PSI and DInSAR (2)

After an Earthquake earth observation methods can support the damage assessment. In this contribution we describe an earthquake damage mapping methodology that is based on the coherence of persistent scatterers. The comparison of the damage map generated for Christchurch, New Zealand, after the Darfield Earthquake on 3-Sep-2010 with liquefaction maps resulting from in-situ assessments indicates a good potential of this methodology.

In Persistent Scatterer Interferometry (PSI) the temporal and spatial characteristics of interferometric signatures collected from temporally persistent point-like scatterers are exploited to accurately map surface deformation histories, terrain heights, and relative atmospheric path delays. The phase model used in PSI is identical to that of conventional differential interferometry, but targets with point like scatter characteristics are much less affected by geometric decorrelation, which permits phase interpretation even for large baselines above the critical one. Consequently, more image pairs may be included in the analysis improving the temporal sampling. Another important advantage is the potential to find scatterers in low-coherence areas permitting filling spatial gaps in the deformation maps. The point-like scatterers very often correspond to infrastructure as buildings, or other temporally rather stable targets as rocks. Due to their specific nature, targets with a point like scattering characteristics very often maintain coherence over long time periods. In an urban environment usually many persistent scatterers are present.

Before presenting the damage mapping methodology we need to consider the “coherence” in PSI. There is not a unique definition of coherence in PSI. To calculate a coherence value multiple interferogram values are necessary. Typically, the non-random phase terms are modeled and subtracted before calculating the coherence. In a PSI processing one coherence value regularly used is the “temporal coherence” that characterizes the random deviation of the phase values of a pixel from a modeled phase history. One way to calculate the temporal coherence is to consider only the phase values of a single scatterer. After subtracting terms as the topographic and atmospheric phase the coherence is calculated from the phase deviations from a (typically linear) phase model. Another way to calculate the temporal coherence is to consider the phase deviations from a spatially filtered phase. As a result the coherence does not only depend on the values of one scatterer, but also on its neighbors that are used as reference. Again a single temporal coherence value is calculated per scatterer. To characterize the coherence of a set of points in a single interferometric pair we use a “spatial coherence” that is calculated in the same way as in a 2D differential interferogram, but just considering the persistent scatterers in an area instead of all pixels. This “spatial coherence” indicates how much the residual phase values vary spatially. In areas with very high quality persistent scatterers the temporal coherence as well as the spatial coherence of each interferometric pair show values close to 1.0. Reasons for a reduced temporal coherence can either be generally reduced spatial coherence for all pairs (e.g. as a result of significant scatter fraction coming from the radar clutter) as well as a significant reduction for only a few pairs. If the coherence is too much reduced for too many pairs the scatterer is no longer considered a persistent scatterer and is therefore not included in the solution.

For the proposed damage mapping methodology we use a stack with many acquisitions before the earthquake and at least one acquisition after the earthquake. Considering the pre-seismic stack only we perform a PSI processing to determine corrected point heights, deformation histories and atmospheric phases. To include the post-seismic scene(s) we apply the point heights found and expand the pre-seismic deformation history to the post-seismic scene(s). The point differential interferogram for the co-seismic pair between the pre-seismic temporal reference and the post-seismic scene will include the co-seismic deformation phase and the atmospheric phase of the post-seismic scene. From this point differential interferogram we calculate the spatial coherence. For areas with severe damage this spatial coherence is significantly reduced. To better discriminate the seismic damage effects only we consider the coherence reduction relative to the spatial coherence of a scene before the earthquake. A high reduction in the spatial coherence indicates the loss of the persistent scatterers which is a clear indication of significant damage.

The described methodology was applied to a stack of ENVISAT ASAR data to get over Christchurch, New Zeeland, a damage indicator map for the Darfield Earthquake on 3-Sep-2010. For a section of the city  the coherence change is shown in Figure 1. Red areas indicate a significant coherence reduction which is a strong indicator for damaged infrastructure. These areas correspond well to liquefaction areas identified during in-situ surveys (Figure 2).

