there is a delay of the subsidence at the surface …...1university of mining and technology,...

RADAR INTERFEROMETRIC ANALYSIS OF MINING INDUCED SURFACE SUBSIDENCE USINGPERMANENT SCATTERER

D. Walter1, J. Hoffmann2, B. Kampes3, and A. Sroka1

1University of Mining and Technology, Department of Mine Surveying and Geodesy, 09599 Freiberg, Germany,[email protected], [email protected]

2German Aerospace Center (DLR), German Remote Sensing Data Center (DFD), 82234 Wessling, Germany,[email protected]

3German Aerospace Center (DLR), Remote Sensing Technology Institute (IMF), 82234 Wessling, Germany,[email protected]

ABSTRACT

We apply the permanent scatterer (PS) technique to inter-ferometric ERS SAR observations to analyse the surfacesubsidence induced by hard coal mining activities at the”Prosper-Haniel” mine (Ruhr region, Germany). Under-ground mining causes extensive subsidence of serveralmeters and typically high subsidence rates at the earth‘ssurface. We show that this approach is applicable forthe measurement of displacements in underground min-ing based on long time-series. A condition for a success-ful derivation of subsidence on the PS is the integrationof model data in the processing of the PS system. Weuse about 78 ERS-1/-2 scenes for our analysis. Extensivevalidation data are also used to constrain the spatial andtemporal displacement field and verify the interferomet-ric results.

Key words: subsidence, hard coal mining, SAR interfer-ometry, permanent scatterer.

1. INTRODUCTION

Underground mining usually causes extensive subsidenceof serveral meters at the earth‘s surface. Particulary indensely populated areas these effects result in signifi-cant damages to houses and urban infrastructure. Miningcompanies in Germany are required by law to compen-sate for the damages. To prevent unjustified claims themining companies are interested in the area-wide accu-rate monitoring of the surface subsidence. At the momentthe coverage of subsidence information with precise lev-elling is very expensive and time consuming. Due to thepointwise measurement, this procedure cannot providearea-wide spatial information and the high costs inhibitthe frequent updating of the data.

An alternative method for detecting and analysing subsi-dence is provided by radar remote sensing, namely differ-ential radar interferometry (DInSAR). Differential radarinterferometry is well suited to detect small relative dis-placements of the surface. This fact is mainly due tothe short wavelenght of radar signals (cm). The funda-mental measurement value of this method is the phaseof the radar signal. An important condition for success-ful interferometric analysis is a high coherence betweenthe radar signals. Unfortunately, interferometric analy-sis of radar data in central Europe is often hampered byextensively vegetated land surfaces that can destroy thedeterministic phases differences in temporally separatedimages. Longer temporal separations between two radaracquisitions typically reduce the ability to interpret themeasured phase differences. Another source of reducedsignal coherence or decorrelation, is the geometric dif-ference in the incidence angles between two aquisitions[11]. Furthermore high subsidence rates, which are typi-cal for mining, can reduce the deterministic coherence ofradar data [7].The recently developed ”permanent scatterer” technique[2] now enables the construction of much longer time-series of displacement measurements than previously fea-sible. This method identifies scatterers in the radar im-ages that remain coherent over a long time and a widerange of viewing angles by means of statistical analysis.Displacement measurements are then exclusively made atthese points.In this study we use the DLR interferometric systemextented for permanent scatterer processing technique[1, 4]. We demonstrate the possibility for appling the PStechnique to derive mining induced subsidence with highsubsidence rates. The analysis was carried out using 78ERS-1/-2 scenes acquired between 1992 and 2000. Thearea under investigation is located in the Ruhr region ofGermany over a hard coal working area (panel) of the”Prosper-Haniel” underground mine of the DSK AG. Insitu hard coal seams occur in inclined bedding. In themine the thickness of extracted hard coal seams reached 4

meters in a middle depth of 890 meters in longwall work-ing with a face width of 400 meters and lenghts of 1 to2.5 kilometers. The maximum subsidence at surface inthis mining area was 4 meters during 1992-2000. Theactive panels of about 55 km2 are mostly located underthe ”Kirchheller Heide” nature preserve. Since perma-nent scatterer points are primarily found on man-madeobjects, the permanent scatterer analysis could only beperformed for one investigated active panel covering sev-eral small towns. A key element of the presented study isthe integration of model data into the permanent scatterersystem. This was necessary for the accurate derivationof the high subsidence rates occuring in the context ofmining. The first part of this paper provides an overviewof the fundamentals of mining surface subsidence andthe possibility of a calculation of expected subsidence.Thereafter we present the integration of this calculationinto the DLR permanent scatterer system in the interfer-ometric data processing. In the last sections the expectedand obtained results of the subsidence estimation in min-ing using PS technique are presented and discussed.More details on the study presented in this paper is foundin [9].

