1. TELESEISMIC BODY WAVE INVERSION Alexandra Moshou, Panayotis Papadimitriou and Konstantinos Makropoulos Department of Geophysics-Geothermics National and Kapodistrian University of Athens Athens, 24 – 26 May 2007

2. Geoenvironment Past Present FutureMethodology Body wave inversion in teleseismic distances to calculate the seismic moment tensor M ij using the generalized inverse method. The proposed methodology is applied for the largest earthquakes that occurred in Greece from 1995 – 2006 and located in different seismotectonics settings Aigio (1995), Kozani (1995) – shallow events Skyros(2001), Lefkada(2003) – shallow events Karpathos(2002), Kythira(2006) – deep events

3. Geoenvironment Past Present FutureMethodologies Different Methodologies  MT5 McCaffrey et all. (1988)  Kikuchi and Kanamori (1991)  A methodology is developed to calculate the seismic moment tensor  P, SV, SH waveform selection  Body wave inversion of the selected waveforms  Graphical presentation of the solution

4. Geoenvironment Past Present Future Calculation of body wave synthetic seismograms ρ : the density at the source c: the velocity of P, S-waves g(Δ,h) : geometric spreading r 0 : the radius of the earth R i : the radiation pattern in case of P, SH, SV-waves (i=1, 2, 3) respectively the moment rate

5. Geoenvironment Past Present Future Forward problem d : a vector of length m, which corresponds the observed displacements G : a non – square matrix, with dimensions mxn, whose elements are a set of five elementary Green’s functions m : a vector of length n, which corresponds the moment tensor elements

6. Geoenvironment Past Present Future Inverse problem  d : m x 1 matrix," lives” in data – space of n – components, represents the observed data set  G : non - square m x n matrix, green’s function  m : n x 1 vector, the model vector m “lives” in model – space of m – components

7. Geoenvironment Past Present Future Moment Tensor Inversion where a 1,…,a 5 are the components of the model m

8. Geoenvironment Past Present Future Moment Tensor Inversion ~ Normal Equations n < 5 : under – determined system n > 5 : over – determined system G non – square matrix G T ·G = square matrix pseudo inverse

9. Geoenvironment Past Present Future Singular value decomposition G = U S V T mn G = nn n x m m U S m m n VTVT

10. Geoenvironment Past Present Future Moment Tensor Inversion ~Singular Value Decomposition  U, V : orthogonal matrices (nxn) and (mxm) corresponding, which elements are the eigenvectors of the matrices G T G and GG T respectively.  S : diagonal matrix, (nxm) which element, σ i are the singular values of the G T G or GG T The singular values σ i [i=1, 2, …, min(m,n)] are real, non – zero and non – negative,

11. Geoenvironment Past Present Future Calculation of model parameters G T G = square matrix G = U·S·V T

12. Geoenvironment Past Present Future Elementary moment tensors Elementary moment tensors

13. Geoenvironment Past Present Future General Moment Tensor a m are the calculated components of the model parameters, m

14. Geoenvironment Past Present Future Applications  Aigio 1995 and Kozani 1995  Skyros 2001 and Lefkada 2003  Karpathos 2002 and Kythira 2006

15. Geoenvironment Past Present Future The June 15, 1995 Aigion earthquake, M w =6.2

16. Geoenvironment Past Present Future The June 15, 1995 Aigion earthquake, M w =6.2 ~ inversion D.C=97% CLVD=3%

17. Geoenvironment Past Present Future The May 13, 1995 Kozani earthquake, M w =6.5 P SV SH P SV SH SV P P P P P SH P SV

18. Geoenvironment Past Present Future The May 13, 1995 Kozani earthquake, M w =6.5 ~ inversion D.C=98% CLVD=2%

19. Geoenvironment Past Present Future The July 26, 2001 Skyros earthquake, M w =6.5 P P P P SV SH P SV SH SV P P P SH P P

20. Geoenvironment Past Present Future The July 26, 2001 Skyros earthquake, M w =6.5 ~ inversion D.C=98% CLVD=2% P SV P SH SV P P P P P P SH SV SH

21. Geoenvironment Past Present Future The August 14, 2003 Lefkada earthquake M w =6.3 The August 14, 2003 Lefkada earthquake M w =6.3 P P SV SH P SV P P P P P SH P P

22. Geoenvironment Past Present Future The August 14, 2003 Lefkada earthquake M w =6.3 ~ inversion D.C= 90% CLVD=10% P SV SH P SV SH P P P P SV

23. Geoenvironment Past Present Future The January 22, 2002 Karpathos earthquake M w =6.2 P P SV SH P SV SH P P SV SH P SV SH P P SV

24. Geoenvironment Past Present Future D.C=90% CLVD=10% The January 22, 2002 Karpathos earthquake Mw=6.2 ~ inversion P SV SH SV SH P P SV SH P P P P

25. Geoenvironment Past Present Future The January 08, 2006 Kythira earthquake M w =6.7 P P P P SH SV P P SH P SV SH SV SH P P SV

26. Geoenvironment Past Present Future The January 08, 2006 Kythira earthquake M w =6.7 ~ inversion D.C=93% CLVD=7%

27. Geoenvironment Past Present Future Moment tensor solutions Forward – InversionProblem Moment tensor solutions Forward – Inversion Problem Forward ProblemInverse Problem Aigion 1995 φ=277, δ=33, λ=-76 (Pascal etall. 1997) φ=270, δ=28, λ=-89D.C= 97% CLVD=3% Kozani 1995 φ=260, δ=45, λ=-90 (Hatzfeld etall. ) φ=264, δ=45, λ=-93D.C=99% CLVD=1% Skyros 2001 φ=160, δ=65, λ=7φ=154, δ=42, λ=6D.C=99% CLVD=1% Lefkada 2003 φ=15, δ=80, λ=170 (Papadimitriou etall. 2006) φ=7, δ=64, λ=178D.C=90% CLVD=10% Karpathos 2002 φ=95, δ=89, λ=50φ=94, δ=89, λ=60D.C=90% CLVD=10% Kythira 2006 φ=205, δ=45, λ=55φ=215, δ=49, λ=48D.C=93% CLVD=7%

28. Geoenvironment Past Present FutureConclusions:  It has developed a new procedure based upon the moment tensor inversion, to obtain the source parameters of an earthquake, taking to account a specific depth.  This methodology is based in two numerical methods, in the normal equations and in singular value decomposition  The method of Singular Value Decomposition is based in the eigenvalues and eigenvectors of the matrix (G T G) or (GG T ). For this reason this method is more stable than the method of normal equations.  In all the applications the Singular Value Decomposition give up to 90% Double Couple and a very good fit between observed and synthetics seismograms.  Our solution was compared with others than proposed from others institutes and it was in very good agreement.  At this time, our interest is to include the depth in this procedure automatically

29. Geoenvironment Past Present Future THE END THANK YOU FOR YOUR ATTENTION