A COMPARISON OF SBAS AND PS ERS INSAR FOR SUBSIDENCE MONITORING IN
OSLO, NORWAY
Tom R. Lauknes (1), John Dehls (2), Yngvar Larsen (1), Kjell A. Høgda (1), Dan J. Weydahl (3)
(1)
Norut IT, P.O. Box. 6434, NO-9294 Tromsø, Norway, {tomrune,yngvar,kjella}@itek.norut.no
(2)
(3)
Geological Survey of Norway (NGU), NO-7441 Trondheim, Norway, [email protected]
Norwegian Defence Research Establishment (FFI), P.O. Box 25, NO-2027 Kjeller, Norway, [email protected]
ABSTRACT
In this paper, we present the results achieved in the long-term subsidence project in Norway, ESA AO-1104, which have
made use of ERS SAR data. By applying the differential SAR interferometry technique referred to as Small Baseline
Subset (SBAS) approach to a test area covering the city of Oslo, Norway, we show significant subsidence in several areas
of more than 5 mm/year in the time period 1992–1999. The results are compared with a similar analysis making use of
the Permanent Scatterers (PS) technique. The presented results demonstrate the capability of the SBAS method to detect
and monitor urban land subsidence at Nordic latitudes.
1
INTRODUCTION
The differential interferometric SAR (InSAR) technique has been shown as a valuable tool for subsidence monitoring in
many places of the Earth by using several techniques of multi-temporal InSAR processing [1,12,21,18].
For long-term subsidence monitoring, and in most general cases where we want to monitor deformations with a low
velocity, we are forced to have long time gaps between the acquisitions. Consequently, large areas are decorrelated, making
the interferometric phase useless. An additional limitation for all interferograms are atmospheric artifacts. However, some
advances have been made in the field. Man-made structures found in urban areas are found to be coherent over long time
intervals [20]. Obviously, interferograms covering urban areas have sparsely coherent patches with information.
When a multi-temporal data set is available, different methods to overcome the mentioned limitations have been published. A technique which makes use of these coherent point targets is referred to as Permanent Scatterers (PS) [12]. The
PS method uses large stacks of images to generate differential interferograms with respect to one common master. All
combinations are employed, even those exceeding the critical baseline. Only the coherent pixels (permanent scatterers)
are considered. For nonurban areas, the density of the PS may be low.
For our study, we have chosen the alternative Small Baseline Subset (SBAS) technique [1]. The SBAS technique relies
on an appropriate combination of differential interferograms created by using SAR image pairs characterized by a small
orbital separation (baseline). This reduces the spatial decorrelation phenomena. However, for the ERS-1/2 satellites, the
available acquisitions are generally distributed in several small baseline subsets, separated by large baselines. The singular
value decomposition technique is used to “link” the separate small baseline subsets, clearly increasing the temporal sampling rate. Atmospheric artifacts are filtered out based on the availability of both spatial and temporal information. The
topographic phase contribution is removed by using a backward phase simulation, starting from an externally available
digital elevation model.
Fig. 1. The approximate ERS SAR coverage over the Oslo region in south Norway.
2
METHODOLOGY
The details of the processing are described in [17]. In this section, we give a short description of the methodology used to
process the data set.
The raw ERS SAR scenes were processed to single-look complex (SLC) images by using the fourth order Extended Exact
Transfer Function (EETF) developed by FFI [8]. This SAR processor is preserving the phase very well, and has previously
been tested on large volumes of ERS SAR data [9]. All SLC images were processed in the zero-Doppler coordinate
system, resulting in congruent geometry for repeat orbit images, significantly simplifying the interferometric processing.
The co-registration and the differential InSAR processing has been performed by using the Generic SAR (GSAR) software
developed by Norut IT [16]. This software has been tested extensively through the ESA projects [10,15,17].
2.1
SBAS technique
The SBAS technique is described in detail in [1], however, for the clarity of this paper, the basic rationale will be outlined
here. As already mentioned, the SBAS technique relies on an appropriate combination of multiple small baseline interferograms. Based on the available image combinations, interferograms having mutual small baselines are created. Obviously,
this can lead to different subsets of InSAR pairs, linked in time and separated by large baselines.
The computed small baseline differential interferograms are organized in a linear model
Bv = δφ,
(1)
where B is a matrix defining the small baseline combinations used, δφ is the vector of (unwrapped) differential interferometric phase values, and v is the vector of the unknown mean phase velocities associated with the deformation. However,
because of the separation in different subsets, the rank of B will be N − L + 1, where N is the number of images used
and L is the number of subsets, and Eq. 1 will have infinite solutions.
