The SISTEM method. LOS ascending

Transcription

1 The SISTEM method Simltaneos and Integrated Strain Tensor Estimation from geodetic and satellite deformation Measrements A new global approach to obtain three-dimensional displacement maps by integrating GPS and DInSAR data GPS data LOS ascending 3D Displacement vectors F Gglielmino, G nnari, G Pglisi, A Spata Istitto azionale di Geofisica e Vlcanologia Sez di Catania, Italy Department of Electrical, Electronic and System Engineering, University of Catania, Italy

2 Grond deformation monitoring Global Positioning System DInSAR data Low temporal resoltion Spatial distribted D (Line of Sight Goal: to take advantage of their complementary natre High temporal resoltion Pntal measre 3D

3 + Grond Deformation Map Over the Whole Intestigated Area

4 The concept of the integration of GPS and DInSAR data to obtain 3D grond deformation maps GPS measrements GPS data 3D grond deformation map D Displacement vectors DInSAR data LOS ascending

5 Two different methodologies have been proposed by: Gdmndsson et al (, Three-dimensional srface motion maps estimated from combined Interferometric synthetic apertre radar and GPS data Jornal of Geophysical Reseach Samsonov, Tiampo et al (6, Analytical Optimization of a DInSAR and GPS Dataset for Derivation of Three-Dimensional Srface Motion IEEE Geoscience and Remote Sensing Letters

6 Gdmndsson et al ( GPS data DInSAR Data Kriging Interpolation Interpolated GPS data Random Markow Field Theory Simlated Annealing Optimization 3D Srface Motion Map Samsonov, Tiampo et al (6 GPS data DInSAR Data Kriging Interpolation Interpolated GPS data Analytical Optimization 3D Srface Motion Map Gglielmino, nnari, Pglisi, Spata (9 sbmitted to IEEE GPS data DInSAR Data Weighted Least Sqares Method 3D Srface Motion Map

7 Kriging Interpolation and Variogram model The method we propose does not reqire a preventive interpolation of the GPS points, sally performed throgh kriging algorithm, ths avoiding the choice of a theoretical semivariogram, which is one of the main critical points in geostatistics This choice, which is sally performed by spervising a preliminary statistic analysis of the eperimental data, strongly affects the final reslt Every components needs an appropriately choosen variogram model

8 Small Deformation Theory Let o (,, 3 the position of an arbitrary point P srronded by points whose position and displacements are respectively (n ( (n, (n, 3(n and (n ( (n, (n, 3(n In a linear approach the small motions arond a point P can be modelled by the eqations: i( n H ij j( n + Ui ( i, j 3 P P Displacement gradient ji H ij Eij + Ω ij i j Relative position j( n j( n j P 6 P 5? P 3 P 4 Strain tensor E ij ( H ij + H ji e i e j Rigid body rotation tensor Ω ω ij ( H ij H ji e i e j ω3 ω ω ω 3 ω ω

9 Small Deformation Theory In a compact form the system of eqation can be written as: Design Matri i( n H ij j( n + Ui ( i, j 3 Al + e A ( ( Unknown parameters l ( ( ( ( ( ( 3( 3( ( ( ( ( 3( 3( 3( 3( ( ( ( ( [ U U U ω ω 3 ω 3 ] Observation vectors [ ( ( 3( ( ( 3( ( ( 3( 3( ( 3( ( 3( ( 3( ( } } ] T T First GPS point Last GPS Point

10 In a compact form the system of eqation can be written as: i( n H ij j( n + Ui ( i, j 3 Al + e Weighted Least Sqares approach l ( A T WA A T W Weigh Matri W is the inverse of the data covariance matri

11 Can we enter the DInSAR data in the small deformation system eqations? A DInSAR interferogram can be related to the components U, U and U 3 of the displacement vector of an arbitrary point P according to the following eqation: D P P P P S U + S U + LOS y S z U 3 where D LOS is the LOS displacements, at the point P on the Earth s srface and V[S S y S z ] is a nit vector pointing from the point P toward the satellite

12 ] [ P z P y P S S S S l S D p LOS T U U U l [ 3] ω ω ω t losi D ] [ 3( ( ( 3( ( ( 3( ( ( ( ( 3( ( ( ( 3( 3( ( ( ( 3( 3( ( ( ( ( 3( ( ( ( 3( 3( ( ( ( 3( 3( ( ( P z P y P S S S A 3 U S U S U S D P z P y P p LOS + + SISTEM Approach Simltaneos and Integrated Strain Tensor Estimation from Geodetic and satellite deformation Measrements W A WA A l T T ( e Al +

13 We emphasize that the SISTEM method is a point-wise oriented approach This means that, at the nknown point P, SISTEM solves the WLS problem by taking into accont the srronding GPS points and only the DInSAR data coincident with the point P Therefore, the spatial correlation of DInSAR data is not taken into accont The variance of DInSAR data points was estimated directly from the interferogram by sing a sample semi-variogram γ(h c (Chiles and Delfiner 999, Sdhas and Jonsson, 8 γ ( hc i [ ] d( r d( s i i where h c is a classified separation distance

