LAND SUBSIDENCE MAPPING WITH ERS INTERFEROMETRY: EVALUATION OF MATURITY AND OPERATIONAL READINESS

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1 LAND SUBSIDENCE MAPPING WITH ERS INTERFEROMETRY: EVALUATION OF MATURITY AND OPERATIONAL READINESS URS WEGMULLER, TAZIO STROZZI, ANDREAS WIESMANN, AND CHARLES WERNER Gamma Remote Sensing, Thunstrasse 130, 3074 Muri, Switzerland, Tel: , Fax: , ABSTRACT Differential SAR interferometry with ERS data has a high potential for surface displacement mapping in the mm to m range. Such displacement information is of interest for the monitoring of phenomena as land subsidence, land slides, earthquakes, volcano swelling, and ice motion. In this contribution the maturity and operational readiness of the SAR interferometric technique are discussed, focusing on the subsidence application. The investigation is based on examples representing displacement velocities between a few mm/year and several m/year. Based on the investigated examples it is concluded that SAR interferometric subsidence mapping reached operational readiness. INTRODUCTION In recent years ERS differential SAR interferometry has demonstrated a high potential for surface displacement mapping in the mm to m range. Such displacement information is of interest for the monitoring of phenomena as land subsidence, land slides, earthquakes, volcano swelling, and ice motion. The main objective of Gamma's project "Differential Interferometric Applications in Urban Areas" in the frame of ESA's Data User Program (DUP) is to approach operational readiness with differential interferometric applications. During the first two years of the project the focus has been on the land subsidence application. After a short overview of the methodology used, a number of cases investigated will be presented and used to evaluate the maturity and operational readiness of land subsidence mapping with ERS differential SAR interferometry. This evaluation includes several aspects. First, the feasibility is assessed and used to determine the potential and limits of the selected methodology. Then, the robustness of the technique is investigated and the results achieved for the different cases will be used to discuss the accuracy of the technique. The specification of requirements for the successful application of the technique is another important aspect for the operational use of the technique. METHODOLOGY The interferometric phase is sensitive to both surface topography and coherent displacement along the look vector occurring between the acquisition of the interferometric image pair. Inhomogeneous propagation delay ("atmospheric disturbance") and phase noise are the main error sources. The unwrapped interferometric phase φ unw can be expressed as a sum of a topographic term φ topo, a displacement term φ disp, a path delay term φ path, and a phase noise (or decorrelation) term φ noise : φunw = φtopo + φdisp + φ path + φnoise (1) The phase to height sensitivity 4π B δφtopo = λ r θ δ h (2) cos with the wavelength, λ, the baseline component perpendicular to the look vector, B, and the incidence angle, θ, and the slant range, r, characterizes the topographic term. Knowing the baseline geometry and φ topo allows to 1

2 calculated the exact look angle and together with the orbit information the 3-dimensional position of the scatter elements (and thereby the surface topography). The displacement term, φ disp, is related to the coherent displacement of the scattering centers along the radar look vector, r disp : = 2 kr (3) φ disp disp where k is the wavenumber. Here coherent means that the same displacement is observed of adjacent scatter elements. Changes in the effective path length between the SAR and the surface elements as a result of changing permittivity of the atmosphere, caused by changes in the atmospheric conditions (mainly water vapor), lead to non-zero φ path. Finally, random (or incoherent) displacement of the scattering centers as well as noise introduced by SAR signal noise is the source of φ noise. The standard deviation of the phase noise σ φ (reached asymptotically for large number of looks N) is a function of the degree of coherence, γ, σφ = 1 2N 1 γ γ 2. (4) Multi-looking and filtering of the interferogram reduce phase noise. The main difficulty with high phase noise is not so much the statistical error introduced in the estimation of φ topo and φ disp but the problems it causes in the unwrapping of the wrapped interferometric phase. Ideally, the phase noise and the phase difference between adjacent pixels are both much smaller than π. In reality this is often not the case, especially for areas with a low degree of coherence combined with rugged topography, as present in the case of forested