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The 2D modeling algorithm

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). The 2D modeling algorithm. 2-D Equations of Motion. Euler-Newton’s Equations:. Constitutive Equations:. Memory Variables:.

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The 2D modeling algorithm

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

  2. The 2D modeling algorithm

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

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

  5. Inhomogeneous waves Elliptical polarization Plane wave

  6. Reflection and transmission

  7. From a stiff ocean floor...

  8. to a soft ocean floor

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

  10. Test with the analytical solution

  11. AVA analysis Elastic case Anelastic case

  12. Rayleigh Window:Water/stainless steel

  13. Water/oceanic crust

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

  15. Water/glass (stiff bottom)

  16. Test with analytical solution Water/plexiglass interface

  17. Test with analytical solution Water/glass interface

  18. Dispersive Scholte waves

  19. Dispersive Scholte waves North Sea. 70 m water depth. Airgun source. Elastic case Anelastic case

  20. Ocean overlying the crust Phase velocity

  21. Ocean overlying the crust Group velocity Dissipation factor

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

  23. Ocean overlying the crust Phase/group velocities

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

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

  26. Sediment layer overlying the crust Low-frequency case Elastic Anelastic

  27. January 7 (2000) Earthquake

  28. Real seismograms

  29. Geological model From CRUST 5.1

  30. Synthetic seismograms

  31. The 3D modeling algorithm

  32. The Kelvin-Voigt stress-strain relation s =stress components e= strain components u=displacements l, m=Lamé constants l’, m’=damping Lamé constants

  33. Input damping parameters w0=reference frequency QP0 = reference P-wave quality factor QS0 = reference S-wave quality factor

  34. The equations of motion

  35. The equations of motion v = particle velocity r= density f=body forces

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

  37. Simulation of Rayleigh waves. Model.

  38. Simulation of Rayleigh waves. Seismograms. Lossless case

  39. Simulation of Rayleigh waves. Seismograms. Lossy case

  40. Simulation of Love waves. Model.

  41. Simulation of Love waves. Seismograms. Lossless case Lossy case

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

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