Estimating crustal deformations using GNSS. Riccardo Barzaghi DICA-Politecnico di Milano

Transcription

1 Estimating crustal deformations using GNSS Riccardo Barzaghi DICA-Politecnico di Milano

2 GNSS non-permanent campaigns The local campaigns require a dense GNSS network in a quite small area a careful distribution of the GNSS sites in the studied area a stable monumentation of the GNSS sites a significant observation window Three test areas the GNSS networks have been monumented in three seismic areas several GNSS campaigns have been already performed two different earthquake cycles: inter-seismic and post-seismic phases

3 The three test areas

4 The antenna mounting device

5 The available campaigns The observation scheme 10 points monumented in each test area 4 days campaigns at least 8 hours/day some points have continuous 4 day observations data analysis using the Bernese software Area Tot. Colfiorito X X X X X 5 Pollino X X X X X X 6 Gemona del Friuli X X X X X 5

6 The processing steps 1 Step: estimation of GNSS solutions: GAMIT/GLOBK and Bernese 2 Step: linear parameter estimations (velocity displacements) by least square adjustment 3 Step: Common Mode Error reduction (Widowinski et al., 1997) 4 Step: unique solution for each campaign 5 Step: velocity re-estimations by least square adjustment The critical point It is difficult to take into account time series discontinuities (e.g. antenna change, Reference Frame residual, co-seismic event)

7 The Umbria-Marche non-permanent network (post-seismic deformation) The network consists of 10 points (only the 6 points belonging to transept A are plotted) and has been measured five times ( )

8 Displacements in the Umbria-Marche area (post-seismic deformation)

9 The baselines lenght variation (post-seismic phase) [Aoudia A., Borghi A., Barzaghi R., Riva R., Sabadini R., Ambrosius B.A.C., Vermeersen L.L.A., Panza G.F. (2003): Postseismic deformation following the 1997 Umbria-Marche (Italy) moderate normal faulting earthquakes. Geophysical Research Letters, vol.30, n.7, ] 9

10 Antenna change + relative PCV (z) absolute PCV(a,z) 10

11 The Castrovillari (CS) non-permanent network (inter-seismic phase) The network consists of 10 points and has been measured six times ( )

12 Some results in the Pollino area The pattern is in good agreement with the model presented by Cinti et al. (Journal of Seismology, 2002) Slip rate over the Castrovillari fault from the inversion of GNSS velocities. Mean strain-rates from GNSS surveying, at the ten sites in the Pollino Range. The thin grey lines indicate the Castrovillari fault scarps (Cinti et al. 2002)

13 GNSS permanent stations for crustal deformation analysis The RING GNSS network (INGV) The seismicity in Italy

14 The GAIN network in the Alpine area The FReDNet network (OGS)

15 Permanent station monuments Monument Type Characteristics Rebar Reinforced Concrete Pillar Long Term Survivability, Good for non-bedrock installations, Low cost C Bar Reinforced Concrete Pillar Long Term Survivability, Good for non-bedrock installations, Low cost Short Drilled Braced Good for remote bedrock installations, Long Term Survivability, Low cost Deep Drilled Braced Good for bedrock and nonbedrock installations, High cost Stainless Steel GPS Pedestal, Long Term Stability Minimal effects from solar radiant heating INVAR rod encased in concrete Low thermal expansion Low Multipath Good Stability The UNAVCO guidelines (

16 GNSS coordinate time series data processing 1 Step: outliers rejection and analysis of known discontinuities : instrument changes (i.e. GNSS antennas) Reference Frames changes possible co-seismic effects 2 Step: least square fitting with a suitable functional model 3 Step: generalised KPSS test on residuals for assessing possible stationary behaviour 4 Step: account of coordinate time series correlations Stationary residuals Estimate of the Empirical Covariance Function Non-stationary residuals White Noise + Flicker Noise model (Williams, S.D.P., 2003) 5 Step: functional model parameters re-estimations by least square adjustment applying the proper stochastic model

17 The functional model for GPS time series analysis y i a bt i m 0 Amcos mti Bmsen mti m 0 C yy = diag( C yy ) j k 1 H( t i T k ) g k i H(t i -T k ) is the Heaviside function, which equals 1 for t i > T k g k are the amplitude of any offset due to co-seismic events, Reference System, GNSS Antenna/Receiver changes The frequencies f m and their maximum number m 0 are chosen among the most significant Lomb s periodogram peaks.

