Simulation of Time Series Deformation Analysis for Verifying a Refined Small BAseline Subset (SBAS) Technique
Chang-Wook Lee(1), Zhong Lu(2) and Hyung-Sup Jung(3)
(1) ASRC
SBAS result
Research and Technology Solutions, Contractor to U.S.Geological Survey (USGS) Cascades Volcano Observatory (CVO), Vancouver, WA, USA; cwlee@usgs.gov
(2) USGS CVO, Vancouver, WA 98683, USA; lu@usgs.gov
(3) University of Seoul, Seoul, Korea; hsjung@uos.ac.kr
Abstract
A small baseline subset (SBAS) InSAR method has been developed to estimate time series surface deformation through a mutli-interferogram processing scheme. Using a synthetic dataset that takes into account two
time-varying deformation sources, topography-induced errors, atmospheric delay anomalies, orbital errors and temporal decorrelation, we validate our SBAS codes. The simulated deformation and various artifacts are
based on realistic ERS-1/ERS-2 SAR image acquisition dates and baseline configuration over Seguam volcano, Alaska. Detailed comparison between SBAS-derived products including time-series deformation maps,
atmospheric delays, and baseline errors with those synthetic values attest the robustness of our SBAS technique.
Introduction
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The small baseline subset (SBAS) interferometric synthetic aperture (InSAR) technique (Berardino et al., 2002) has been
developed to map ground surface deformation using a multi-interferogram approach. To achieve deformation time-series
information from multiple interferograms, the SBAS algorithm estimates the mean deformation rate and the topographic
error. The atmospheric artifacts are mitigated through temporal high-pass and spatial low-pass filtering of interferograms
after the mean deformation rates have been removed. SBAS InSAR uses the singular value decomposition (SVD)
approach based on a minimum-norm criterion of the deformation rate to derive time-series deformation measurements.
Although the SBAS algorithm (Berardino et al., 2002) is very effective for measuring time-series deformation, the
suppression of errors caused by temporal decorrelation and other noise effects is not properly addressed. Linear
deformation rates estimated using interferograms having unwrapping errors often lead to misestimates of the actual
deformation history. Estimates of atmospheric artifacts and topographic errors based on the assumption of linear
deformation rate during the periods spanned by individual interferograms can further detract from the retrieval of accurate
time-series deformation measurements.
A refined SBAS InSAR algorithm (Lee et al., 2010) (Figure 1) has been developed to improve estimates of time-series
deformation through iterative processing. Phase unwrapping errors can be corrected by distinguishing between highquality (HQ) images in which no unwrapping errors could be found and low-quality (LQ) ones where phase jumps due to
unwrapping errors are possible. Estimating atmospheric artifacts, topographic errors, and time-series deformation
measurements are refined through an iteration procedure. The temporal noise is further mitigated by the finite difference
smoothing approach (Schmidt and Burgmann, 2003). In this study, we systematically validate our SBAS technique using
synthetic datasets (Table 1) that are based on realistic ERS-1/ERS-2 SAR image acquisitions over Seguam volcano,
Alaska where time-variant ground surface deformation have been observed (Lee et al., 2011).
Figure 1. Block diagram of the refined SBAS
InSAR processing algorithm
Mission
ERS1
ERS1
ERS1
ERS1
ERS1
ERS1
ERS1
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
ERS2
Orbit
9865
10366
10867
11368
11869
20229
21732
12580
13081
18091
18592
22099
22600
23101
28111
29113
33121
38131
38632
39133
42640
43141
44143
44644
47650
49153
49654
53662
58171
58672
59674
60175
63682
64183
Date
1993-06-04
1993-07-09
1993-08-13
1993-09-17
1993-10-22
1995-05-28
1995-09-10
1997-09-15
1997-10-20
1998-10-05
1998-11-09
1999-07-12
1999-08-16
1999-09-20
2000-09-04
2000-11-13
2001-08-20
2002-08-05
2002-09-09
2002-10-14
2003-06-16
2003-07-21
2003-09-29
2003-11-03
2004-05-31
2004-09-13
2004-10-18
2005-07-25
2006-06-05
2006-07-10
2006-09-18
2006-10-23
2007-06-25
2007-07-30
Baseline
0
-57
823
1394
1661
731
143
977
953
1430
1768
1034
2100
980
998
919
901
128
1369
1251
470
635
1756
1110
444
832
1685
1025
627
974
993
1387
1127
1740
Table 1. Characteristics of ERS-1 and
2 data used in this study
Data processing
We generate 48 synthetic interferograms that maintain good coherence during 1992-2007. These interferograms have perpendicular baselines of less than 300 m and temporal separations of less than 5 years. Image
acquisition dates and baseline configuration are based on ERS-1/ERS-2 Track 201 acquisitions over Seguam volcano, Alaska. Each of synthetic interferograms contains ground surface deformation, atmospheric
contribution, orbit error, topographic error, temporal decorrelation and noise. The phase components due to deformation, atmospheric delay, orbit error, DEM error and temporal decorrelation are simulated separated
and then combined to produce the synthetic interferograms for SBAS processing (Figure 2).
