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(1) ASRC 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 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) 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. 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 high- quality (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). Table 1. Characteristics of ERS-1 and 2 data used in this study #MissionOrbitDateBaseline 1ERS198651993-06-040 2ERS1103661993-07-09-57 3ERS1108671993-08-13823 4ERS1113681993-09-171394 5ERS1118691993-10-221661 6ERS1202291995-05-28731 7ERS1217321995-09-10143 8ERS2125801997-09-15977 9ERS2130811997-10-20953 10ERS2180911998-10-051430 11ERS2185921998-11-091768 12ERS2220991999-07-121034 13ERS2226001999-08-162100 14ERS2231011999-09-20980 15ERS2281112000-09-04998 16ERS2291132000-11-13919 17ERS2331212001-08-20901 18ERS2381312002-08-05128 19ERS2386322002-09-091369 20ERS2391332002-10-141251 21ERS2426402003-06-16470 22ERS2431412003-07-21635 23ERS2441432003-09-291756 24ERS2446442003-11-031110 25ERS2476502004-05-31444 26ERS2491532004-09-13832 27ERS2496542004-10-181685 28ERS2536622005-07-251025 29ERS2581712006-06-05627 30ERS2586722006-07-10974 31ERS2596742006-09-18993 32ERS2601752006-10-231387 33ERS2636822007-06-251127 34ERS2641832007-07-301740 Introduction Data processing Figure 1. Block diagram of the refined SBAS InSAR processing algorithm 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. 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). 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). SBAS result 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 R 2 =0.963, suggesting the SBAS can retrieve the time-variant deformation very well. Figure 4. Deformation and error images retrieved from SBAS processing of multi-temporal simulated interferograms with error components. Figure 5. Average deformation map between simulated (a) and SBAS result (b). (c) represents residual image from (a) and (b). - Mean = 0.6 mm - Standard deviation = 2.4 mm - Mean = 0.6 mm - Standard deviation = 2.2 mm - Mean = 0.6 mm - Standard deviation = 0.2 mm Figure 6. Profile of true mean deformation and SBAS-derived deformation over profile A-A’ in Figure 5. Figure 7. Scattergrams between simulated (true) time- series deformation and SBAS-derived time-series deformation. 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. 1.5 cm 0 Conclusions 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 8. Time-series Surface deformation maps from SBAS processing. Figure 9. Time series deformation of simulated (true) interferograms and SBAS result at two locations (Site 1 and 2 in Figure 5). 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.

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