1. Seismic Wave Propagation

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

3. Acoustic Waves F = Mass*Acceleration (Newton rules!) u u+ du x x + dx A F(x) F (x+dx) Net force = F(x+dx) – F(x) =  F = [  *A*dx] *acc  F/  x =  * acc * A] but F = k *  u/  x (Hookes law) and S = F/A, so K *  u/  x  x =  *  u 2 /  t 2 i.e. wave equation where V= (k  ) 1/2

4. Seismic Wave Equation k *  u/  x  x =  *  u 2 /  t 2 or d 2 u/dx 2 = (  /k) du 2 /dt 2 which has solutions of the form u = A e +ikt + Be -ikt

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

6. Rayleigh Waves

7. Seismic Wave Speeds MaterialP wave Velocity (m/s)S wave Velocity (m/s) Air332 Water1400-1500 Petroleum1300-1400 Steel61003500 Concrete36002000 Granite5500-59002800-3000 Basalt64003200 Sandstone1400-4300700-2800 Limestone5900-61002800-3000 Sand (Unsaturated)200-100080-400 Sand (Saturated)800-2200320-880 Clay1000-2500400-1000 Glacial Till (Saturated)1500-2500600-1000

8. Seismic Velocities

9. Wave Simulations Colorado School of Mines Tutorial Colorado 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  1 = sin  2 = sin  3 Vp 1 Vp 2 Vs 3

13. Critical Refraction sin i c = sin (90º) V 1 V 2 sin i c = V 1 V 2

14. Seismic Refraction Waves passing from slow to fast medium

15. Snell’s Law

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

17. Refraction: Two Layers

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

19. Refraction: 3 layer case

20. Refraction: Dipping Layer

21. Refraction: Hidden Layers

22. Refraction: Lateral Offset

24. Refraction: Many Layers

25. Refraction: Multiple Layers

26. Refraction: Linear V(z)

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

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

29. Diffraction

30. Reflection: Basic Geometry T 2 = X 2 + ( 2Z/V) 2 V 2 T 2 = X 2 + T 0 2 V 2

31. Reflection Hyperbola

32. Reflection from Dipping Layer

33. SHOT * Reflection display convention

34. Sample shot gathers offend split spread

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

36. Rayleigh Waves

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