2. MINING INDUCED SUBSIDENCE

The underground mining of mineral deposits from therock mass system of the earth creates large undergroundexcavations. In mining without back-filling (clastic rock,sand, ash etc.), the openings are closed sooner or laterbecause of the overburden pressure of the top and siderock mass layers. As a result, the subsidence of the roofabove the opening has an effect on the earth‘s surface.The deeper the opening the shallower and wider the sub-sidence basin is, depending on the structure of rock mass[5].Typical of the german deep-level hard coal mining isthe formation of an extensive and shallow subsidencetrough. The shape of this depends on mining depth, theworked seam thickness and the extent of the mining, aswell as on tectonic faults and the method of mining, thespeed of advance, the back-filling and the rate of stressto strata due to multiple-seam mining. The basic theoryof the ground movement due to mining operations wasadvanced by Lehmann‘s trough theory in 1919 [6]. Themaximum vertical subsidence is reached in the centre ofthe affected area. The amount of maximum subsidencedepends on the mining depth and extent. For mining ofthe so-called ”critical area of extraction” the maximumsubsidence∆zMax can be computed from the workingthicknessm and an empirical subsidence factora. Thesubsidence factora is an empirical value for the loos-ening of overlying rock depending on filling and is 0.9for mining with self-filling (without back-filling) for ex-ample [5]. For any pointi on the surface the maximumsubsidence∆zMax will be reduced by a ”factor of ef-fect” e(i) (see eq. 1).

∆z(i) = e(i) ·∆zMax = e(i) · a ·m (1)

There is a delay of the subsidence at the surface with re-spect to the advancing coal face (see fig. 1) [5]. Curve 1shows the temporal subsidence at point P at the earth sur-face above the excavation. The temporally increasing ef-fect of mining on point P relative to the maximum subsi-dence at this point can be seen in curve 2. The differenceof these two curves is the time delay curve. For min-ing induced subsidence the rate of subsidence typicallyincreases initially, while the mining approaches point P,and decreases during the departing phase of the movingcoal head (face). This results in a highly non-linear sub-sidence history.

Fig. 1. The subsidence history of a point P in relation tothe moving coal head (curve 1) and the temporal effect ofmining in terms of the maximum subsidence at the pointP (curve 2). The other curves show the velocity and timedelay of subsidence. [5].

2.1. Calculation of expected subsidence

The calculation of expected subsidence is very importantfor the estimation of potential mining damages andparticularly to determine the extent of subsidence.Furthermore it is interesting with respect to preventingstructure damages prior to mining and reparation after-wards [5]. For the calculation mathematical models arenecessary. These should be described by the correlationbetween the compression of excavation and the groundmovement (cause⇔ effect). The difficulty is the insuffi-cient knowledge about the mechanical properties of therock mass deforming due to mining activities. There aremany methods for calculating expected subsidence [5].

The DSK AG predicts the ground movements (verticaland horizontal displacement, tilt, tension and compres-sion etc.) using the AutoCAD applicationCadBERG[10]. This system is based on a stochastic method con-sidering mining parameters, including the geometry ofthe excavation and the temporal development (see sec-tion 2). The effect of an elementary excavation on a pointat the surface can be described using a transfer function,in this case a Gaussian distribution. The mining block israsterized and a mining depth, the limit angles of the sub-sidence effect and other mining parameters are assignedto each raster element. The dynamics of temporal subsi-dence is included using an e-functionq(t) developed byKnothein 1953:

q(t) = 1− e−c·(t−t0) (2)

The exponential time coefficientc characterizes the prop-agation behavior of the rock mass system in the openingprocess. The dynamic subsidence of a surface point at aparticular time results from the product of eq. 1 and eq.2. The total effect of the mining at the surface is the resultof the sum of the effects of all raster elements.

