1. Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis of the wave profiles near the fronts appearing in Tsunami problems

2. “Gaussian” source of Earthquake

3. Level curves of perturbation

4. Wave profiles at the front at time t at different angles

5. 3D wave profile for elliptic source

6. “Modulated gaussian” source of Earthquake

7. Level curves of perturbation

8. Wave profiles at the front at time t at different angles

9. 3D wave profile for elliptic source

10. The ridge near the source of Eathquake

11. Fronts at different times

12. The set of profiles

16. Simulations for Tyrrhenian Sea Relief data: National Oceanic and Atmospheric Administration (NOAA) National Geophysical Data Center (NGDC) ETOPO2 2-minute Global Relief http://www.ngdc.noaa.gov/mgg/gdas/gd_designagrid.html

17. Rays for imaginary source at Stromboli: 38.8 N, 15.2 E

18. Amplitudes of wave at different points of the coast

19. 3D wave profile

20. Density plot

21. DD7-29/05/07-01/06/07 Special session on tsunami and typhoons Scattering of tsunami on the beach S.Dobrokhotov Inst. Probl. of Mechanics R. Ac Sc. Moscow Petya Zhevandrov Escuela de Ciencias Fisico-Matematicas, Morelia, Mexico Brunello Tirozzi Department of Physics, Univ. “La Sapienza”, Rome

22. ... Workshop on Extreme Events... Max Planck Institut for Complex System Dresden, 30 October-2 November 2006 Analysis of the tsunami event in Algeria 2003 B. Tirozzi (1),F. Raicich (2) (1) Department of Physics, University “La Sapienza”, Rome, Italy (2) CNR, Institute of Marine Sciences, Trieste, Italy

23. Valencia Barcelona Ibiza Earthquake data (USGS): t0: 18:44:19 GMT, 21 may 2003 USGS: epicenter 36.96°N, 3.63°E, M=6.9, hf=12 km Borerro: epicenter 36.90°N, 3.71°E, M=6.8, hf=10 km, strike=56°

25. Ellipsoidal deformation M = 6.9 h f = 12 km (Pelinovsky et al., 2001) a = 34 km b = 12 km b 56° a Coordinates: model gridpoints

26. (Dobrokhotov et al., 2006) a 1 = 1.2 10 -2 km -1 Gaussian*cosine deformation = 0 a 2 = 2.7 10 -2 km -1 b 1 = 0.5 10 -2 km -2 b 2 = 4.0 10 -2 km -2 = 56° Coordinates: model gridpoints

33. Linear theory of the scattering of localized waves on a beach of constant slope S. Dobrokhotov, Petya Zhevandrov, Brunello Tirozzi

36. Shape of perturbation

37. Amplitude of the waves at tsunami front

39. Average of the too fast oscillating WKB solution

40. Example: beach of costant slope

41. Momentum equation

42. Singular Lagrangian manifold

43. Dynamic on the lagrangian manifold

44. Dynamic on the phase space

45. Solutions before and after the scattering of the beach (1/2)

46. Solutions before and after the scattering of the beach (2/2)

47. Graphics 1

48. Graphics 2

49. Graphics 3

50. End