Introduction: the Abruzzo earthquake The network and the processing strategies. displacements estimation at earthquake epoch. horizontal displacements

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1 The Abruzzo earthquake: temporal and spatial analysis of the first geodetic results L. Biagi, S. Caldera, D. Dominici, F. Sansò Politecnico di Milano Università degli studi de L Aquila

2 Outline Introduction: the Abruzzo earthquake The network and the processing strategies Time modelling of daily results: displacements estimation at earthquake epoch Spatial interpretation of the horizontal displacements The vertical displacements Future works

3 Abruzzo earthquake Main event: 6th april, 1:33 UTC Location: N, E, Depth: 8.88 km Magnitude: 5.8 Richter

4 Abruzzo earthquake Main event: 6th april, 1:33 UTC Location: N, E, Depth: 8.88 km Magnitude: 5.8 Richter Before and after the main event: many other pre seismic and after seismic events

5 The geodetic network 3 Italian IGS stations 32 stations in Abruzzo region 17 other stations within a distance of 50 km from Abruzzo boundaries

6 The geodetic network 3 Italian IGS stations 32 stations in Abruzzo region 17 other stations within a distance of 50 km from Abruzzo boundaries Data from 1st February y( (DOY 32) to 2nd, May y( (DOY 122) have been adjusted up to now from 32 to 95 (64 days): before earthquake from 96 to 122 (27 days): after earthquake

7 The geodetic network ASI-Geodaf, INGV-RING, Leica-ItalPos, TopCon-Geotop, GPSAbruzzo, GPSUmbria, ResNap

8 The processing strategies 1/2 IGS stations stochastically constrained: coordinates: interpolation of last 52 IGS05 weekly solutions, constraints: 2 mm horizontally, 4 mm in height

9 The processing strategies 1/2 IGS stations stochastically constrained: coordinates: interpolation of last 52 IGS05 weekly solutions, constraints: 2 mm horizontally, 4 mm in height Final IGS EOP, EPH and PCV s Adoption of the international standards in the raw data processing by BSW 5.0 software

10 The processing strategies 2/2 Outlier rejection

11 The processing strategies 2/2 Outlier rejection Modelling the time series to estimate discontinuities

12 The processing strategies 2/2 Outlier rejection Modelling the time series to estimate discontinuities Spatial analysis of the discontinuities and clustering in subregions

13 Examples of time series: MATE

14 Examples of time series: MATE Bad data quality (some adjusted d station) ti

15 Examples of time series: MEDI

16 Examples of time series: TERA

17 Examples of time series: TERA Earthquake

18 Examples of time series: OCRA

19 Examples of time series: PAGA

20 Examples of time series: AQRA

21 Outliers rejection Permanent networks are intrinsically redundant to improve coordinates repeatabilities a severe automated outliers rejection is useful

22 Outliers rejection Permanent networks are intrinsically redundant to improve coordinates repeatabilities a severe automated outliers rejection is useful This is a particular case: few data, manual analysis, conservative approach in outlier rejection just bad quality sessions before earthquake removed

23 The results of IGS stations 3 stochastically constrained stations: CAGL, MATE, MEDI Residuals of daily results wrt apriori coordinates (mm) East North Height Mean Min Max

24 Time series interpretation (1/2) Short time series in the geodetic analysis constant model to avoid propagation of seasonal effects and localized in time variations into meaningless estimated velocities

25 Time series interpretation (2/2) Before earthquake: not a clear presence of pre seismic signal, just linear trend linear trend estimation and removal not to estimate velocities but to better model daily solutions

26 Time series interpretation (2/2) After earthquake: a postseismic signal is often clear, but few days are available at the present, simple costant model applied, with more data: linear and 2nd order polynomial

27 One example (mm) DE DN Dh Constant Linear

28 Residuals statistics of daily solutions Before (mm) E N h Mean Min After (mm) E N h Mean Min Max Max Worse height results after earthquake: Worse height results after earthquake: post seismic assessment of 4 stations near L Aquila

29 Parameters and covariances estimation Daily coordinates models in time Model parameters estimated by LS Formal daily covariances typically underestimated and final covariances too much optimistic Empirical i covariances estimation needed d

30 Parameters and covariances estimation Few observations Simplified hypotheses on time series models and covariances

31 Parameters and covariances estimation Few observations Simplified hypotheses on time series models and covariances Joint estimation of parameters and covariances Typically an iterative process up to final results y, C xˆ, Cˆ y Cˆ xˆ, Cˆ... xˆ, Cˆ 0 yy I yy 0 yy II yy F yy I I II F

32 Hypotheses on network covariances 1. daily network covariance constant in time 2. no correlations between consecutive days C11 C12... C1P C21 C22... C 2P C ( t k ) C k 1,..., T, C, 3P3P CP1 CP2 C PP cx 1 x c 1 x 1 x c P P P 2 P x 1 Px 3 P i j i j i j c c c c C ij x 2P x i 1P x j 2P x i 2P x j 2P x i 3P ij j 33 l m l, m123 1,2,3 c x3px c i 1P x j 3Px c i 2P x j 3Px i 3 Pj

33 Estimation of the model parameters Constant or linear model x P i () t x P i x P i ( t ) ( t ) x ( tt ) P i

34 Estimation of the model parameters Constant or linear model x P i () t x P i x P i ( t ) ( t ) x ( tt ) 1. For each point i=1,,p, each component l=1,2,3 an independent regression is estimated by Least Squares xl i ( t1 ) 0 x ˆ t x ( t ) l ( 2) i 0 2 l i y ˆ 0, yy 0 I... C I LS x xˆ l i x ( ) l t i 0 T P i I