A minimum-norm least squares (LS) solution of Eq. 1 is obtained by using the singular value decomposition (SVD)
method


Σ−1 0
 UT δφ,
(2)
v̂ = V 
0 0
−1
where V, U and Σ−1 = diag(σ1−1 , . . . , σN
−L+1 ) are the SVD decompositions of B [19].
The generation of a linear model, and the solution via the SVD method clearly increases the sampling rate, allowing the
use of all acquisitions included in the different small baseline subsets. By using complex multi looking in the InSAR
processing, together with a coherence threshold, phase noise is reduced and spatial resolution is preserved. This is a key
feature of classical differential SAR interferometry.
The SBAS method is based on the availability of unwrapped differential interferograms. In order to facilitate the phase
unwrapping (on the sparse grid), only the phase in coherent pixels is used. Following this, the phase values located in the
(a)
(b)
Fig. 2. Baselines and InSAR combinations (a) and mean estimated coherence (b).
coherent sparsely distributed patches are triangulated and interpolated by using a Delauney triangulation, similar to [3].
The final unwrapping is done by using the SNAPHU software [2].
In order to mitigate any DEM errors, an estimate of topographic errors is also incorporated in the SBAS method [1].
Finally, atmospheric and orbital artifacts are estimated and removed based on the space-time information available, similar
to the PS approach [11,12].
3
TEST AREA AND DATA SET
In order to validate the SBAS method, a test area located in the region around Oslo, the capital of Norway, has been
chosen, see Fig. 1 and Fig. 2(b).
The elevations are ranging from sea level up to 700 m. The higher elevations in the Oslo region will normally be covered
by snow several months during the winter season. However, for the built-up areas, the winter conditions in the 1990’s have
varied considerably from snow to sleet and rain.
A total of 43 ERS SAR raw data sets from descending satellite track 337 and frame 2394 were received from ESA,
covering the Oslo region. The SAR images covered the time period between May 1992 and September 1999. Among the
images, 20 were from the ERS-1 sensor and 23 from ERS-2. The data also incorporates 5 tandem pairs from 1995/1996.
A total of 12 scenes were from the winter season (November to April), and 31 scenes from the spring/summer/autumn.
Meteorological weather data from the station Blindern was used as a reference in order to exclude images with a possibility
of snow cover. The SAR images were delivered from both the Italian PAF, and the UK PAF.
4
EXPERIMENTAL RESULTS
All SAR processing has been performed by FFI, while all InSAR processing has been performed using the Norut IT
developed GSAR software [16].
All images were first coregistered to the July 12, 1995 scene. In order to select which InSAR pairs to use for the SBAS inversion algorithm, the baselines for all combinations were estimated. Following this, we selected the InSAR combinations
that exhibited a mutual perpendicular baseline less than 300 m, and a temporal baseline less than 4 years. The dataset was
then contained in one subset, including all 129 combinations, as indicated by the connecting lines in Fig. 2(a).
When the set of 129 InSAR pairs was established, the SBAS processing was carried out. The overall processing was
performed by applying a complex multi-look operation with four and sixteen looks in range and azimuth, respectively.
The ground range pixel dimensions of all products is therefore about 80 × 68 m in the range and azimuth directions.
(a)
(b)
Fig. 3. The false-color maps represent the average relative velocity estimated between 1992–1999. Each color interval
represent 1 mm of range change. An orbital trend in the range direction can clearly be seen in (a), while (b) shows the
deformation velocity after removing the orbital plane from all interferograms. The full ERS radar scene is shown.
In the results provided, an a priori available DEM from Statens Kartverk was used to remove the topographic phase. This
DEM has a grid size of 25 × 25 m and a height standard deviation of ± 5–6 m, and is given in the UTM coordinate
system. We used the backward phase simulation [6] to simulate the topographic phase, layover mask, radar intensity, and
to convert the DEM, to the radar coordinate system, range and azimuth.
Furthermore, in order to exclude decorrelated areas from the study, we performed a pixel thresholding, selecting only the
pixels that exhibited an estimated coherence value larger than 0.1 in at least 80% of the interferograms. In order to ease
the phase unwrapping of the selected set of interferograms, a Delauney triangulation and interpolation as described by [3]
was done for all images, based on the selected pixels. After the phase unwrapping, all pixels were calibrated with respect
to an area that was assumed stable. The zero deformation value was taken as the mean of the phase values located within
a 3 × 3 neighborhood in an area with high coherence. In order to select this stable area, an a-priori available deformation
map created by the NGU [5] was used.
