Combining InSAR, Levelling and GNSS for the Estimation of 3D Surface Displacements

Combining InSAR, Levelling and GNSS for the Estimation of 3D Surface Displacements Thomas Fuhrmann (1), Miguel Caro Cuenca (2), Freek van Leijen (3), Malte Westerhaus (1), Ramon Hanssen (3), Bernhard Heck (1) (1) Karlsruhe Institute of Technology, (2) Netherlands Organisation for Applied Scientific Research (TNO), (3) Delft University of Technology 0 Introduction Database Combination Results KIT University of the State of Baden-Wuerttemberg and www.kit.edu National T. Fuhrmann Research Center et al. of thecombining Helmholtz Association InSAR, Levelling and GNSS Fringe Workshop 2015, Frascati March 24, 2015

Motivation Major drawbacks of SAR-Interferometry 1-dimensional measurements along the LOS direction Decomposition into horizontal and vertical components not possible Accuracy of estimated displacement/rate not easily accessible (filtering) Results relative to a reference point/area 1 Introduction Database Combination Results

Research objectives GNSS Levelling InSAR 3D velocity field Derivation of horizontal and vertical surface displacements Robust combination of InSAR, levelling and GNSS Focus on linear movements (displacement rates) Realistic information on the accuracies of the estimates Area of interest: Upper Rhine Graben 2 Introduction Database Combination Results

Upper Rhine Graben Most prominent segment of the Cenozoic rift system Significant probability for large earthquakes 3 Introduction Database Combination Results

Upper Rhine Graben Most prominent segment of the Cenozoic rift system Significant probability for large earthquakes Basel 1356: M W = 6.7 7.1 (Fäh et al., 2009) 3 Introduction Database Combination Results

Upper Rhine Graben Most prominent segment of the Cenozoic rift system Significant probability for large earthquakes Mahlberg 1728: M W = 5.3 (Meidow, 1998) Basel 1356: M W = 6.7 7.1 (Fäh et al., 2009) 3 Introduction Database Combination Results

Upper Rhine Graben Most prominent segment of the Cenozoic rift system Significant probability for large earthquakes Mahlberg 1728: M W = 5.3 (Meidow, 1998) Waldkirch 2004: M W = 4.6 (Häge et al., 2009) Basel 1356: M W = 6.7 7.1 (Fäh et al., 2009) 3 Introduction Database Combination Results

Upper Rhine Graben Most prominent segment of the Cenozoic rift system Significant probability for large earthquakes Tectonic motion: Small (< 1mm/a), but still not well constrained from Geodesy Mahlberg 1728: M W = 5.3 (Meidow, 1998) Waldkirch 2004: M W = 4.6 (Häge et al., 2009) Basel 1356: M W = 6.7 7.1 (Fäh et al., 2009) 3 Introduction Database Combination Results

Database 3 Introduction Database Combination Results

Properties of the techniques Spatial distribution: InSAR: high in urban areas Levelling: high along lines GNSS: low (30 40 km) Temporal distribution: InSAR: 35 days Levelling: campaigns ( 20a) GNSS: permanent (daily) InSAR desc. InSAR asc. Temporal coverage, representative example GPS Levelling 1940 1950 1960 1970 1980 1990 2000 2010 Year 4 Introduction Database Combination Results

Single technique analysis InSAR: PS analysis using StaMPS (Hooper et al., JGR 2007) Data: 2 ascending, 1 descending track; ERS-1/2, Envisat Result: LOS displacement w.r.t. a master scene and a reference area Levelling: Kinematic adjustment of repeatedly measured levelling data Data: 40049 height differences at 15592 levelling benchmarks Result: Linear displacement rates (vertical) w.r.t. a reference point GNSS: Differential processing using Bernese GPS software (Dach et al., 2007) Data: GPS observations, daily coordinates at 76 sites Result: Linear displacement rates (horizontal) w.r.t. ITRF05 (block mean subtracted) 5 Introduction Database Combination Results

Combination approach PS interpolation @ levelling / GNSS locations Interferograms 1,2,...,n ------------------------------- ERS ascending ERS descending Envisat ascending Envisat descending PS interpolation @ PS grid Estimation of linear velocities Using time series of ERS/Envisat ------------------------------- ascending descending Estimation of linear velocities Interpolation of levelling velocities @ PS grid Interpolation of GNSS velocities @ PS grid Calculation of Up / East component Step 1 Step 2 Estimation of offset and trend (Up / East) Estimation of East, North and Up components 6 Introduction Database Combination Results

