Measuring 3-D Ground Movement from Differential Interferometry: Technique and Validation

Measuring 3-D Ground Movement by Differential Interferometry: Technique and Validation.

S.Sircar1, 2, C.Randell1, D.Power1, J.Youden1 and E.Gill2

Remote Sensing Group C-CORE1 / Faculty of Engineering and Applied Science2

Memorial University

St. Johns NF Canada.

email:-

Abstract

Interferometry is a phase-based technique, which uses a coherent imaging system to extract topographical information from image pairs. This paper will derive a technique for extracting lateral ground displacement using interferometry with data from satellite Synthetic Aperture Radar (SAR). Ground movement derived from a single look direction (e.g., subsidence only) will contain errors if it is incorrectly assumed that the other two components (i.e., East-West and North-South) are zero. The advanced technique presented can be used to improve the accuracy of single-pair subsidence estimates by fusing two non-parallel pass images and measuring the lateral movement and subsidence. It is shown that three dimensional movement estimates can be derived from two satellite look directions by combining the look geometry with standard least squares estimation technique.

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.

Figure 1. Image acquisition geometry of SAR. 1 and 2 are the phase differences obtained from the two image scenes related to slant range change D and  is the wavelength. +j 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 or Digital Elevation Model (DEM) and then this model can be used to remove the topographical phases from the subsequent pair to obtain movement information. This technique is called differential interferometry. In principle, phase relating to range change can be written as

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

North Belridge Oil Field located in San Joaquin Valley in southern California is known to be experiencing significant ground movement due to oil production based on historical surveys. This ground movement has resulted in significant problems for companies operating in the region. For example, one gas pipeline company has experienced several ruptures to a pipeline that runs directly through the subsiding region.

The measurements of ground position via global positioning satellites or GPS is a popular and convenient method for measuring ground movement. Although it does not achieve the same accuracy as a rigorous theodolite derived survey, differential GPS measurements with a fixed and moving station can achieve reasonably accurate positional estimates. The accuracy of these estimates increase with the amount of time the roving station collects its data at a single point and accuracies of 1-2 cm in x, y and 2-5 cm in z are achieved respectively if data is collected for greater than 20 minutes or so.

GPS surveys were made of 65 monuments during the period of 2000 to 2001, with six surveys conducted in 2000 and four surveys conducted in the year 2001. The area of coverage for this survey was approximately ~10km2 where measurements from these 65 monuments were recorded. The recording of these GPS surveys was not periodic and there were some instances where the interval of readings exceeded many months. To normalize these inconsistencies in the GPS survey, standard slope fitting techniques were used to estimate a general movement trend for each monument from the GPS measured data set. These data were used to validate ground movement data derived from a series of SAR images using DInSAR over the same period.

The DEM required to remove topographical information with the DInSAR technique was obtained from a tandem mode ERS-1 and ERS-2 pair. The time interval between interferometric acquisitions of ERS-1/2 is only one day and is suitable for DEM, since decorrelation in the phase due to changes in the scattering properties of the ground is limited over that period. The interferogram shown in Figure 3 is obtained after processing ERS-1/2 interferometric pair, which contains only topographical information. Five RADARSAT-1 both ascending and descending scenes were obtained over a 7 month period during 2001 for application of differential interferometry. The area of interest containing the 65 monuments is well contained by the coverage region of all the obtained scenes.

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), 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/D-InSAR processing includes co-registration of SLC images and generation of a coherence image, 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 2. Interferogram or fringe image. Every cycle from red to red is (half wavelength) shift of the propagation path.

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 slant range change measurements [4]. 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].

Typically DEM contains spatial elevation change information. A 3-D perspective of the area under investigation is shown in Figure 5, which is a DEM.

Figure 3 (DEM San Joaquin Valley. InSAR processing of ERS-1/2 data)

3. Fusion of Ascending and Descending Passes for estimating 3-D ground movement.

The synthesis equations that were derived in [7] for extracting ground movement from the two non-parallel passes can, in general, be used to derive two dimensional ground movement. The equation derived in [7] for extracting 2-D ground movement is as follows:

.=, and is clearly underdetermined. It is possible to estimate Subsidenceand

East-West by neglecting North-South movement.

In principle, only one component of the displacement vector can be obtained from a single interferometric pair of similar viewing geometry (either ascending or descending). To measure three components of displacement one must have three sets of interferometric pair each of which have different look directions, unless additional information (e.g., from ground observations) are available to determine the full three-dimensional displacement field. To extract the third component of movement some assumptions have to be made in the absence of a third pair of differential interferogram with unique look direction. With Satellite interferometry, it is not possible to obtain this third unique pair. However, under certain conditions it may be possible to estimate three dimensional ground movement using least squares techniques. These conditions include regions experiencing well-behaved ground movement, in which the movement is generally homogeneous over many resolution cells of the SAR sensor.

Consider a small area on ground viewed by a varying incidence angle to + where the surface change is a small-scale coherent change common to several adjacent pixels.

Figure 4: Bounded region of n pixels that coherently move together.