Compared to more consolidated methodologies based on the degree of correlation of a single interferogram computed with two acquisitions before respectively after the event, using a significant data stack to determine change between the last two observations appears as a tremendous effort. On the other hand PSI techniques are quite well established and using the entire stack instead of just two or a few more scenes adds some information. For the persistent scatterers a high coherence is confirmed over many different time intervals – consequently a strong reduction of the spatial coherence is a more clear indication that significant change occurred to the scatterer. And in-spite of the relatively coarse resolution of the satellite SAR  data used (20m in ground range) the information is at single building level. But it is also clear that information is not available for every building.

Persistent scatterer interferometry (PSI) [4, 5] has emerged as a valuable tool for radar-based deformation assessment in urban areas. PSI inherently assumes the presence of a single temporally coherent scatterer in a range-azimuth resolution cell. This restriction results in the rejection of numerous persistent scatterer (PS) candidates, particularly in urban areas where layovers occur frequently. SAR tomography has the potential to overcome this limitation. It estimates scatterer reflectivity along the direction perpendicular to the line-of-sight (PLOS/elevation), thus allowing a spatial discrimination of the scatterers in layover. Differential tomographic techniques [6,7,8,9] have the potential to retrieve the elevation as well as the deformation parameters. Extending the ideas presented in [1,2], this paper investigates the combined use of PSI and tomographic inversion techniques for resolution of the layovers as well as the estimation of the deformation parameters. The results obtained promise increased deformation sampling.

Experiments have been performed on an interferometric data stack comprising of 50 TerraSAR-X stripmap images acquired over the city of Barcelona. The data is multi-baseline and multi-temporal, acquired over a span of five years. Prior to tomography, it is necessary to perform a preliminary PSI analysis to obtain precise phase calibration of the interferometric data stack, removing atmosphere induced phase variations [3]. In our work, we obtained a preliminary PSI solution using the Interferometric Point Target Analysis (IPTA) [2] framework. During the PS candidate selection process, IPTA observes the temporal variability of the backscatter and spectral diversity for each resolution cell. Layovers cases, especially when none among the interfering scatterers is dominant, tend to get rejected owing to a wider spectral diversity than otherwise. We present the case of the Torre Agbar tower in Barcelona as a typical example of a high-rise building appearing in layover in the SAR images. Fig. 1 shows the tower and its surroundings; the top image is an optical view from Google Earth, while the lower image is the average SAR backscatter.

We selected a point (non-PS) at the tip of the building (as marked with a blue cross in Fig. 1) . Next we performed tomographic inversions using three different phase models: #1) for elevation only, as for conventional SAR tomography ; #2) for both elevation and average deformation velocity, as for the general differential tomography, and #3) for elevation, average deformation velocity, as well as a thermal-expansion induced phase term (phase-to-temperature sensitivity). The latter case constitutes an extended phase model for differential tomography. The results are presented in Fig. 2. The elevation profiles for each phase model are given in Fig 2a. The conventional tomographic inversion, which takes into account only the geometry induced phase (elevation), does not produce a well-focused peak. We next perform tomographic inversion with the second phase model where a deformation-velocity term is modeled as well. The deformation velocity-elevation plane is shown in Fig. 2b. The inversion is still not satisfactory. In addition, it can be seen in Fig. 2a (for phase model #2) that the elevation profile is not correct either. It seems that the building elevation (in PLOS direction) is around 160 m, though in truth it is around 251 m (corresponding to a true vertical height of 145 m). Only when a thermal-expansion induced phase change is modeled do we see both a well-focused elevation profile (Fig. 2a, phase model 3), as well as a nicely focused peak in the elevation-deformation plane (Fig. 2c). The scatterer is now focused at the correct elevation. This result clearly highlights the importance of appropriate phase modeling, particularly for high-rise buildings.

Tomographic inversion with extended phase model is then applied to all the scatterers along a cross-section through the Torre Agbar tower (as marked with a red line in Fig. 1). The results are provided in Fig. 3. We now have estimates of the scatterer elevation positions in PLOS, average deformation velocity as well as the phase-to-temperature sensitivity for these scatterers. It is worthwhile to mention here that the local temperature values used in the tomographic analysis itself are based on an iterative PSI solution obtained with IPTA.

