( ϕ a ) x + sin ( θ a ) sin ( ϕ a ) y +cos (180 - θ a ) z -(2) where B.Ă is the component of B in A s direction as illustrated in Figure 7, θ a and ϕ a are the corresponding incidence and orientation angles respectively, for the ascending pass. Figure 10. InSAR VS GPS with lateral movement accounted for and this reduces the errors in estimating the subsidence. The lateral movement observed from the GPS are in the order of ± 15 mm as shown in Figure 11 and is close to the system error. Though there is a trend and the correlation is quite good, the slope is not unity. From the calculation of the 4

5 slope of the trend line, it appears that InSAR overestimates lateral movement by a factor of 4. This over estimation may be due to the assumption that North-South movement is zero. However it is more likely that this difference is due to measurement errors in the GPS. It is known to the authors that the oil production was increased substantially in 2001 in this area, and the low frequency of GPS measurements (only 3 over the entire time period of 4 months) may have contributed to these errors. This inconsistency is not evident when observing subsidence (which has a 1:1 correlation between InSAR and GPS, see Figure 10). Further investigation is now being done to determine the source of this inconsistency and why it influences lateral movement more than subsidence. In Figure 12, GPS measured movement of identified monuments on the ground are plotted on top of InSAR measured movements. 5. Conclusion This paper has demonstrated the possibility of fusing ascending/descending pass SAR images in order to extract lateral ground displacement. The results give a satisfactory indication of the capability of InSAR to measure lateral ground movement. North-south ground movement was assumed to be zero in order to solve the equations derived in Section 3.1. However, to be able to measure all dimensions of movement, there is a need for another interferometric pair of a different acquisition angle other than the two already considered. In the absence of another interferometric pair, attempts can be made to model the movement parameters already obtained to estimate the third component. Least square techniques may also be used to estimate the North-South movement, and these will be investigated in the near future. 6. References [1] Zebker, H. A., and R.M. Goldstein, Topographic Mapping From Interferometric Synthetic Aperture Radar Observations, J. Geophys. Res., 91, ,1986. [2] Soren, N.M, H.A. Zebker, and J.Martin, Topographic mapping using radar interferometric processing techniques, IEEE Trans. Geosci. Remote. Sens., 30(3), ,1992. Figure 11. InSAR VS GPS East-West estimated movement in cm. [3] Gabriel, A.K., R.M. Goldstein, and H.A. Zebker, Mapping small elevation changes over large areas: differential radar interferometry, J.Geophys.Res., 94(B7), , [4] Gabriel, A.K., and R.M. Goldstein, Crossed orbit interferometry theory and experimental results from SIR-B, Int. J. Remote Sens., 9(5), ,1988. [5] Qian, L., J.F. Vesecky, and H.A. Zebker, New Approaches in Interferometric SAR data processing, IEEE Trans. Geosci. Remote. Sens., 30(5), ,1992. [6] Prati, C., Report on ERS-1 SAR Interferometric Techniques and Applications, June [7] Giani, M., C. Prati, and F. Rocca, SAR interferometry and its applications, ESA report., N.8928/90/F/BZ,1992. Figure 12. InSAR VS GPS subsidence trends over the region of analysis. 5