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Quiz results

Quiz results. a) P-wave c) Love wave d) Rayleigh wave b) 6378 km c) 4300C. http://www.youtube.com/watch?v=ZO7zPEr8sDk. hypocenter. Earth surface. expanding. wavefront. ray. epicentral. distance, D. receiving. station. Earth. center. hypocenter. Earth surface. expanding.

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Quiz results

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  1. Quiz results • a) P-wave • c) Love wave • d) Rayleigh wave • b) 6378 km • c) 4300C

  2. http://www.youtube.com/watch?v=ZO7zPEr8sDk

  3. hypocenter Earth surface expanding wavefront ray epicentral distance, D receiving station Earth center

  4. hypocenter Earth surface expanding wavefront ray epicentral distance, D receiving station ray Earth center wavefront

  5. hypocenter Earth surface expanding wavefront ray epicentral distance, D receiving station ray Earth center wavefront straight ray plane wavefront

  6. hypocenter Earth surface expanding wavefront ray epicentral distance, D receiving station ray set up cartesian coordinate system in small region near wave front Earth center wavefront y ray x

  7. hypocenter Earth surface expanding wavefront ray epicentral distance, D receiving station ray Earth center S wave polarization: SV = particle motions in the plane of the ray SH = particle motions perpendicular to plane of ray

  8. hypocenter Earth surface wavefront incident on boundary next slide Ra ray receiving station Earth center internal boundary at radius Ra

  9. We can treat this as plane waves interacting with plane boundaries and straight rays, governed by SNELL’S LAW incident ray internal boundary refracted ray Ra

  10. Let’s consider an incident P wave reflected SV ray incident P ray reflected P ray is ip ip homogeneous medium 1 r1, Vp1, Vs1 boundary r2, Vp2, Vs2 rp refracted P ray homogeneous medium 2 rs refracted SV ray Ra

  11. Now view the wave fronts incident P wave front reflected P wave front reflected SV wave front internal boundary refracted SV wave front refracted P wave front

  12. Apparent Velocity = Va incident P wave front Incident P ray wavefront velocity = Vp1 ip Dt · Vp1 ip internal boundary Dt · Va

  13. Finally, Snell’s law reflected SV ray incident P ray reflected P ray is ip ip homogeneous medium 1 r1, Vp1, Vs1 boundary r2, Vp2, Vs2 rp refracted P ray homogeneous medium 2 rs refracted SV ray Ra

  14. Snell’s law in spherical geometry i1 i1’ V1 V2 i1’ R1 i2 R2 seismic ray Two concentric spherical shells with radii R1 and R2 B Earth’s center

  15. Snell’s law in spherical geometry What is the relationship between i1 and i1’ ? i1 i1’ V1 V2 i1’ R1 i2 R2 seismic ray Two concentric spherical shells with radii R1 and R2 B Earth’s center

  16. Snell’s law in spherical geometry What is the relationship between i1 and i1’ ? i1 i1’ V1 V2 i1’ R1 i2 R2 seismic ray Two concentric spherical shells with radii R1 and R2 B Earth’s center

  17. Snell’s law in spherical geometry How about i1’ and i2 ? i1 i1’ V1 V2 i1’ R1 i2 R2 seismic ray Two concentric spherical shells with radii R1 and R2 B Earth’s center

  18. Snell’s law in spherical geometry Now substitute for sin(i1’) i1 i1’ V1 V2 i1’ R1 i2 R2 seismic ray Two concentric spherical shells with radii R1 and R2 B Earth’s center

  19. D = 2 cos-1(R1/R0) R0 Travel time R1 rays reflected from boundary V0 V1 tt = (R0 - R1)/V0 rays above boundary R1 dist=2sin(D/2)(R0-R1) R0 D = 2 cos-1(R1/R0)) 0 distance, D Simple velocity increase: V1 > V0 V0 V1 R1 R0

  20. D = 2 cos-1(R1/R0) R0 Travel time R1 rays reflected from boundary V0 V1 tt = (R0 - R1)/V0 rays above boundary R1 dist=2sin(D/2)(R0-R1) R0 D = 2 cos-1(R1/R0)) 0 distance, D Simple velocity increase: V1 > V0 travel time tt/dD = 0 rays reflected from boundary V0 V1 rays refracted below boundary R1 tt/dD = R0/V0 rays above boundary R0 0 distance, D 180 or 

  21. Elastic moduli • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains L 11=E(L/L)

  22. Elastic moduli • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains K=-V dP/dV =  dP/d

  23. Elastic moduli • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains  = xy/xy/2

  24. Elastic moduli • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains =-22/11

  25. Elastic moduli Auxetic material • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains =-22/11

  26. Gradient T T T gradT = [0 0] gradT = [1 0] gradT = [1 1]

  27. Vector fields • Divergence of a vector field: • No rotation • Just volume change • Which body wave?

  28. Vector fields • Curl: • No volume change • Just rotation

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