In short, this paper provides an initial investigation towards the combined use of PSI and advanced tomographic techniques for improved spatiotemporal inversion. It has been highlighted that insufficient phase modeling may lead to improper inversion, resulting in inaccurate estimation of elevation and/or deformation velocity. The results for the high-rise buildings suggest that phase changes induced by thermal expansion have to be modeled. In the final paper, we present the detailed data model for tomographic inversion. Results are provided for wider areas, and the analysis is extended further.

References

[1] O. Frey, M. Siddique, I. Hajnsek, U. Wegmuller, and C. Werner, “Combining SAR tomography and a PSI approach for high-resolution 3-D imaging of an urban area,” in Proc. 10th European Conf. on SAR, 2014, pp. 1045–1048.

[2] O. Frey, I. Hajnsek, U. Wegmuller, and C. Werner, “ SAR tomography based 3-D point cloud extraction of point-like scatterers in urban areas,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., 2014, pp. 1313–1316.

[3] O. Frey, I. Hajnsek, and U. Wegmuller, “Spaceborne SAR tomography in urban areas,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., July 2013, pp. 69–72.

[4] A. Ferretti, C. Prati, and F. Rocca, “Permanent scatterers in SAR interferometry,” IEEE Trans. on Geosc. and Remote Sens., vol. 39, no. 1, pp. 8–20, 2001.

[5] C. Werner, U. Wegmuller, T. Strozzi, and A. Wiesmann, “Interferometric point target analysis for deformation mapping,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., pp. 4362–4364.

[6] F. Lombardini, "Differential tomography: a new framework for SAR interferometry," IEEE Trans. on Geosc. and Remote Sens. , vol. 43, no. 1, pp. 37-44, Jan. 2005

[7] F. Lombardini, D. Pasculli, F. Viviani, and F. Cai, "Tomo and diff-tomo superresolution degarbling improvements and first results with COSMO-SkyMed urban data," in Proc. 9th Euro. Conf. on SAR., 2012, pp.155-158

[8] G. Fornaro, D. Reale, and S. Verde, "Bridge Thermal Dilation Monitoring With Millimeter Sensitivity via Multidimensional SAR Imaging," IEEE Geosc. and Remote Sens. Letters, vol.10, no.4, pp. 677-681, July 2013

[9] X. Zhu, and R. Bamler, "Superresolving SAR Tomography for Multidimensional Imaging of Urban Areas: Compressive sensing-based TomoSAR inversion," IEEE Signal Processing Magazine, vol. 31, no. 4, pp. 51-58, July 2014

Differential Synthetic Aperture Radar Interferometry (DInSAR) technique [1] for the monitoring of Earth surface deformation has evolved over the years to represent nowadays a powerful tool in scientific and operational contexts. Historically developed to study single deformation episodes, DInSAR is now mostly used to follow the temporal evolution of surface deformation through the generation of displacement time-series, retrieved by applying advanced multi-temporal DInSAR approaches. These methods are based on the inversion of properly-generated sequences of DInSAR interferograms, and allow the computation of Line Of Sight (LOS)-projected deformation time-series in areas that are not significantly affected by decorrelation noise [2]. Advanced DInSAR techniques are usually grouped into two main categories: the Persistent Scatterer (PS) methods [3]-[4], mostly focused on investigating point targets, and the Small Baseline (SB) techniques [5]-[6], which, instead, are designed to analyze distributed targets (DS).