Combination approach PS interpolation @ levelling / GNSS locations Estimation of linear velocities Interferograms 1,2,...,n ------------------------------- ERS ascending ERS descending Envisat ascending Envisat descending Using time series of ERS/Envisat ------------------------------- ascending descending PS interpolation @ PS grid Joint ERS/Envisat Interpolation displacement Interpolation Estimation of levelling of time linear series (Caro Cuenca et al., 2010) of GNSS velocities velocities velocities @ PS grid @ PS grid Calculation of Up / East component Step 1 Step 2 Estimation of offset and trend (Up / East) Estimation of East, North and Up components 6 Introduction Database Combination Results

Combination approach PS interpolation @ levelling / GNSS locations Estimation of linear velocities Interferograms 1,2,...,n ------------------------------- ERS ascending ERS descending Envisat ascending Envisat descending Using time series of ERS/Envisat ------------------------------- ascending descending PS interpolation @ PS grid Joint ERS/Envisat Interpolation displacement Interpolation Estimation of levelling of time linear series (Caro Cuenca et al., 2010) of GNSS velocities velocities velocities @ PS grid @ PS grid Calculation of Up / East component Step 1 Step 2 Estimation of offset and trend (Up / East) Estimation of Different reference East, North frames Residual atmospheric/orbit and Up effects Validation ofcomponents InSAR results 6 Introduction Database Combination Results

Interpolation of PS points (using Kriging) Step 1: At location of levelling/gnss points Step 2: At a 200 m grid (only in vicinity of PS points) 7 Introduction Database Combination Results

Interpolation of PS points (using Kriging) Step 1: At location of levelling/gnss points Step 2: At a 200 m grid (only in vicinity of PS points) for every Ifg 7 Introduction Database Combination Results

Linear velocities from PS time series y A,1 ta,1 3 t 2 A,1 t A,1 1 0...... x 3 y A,NA ta,n 3 t y B,1 = A A,N 2 t A,NA 1 0 A x 2 t B,1 3 tb,1 2 t B,1 1 1 x 1 + x. 0 e x..... y B,NB tb,n 3 t 2 B B,N t B,NB 1 1 B y A,i : Displacement in interferogram i, sensor A (ERS) y B,i : Displacement in interferogram i, sensor B (Envisat) N A : Number of interferograms of sensor A N B : Number of interferograms of sensor B t A : Acquisition time of sensor A t B : Acquisition time of sensor B x 0, x 1, x 2, x 3 : Parameters of a polynomial function x : Offset between sensor A and sensor B s 8 Introduction Database Combination Results

Linear velocities from PS time series y A,1 ta,1 3 t 2 A,1 t A,1 1 0...... x 3 y A,NA ta,n 3 t y B,1 = A A,N 2 t A,NA 1 0 A x 2 t B,1 3 tb,1 2 t B,1 1 1 x 1 + x. 0 e x..... y B,NB tb,n 3 t 2 B B,N t B,NB 1 1 B mm mm 20 10 0 10 20 1992 1994 1996 1998 2000 2002 Year 20 Envisat 10 0 ERS y A,i : Displacement in interferogram i, sensor A (ERS) y B,i : Displacement in interferogram i, sensor B (Envisat) N A : Number of interferograms of sensor A N B : Number of interferograms of sensor B t A : Acquisition time of sensor A t B : Acquisition time of sensor B x 0, x 1, x 2, x 3 : Parameters of a polynomial function s x : Offset between sensor A and sensor B 8 Introduction Database Combination Results 10 20 2002 2004 2006 2008 2010 2012 Year

Linear velocities from PS time series y A,1 ta,1 3 t 2 A,1 t A,1 1 0 0...... x 10 3 y A,NA ta,n 3 t y B,1 = A A,N 2 t A,NA 1 0 A x 2 20 t B,1 3 tb,1 2 t B,1 1 1 x 1 + x. 0 e 1992 1994 1996 1998 2000 2002 Year 20 Envisat x..... 10 y B,NB tb,n 3 t 2 B B,N t B,NB 1 1 B mm mm 20 10 0 10 ERS 10 0 ERS Envisat 20 2002 2004 2006 2008 2010 2012 Year mm 10 s 20 1st order (linear) 30 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Year 8 Introduction Database Combination Results

Linear velocities from PS time series mm s y A,1 ta,1 3 t 2 A,1 t A,1 1 0 0...... x 10 3 y A,NA ta,n 3 t y B,1 = A A,N 2 t A,NA 1 0 A x 2 20 t B,1 3 tb,1 2 t B,1 1 1 x 1 + x. 0 e 1992 1994 1996 1998 2000 2002 Year 20 Envisat x..... 10 y B,NB tb,n 3 t 2 B B,N t B,NB 1 1 B 10 0 10 1st order (linear) 20 2nd order 3rd order 30 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Year 8 Introduction Database Combination Results mm mm ERS Envisat 20 10 0 10 ERS 20 2002 2004 2006 2008 2010 2012 Year Statistical test on linearity