slopes. In the general case, φ topo 0, surface displacement mapping requires the estimation of the topographic phase term. This is done based on an independent digital elevation model in the 2-pass approach or based on an independent interferogram with negligible (or known) surface displacement in the multi-pass approach [1]. EXAMPLES OF SAR INTERFEROMETRY BASED SUBSIDENCE MAPS While a single successful example is sufficient to demonstrate the potential of a technique such an example is not sufficient to assess its maturity and operational readiness. Important aspects as the feasibility, robustness, and accuracy need to be investigated. To conduct such an investigation four sites characterized by different subsidence velocities (see Table 1) were selected: the Euganean Geothermal Basin (Italy), Bologna (Italy), Mexico City (Mexico), and the Ruhrgebiet (Germany). In addition, the temporal and spatial dependence of the movement, the availability of ERS data, and the availability of a Digital Elevation Model (DEM) differ from case to case. In the following the results achieved for the four sites will be summarized. Table 1: Subsidence velocities for the selected sites. Velocities [cm/year] Monitoring interval Data used Approx. accuracy [cm/year] Euganean Geothermal Basin (Italy) years 10 ERS, DEM 0.1 Bologna (Italy) year 6 ERS, DEM < 1 Mexico City (Mexico) months 4 ERS 5 Ruhrgebiet (Germany) month 4 ERS 10 2

3 Euganean Geothermal Basin Land subsidence of the Euganean Geothermal Basin, Italy, is related to the geothermal groundwater withdrawal. Up to 1991 the maximum rate of land subsidence has been 1 cm/year as observed from precision levelling surveys. After 1991 the subsidence velocity decreased as a consequence of a regulation of the groundwater withdrawal. To map the land subsidence a time series of ERS-1 and ERS-2 SAR data from 1992 to 1996 was selected. Multiple interferograms covering in total a time span of more than 20 years were combined into a single subsidence map in order to reduce errors caused by atmospheric phase distortions, to a level significantly below the differential phase for the expected slow subsidence. This technique was successful and revealed a clear subsidence signal over Abano Terme with a maximum annual subsidence velocity of 4 mm/year, in agreement with the results of the last levelling surveys performed in 1991 and 1995 (Figure 1). The correspondence of the results of the two different surveying techniques is high, as confirmed by a direct quantitative comparison of the interferometry based subsidence values and levelling lines, an example of which is shown in Figure 2. For 17 points where we had values available from both surveying techniques the average difference of the vertical displacement velocity values was 0.2 mm/year with a standard deviation of 1.0 mm/year. The minimum and maximum differences were 1.5 mm/year and +2.2 mm/year, respectively. A more detailed description of this case was given by Strozzi et al., 1999 [2]. Figure 1. Map of the vertical ground movements (in mm/year) from two levelling surveys in 1991 and 1995 in the urban areas of Abano and Montegrotto Terme (data from Comune di Abano Terme and Regione del Veneto) superposed to the map of the vertical displacement velocity derived from ERS differential SAR interferometry between 1992 and Also shown is the position of the benchmarks. 3

4 bis 19 19bis 20 20bis 21 21bis 22 22bis 23 23bis Vertical displacement velocity (mm/year) Position Figure 2. Profiles of the vertical displacement velocity from SAR interferometry (blue line, period ) and levelling surveys (red line, period , data from Comune di Abano Terme and Regione del Veneto) along the yellow levelling line Abano Terme Montegrotto Terme. Bologna At Bologna, Italy, the subsiding area is large with maximum subsidence velocities of 6 to 8 cm/year and characteristic spatial gradients of the vertical movement. A large scientific community is involved in the study of the subsidence. Levelling surveys are being conducted at intervals of several years. For the SAR interferometric subsidence mapping we selected a time series of ERS-1/2 data from August 1992 to May To reduce the errors introduced by atmospheric inhomogeneity three long-time interferograms were combined. The crosscomparison of the subsidence maps derived from the independent ERS pairs served also as an immediate consistency test. The final interferometry based subsidence map was validated with levelling data. The values and shapes of the contour lines of land subsidence derived from ERS differential SAR interferometry in the urban area of Bologna (Figure 4) are in good agreement with those derived from levelling surveys (see Figure 3). Particularly in the