35 Empirical estimation of the covariances Estimated vector of the residuals x ( t ˆ ˆ l 0 1) [ x ( t ) ( 1 )] i l x i l t t I ii x ( ) [ ˆ ( ) ˆ ( )] l t i0 2 xl t x i l t i 2 t ˆ I I rl i I... x ( t ) [ x ˆ ( t ) x ˆ l ( t t )] i0 T l ii l ii T

36 Empirical estimation of the covariances Estimated vector of the residuals x ( t ˆ ˆ l 0 1) [ x ( t ) ( 1 )] i l x i l t t I ii x ( ) [ ˆ ( ) ˆ ( )] l t i0 2 xl t x i l t i 2 t ˆ I I rl i I... x ( t ) [ x ˆ ( t ) x ˆ l ( t t )] i0 T l ii l ii T Estimated covariances and correlations ˆ c ij I T 1 N T rˆ rˆ lm li I m j I (N=1/2 for the constant/ linear model)

37 Final results Final results With the above hypotheses, no need of iterations Final parameters ˆ ˆ ( ) t 1,2,3; 1,..., ( ), ˆ ˆ i i l l l i P F I x t x x x 123; 1 ˆ ( ) i F I l l i P x t 1,2,3; 1,..., l i P

38 Final results With the above hypotheses, no need of iterations Final parameters Related covariances ˆ ˆ ˆ x, 0 ˆ ) ˆ x c x x x x l i mj li mj l i m j x ( ), l t x i l T i l1,2,3; i1,..., P xˆ ˆ 2 2 x 1 F I ˆ ˆ x c l xm 2 xl x i j i mj xˆ mt t l ( t ) i l 123; 1,2,3; i 1,..., P mt ( ti t ) N i

39 Propagation of coordinates and covariances Displacement at earthquake epoch x ˆ ( t ) x ˆ ( t ) x ˆ i E i B i( t t E B) B xˆ ( ) ˆ i te xi ( t ) A A A xˆ ( t ) xˆ ( t ) xˆ ( t ) i E ia E ib E

40 Propagation of coordinates and covariances Displacement at earthquake epoch x ˆ ( t ) x ˆ ( t ) x ˆ i E i B i( t t E B) B xˆ ( ) ˆ i te xi ( t ) A A A xˆ ( t ) xˆ ( t ) xˆ ( t ) i E ia E ib E Covariance of the displacement C ( t ) C C ( t t ) C i B E xx ib xxi E B ( t ) C ia E xxia Ci ( te ) Ci ( te ) Ci ( te ) A B 2

41 Covariances of the two propagations Few data

42 Horizontal displacements map

43 Horizontal displacements map No smooth deformation field but a discontinuity line

44 Separation of rigid motion from deformation BAD SPATIAL INTERPOLATION

45 Separation of rigid motion from deformation BAD SPATIAL INTERPOLATION GOOD SPATIAL INTERPOLATION PIECEWISE INTERPOLATION INVOLVES DISCONTINUITIES = FAULTS!

46 Spatial covariances and interpolation A signal could be isolated, but quite arbitrarily a preliminary clustering of homogeneous areas needed

47 Spatial clustering 1. L Aquila sites: mm W displacements

48 Spatial clustering 1. L Aquila sites: mm W displacements 2. Around them: smaller S-W displacements

49 Spatial clustering 1. L Aquila sites: mm W displacements 2. Around them: smaller S-W displacements 3. East region: 2-30 mm NE displacements

50 Spatial clustering 1. L Aquila sites : mm W displacements 2. Around them: smaller S-W displacements 3. East region: 2-30 mm NE displacements 4. Around it: no significant displacements, but consistent directions.

51 Spatial clustering 1. L Aquila sites : mm W displacements 2. Around them: smaller S-W displacements 3. East region: 2-30 mm NE displacements 4. Around it: no significant displacements, but consistent directions. 5. No other significant displacements

52 Separation of rigid motion from deformation Horizontal motion of a network on earth surface: rotation o of all the points around an axis with angular velocity v [ ω] x i i x v

53 Separation of rigid motion from deformation Horizontal motion of a network on earth surface: rotation o of all the points around an axis with angular velocity v [ ω] x i i x v can be estimated by minimization of relative kinetic energy of the network ap vv T i i i1,..., P T min Realization of a Realization of a Discrete Tisserand reference system

54 Horizontal analysis in separate regions Probably no significant rotation of networks but differential i displacements up to now no Tisserand analysis but statistics on displacements for the two main regions East (14 stations) ti L Aquila (4 stations) ti (mm) E N 2D (mm) E N 2D Mean Mean Min Min Max Max

55 Vertical displacements

56 Vertical displacements Significant displacements for L Aquila stations: -25, -76, -107, -123 mm No significant ifi displacements in other regions: mean: 0.5 mm, range -3/+3mm

57 Conclusions 6th April earthquake in L Aquila has been accompanied by an extension along an axis oriented NW-SE: L Aquila area and an Eastern Adriatic area interested by significant opposite horizontal displacements

58 Conclusions 6th April earthquake in L Aquila has been accompanied by an extension along an axis oriented NW-SE: L Aquila area and an Eastern Adriatic area interested by significant opposite horizontal displacements Significant gradients in the horizontal displacements of the Eastern Adriatic area L Aquila sites interested by vertical displacements of about 10 cm

59 Future analyses Longer time series, to: increase the populations after the earthquake, analyze the post seismic time series

60 Future analyses Longer time series, to: increase the populations after the earthquake, analyze the post seismic time series More rigorous clustering in separate regions, rigorous Tisserand analysis, geometric analysis in Adriatic region

61 Future analyses Longer time series, to: increase the populations after the earthquake, analyze the post seismic time series More rigorous clustering in separate regions, rigorous Tisserand analysis, geometric analysis in Adriatic region Cross comparison in L Aquila with SAR interferograms