Linear velocities from PS time series Temporal covariance matrix for the estimation: 6 10 20 30 40 5 4 3 [mm 2 ] 54 ERS Interferograms 17 Envisat Interferograms 50 2 60 1 70 0 10 20 30 40 50 60 70 8 Introduction Database Combination Results s

Linear velocities from PS time series Temporal covariance matrix for the estimation: 6 10 20 30 40 5 4 3 [mm 2 ] 54 ERS Interferograms 17 Envisat Interferograms 50 60 70 10 20 30 40 50 60 70 8 Introduction Database Combination Results 2 1 0 Correlation length from atmospheric filtering Variances q ii scaled w.r.t. relative Ifg and PS accuracy s

Linear velocities from PS time series mm mm 20 10 0 10 20 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Year 20 10 0 10 20 ERS/Envisat combination: Accurate estimates for linear rates asc desc 9 Introduction Database Combination Results ERS Envisat ERS Envisat 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Year

Linear velocities from PS time series mm mm 20 10 0 10 20 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Year 20 10 0 10 20 Separation of non-linear movements asc desc 9 Introduction Database Combination Results ERS Envisat ERS Envisat 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Year

Linear velocities from PS time series LOS velocities (desc) 9 Introduction Database Combination Results

Linear velocities from PS time series LOS velocities (desc) + non-linear grid points 9 Introduction Database Combination Results

Interpolation of levelling and GPS velocities 10 Introduction Database Combination Results

Interpolation of levelling and GPS velocities Standard dev. 10 Introduction Database Combination Results

Interpolation of levelling and GPS velocities Standard dev. High weight close to the data points Low weight in between 10 Introduction Database Combination Results

Mathematical fusion Using least squares adjustment: y = Ax + e y : Velocities from InSAR (asc and desc), GPS (East and North comp.) and levelling x : Velocities in East, North, Up V asc S asc,1 S asc,2 S asc,3 V desc V GPS,E = S desc,1 S desc,2 S desc,3 v E 1 0 0 v N + e V GPS,N 0 1 0 v U V lev 0 0 1 sin θ asc cos α asc S asc = sin θ asc sin α asc cos θ asc sin θ desc cos α desc S desc = sin θ desc sin α desc cos θ desc 11 Introduction Database Combination Results

Mathematical fusion Using least squares adjustment: y = Ax + e y : Velocities from InSAR (asc and desc), GPS (East and North comp.) and levelling x : Velocities in East, North, Up V asc S asc,1 S asc,2 S asc,3 V desc V GPS,E = S desc,1 S desc,2 S desc,3 v E 1 0 0 v N + e V GPS,N 0 1 0 v U V lev 0 0 1 σ 2 V asc 0 0 0 0 0 σv 2 0 0 0 desc Q yy = 0 0 σv 2 σ VGPS,E,N 0 GPS,E 0 0 σ VGPS,E,N σv 2 0 GPS,N 0 0 0 0 σ 2 V lev sin θ asc cos α asc S asc = sin θ asc sin α asc cos θ asc sin θ desc cos α desc S desc = sin θ desc sin α desc cos θ desc Covariance matrix using standard deviations of single technique estimates 11 Introduction Database Combination Results

Results Two test areas: Northern part, Southern part 3D velocity field Standard deviations 12 Introduction Database Combination Results

Results Northern Upper Rhine Graben 13 Introduction Database Combination Results

Results Northern Upper Rhine Graben Mean standard deviation Up: 0.10 mm/a 13 Introduction Database Combination Results

Results Northern Upper Rhine Graben 13 Introduction Database Combination Results

Results Northern Upper Rhine Graben Mean standard deviation East: 0.20 mm/a North: 0.24 mm/a 13 Introduction Database Combination Results

Results Southern Upper Rhine Graben 14 Introduction Database Combination Results

Results Southern Upper Rhine Graben Mean standard deviation Up: 0.12 mm/a 14 Introduction Database Combination Results

Results Southern Upper Rhine Graben 14 Introduction Database Combination Results

Results Southern Upper Rhine Graben Mean standard deviation East: 0.30 mm/a North: 0.36 mm/a 14 Introduction Database Combination Results

Conclusions Consistent approach to combine velocities from Different SAR sensors (ERS, Envisat) Different SAR tracks (asc, desc) Permanent GNSS sites Repeated levelling measurements Consideration of realistic covariance information Results for two test areas in the URG: Tectonic movements are well below 1.0 mm/a Standard deviations: 0.3 mm/a (horizontal) / 0.1 mm/a (vertical) Next steps: Combined velocity solution for the whole URG area (300 km SAR stripes) Special cases: Overlapping SAR tracks, only ascending/descending 15 Introduction Database Combination Results