historical center of the city the correspondence between the two methods is very high resulting in a similar shape of the sharp gradient of movements with. For a quantitative validation, the difference between the two measurements was calculated for 215 points distributed over the urban area of Bologna. The average of the difference of the subsidence velocity values determined from levelling surveys (period ) and SAR interferometry (period ) was 1.1 cm/year with a standard deviation of 1.1 cm/year. The small standard deviation of 1.1 cm/year between the two methods indicates a good performance of ERS differential SAR interferometry for subsidence mapping in urban areas. The discrepancy between the two data sets, with a systematic behavior in the majority of the area, can be explained by the different time period, indicating a decrease of the subsidence velocity. These findings are confirmed by a detailed comparison performed along three levelling lines. The profiles (Figure 5) indicate similar spatial dependence with smaller subsidence velocities found with SAR interferometry. More recent levelling data with a better correspondence to the time interval covered with SAR interferometry will be used for an improved validation, as soon as such data becomes available. For a more detailed description of this case see [3,4]. Considering on one hand the temporal development of the subsidence at Bologna indicated by the differences between the older levelling data ( , Figure 3) and the newer SAR interferometry based results ( ) and the small relative error caused by atmospheric distortions for interferograms with acquisition intervals of several years indicated some potential to annually map the subsidence at Bologna. To investigate this potential we produced two individual subsidence maps for the time periods and To generate the subsidence map six interferograms covering in total a time span of more than four years were used. For the the subsidence map is based on seven interferograms again covering in total a time span of more than four years. Thanks to the support of the University of Bologna the map could be validated with corresponding levelling data, confirming the usefulness of the technique for the annual subsidence monitoring. Up to present the result could not be validated. 4

5 Fig. 3. Map of the vertical ground movements from two levelling surveys in 1987 and 1992 in the urban area of Bologna [1]. The contour lines indicate the total subsidence between 1987 and 1992 with 2 cm contour line interval and the southernmost contour line corresponding to 2 cm. Fig. 4. Subsidence map of the urban area of Bologna from ERS differential SAR interferometry. One color cycle corresponds to a subsidence velocity of 1 cm/year starting from the base of the Appennini (in the south) that is considered stable. (a) West-East line #1 (b) Southwest -Northeast line #2 (c) South-North line #3 Fig. 5. Profiles of the subsidence velocities determined from ERS SAR interferometry (normal line) and levelling surveys (bold line) along three levelling lines. Mexico City Mexico City is built on highly compressible clays and by reason of strong groundwater extraction a total subsidence of more than nine meters has been observed over the last century. The selection of ERS data to map subsidence at Mexico City is strongly restricted by the relatively few acquisitions found in the archive. From the available data acquisitions, three independent differential interferograms, one in ascending and two in descending mode, were selected. For Mexico City and the time period between January 1996 and September 1997 SAR interferometry led to a consistent results with high subsidence velocities above 30 cm/year for some areas and strong spatial subsidence velocity gradients for large parts of the city. The subsidence maps derived from the three independent interferograms are consistent. For the period January 1996 May 1996 (Figure 6) the observed maximum subsidence velocities are about 7cm/year higher than for the period June 1996 September 1997, indicating some temporal or seasonal variation. The values of land subsidence measured in Mexico City with differential SAR interferometry are also in general agreement with those reported in the literature. For a more detailed description of this case see [5]. 5