The growing availability of large archives of SAR images collected by several sensors, mounted onboard to constellations of space-based platforms operating at different wavelengths, and with complementary looking angle geometries (and also possibly through different acquisition modes) poses the problem to effectively combine the pieces of information coming from them. In particular, the combination of multi-platform/multi-looking angle DInSAR-based displacement measurements can improve our ability in mapping surface deformation in three dimensions, thus overcoming the inherent limitation of InSAR to measure, exclusively, the sensor’s LOS projection of the deformation. Noteworthy, all modern space-based SAR platforms are in a quite near-polar orbits and acquire images over ascending and descending passes; accordingly, the ability to discriminate the north-south components of deformation is quite limited. However, the combination of ascending/descending mean displacement velocity maps is still possible [7], and allows retrieving the rate of deformation w.r.t. the Up-Down and East-West directions, respectively. More challenging is the problem to recover, not only, the Up-Down and East-West mean displacement rate maps, but also to follow the temporal evolution of deformation via the retrieval of Up-Down and East-West time-series, covering the overlapped time span between ascending and descending passes. This problem has been faced, and a few solutions have already been proposed in literature in recent years [8]-[9]. In particular, the algorithm presented in [8], referred to as MSBAS, is thought as an extension of the Small BAseline Subset (SBAS) method [5], and consists in acquiring and simultaneously processing a very large sequence of multiple-sensor interferograms, which are then inverted to recover the (2-D) displacement time-series by using a regularized Singular Value Decomposition (SVD)-based approach.

In our work, we investigate the potential of an alternative solution, which does not require the simultaneous process of large archives of DInSAR interferograms, and consists in the development of a post-processing step to be carried out on sets of already independently processed (potentially, with different DInSAR processing tools) of (geocoded) multi-sensor LOS displacement time-series. The presented method relies on a minimum curvature combination scheme [10], here adapted to work with the problem at hand. A comprehensive description of the algorithm will be provided in the full paper. Here, we only give a few hints about the main characteristics of the inversion scheme.

Let us consider K sets of independently retrieved (by applying either the SBAS approach or other alternative DInSAR techniques) geocoded LOS-projected deformation time-series, namely φ₁(t₁),φ₂(t₂),...,φ_K(t_K), corresponding to the time vectors t₁,t₂,...,t_K, each of them consisting of M_K distinctive time acquisitions. By considering the general guidelines of [5],[8], for each pixel of the (geocoded) grid, a system of linear equations with respect to  unknowns representing  the Up-Down and East-West deformation velocities between consecutive (wholly) time acquisitions can be written. With respect to previous solutions, the obtained ill-posed system of equations is now regularized introducing a set of additional equations, imposing the condition that the expected solutions are with the minimum curvature, that is the difference between consecutive velocities is minimal.

The main advantages in using the proposed combination scheme arise in: i) the possibility to use “conventional” processing tools for the retrieval of LOS displacement maps, thus also making it possible the combination of DInSAR displacement time-series produced by different, and inherently complementary, InSAR tools; ii) the possibility to integrate in the post-processing “minimum curvature” combination scheme information on the quality of reconstruction of the deformation inherent to the different used processing tools (e.g. the information on the temporal coherence of investigated pixels [11]); iii) the capability to further refine the estimates of residual topography in the DInSAR time-series; iv) its ability to be simply adapted to “update” previously achieved 2-D displacement time-series as soon as new SAR acquisitions are available: this is particularly important in the light of new SAR systems, such as the Sentinel-1 SAR platform, planned to collect data with a only few days repetition frequency.

The experiments carried out both on simulated and real SAR datasets demonstrate the validity of the presented approach. In particular, the area of Piton La Fournaise (Reunion Islands) has been selected to perform the experiments on real SAR data. Indeed, over this area, three independent sets of SAR acquisitions collected by the ENVISAT/ASAR (C-band) instrument along ascending (48 images) and descending passes (35 images) and by the ALOS/PALSAR (L-band) sensor (11 images) were available. These three sets of SAR data were independently processed by the SBAS processing chain, thus first obtaining the corresponding LOS-projected (geocoded) displacement time-series. Then, they have been combined (in a post-processing phase) to discriminate the different components of the deformation.

References 

[1]       R. Bürgmann, P. A. Rosen, and E. J. Fielding, “Synthetic aperture radar interferometry to measure Earth's surface topography and its deformation,” Annu. Rev. Earth Planet. Sci., vol. 28, pp. 169–209, May 2000.

[2]       H. A. Zebker and J. Villasenor, “Decorrelation in interferometric radar echoes,” IEEE Trans. Geosci. Remote Sens., vol. 30, pp. 950–959, Sep. 1992.

