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Seismic Wave Propagation

Seismic Wave Propagation. Elastic Materials. L. F. strain. D L. F = k * D L/L (Hooke’s Law) k = Young’s modulus. strain. Rand quartzite. Acoustic Waves. F = Mass*Acceleration (Newton rules!). F(x). F (x+dx). A. u+ du. x. u. x + dx.

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Seismic Wave Propagation

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  1. Seismic Wave Propagation

  2. Elastic Materials L F strain DL F = k *DL/L (Hooke’s Law) k = Young’s modulus strain Rand quartzite

  3. Acoustic Waves F = Mass*Acceleration (Newton rules!) F(x) F (x+dx) A u+ du x u x + dx Net force = F(x+dx) – F(x) = DF = [r *A*dx] *acc DF/Dx = [r * acc * A] but F = k *Du/Dx (Hookes law) and S = F/A, so K * D(Du/Dx)Dx = r * Du2/Dt2 i.e. wave equation where V= (k/r)1/2

  4. Seismic Wave Equation k * D(Du/Dx)Dx = r * Du2/Dt2 or d2u/dx2 = (r/k) du2/dt2 which has solutions of the form u = A e+ikt + Be-ikt

  5. Seismic Waves P Body waves S Surface Waves Love “Ground Roll” Rayleigh

  6. Rayleigh Waves

  7. Material P wave Velocity (m/s) S wave Velocity (m/s) Air 332 Water 1400-1500 Petroleum 1300-1400 Steel 6100 3500 Concrete 3600 2000 Granite 5500-5900 2800-3000 Basalt 6400 3200 Sandstone 1400-4300 700-2800 Limestone 5900-6100 2800-3000 Sand (Unsaturated) 200-1000 80-400 Sand (Saturated) 800-2200 320-880 Clay 1000-2500 400-1000 Glacial Till (Saturated) 1500-2500 600-1000 Seismic Wave Speeds

  8. Seismic Velocities

  9. Wave SimulationsColorado School of Mines Tutorial Body waves in half space

  10. Huygen’s Principle

  11. Snell’s Law*(acoustic) *Fermat’s Least Time Principle

  12. Snell’s Law(elastic) sin f1 = sin f2 = sin f3 Vp1 Vp2 Vs3

  13. Critical Refraction sin ic = sin (90º) V1 V2 sin ic = V1 V2

  14. Seismic Refraction Waves passing from slow to fast medium

  15. Snell’s Law Snell’s Law

  16. 400 Reflection & Refraction 200 Refracted T, msec Reflected Direct 0 Distance, km

  17. Refraction: Two Layers

  18. Travel Time Curve(Shotpoint Gather Engineering Quad 1/27/00 12 gauge source 1m geophone spacing, 1 m minimum offset

  19. Refraction: 3 layer case

  20. Refraction: Dipping Layer

  21. Refraction:Hidden Layers

  22. Refraction: Lateral Offset

  23. Refraction: Lateral Offset

  24. Refraction: Many Layers

  25. Refraction: Multiple Layers

  26. Refraction: Linear V(z)

  27. Refraction: + Gradients V x z z t x

  28. Refraction: - Gradients V x LVZ z z t x Low velocity zone

  29. Diffraction

  30. Reflection: Basic Geometry T2 = X2 + (2Z/V)2 V2 T2 = X2 + T02 V2

  31. Reflection Hyperbola

  32. Reflection from Dipping Layer

  33. SHOT * Reflection display convention

  34. Sample shot gathers split spread offend

  35. Seismic Waves P Body waves S Surface Waves Love “Ground Roll” Rayleigh

  36. Rayleigh Waves

  37. x Ground Roll(Rayleigh Waves) t Dispersion Ewing, Jardetzky and Press (1957)

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