6 Fig. 6. SAR interferometric subsidence map of Mexico City derived from ERS data of 29-Dec-95 / 16-May-96. One color cycle corresponds to a subsidence velocity of 5 cm/year. A backscattering image is used as image brightness. Ruhrgebiet Coal mining in the Ruhrgebiet causes significant surface movement. Due to legal requirements the mining companies are obliged to assess the environmental impact of the excavations. Surface movement caused by mining is a very dynamic process with high spatial and temporal variability. For mining areas with high subsidence velocities, interferometric pairs with acquisition intervals of only one or a few 35 day repeat cycles are preferred. Subsidence maps of different time intervals clearly indicate the progress in the sub-surface coal excavation. Detailed studies and a validation with excavation plans are ongoing. MATURITY AND OPERATIONAL READINESS OF THE TECHNIQUE The successful application of interferometric surface displacement mapping depends on factors related to the phenomenon itself (displacement velocity field, temporal and spatial gradients), scene parameters (topography, landuse), sensor parameters (data availability, acquisition intervals, baselines), the availability and accuracy of a digital elevation model, and data processing related factors (phase filtering, phase unwrapping, geocoding accuracy, averaging scheme for multiple results, to name just a few important ones). The investigation of the dependence of the technique on these factors is essential for us as a provider of related value-added products and services. As described above, several complementary cases were studied for this purpose. The focus was on land subsidence mapping, but the most of the conclusions will also apply for other types of surface displacement. Factors related to the phenomenon itself The four investigated cases Euganean Geothermal Basin (Italy), Bologna (Italy), Mexico City (Mexico), and Ruhrgebiet (Germany) are characterized by different subsidence velocities (see Table 1). In addition, the temporal and spatial dependence of the displacement velocities differ from case to case. While no steep velocity gradients are observed for the Euganean Geothermal Basin, this is the case for the other sites. For Bologna a temporal variation of the subsidence was detected. For Mexico City an even stronger variation is expected and for the Ruhrgebiet with mining related subsidence the temporal and spatial variability is highest, depending on the local coal extraction history. 6

7 To obtain reliable displacement values with SAR interferometry the subsidence signal should dominate over the error terms. Usually, spatial heterogeneity of the atmospheric and ionospheric path delay (often called 'atmospheric distortions') presents the main error source in single interferograms. To consider a relatively strong atmospheric distortion we assume a phase error of the single interferogram of π 2. The displacement term of the interferometric phase, on the other hand, depends on the absolute displacement along the radar look vector occurring during the interval enclosed by the interferometric pair. The absolute displacement corresponds to the average displacement velocity multiplied with the time interval. As a consequence the relative error caused by the atmospheric distortion decreases with increasing acquisition interval. To keep the expected error in the order of 5% of the maximum displacement the displacement phase term should be 20 times the assumed atmospheric distortion, i.e. 10π, corresponding to 5 fringes or about 15 cm of vertical subsidence. This means that we preferably select an interferogram with 3 or more years acquisition interval to map the subsidence of an area with velocities up to approximately 5 cm/year. The Bologna results confirm this strategy. To map faster moving subsidence, shorter intervals are preferred, as selected for Mexico City and the Ruhrgebiet. To map slow subsidence, such as in the case of the Euganean Geothermal Basin, even longer intervals would be required. The intervals cannot be much extended above the 3 years because of data availability. In addition, the use of very long intervals introduces excessive temporal decorrelation, which precludes interpretation of data except for urban areas. A welcome approach improving the subsidence signal to atmospheric phase error ratio is the stacking of multiple interferograms. Under the assumption of a stationary process the subsidence term adds up linearly, i.e. the addition of the unwrapped phases of two interferograms with one and two years acquisition intervals results in an unwrapped phase with a covering an effective time interval of 3 years. For the error term, on the other hand, we can assume statistical independence between the independent interferograms. As a consequence the atmospheric error increases only with the square root of the number of pairs and not with the number of pairs. In the case of the Euganean Geothermal Basin 10 interferograms covering a total time interval of more than 20 years were combined, resulting in an estimated atmospheric phase error of 10π 2. With a subsidence velocity of 4 mm/year the total subsidence phase corresponding to the 20 years of accumulated subsidence amounts 5. 