14 Scaling Fnction According to the modified least sqares (MLS approach proposed by Shen et al (996, based on the adjstment of the matri W, we se the matri W I which is a weighted version of the matri W Following the sggestion of literatre [Teza et al, 7, Shen et al 996] the weight fnction considered here is: W W I ij ij f ( d / do f ( d / d ep( d / d d is the level of locality of the estimation Shen, 996, Crstal deformation across and beyond the Los Angeles basin from geodetic measrements, Jornal of Geophysical Research Locality Effects Only the point closer than abot d to P give a significant contribtion to the strain estimate on P The niform distribtion of the strain is reqired only in a neighborhood of each comptation point For points P far away from GPS measmerent the DInSAR data becomes the dominant information sorce

15 In this method, the only parameter that needs to be appropriately chosen is the parameter d in order to define the level of locality of the estimation As sggested by Pesci and Teza (7 we have related d with the mean inter-distance between neighbor stations In particlar let be the nmber of EPs point of the network and K i be the set of M nearest stations to the i station We propose the following empirical formla to evalate d : P P d M i j K i d ij P 6 P 3 P 5 P 4 The optimal vale of M depends on the topology of the network; based on several trials, we have empirically fond that for random configrations M ranges between 4 and 6

16 Application of SISTEM: A synthetic case stdy ( ( ( w y e z y z /, + Synthetic topography Point pressre sorce (Mogi sorce 3/ 3 ( 4 3 d f d P a + μ 3/ 3 ( 4 3 d f f P a z + μ μ3 GPa f5m a 3 P 7 Pa*m 3

17 (a, (b, (c,(d : East, orth, Up and LOS components of the displacement field generated on the synthetic topography sing the Mogi sorce (e, (f, (g,(h: the three displacements components and the projected LOS calclated by the proposed GPS InSAR integration method (i, (l, (m,(n: residals of the east, north and p component respectively (o, (p, (q,(r: normalized histograms of the corresponding residals errors, the mean vale and standard deviation A hge nmber of eperiments performed allows to point ot that the error distribtion depends on the spatial distribtion of the GPS point In particlar it was fond that the best performance are obtained when a reglar grid of GPS point is considered Instead, if a randomly generated distribtion of GPS point is considered the error distribtion may reslt biased

18 (a dilatation; (b differential rotation magnitde; (c maimm shear strain Error as a fnction of the nmber of EP Locality parameter considered How it was epected accracy increase with larger nmber of GPS points However it can be appreciated that there are not sensible advantages in sing a nmber of GPS point greater than 5-6 (see the platea Frthermore the best accracy is achieved for the vertical component; this was an epected reslts which can be eplained bearing in mind that the DInSAR images have an average vertical directional cosine of abot 9 and therefore is particlar sensitive to vertical movements

19 Application of SISTEM: the Mt Etna 3-4 case stdy This GPS dataset shows a significant inflation affecting the western and pper flanks, with a maimm of abot 5 cm located on the pper sothern flank, copled with an eastward movement of the benchmarks located on the eastern flank of the volcano An appropriate pair of ascending ERS SAR images was selected; they refer to the Agst 3 to 3 Jne 4 interval and have a 7 m of perpendiclar baseline Interferogram was processed sing the Jet Proplsion Laboratories (JPLs/Caltech Repeat Orbit Interferometry Package (ROI_PAC, version 3

20 The East component map show an evident displacement of the eastern flank The most evident vertical movement (plift is localized in the smmit western area according to a recharging phase of the plmbing system of the volcano dring the investigated period [Bonaccorso et al 6] The error maps of the horizontal components have similar patterns and show smallest error (bl area where dense GPS coverage is achieved The errors of the vertical component have a lower magnitde with respect to horizontal errors

21 RMSE East orth Up GPS points RMSE (in mm between the SISTEM otpt and the GPS data calclated at the GPS site locations as a fnction of the nmber of GPS stations Discrepancy relevant to the East, orth and Vertical components respectively, compted for the whole network configration (ie 5 GP stations SISTEM GPS stations 6 4 SISTEM GPS stations 6 4 SISTEM GPS stations 8 East (mm 6 4 orth - Up GPS stations GPS stations GPS stations

22 SISTEM Applications 3D clstering analysis performed by the Kohonen maps This analysis was aimed to partition the whole displacement field into sbsets sharing some common displacements featres in order to recognize and classify deformation patterns affecting different sectors of Etna volcano 4,96, 4,94, 4,9, 4,9, 4,88, 4,86, 4,84, 4,8, 4,8, 4,78, 4,76, 4,74, 4,7, 4,7, 4,68, 4,66, 4,64, 4,6, 4,6, 4,58, 4,56, 4,54, 4,5, 48, 485, 49, 495, 5, 55, 5, 55, 5, Abrzzo Earthqake case stdy: GPS, ALOS (ascending, EVISAT(ascending and descending + + +

23 Conclsions GPS and DInSAR integration based on small deformation theory GPS and DInSAR data are simltaneos integrated withot the preliminary step of the Kriging interpolation Prodcts: Deformation field and relevant standard errors Strain tensor and relevant standard errors Rigid body rotation tensor and relevant standard errors The proposed method was applied on the Mt Etna area where the GPS network well cover the area and freqent SAR passes are available