5
DEFORMATION ESTIMATE
Based on the spatially sparse grid of unwrapped phase values, we carried out, for each selected pixel, a joint estimation of
DEM errors and a temporal low pass (LP) deformation signal.
Atmospheric phase contributions were then estimated. For each considered pixel, the following space-time filtering operation was carried out. The temporal time series, composed of 30 irregularly spaced samples, was interpolated to a length
of 2789 points, corresponding to the number of days in the time series. The time series was then smoothed by using a
Bartlett window of length 300 days, followed by a removal of the low pass component. A spatial Delauney triangulation
and interpolation step was then carried out on the remaining high pass (HP) phase residuals. The interpolated 2D data
were then LP filtered by using a 2 × 2 km Hanning moving average window. All differential interferograms were then
compensated for the estimated atmospheric contribution.
The average estimated deformation velocity is shown in Fig. 3(b). The deformation signal is shown superimposed on a
grayscale SAR intensity image. The areas that are subsiding are clearly shown with red color. Note that only the pixels
fulfilling the coherence criterion are displayed.
Based upon the large-scale deformation velocity map shown in 4, areas of special interest can be defined. These areas can
be further investigated by generating displacement time series for selected points inside these areas. Fig. 5(a–d) shows
time series for four selected points.
(a)
(b)
(c)
(d)
Fig. 4. The figures show the orbital plane removal: (a) estimated interferometric phase (B⊥ =192 m, BT =1389 days), (b)
triangulated phase, (c) estimated orbital fringe frequency, and (d) coherent phase after removal of orbital plane.
5.1
Orbital errors
After processing using the standard SBAS algorithm, the final deformation velocity map showed a large phase ramp in the
range direction, see Fig. 3(a). This phase signal is not related to any physical signal due to the large magnitude (several
mm/yr across the image). A possible comparable signal due to the post glacial rebound of Fennoscandia would be on the
order of about 1 mm/yr across the radar scene [13,4].
The prominent fringe gradient due to incorrect orbital information coincides with the trend seen in the final velocity
estimate map.
In order to correct for the orbital plane, we performed the following processing steps. The triangulated and interpolated
phase values were used as input to a Maximum-Likelihood (ML) frequency estimator. The complex plane was then
removed from the interferogram. An example of the results of this correction is shown in Fig. 4(a–d). Starting from
the decorrelated interferometric phase in Fig. 4(a), the Delauney triangulated and interpolated interferogram is shown in
Fig. 4(b). Fig. 4(c) shows the estimated orbital fringe frequency, and Fig. 4(d) shows the corrected interferometric phase
for the coherent points chosen.
After removal of the complex orbital plane for all InSAR combinations, the standard SBAS processing as described was
applied. The final deformation velocity shown in Fig. 3(b).
More elaborate methods for understanding the orbital effects, such as for example the proposed Orbital Tuning Approach
(OTA) [14] is being investigated.
(a) Stable point
(b) Alnabru
(c) Bjørvika
(d) Hellerud
Fig. 5. Deformation time series for four selected points.
Fig. 6. The mean deformation velocity map processed by TRE (Italy) & NGU by using the permanent scatterers technique
(PS) [5]. The color scale is from -5 mm/yr (red) to 5 mm/yr (blue).
5.2
Comparison with a PS study
The deformation velocities detected compare well with an independent study done by Tele-Rilevamento Europa (TRE)
and NGU [5]. Fig. 6(b) shows the average relative velocity estimated by using the PS technique (processing by TRE, Italy).
Some comments on the results are in order. Both studies have been performed by using ERS-1/2 data from descending
track 337 and frame 2394. NGU has used 49 images while we have used 30 images. If we compare Fig. 3(b) and Fig. 6, we
see that largely the same areas are coherent, and comparable deformation patterns. Different selection of stable points will
give slightly different velocity values when comparing the two results. However, the subsidence pattern is nearly identical
using both methods. Further comparisons are ongoing.
6
CONCLUSIONS
We have demonstrated that the SBAS technique is applicable for long-term surface deformation monitoring in Nordic
environments. By analyzing a data set of 30 ERS-1/2 SAR images covering the city of Oslo (Norway), significant subsidence of more than 5 mm/year has been detected in the time period 1992–1999. The deformation estimates compare well
with results from an independent study and geodetic measurements.
ACKNOWLEDGEMENTS
The SAR data have been provided by ESA within the AO-1104 project.
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