2π resulting in a relative error of 30% or 1.2 mm/year, in general agreement with the validation of the subsidence map of the Euganean Geothermal Basin. To consider this relatively high atmospheric phase error is not just motivated by a rather conservative assessment of the accuracy, but also to achieve a more operational and more robust technique. High atmospheric errors can often be identified by its specific shape, by cross-comparison of multiple interferograms, or possibly based on meteorological data. Interferograms with high atmospheric errors can then be excluded from a combination of multiple interferograms. It is not clear, though, how to best integrate such tests in an operational processing chain. So far the discussion was mainly addressing vertical subsidence, i.e. assuming a known displacement direction. This assumption is usually appropriate in the case of subsidence caused by ground water extraction. In the case of the mining induced ground movement shows a more complicated geometry. Even a combination of ascending and descending data does not allow to resolve the complete three dimensional displacement vector field, without use of additional information. For the transformation of the displacement phase term to displacement velocities a reference point with known displacement velocity is required. Often the scene content allows to find stable points, as in the case of Bologna, where the nearby Appeninian mountains can be assumed to be stable. Nevertheless it has to be kept in mind that the availability and accuracy of one or several reference points is important for the accuracy of the interferometric displacement map. Factors related to scene parameters The scene topography has an influence on the robustness of the interferometric technique. The estimation of the displacement phase term requires the prior estimation of the topographic phase term. The latter is either simulated based on an available digital elevation model or estimated from an independent interferogram with a 7

8 short acquisition interval, such as an ERS Tandem pair. In many cases the use of a digital elevation model turns out to be more robust and operational. The phase unwrapping required in the multi-pass approach, on the other hand, is often difficult to resolve and far from operational for low coherence areas, especially in rugged terrain. In addition, gaps in the unwrapped topographic phase for areas of too low coherence may be present, depending on the phase unwrapping method used. The degree of coherence depends on the landuse. For Tandem pairs the coherence is very low for open water and forest. For most other classes the coherence is higher, allowing a more reliable interpretation of the interferometric phase. For a 35 day time interval the coherence is still quite high over sparsely vegetated terrain. For acquisition intervals longer than one year the areas with higher coherence levels are further reduced mainly to urban and sub-urban areas. Factors related to sensor parameters Of course sensor parameters as the wavelength, the spatial resolution, incidence angle, etc. have a strong influence on the feasibility, robustness, and operationality of SAR interferometric displacement mapping. Such factors are not discussed here, but only effects related to subsidence mapping with the SAR on ERS-1/2. For Mexico City only relatively few acquisitions are available in the archive. As a consequence the data availability limits the flexibility in the data selection and does not allow the generation of a complete temporal sequence of subsidence maps. For the investigated European sites in Italy and Germany a large number of ERS acquisition are available, allowing to optimize the data selection with respect to acquisition dates and interferometric baselines. This valuable archive of data useful for the subsidence application is the result of the operation of the ERS satellites in the single mode (35-day repeat orbits) for most of the time. For the planned ENVISAT mission this means that the robustness and operationality of the subsidence application depends very much on the operation of the SAR in a single interferometric mode for most of the time. Data processing related factors Data processing related aspects which influence the robustness and operationality of the application include processing steps as phase filtering, phase unwrapping, geocoding, and the averaging scheme for multiple results. Not so much the optimization of the processing for a specific example but a robust processing scheme which works under most circumstances is in the foreground. In our own processing chain we