We apply SBAS processing on a set of 48 simulated interferograms (e.g., Figures 4b and 4g). The retrieved surface deformation images from the SBAS processing are shown in Figures 4d and 4i. The difference
between the simulated interferograms (Figures 4b and 4g) and the retrieved deformation interferograms (Figures 4d and 4i) contains primarily atmospheric artifacts, orbit errors and decorrelation noise (Figures 4c and
4h). The SBAS-retrieved deformation images (Figures 4d and 4i) are compared with the original deformation images (Figures 4a and 4f), and the results are shown in Figure 4e and 4j. We also compare the mean
surface deformation during 1993-2007 between the simulated and SBAS-retrieved (Figure 5). Figure 6 represents surface deformation between the retrieved and the “truth” corresponding to profile A-A’ of the spatial
domain on the figure 5a and 5b. The difference of two results has less than 1.1 mm and standard deviation is 0.2 mm. The scattergram between the SBAS-retrieved deformation rates and the truth is shown in Figure 7.
The correlation coefficient reaches to R2=0.963, suggesting the SBAS can retrieve the time-variant deformation very well.
- Mean = 0.6 mm
- Standard deviation = 2.4 mm
Figure 6. Profile of true mean deformation and SBAS-derived deformation
over profile A-A’ in Figure 5.
- Mean = 0.6 mm
- Standard deviation = 2.2 mm
Figure 4. Deformation and error images retrieved from SBAS
processing of multi-temporal simulated interferograms with error
components.
- Mean = 0.6 mm
- Standard deviation = 0.2 mm
Figure 5. Average deformation map between simulated (a) and
SBAS result (b). (c) represents residual image from (a) and (b).
Time-series deformation
Figure 7. Scattergrams between simulated (true) timeseries deformation and SBAS-derived time-series
deformation.
Figure 8 displays time-series surface deformation maps from SBAS processing. Figure 9 shows time-series deformation at two locations over the western caldera and eastern caldera, respectively. SBAS processing
produces time-variant deformation patterns that agree well with the “truth” data. While the difference between the retrieved and the “truth” at the west caldera point (Figure 5a) reaches a maximum of 3.4 mm and a
standard deviation of 0.8 mm, it is less than 6±1.3 mm on the east caldera.
 temporal  exp(  0 . 2  T )
2
4

d ( x, r ) 
4
B
 r sin 
 z ( x , r )    atmo ( x , r )    orbit ( x , r )    temp ( x , r )    n ( x , r )    ( x , r )
0
1.5 cm
Figure 8. Time-series Surface deformation maps from SBAS processing.
Conclusions
Figure 9. Time series deformation of simulated
(true) interferograms and SBAS result at two
locations (Site 1 and 2 in Figure 5).
We validate our SBAS processing method using simulated deformation observations. The simulated InSAR images contain time-variant deformation due to two different deformation sources, atmospheric delay
anomalies, orbital errors, DEM errors and decorrelation errors. The simulated InSAR observations are based on realistic SAR image acquisition time and baseline configuration from ERS-1/ERS-2 track 201 over
Seguam volcano, western Alaska. Comparison between the retrieved ground surface deformation and theoretic (true) deformation confirms the effectiveness of this algorithm, suggesting that our SBAS processing can
remove and suppress most of the atmospheric delay artifacts and orbital errors.
Figure 2. Two examples of (a, g) simulated deformation-only interferograms, (b, h) simulated topographic residual errors of interferograms, (c, i) simulated
atmospheric artifacts, (d, j) simulated orbital errors, (e, k) simulated temporal decorrelation noise, and (f, l) summation of simulated deformation and all error
components. The phase images are plotted on a SAR amplitude map.
Figure 3. (a) Temporal decorrelation observations (blue dots)
and model (red curve) using observed ERS-1/ERS-2
interferograms over seguam volcano (Lee et al., 2011). (b)
Standard deviation of InSAR phase measurements based on
temporal decorrelation model in (a).
 References
• Berardino, P., G. Fornaro, R. Lanari, and E. Sansoti (2002), A new algorithm for surface deformation monitoring based on small baseline Differential SAR Interferograms, IEEE Trans. Geosci. Remote Sens., 40(11), 2375-2383.
• Lee C.W., Lu, Z., Jung, H.S., Won, J.S., Dzurisin, D., 2010. Surface Deformation of Augustine Volcano (Alaska), 1992-2005, From Multiple-Interferogram Processing Using a Refined SBAS InSAR Approach, USGS Professional Papers 1769, 453-465.
• Lee C.W., Lu, Z., Won, J.S., Jung, H.S., Dzurisin, D., 2011. Dynamic deformation of Seguam Volcano, Alaska, 1992-2008, from multi-interferogram InSAR processing, Journal of Volcanology and Geothermal Research, (Review).
• S chmidt, D., and R. Burgmann (2003), Time-dependent land uplift and subsidence in the Santa Clara valley, California, from a large interferometric synthetic aperture radar data set, J. Geophys. Res., 108(B9) , doi: 10.1029/2002JB002267.