18 The stochastic model for GNSS time series analysis y i a bt i m 0 Amcos mti Bmsen mti m 0 j k 1 H( t i T k ) g k i Stationary residuals: C yy = é ù ë Ĉyyû Residuals m Empirical covariance Model covariance function Non-stationary residuals: C yy 2 w I 2 f Q f (Williams, S.D.P., 2003)

19 Final parameter estimates y i a bt i m 0 Amcos mti Bmsen mti j H( t i T k ) g k i m 0 k 1 C yy = é ù ë Ĉyyû or C yy 2 w I 2 f Q f Stochastic model North East Up AMUR GPS Permanent station Velocity estimate under in-correlation hypothesis / / / Velocity estimate by ECF / / /- 0.59

20 U E N aqui: vel= / (mm/yr) day aqui: vel= / (mm/yr) day aqui: vel= / (mm/yr) day

21 Residuals filtering for estimating transient phenomena 1) In case of stationary residuals, the collocation filtering method can be applied e(t i ) = s(t i )+n(t i ) ŝ(t) = N å i,k=1 C( t - t k ) C +s 2-1 é ë 0 Iù e(ti ûki ) C is the covariance function of the signal s(t) which is estimated using the sampled data ε(t) The linear estimator DOES NOT give the observed values in t j and,in the observation points, the noise can be estimated ˆn(t k ) = e(t k ) - ŝ(t k ) = e(t k ) - é ë I +s 2 n C -1-1 ù e(ti ûki ) N å i=1

22 2) Low-pass filtering of the collocation filtered values with kriging moving average N å ˆm = w i ŝ(t i ) i=1 the N values are selected in a window which is shaped on the correlation length of the covariance function C of. The estimator is obtained by solving the system of equations (η is the Lagrange multiplier) ŝ(t) ì ï ï í ï ï î N å j=1 w j C(t i - t j ) -h = 0 N å j=1 w j -1= 0 i=1,,n

23 (m) (m) Post-fit residuals filtering time time

24 The L Aquila area

25 The strain pattern on March 13th, 2009 (before the L Aquila earthquake - April 6th, 2009)

26 The FReDNet test The (13 red) stations of the FReDNet network have been analysed following the described procedure (we acknowledge Dr. David Zuliani from OGS for providing us with the data)

27 An example of post-fit residuals: the JOAN station North East days days Up days

28 Two examples of filtered residuals residuals collocation kriging days residuals collocation kriging days

29 The PCA on the kriging filtered time series The Principal Component Analysis (PCA) can be used for finding possible spatial correlated behaviours. It is based on the SVD of the matrix (in each component) é ê êê ˆm 1 k (t 1 ) ˆm 2 k (t 1 ).. ˆm p k (t 1 ) ˆm 1 k (t 2 ) ˆm 2 k (t 2 ).. ˆm p k (t 2 ) ù ú úú é ê êê k x 11 k x 21 k x 12 k x 22 k.. x 1p k.. x 2 p ù ú úú X k = ê êê ê ê ë ˆm k 1 (t N ) ˆm k 2 (t N ).. ˆm k p (t N ) ú = ê úú êê ú ê ú ê û ë k x N1 k x N 2 k.. x Np ú úú ú ú û k=component index (East or North) p=number of stations involved in the analysis The smoothed signal can be suitably analysed while the original residuals are too noisy

30 Given the SVD decomposition of X X k =ULV t where U and V are suitable orthogonal matrices and L is a diagonal matrix having a dimension equal to the rank r of X. The columns of U and V are called left and right singular vectors for X and the diagonal elements in L are called singular values of X Thus x ij = r å m=1 u im l m v jm and one can approximate x ij by considering only the first L<r singular values

31 The singular values of X E and X N East North The first singular value is remarkably larger than the remaining values (particularly in the North component)

32 The signal approximation using only the first singular value (in both components) North CANV East days The signals in any other station is not properly reproduced (not even using the first two singular values - see e.g. the NOVE station below) NOVE days North East days days The CANV signal is a local effect related to groundwater storage in the Cansiglio plateau area (Devoti et al., 2015)

33 The singular values of X E and X N without CANV East North

34 There are no sharp differences among the singular values and the filtered signals based on the first larger singular values don t cluster so clearly in a specific area. There are however some (weak) indications of a better fit between signals and filtered signals in the SE area (using the two larger singular values)

35 North The filtered MDEA signal East days days North The filtered JOAN signal East days days

36 The Gradisca d Isonzo seismic event on December 6 th, 2011 (0.8-magnitude seismic event)

37 The filtered time series in the Gradisca d Isonzo area (East component) CODR MDEA UDI1 JOAN TRIE PAZO