[3]       A. Ferretti, C. Prati, and F. Rocca, “Permanent scatterers in SAR interferometry,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 1, pp. 8–20, Jan. 2001.

[4]       C. Werner, U. Wegmüller, T. Strozzi, and A. Wiesmann, “Interferometric point target analysis for deformation mapping,” in Proc. of  IGARSS, Toulouse, France, Jul. 21–25, 2003, vol. 7, pp. 4362–4364.

[5]       P. Berardino, G. Fornaro, R. Lanari, and E. Sansosti, “A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms,” IEEE Trans. Geosci. Remote Sens., vol. 40, no. 11, pp. 2375–2383, Nov. 2002.

[6]       S. Usai, “A Least Squares Database Approach for SAR Interferometric Data,” IEEE Trans. Geosc. Remote Sens., vol. 41, no 4, pp. 753-760, April 2003.

[7]       M. Manzo, Ricciardi, G. P., Casu, F., Ventura, G., Zeni, G., Borgström, S., Berardino, P., Del Gaudio, C., and Lanari, R., “Surface deformation analysis in the Ischia island (Italy) based on spaceborne radar interferometry”, Journal of Volcanology and Geothermal Research, 151, pp. 399–416, 2006.

[8]       S. Samsonov, N. d’Oreye , “Multidimensional time-series analysis of ground deformation from multiple InSAR data sets applied to Virunga Volcanic Province”, Geophysical Journal International 191, pp. 1095-1108, 2012.

[9]       J. Hu, X. L. Ding, Z. W. Li, J. J. Zhu, Q. Sun, and L. Zhang, “Kalman-Filter-Based Approach for Multisensor,Multitrack, and Multitemporal InSAR”, IEEE Trans. Geosc. Remote Sens., vol. 51, no. 7, July 2013.

[10]      M. Costantini, F. Miniati and L. Pietranera, “Combining Multi-Temporal SAR Differential Interferograms: A Curvature based method”, Fringe Symposium, Frascati, 2004.

[11]      A. Pepe, and R. Lanari, “On the extension of the minimum cost flow algorithm for phase unwrapping of multitemporal differential SAR interferograms,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 9, pp. 2374-2383, Sept. 2006.

Demonstration of TerraSAR-X ScanSAR Persistent Scatterer Interferometry

Fernando Rodriguez Gonzalez, Ramon Brcic, Nestor Yague‐Martinez,
Robert Shau, Alessandro Parizzi and Nico Adam

Remote Sensing Technology Institute (IMF), German Aerospace Center (DLR),
Oberpfaffenhofen, D‐82234 Wessling, Germany

Abstract

The concept of PSI Wide Area Product was introduced in ESA´s GMES Terrafirma project [1] in preparation for the upcoming Sentinel-1 Mission. The extension of the PSI technique to wide area deformation mapping presents many technical challenges, especially in non-urban areas and in mountainous areas [2]. The Integrated Wide Area Processor (IWAP) [3] has been developed at DLR for this purpose. Wide area deformation mapping has been demonstrated in Greece [3].

The Sentinel 1 system has been conceived in order to provide wide swath SAR interferometric capabilities. A wide swath is achieved by the TOPS (Terrain Observation by Progressive Scan) SAR acquisition mode [4], which cyclically scans a group of neighboring swaths, as performed in the ScanSAR acquisition mode. Furthermore, by means of its forwards azimuth antenna steering it eliminates the main drawbacks of ScanSAR, namely the effects of scalloping and the azimuth varying SCR, NESZ and azimuth-ambiguities. Nevertheless, the spectral characteristics (linear Doppler Centroid variation over azimuth) and the processing strategies for ScanSAR and TOPS SAR are analogous [5][6], the main difference been the higher azimuth co-registration accuracy required for TOPS SAR. This is due to its higher Doppler Centroid variations caused by the antenna steering.