identified phase unwrapping as the most critical point. This is not surprising as the coherence levels in long time interferograms tend to be very low for large parts of the image. Patches of sufficiently high coherence to reliably interpret the interferometric phase are disconnected in space separated by areas with high phase noise. Phase filtering reduces the phase noise but tends to lead to phase unwrapping errors in areas of high fringe densities. Our geocoding scheme on the other hand turns out to be operational and robust in the case an external DEM is used. Because of the scaling of the topographic phase with the perpendicular baseline component the precision baseline estimation is another essential processing step. At present we use various estimation methods based on the orbits data, the registration offsets, and the fringe rate of the interferogram. The baseline estimation accuracy required increases with increasing size of the area investigated. Therefore the study area size is another important factor. Processing related factors depend on the processing software and processing parameters used. Status of maturity and operational readiness of subsidence application at Gamma Based on the investigated examples we gained a lot of insight and experience putting us in the position: to assess the feasibility and robustness of SAR interferometric subsidence mapping for a new specific case to decide on an appropriate strategy (data selection, processing scheme) to give an estimate of the achievable accuracy to estimate the expected processing effort to estimate the overall costs, allowing us to offer related value adding services In conclusion this means that interferometric subsidence mapping reached operational readiness at Gamma. 8

9 SUMMARY AND CONCLUSIONS Four different cases representing subsidence velocities between a few mm/year and several m/year were used to discuss the feasibility, robustness, and accuracy of subsidence mapping with ERS SAR interferometry. With our current understanding of the influence of several important factors, including factors related to the subsidence phenomenon, sensor related factors, scene related factors, and processing related factors, we succeeded in all four cases to generate useful subsidence maps. This allowed us to conclude that the application reached operational readiness. This does not mean that all subsidence mapping problems are solved with SAR interferometry, but rather that the technique has a good potential, that it reaches some robustness, and that our understanding is sufficient to more easily evaluate its potential for new cases, i.e. to decide on the strategy to use, to assess the feasibility, to assess the expected processing effort and data costs, and to indicate an expected accuracy. In spite of this operational readiness it is important to keep the limitation of the technique in mind. In most cases it was not possible, for example, to generate a subsidence map with complete coverage due to temporal decorrelation for certain surface types during the selected acquisition intervals. ACKNOWLEDGMENTS This work was supported by the ESA Data User Program (DUP). The Italian National Geologic Survey is acknowledged for the DEMs of the Italian sites. Arch. Benetetto Vettore of the Comune di Abano Terme and Ing. Andrea Costantini of the Regione del Veneto are acknowledged for the high precision levelling data used for validation purposes at the Euganean Geothermal Basin. Gabriele Bitelli of the University of Bologna, is acknowledged for his support of the validation of the interferometric subsidence maps of Bologna. ERS data copyright ESA. ERS data over Mexico City courtesy of AO Volker Spreckels and Norbert Benecke of the Deutsche Steinkohle AG, Bottrop, are acknowledged for their support of the validation of the interferometric subsidence maps of the Ruhrgebiet. REFERENCES [1] Wegmüller U., and T. Strozzi, Characterization of differential interferometry approaches, EUSAR'98, May, Friedrichshafen, Germany, VDE-Verlag, ISBN X, pp , [2] Strozzi T., L. Tosi, L. Carbognin, U. Wegmüller, and A. Galgaro, Monitoring Land Subsidence in the Euganean Geothermal Basin with Differential SAR Interferometry, Proceedings of Fringe'99, Liège (B), [3] Wegmüller U., T. Strozzi, and C. Werner, Land subsidence in the Po river valley, Italy, Proceedings of IGARSS'98, 6-10 July, Seattle, WA, USA, [4] Wegmüller U. and T. Strozzi, Validation of ERS Differential SAR Interferometry for Land Subsidence Mapping: the Bologna Case Study, Proceedings of IGARSS'99, Hamburg, 28 June - 2 July [5] Strozzi T. and U. Wegmüller, Land Subsidence in Mexico City Mapped by ERS Differential SAR Interferometry, Proceedings of IGARSS'99, Hamburg, 28 June - 2 July