3. DATA PROCESSING

The measurement of mining induced subsidence wasconducted using the DLR permanent scatterer system[1, 4]. The available ERS scenes, acquired nearly every35 days, were a very good basis for this interferometricanalysis. These radar scenes have perpendicular base-lines from 7 meters to 1037 meters. The steps for thecalculation of differtial interferograms were similar tothose in classical DInSAR processing. All scenes werecoregistered geometrically to a selectedmaster sceneusing an external DEM (SRTM-ERS mosaic, accuracy:2-22m). Subsequently we computed 77 interferograms.The average coherence of most interferograms was verylow with a maximum of 0.31. Vegetation and high rateof subsidence caused severe decorrelations (fig. 2). Theinterferograms were corrected for topography using theexternal DEM. Because of the insignificant topographyin the region of Prosper-Haniel (20-70m), most visiblefringes in the interferograms can be interpreted asmovements of the surface (fig. 2). The fringes indicatedby arrow 1 in the lower frame of fig. 2 are caused bysubsidence within the area of influence of the Prosper-Haniel mine.The permanent scatterers were detected by an analysis ofthe temporal backscattering behavior of point scatterersin calibrated images. The aim of this processing stepwas to find as many scatterers as possible becausea subsidence pattern has to be sampled spatially asdensely as possible [1]. Because of the low density ofPS in the nature preserve above the working area ofthe Prosper-Haniel mine (see fig. 3), we chose a largerarea of estimation to construct a connecting networkon both sides of that region to enable a meaningfulspatial interpolation of subsidence values. The objects,

which were identified as permanent scatterer in thisarea were often industrial buildings, greenhouses andother man-made features with point-like backscatteringcharacteristics.

Fig. 2. The mean radar amplitude of all ERS scenes(above) and the interferogram with a perpendicular base-line of 70 m and a temporal baseline of 175 days (below).The visible fringes were caused by mining induced subsi-dence of the Prosper-Haniel mine (arrow 1) and a neigh-boring hard coal mine (arrow 2).

In general, the next step of PS processing would havebeen the estimation of the parameters at the PS, i.e. thesubsidence rate. But because of the very high rate ofsubsidence in mining a robust estimation of the param-eters was impossible. To circumvent this problem, weintegrated from the CadBERG predictions asdescribedbelow. The next step of PS processing was the temporal

phase unwrapping [3], i.e. the estimation of differencesof DEM errors and the displacement rates in line of sight(LOS) between PS (arcs). Furthermore a least squareadjustment and statistical testing were used to obtain themeasurement values of subsidence rate and DEM errorat the PS. Statistical tests were applied to identify andremove unreliable points and arcs, until a stable solutionfor estimation was reached [4].

Fig. 3. Overlay of the detected permanent scatterers (red)on the intensity image of the working area of the Prosper-Haniel mine.

4. INTEGRATION OF MODEL DATA

The mining caused surface subsidence of serveral meters.For a robust measurement of subsidence using the DIn-SAR method, very frequent radar acquisitions would benecessary. Alternatively radar images recorded by sen-sors with a longer wavelenght than ERS (5.6 cm) couldbe used. But for the available ERS differential interfero-grams a cycle of phase is equivalent to a vertical displace-ment of about 3 cm. For the repeat cycle of ERS of 35days we calculated (using CadBERG) an average maxi-mum subsidence of 23 cm. The radii of the calculatedsubsidence bowls were typically on the order of 1000 m.Furthermore the temporal movement of the points at thesurface is non-linear (see fig. 1), whereas the DLR PSsystem assumes a primarily linear motion. In a recentlydeveloped version an arbitrary base function can be cho-sen, but it proved very difficult to find a sufficiently gen-eral function for the description of mining induced subsi-dence (fig. 4).In this study we used the advantage of stochastical mod-els such as the calculation of expected subsidence withCadBERG. As a recalculation the computations take intoaccount the actual mining and mining geometry.

Fig. 4. The calculation of expected subsidence of a point,near the centre of maximum subsidence caused by themultiply-seam mining of Prosper-Haniel between 1992and 2001.

This model data was calculated dynamically between twosuccessive radar acquisitions with a theoretical time stagefunction for points of a regular grid (25m x 25m) in theGerman Gauss-Krueger projection. The modeled subsi-dence were referenced to the time of the master scene. Inthis way it was possible to simulate theoretical radar in-terferograms with the assumption that coherence equals1 and the differential phase equals the phase of move-ment (deformation). This was realized by common equa-tions of radar interferometry and ERS parameters, see eq.3 with eq. 4. Horizontal displacements were not con-sidered. As a basic principle there maximum is locatedabove the mine working boundary of highest subsidenceand is approximatly 20%-40% of the maximum subsi-dence, i.e. decimeter [8].