In the framework of ESA GMES Terrafirma project as well as in order to support ESA in its Sentinel‐1A Commissioning Phase activities (ESA Contract No. 4000111074/14/NL/MP/lf) [7], the IWAP has been extended to support both burst acquisition modes: ScanSAR and TOPS SAR. Interferometric processing is based on the techniques specified in [6]. PSI processing has been extended to support burst modes, the main update been the PS candidates detection. The further wide area PSI processing methods remain valid [3]. An interesting aspect specific to burst mode PSI is the possibility of obtaining multiple observations from a PS observed with different Doppler Centroids. Moreover, the impact of azimuth residual phase ramps due to azimuth mis-registration on the estimation of inter-burst and inter-beam arcs should be assessed. The feasibility of generating such arcs conditions the overall processing strategy: full scene processing versus single burst processing and a posteriori mosaicking. The inter-burst and inter-beam arcs are essential for ScanSAR PSI, since the reduced azimuth burst overlap does not support a posteriori mosaicking of individual processing of bursts.

At the moment of writing this abstract, no Sentinel data stack is available. As a consequence and due to the analogies of modes and processing, a stack of 65 TerraSAR-X images has been selected for this demonstration. The test site is a 100x100km area around Lake Mead (USA), an artificial water reservoir impounded by the construction of Hoover dam. The water level variation during the stack time span [8] and the master acquisition coverage are depicted in Figure 1. The water level exhibits a clear descent trend and a seasonal modulation. Deformations caused by water level variations have been previously reported [9].

Selected interferograms illustrating the variety of atmospheric effects are shown in Figure 2. Due to the large height variations within the covered area (from 150 m to 2400 m ellipsoid heights) and to the variation of weather conditions, the effect of the stratified atmosphere is very high (see Figure 2 (b)). Data-based stratification estimation and mitigation has been applied. The remaining APS has been conventionally estimated in PSI processing.

The estimated linear deformation rate is shown in Figure 3 (a). A big oval deformation pattern in the northern part was already reported for the period 1992-2002 [9]. According to the authors, movement in this area might be due to the poroelastic response of a sedimentary layer adjacent to the lake, in which ground water communicates with the lake. Thus, when the water level goes down, water is expelled from this layer and thus the area subsides, as in the case of the ScanSAR stack. A landslide phenomenon is shown in Figure 3 (b) and localized uplift and subsidence areas in the Boulder City are depicted in Figure 3 (c).

Finally, it is interesting to evaluate the residual topography estimates. The topography update is with respect to the STRM DEM, which was acquired in February 2000. At that time the average water level was 370, whereas at the time of the master acquisition 334. As a consequence, areas in the perimeter of the lake that in 2000 were in under the water are now new shore areas. The topographic update for such areas is thus negative. Examples of these areas are shown in Figure 4.

Acknowledgements

The WAP is developed within the ESA project Terrafirma with the ESRIN/Contract no. C19366/05/I-EC/DLR.

References

[1]   “GMES Terrafirma: Pan European Ground Motion Hazard Information Service,” www.terrafirma.eu.com.

[2]   N. Adam, W. Liebhart, A. Parizzi, F. Rodriguez-Gonzalez, R. Brcic, “Persistent Scatter Interferometry Wide Area Product Methodology and Final Characteristics,” Terrafirma Stage 3, DLR-IMF – Remote Sensing Technology Institute, 2012.

[3]   F. Rodriguez Gonzalez, N. Adam, A. Parizzi, R. Brcic, “The Integrated Wide Area Processor (IWAP): A Processor for Wide Area Persistent Scatterer Interferometry,” ESA Living Planet Symposium, Edinburgh, September 2013.

[4]   F. de Zan and A. Monti Guarnieri. TOPSAR: Terrain Observation by Progressive Scans, IEEE Transactions on Geoscience and Remote Sensing, Vol. 44, No. 9, September 2006, pp 2352-2360.

[5]   P. Prats-Iraola, R. Scheiber, L. Marotti, S. Wollstadt and A. Reigber. TOPS Interferometry with TerraSAR-X, IEEE Transactions on Geoscience and Remote Sensing, Vol. 50, No. 8, August 2012, pp 3179-3188.

