1. On the Physics and Simulation of Waves at Fluid-Solid Interfaces: Application to NDT, Seismic Exploration and Earthquake Seismology by José M. Carcione (OGS, Italy)

2. Page: 2 The 2D modeling algorithm

3. Page: 3 2-D Equations of Motion Euler-Newton’s Equations: Constitutive Equations: Memory Variables:

4. Page: 4 Scholte wave dispersion equation Relevant roots: Scholte wave Leaky Rayleigh wave

5. Page: 5 Inhomogeneous waves Plane wave Elliptical polarization

6. Page: 6 Reflection and transmission

7. Page: 7 From a stiff ocean floor...

8. Page: 8 to a soft ocean floor

9. Page: 9 Numerical algorithm Two grids (domain decomposition): ocean and oceanic crust Fourier method in the horizontal direction Chebyshev method in the vertical direction Spatial derivatives Time integration 4th-order Runge-Kutta

10. Page: 10 Test with the analytical solution

11. Page: 11 AVA analysis Elastic case Anelastic case

12. Page: 12 Rayleigh Window: Water/stainless steel

13. Page: 13 Water/oceanic crust

14. Page: 14 Water/plexiglass (soft bottom) No leaky Rayleigh wave

15. Page: 15 Water/glass (stiff bottom)

16. Page: 16 Test with analytical solution Water/plexiglass interface

17. Page: 17 Test with analytical solution Water/glass interface

18. Page: 18 Dispersive Scholte waves

19. Page: 19 Dispersive Scholte waves Elastic caseAnelastic case North Sea. 70 m water depth. Airgun source.

20. Page: 20 Ocean overlying the crust Phase velocity

21. Page: 21 Ocean overlying the crust Group velocity Dissipation factor

22. Page: 22 Ocean overlying the crust Attenuation coefficient Ben_Menahem and Singh (1981) Experimental data (Fig. 10.3)

23. Page: 23 Ocean overlying the crust Phase/group velocities

24. Page: 24 Ocean overlying the crust High-frequency case Elastic and anelastic solutions

25. Page: 25 Ocean overlying the crust Low-frequency case Anelastic Elastic

26. Page: 26 Sediment layer overlying the crust Low-frequency case ElasticAnelastic

27. Page: 27 January 7 (2000) Earthquake

28. Page: 28 Real seismograms

29. Page: 29 Geological model From CRUST 5.1

30. Page: 30 Synthetic seismograms

31. Page: 31 The 3D modeling algorithm

32. Page: 32 The Kelvin-Voigt stress-strain relation  = stress components  = strain components u = displacements  = Lamé constants ’  ’ = damping Lamé constants

33. Page: 33 Input damping parameters  0 = reference frequency Q P0 = reference P-wave quality factor Q S0 = reference S-wave quality factor

34. Page: 34 The equations of motion

35. Page: 35 The equations of motion v = particle velocity  = density f = body forces

36. Page: 36 Tests with analytical solutions Rayleigh waves -- Cagniard-de Hoop solution Pekeris (1955) solution -- unbounded media

37. Page: 37 Simulation of Rayleigh waves. Model.

38. Page: 38 Simulation of Rayleigh waves. Seismograms. Lossless case

39. Page: 39 Simulation of Rayleigh waves. Seismograms. Lossy case

40. Page: 40 Simulation of Love waves. Model.

41. Page: 41 Simulation of Love waves. Seismograms. Lossless caseLossy case

42. Page: 42 Conclusions Effects of anelastic attenuation Pseudospectral numerical method Inhomogeneous viscoelastic waves Differences at critical and post-critical angles Rayleigh-window effect Verified for reflection/transmission and interface waves Effective tool for seismic exploration studies, NDT and earthquake seismology