φDInSAR =4π

λ·∆rDiff (3)

∆rDiff = ∆z · cos θ (4)

With λ - wavelength,∆rDiff - displacement in LOS,θ - look angle and∆z - vertical displacement (subsi-dence).

The wrapped phase was computed from the unwrappedphase. The comparison between the simulated theoreticalinterferogram and the result of InSAR processing in fig. 5shows a good agreement in terms of the fringe pattern.Above, in the right side of fig. 5 strong decorrelation inthe centre of the basin of subsidence occurs even in the35day interferogram. This is due to the high subsidencegradient. The poor coherence to the left of this area is dueto the existence of vegetation. The higher the temporalbaselines between master and slave scene, the stronger isthe decorrelation of the differential interferograms.

In integrating the model data the accurate geocodingwas very important. We transformed the radar coor-dinates of the PS to the projection of model data, i.e.Gauss-Krueger coordinates. After this we interpolatedthe simulated subsidence (available in a raster of 25 m×25 m) at the geocoded PS positions. Finally, the modeldata at PS positions were converted to phases accordingto eqs. 3 and 4 and subtracted from the differentialinterferometric phases of PS.

Fig. 5. Comparision of geocoded interferogram (35days)(above) and the simulated theoretical differential inter-ferogram (below) for total effected area the Prosper-Haniel mine.

In the result we used model corrected differential phasesto estimate deviations between model data and preciselevelling on benchmarks (reality) using DLR perma-

nent scatterer system. This means that we estimatedthe residues of subsidence, because the high-subsidence(model) were already substraced from differential phases.

5. ANALYSIS METHOD AND EXPECTEDRESULTS

The subsidence estimates were analysed and assessed bycomparing them to the results of precise levelling sur-veys. Since we estimated only the model deviations (be-cause of previous model integration), we compared ourresults with expected model deviations. The basis wasprecise levelling data on benchmarks, which were bilin-early interpolated at the PS positions. Precise levellingwas conducted every two years (1992, 1994, 1996, 1998,2000) by the mining companies. For the comparison withthe PS estimation and computed model data, the preciselevelling data at PS also had to be temporally interpolatedfrom the nearest satellite acquisition times. Here we useda simple linear interpolation. The difference betweenmodel and levelling data at PS for 4 satellite acquisitiontimes referenced to 1992 was equal to expected model de-viations. The expected model deviations showed that thelinear subsidence model was generally valid. As men-tioned before, mining induced subsidence are non-linear.This non-linearity was largely eliminated for most pointsof the estimation by the model integration. The highermodel deviations migth be due to the effects of multiple-seam mining resulting in a higher velocity of subsidencein the investigated panel of the Prosper-Haniel mine. Thiswas not reflected in the input parameters in the calcula-tion by CadBERG. Consequently, the calculation of ex-pected subsidence in this mining panel was too conserva-tive.

6. RESULTS AND DISCUSSION

We estimated a maximum linear subsidence rate (modeldeviation) of 78 mm/year at the PS with the maximumexpected subsidence rate. A good spatial agreement be-tween the estimated and expected results at the PS wasobserved (fig. 6). This indicates a successful PS estima-tion. However fig. 6 also shows an underestimation ofthe expected model deviations of up to 21 mm/year in thearea of investigation. The estimated DEM error at the PSwas less than 20 meters, which is within the accuracy ofthe DEM. Only at very few PS the DEM error was unre-alistically large.