[6]   N. Yague-Martinez, F. Rodriguez-Gonzalez, U. Balss, H. Breit, T. Fritz. TerraSAR-X TOPS, ScanSAR and WideScanSAR interferometric processing. EUSAR 2014 - 10th European Conference on Synthetic Aperture Radar, pp. 945-948. VDE Verlag. 03-05 June 2014, Berlin, Germany.

[7]   N. Yague Martinez, R. Brcic, and B, Schättler, “Sentinel‐1A Commissioning Phase Technical Assistance forSAR System Verification, Repeat Pass Consistency Analysis,” SAR Signal Processing Team, Remote Sensing. Technology Institute, DLR, Sentinel‐1 Technical Assistance, Document S1‐TR‐DLRIMF‐0004, 2014.

[8]   Bureau of reclamation. http://www.usbr.gov.

[9]   Cavalié, O., M.-P. Doin, C. Lasserre, and P. Briole (2007), Ground motion measurement in the Lake Mead area, Nevada, by differential synthetic aperture radar interferometry time series analysis: Probing the lithosphere rheological structure, J. Geophys. Res., 112, B03403, doi:10.1029/2006JB004344.

Figure captions

Figure 1: Lake Mead test site. (a) Water Level elevation (line), TerraSAR-X ScanSAR acquisitions (red dots) and processed stack time span (blue overlay). (b) Coverage of master acquisition (acquired 2009-12-10). Water level data source: [8]. Visualization of (b): Image Landsat © 2014 Google, Google Earth.

Figure 2: Selected differential intererograms. Slave acquisition date and effective baseline: a) 2009-11-29, 51.6 m; b) 2009-07-09; 107.7 m; c) 2010-10-25, -112.2 m; d) 2009-01-25, 40.4m.

Figure 3: Linear deformation rate estimates: (a) overview; (b) landslide; (c) uplift and subsidence in boulder city. Visualizations of (b)-(c): © 2014 Google, Google Earth.

Figure 4: Residual topography estimates with respect to SRTM. Visualizations of (a)-(b): © 2014 Google, Google Earth.

Figures

See attached PDF.

Advanced Interferometric Synthetic Aperture Radar (InSAR) techniques such as, Persistent Scatterer Interferometry (PSI) and Tomographic SAR inversion (TomoSAR) including SAR tomography and differential SAR tomography have been proven to be valuable tools for three-dimensional (3D) mapping and deformation monitoring of urban areas. TomoSAR coupled with data from modern SAR sensors, such as the German TerraSAR-X (TS-X), that are characterized by accurate orbit determination and high spatial resolution, produces the most detailed multi-dimensional maps of individual buildings by distinguishing among multiple scatterers within a resolution cell. When using TS-X very high resolution spotlight images, the resulting TomoSAR point clouds have a point (scatterer) density in the order of 1 million pts/km2  which is comparable to the point density of point clouds obtained from Light Detection and Ranging (LiDAR).

One of the limitations of using InSAR techniques, including TomoSAR, for deformation monitoring is that they only measure deformation along the radar Line-of-Sight (LOS) direction. In order to enhance the understanding of deformation, a decomposition of the observed LOS displacement into the real 3D deformation vector in the local coordinate system is desired.

In this paper, we propose a method to reconstruct 3D deformation vectors of urban areas from TomoSAR point clouds available from, at least, three different viewing geometries.  Initially, TomoSAR point clouds obtained from multiple viewing geometries are geodetically fused in order to produce an accurate shadow-free detailed point cloud. Then around each scatterer a spatial cube is considered within which the 3D displacement vector of the central point is estimated by L1 norm adjustment. The surrounding points in the cube are participated in the estimation based on the distance they have to the central point and also the standard deviation of the deformation estimate which is the output of TomoSAR.

The methodology is applied on four TS-X very high resolution spotlight image stacks over the city of Berlin from which two stacks are acquired from ascending geometries and two from descending geometries. The linear deformation rate and amplitude of seasonal deformation (induced from thermal dilation of buildings) are decomposed in 3D and the results from some individual buildings with interesting deformation patterns are discussed in details.