In other words, the deformation is well behaved with no discontinuities. With this assumption, the under-determined system can be restructured into an over-determined system for pixels within the region bounded by (,+) as illustrated in Figure 4. Consider n pixels in that neighbourhood where the position of the radar scatter has not changed substantially however, the ensemble of the scatter has moved up, down, or sideways in some correlated fashion. This implies an area on the ground experienced homogenous movement and can be collectively grouped by those n pixels. For the ith pixel in that n pixel region (Figure 4), the 3-D movement , and can now be estimated. The conversion matrix for each ithpixel is given as:

. .=, [1]

where,andare the constraints imposed on the solution , and. The constrained least squared solution would estimate ground movement in all three directions. The constrained matrix can be derived from the knowledge of sensitivity of InSAR in each individual direction. InSAR is insensitive to changes in the direction compared to and directions. As a consequence, the estimated movement in thedirection would be large compared to and . This would require further constraints to the obtained solution in direction. The gradient vector of SRC over a small grid will be proportional with respect to the amount of lateral ground movement of that region. Thus more lateral movement is likely to occur when the rate of change of SRC with respect to distance is observed in a particular region. The solution can be adjusted according to the gradient of the SRC vector.

The grid for the over determined system of equations with overlapping ascending and descending pass images is illustrated in Figure 5. The variation of and over a small area on ground is insignificant thus a relatively large area has to be chosen to provide a meaningful result from the least squares estimation. The rationale for this is based on the convergence of a least squares solution. However, it also reduces the likelihood of having a region of homogeneous ground movement with no discontinuities. To mitigate these potential problems, an optimization routine can be employed to determine the region of most suitable size.

Figure 5: Ascending and Descending pass grid with varying incidence angle. The n neighbourhood identifies region of continuous displacement field used for the least squares solution.

4 Verification and Results

For verification of the fusion least squares technique presented in section 3, an area experiencing ground movement must be first selected. North Belridge Oil Field located in San Joaquin Valley in southern California is known to be experiencing significant ground movement due to oil production based on historical surveys. GPS data were processed of the area to verify the technique. D-InSAR data were processed over the same time frame as that of the GPS survey data. Five satellite scenes February 2001 to September 2001 from ascending and descending were processed. All pairs exhibited excellent coherence, thus DInSAR results were expected to be of very good quality.

The comparison of results between InSAR and GPS illustrate the following:

1.Subsidence, East-West and North-South movements derived from D-InSAR correlate very favourably to GPS.

2.The average variance (scatter of the data) from the trend line achieved in East-West, North-South and Subsidence are <0.22, 0.35 and 0.34>cm respectively and are well with in the expected measurement error. Achieved slope for East-West and Subsidence is close to 1 and a strong correlation indicates validation of the technique.

The estimated North-South movement with the aid of constrained least squares technique seems to work very well.

Figure 5-21: D-InSAR versus GPS East-West movement normalized to 24 days from February – September 2001.

Figure 5-22: InSAR versus GPS North-South movement normalized to 24 days from February – September 2001.

Figure 5-20: InSAR versus GPS Subsidence movement normalized to 24 days from February – September 2001.

Carefully observing the plots it can be seen that the correlation between InSAR measured movement and GPS measured movements have improved over results published in [7] earlier. A noted difference is seen in the East-West displacement, which seems to have improved appreciably from the previous work in [7]. More precise measurements of the monuments with a theodolite would have helped demonstrate better results.

5.Conclusion

In the context of deriving 3-D ground movement from Synthetic Aperture Radar, the possibility of fusing ascending/descending pass SAR images in order to extract ground movement is shown. The results give a satisfactory indication of the capability of D-InSAR to measure 3-D ground movement. The objective of this paper was to be able to show that there exists a trend between D-InSAR estimated lateral ground movements with respect to GPS estimated ground movements. The excellent correlation between the two suggests the success of this technique. Overall it can be said that the technique provides a much improved subsidence estimate and a very favourable lateral movement estimate.

6. References

[1] Zebker, H. A., and R.M. Goldstein, Topographic Mapping From Interferometric Synthetic Aperture Radar Observations, J. Geophys. Res., 91, 4993-4999,1986.

[2] Soren, N.M, H.A. Zebker, and J.Martin, Topographic mapping using radar interferometric processing techniques, IEEE Trans. Geosci. Remote. Sens., 30(3),560-567,1992.

[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), 9183-9191, 1989.

[4] Gabriel, A.K., and R.M. Goldstein, Crossed orbit interferometry theory and experimental results from SIR-B, Int. J. Remote Sens., 9(5),857-872,1988.

[5] Qian, L., J.F. Vesecky, and H.A. Zebker, New Approaches in Interferometric SAR data processing, IEEE Trans. Geosci. Remote. Sens., 30(5),950 - 959,1992.

[6] Prati, C., Report on ERS-1 SAR Interferometric Techniques and Applications, June 1994.

[7] Sircar, S., Power, D., Youden, J., Gill, E. and Han, P., 2002. Lateral Movement Estimation from Space-borne Radar by Differential Interferometry, IEEE NECEC 2002, St. John's, Newfoundland, Canada.