In addition to the linear estimation of model deviationwe analysed the non-linear component of movement.This could be derived from the residual phases at the PS,which were the differences between linearly estimatedphases and the differential phases of DInSAR modulo2π. The residual phases are composed of atmospheric,noise and non-linear motion phase components. The aimof this analysis was the separation of these componentsusing suitable filters. After a phase unwrapping of the

Fig. 6. The comparison between the expected mean(above) and estimated (below) temporal linear model de-viations for the reliable estimated PS in the area of theProsper-Haniel mine

residues, we filtered the total signal, i.e. the sum ofabsolute phase of model data, estimated linear modeldeviation and residues. A small temporal shift of themodeled phases can introduce a high-frequency signalin the total phase. This high-frequence signal can notbe differentiated from atmospheric phase contributions.We eliminated the noise using a small triangle high-passfilter in space, because the atmosphere and the non-linearmovements are correlated either in space. With a smalltriangle low-pass filter in time (35days) we tried todivide atmosphere and noise from the non-linear phasecomponent. A higher filter size would result in theblurring of the times of mining initiations.The overall result of the PS estimation is shown by meansof diagrams of subsidence for a few reliable estimatedPS over the investigation panel of the Prosper-Hanielmine, see PS overview in fig. 7. The results of the PSestimation were added to the substracted model data

at the beginning. As one can see in fig. 8, we couldreached a good accordance between precise levellingand the estimation on this PS. The maximum subsidencedifference between model data and the real measurement(precise levelling) was 12 cm during 1992 and 2000.After the estimation, the maximum difference was only4 cm. The high frequencies of the curve of estimatedsubsidence were the result of the weak filter for non-linear motions in time. The right side of fig. 8 show agood accordance between the expected result and the PSestimation of model deviation. The greater differencesin last times (1998, 2000) could be due to errors in thephase unwrapping of the residues.

Fig. 7. The overview of the mining during 1992-2001 andthe estimated PS in the area of Prosper-Haniel. The anal-ysis of PS estimation was taken along the profiles for thesparse detected PS.

Even if the calculated subsidence was small for a PS,finally we got a good result for PS estimation (seefig. 9a). In comparison to the calculated model data of theProsper-Haniel mine the PS estimation was more precise.A relatively good acquisition of the subsidence was ob-tained in the southern area of the investigated mine panelof Prosper-Haniel (fig. 7, profile A) and in the borderzone of influence of mining. Problems appeared in thecontext of PS with high model deviations. One reasonfor PS estimation errors was an erroneous temporal phaseunwrapping, which could be detected by observations atthe estimated arcs. The different model deviations of twopoints connected by an arc was the reason for this, be-cause the parameters are first estimated for the arcs and

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Fig. 8. Analysis of PS estimation of the profile point A2. The aerial view on the left side shows the object, which wasdetected as PS, mainly due to its the favorable geometry and backscatterer behavior. The first diagram (center) shows thecomparison between the model data, the precise levelling and the PS estimation including the model data. On the rightside, the expected and estimated model deviations are compared.

then integrated to the points. Such differences often ap-peared on tectonic faults (fig. 7), that were not consid-ered in the calculation of the expected subsidence. Anexample for such a phase unwrapping error is illustratedin fig. 9b. Another source of error for the appropriatederivation of subsidence from the PS was a wrong spatialphase unwrapping of the residues and the incomplete sep-aration between atmospheric, noise and non-linear com-ponents of the residues. For example in fig. 9c, the highnoise prevents the successful derivation of subsidence.Nevertheless the trend of estimation corresponded withthe precise levelling data. Biases result from horizon-tal displacements of PS, which were not considered inthe model data integration. An example of this is shownin fig. 9d. The underestimation for this PS as of 1996(∆t=1446 days) suggests the presence of horizontal dis-placements because the point D1 has moved toward theERS sensor against line of sight (fig. 7). Fig. 7 illustratesthe assumed horizontal directions of few PS. Given theradar aquisition geometry the vertical underestimation of9 cm for 2000 at the point D1 corresponds to a minimumhorizontal movement of 21 cm. This is realistic for a min-ing induced subsidence of 92 cm during 1992-2000. Theprofile B in fig. 10 clarifies the effect of horizontal dis-placements on PS estimation. Because of the increase inhorizontal movements in direction of the working bound-ary of mining there was an increasing of underestimationof the real subsidence using the PS system (see fig. 7).The opposite effect is shown of point B3. There is noconsideration of data from 1993, because of inaccuratetemporal interpolation from precise levelling for this year.

