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TELESEISMIC BODY WAVE INVERSION

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

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TELESEISMIC BODY WAVE INVERSION

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

  2. Methodology • Body wave inversion in teleseismic distances to calculate the seismic moment tensor Mij 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. Methodologies 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. Calculation of body wave synthetic seismograms ρ :the density at the source c: the velocity of P, S-waves g(Δ,h) : geometric spreading r0 : the radius of the earth Ri : the radiation pattern in case of P, SH, SV-waves (i=1, 2, 3) respectively the moment rate

  5. 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. 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. Moment Tensor Inversion where a1,…,a5 are the components of the model m

  8. Moment Tensor Inversion ~ Normal Equations • n < 5 : under – determined system • n > 5 : over – determined system G non – square matrix pseudo inverse GT·G = square matrix

  9. Singular value decomposition G = U S VT m m n m S G = VT U n n x m n n m

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

  11. Calculation of model parameters GTG = square matrix G = U·S·VT

  12. Elementary moment tensors

  13. General Moment Tensor am are the calculated components of the model parameters, m

  14. Applications • Aigio 1995 and Kozani 1995 • Skyros 2001 and Lefkada 2003 • Karpathos 2002 and Kythira 2006

  15. The June 15, 1995 Aigion earthquake, Mw=6.2

  16. The June 15, 1995 Aigion earthquake, Mw=6.2 ~ inversion D.C=97% CLVD=3%

  17. The May 13, 1995 Kozani earthquake, Mw=6.5 P SV SH P P P SV SV SH P P SV P SV SV P SH SH

  18. The May 13, 1995 Kozani earthquake, Mw=6.5 ~ inversion D.C=98% CLVD=2%

  19. The July 26, 2001 Skyros earthquake, Mw=6.5 P P SV P P P SH P SV SV P SH SH P P SV SV P SV SH SH

  20. The July 26, 2001 Skyros earthquake, Mw=6.5 ~ inversion P SH SV P P SH SV P P SV SH SV P SV SV P P SH SH D.C=98% CLVD=2%

  21. The August 14, 2003 Lefkada earthquake Mw=6.3 P P P SH SH P P SV SH SH SV P P P SV SH P P

  22. The August 14, 2003 Lefkada earthquake Mw=6.3 ~ inversion P P P P SV SV SH P P SV SH D.C= 90% CLVD=10%

  23. The January 22, 2002 Karpathos earthquake Mw=6.2 SH P P SV SH SV P P SV SH SH P SV P P SV P SH SH

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

  25. The January 08, 2006 Kythira earthquake Mw=6.7 P P P SH P P P SH SV SV SH SV P SV P SH P

  26. The January 08, 2006 Kythira earthquake Mw=6.7 ~ inversion D.C=93% CLVD=7%

  27. Moment tensor solutions Forward – InversionProblem

  28. Conclusions: • 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 (GTG) or (GGT). 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. THE END THANK YOU FOR YOUR ATTENTION

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