7. CONCLUSIONS

The most important limiting factors for the derivation ofmining induced subsidence using the PS technique are thetypically high rate of subsidence and the low density ofdetected permanent scatterers. Nevertheless, this studyhas shown that the estimation of this subsidence usingPS technique can be feasible by integrating model data.Depending on the density of PS there was a good spa-tial differentiation of area influenced by mining or ratherthe area of model deviations. The PS estimation was not

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Fig. 10. Comparison between the subsidence derivedfrom precise levelling and the PS estimation inclusing themodel data along the profile B in reference to 1992.

possible in some areas with vegetation, e.g. in the Kirch-heller Heide, because of a lack of detected PS. Despirethe poor coherence of the differential interferograms andfew visible fringes we could estimate the subsidence onPS for a large time span of 8.5 years. We improved theagreement between the subsidence measured by preciselevelling and the model-estimated results. A quantita-tive specification of accuracy in terms of the derivation ofmining induced subsidence using PS technique is not pos-sible, because of the complexity of the errors. But herewe have tried to show the limitations of the PS method inmining applications by discussing the errors. Under idealconditions, i.e. a high density of detected PS and the in-tegration of model data with higher accuracy, should beable to detect mining induced subsidence with an accu-racy of millimeters or centimeters. A prerequisite for thisis the successful separation of the residual phase compo-nents.Future research should integrate calculations of expectedhorizontal displacements. Furthermore to increase the ac-curacy of the model data, the parameters of the calcula-tion of expected subsidence should reflect for examplethe frequency of extraction in the mining.The application of the PS method in mining regions withmost favorable conditions for the interferometric analysisof subsidence, for example with less vegetation, wouldlead to better results. Mainly we expect a better utili-sation of PS technique in urban areas with undergroundmining for example in other underground hard coal minesof the Ruhr region in Germany, because of the detectionof more PS. In the future it is imaginable to use radar in-terferometric analysis with PS technique in combinationwith the current monitoring for the observation of min-ing induced subsidence. A higher temporal and spatialresolution can be achieved for observations with a higherdensity of permanent scatterers. The integration of themodel calculation in the PS system can also be a inter-esting topic for future studies. This might enable newinsights into rock behaviour or the location of faults.

REFERENCES

[1] N. Adam, B. Kampes, Eineder M., J. Worawattana-mateekul, and M. Kircher. The development ofscientific permanent scatterer system. InProc. IS-PRS Joint Workshop on ”High Resolution Mappingfrom Space” 2003, Hannover, Germany, 6-8 Octo-ber, 2003.

[2] A. Ferretti, C. Prati, and F. Rocca. Permanent scat-terers in SAR interferometry.IEEE Transaction onGeoscience and Remote Sensing, 39(1):8–20, 2001.

[3] R. F. Hanssen. Radar Interferometry - Data in-terpretation and error analysis. Kluwer AcademicPublishers, Dordrecht, Netherlands, 2001.

[4] B. Kampes and N. Adam. Velocity field retrievalfrom long term coherent points in radar interfero-metric stacks. InProc. IGARSS 2003, Toulouse,France, 21-25 July, 2003.

[5] H. Kratzsch. Bergschadenkunde. DeutscherMarkscheider-Verein e.V., Bochum, Germany,1997.

[6] K. Lehmann. Bewegungsvorgaenge bei der Bildungvon Pingen und Troegen.Glueckauf, 20, 1919.

[7] V. Spreckels, U. Wegmueller, T. Strozzi, J. Musied-lak, and H.-C. Wichlacz. Detection and observationof underground coal mining-induced surface defor-mation with differential SAR interferometry. InProc. ISPRS Joint Workshop on ”High ResolutionMapping from Space” 2001, Hannover, Germany,19-21 September, pages 227–234, 2001.

[8] A. Streerath. Analyse und Modellierung gross-raeumiger bergbaubedingter Senkungen aus pho-togrammetrischen Beobachtungen. Ph.D. thesis,TU Clausthal, Germany, 2000.

[9] D. Walter. Untersuchung der vom untertaegigenBergbau induzierten Senkungen unter Verwendungder Permanent Scatterer Technik als Methode derdifferentiellen SAR Interferometrie. diploma thesis,Department of Mine Surveying and Geodesy, Uni-versity of Mining and Technology, Freiberg, Ger-many, 2004.

[10] R. Wieland. CadBERG - Eine kurze Einfuehrungueber das Verfahren zur Vorausberechnung vonGebirgs- und Bodenbewegungen, 2001. User man-ual: CadBERG.

[11] H. A. Zebker and J. Villasenor. Decorrelation in in-terferometric radar echoes.IEEE Transaction onGeoscience and Remote Sensing, 30(5):950–959,1992.

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