Thailand Training Program in Seismology and Tsunami Warnings, May 2006

1. Theoretical Seismology 2: Wave Propagation Thailand Training Program in Seismology and Tsunami Warnings, May 2006

2. Theoretical Seismology 2: Wave Propagation • Seismic waves in an elastic medium • ・ Rays and Ray Paths • How they propagate in the Earth • Travel-time curves • ・ Near-Field Terms (Static Displacements) • Far-Field Terms (P, S, Surface waves) • Surface Waves • ・ Normal modes • (Free oscillations of the Earth)

3. Explosion P waves

4. Psychology test Homogeneous Earth (seismologist) (engineer) (tsunamicist?)

5. a1 q1 q2 a２ a1 > a2 Ray Paths in a Layered Medium Snell’s law: sin a1 / sin a2 = a1 / a2 Faster a1 q1 Slower Slower q2 Faster a２ a1 < a2

6. Time Travel-timecurves 1/a3 1/a2 1/a1 Distance (D=T/velocity) Travel-time Curves for Ray Paths in a Layered Medium a1 head wave a2 a3

7. Velocity structure of the Earth

8. Time Travel-time curves 1/a3 1/a2 1/a1 Distance (D=T/velocity) Ray Paths in a Gradient Velocity gradient can be treated as a series of thin homogeneous layers. a1 a2 a3

9. Moho Andrija Mohorovicic (1857-1936) Found seismic discontinuity at 30 km depth in the Kupa Valley (Croatia). Mohorovicic discontinuity or ‘Moho’ Boundary between crust and mantle

10. Structure in the Earth Conrad and Moho Discontinuities Low velocity zone

13. Forward Branch Receding Branch

14. Forward Branch Shadow Zone Forward Branch (PKPbc) Receding Branch (PKPab)

15. PcP Shadow Zone Not shown: PKP(DEF) and PKiKP Other notation for core phases: ABC branch known as P2l DEF branch known as P1ll PKP(DEF) known as PKIKP Point B is a caustic Receding Branch A Forward Branch PKP C B Forward Branch PcP Shadow Zone P Forward Branch Forward Branch Receding Branch

16. PcP Core Reflections

18. Faulting Seismic waves

19. Other aspects of wave propagation: • Diffracted Waves • ・ Surface Waves • ・ Static Displacements • ・ Frequency content • Normal Modes

21. Other aspects of wave propagation • Diffracted Waves • ・ Surface Waves • ・ Static Displacements • ・ Frequency content and wavelength • Normal Modes

22. 1-D Wave Equation 1-D wave equation c = propagation speed

23. Solution T = wave period w = angular frequency LW 3.2.1

24. Wave Period and Wavelength Velocity = Wavelength / Period Space x Velocity 6 km/s wavelength period 50 s Wavelength 300 km Time t period 50 s frequency = 1/period= 0.02 hz period

25. Period Wavelength

26. Other aspects of wave propagation • Diffracted waves • ・ Surface waves • ・ Static Displacements • (amplitude at zero frequency) • ・ Frequency content • Normal modes

27. 3-D Wave Equation with Source source spatial 2nd derivative Near-field Terms (Static Displacements) Solution Far-field Terms (P, S Waves)

28. r/a r/b r/a r/b Near-field terms • ・ Static displacements • ・ Only significant close to the fault • ・ Source of tsunamis t　→

29. Static Displacements Bei-Fung Bridge near Fung-Yan city, 1999 Chi-Chi, Taiwan earthquake

30. Static displacements Co-seismic deformation of 2003 Tokachi-oki Earthquake (M8.0)

31. Generation of Tsunami from Near-field Term EA PAC

32. Far-field Terms • ・ Propagating Waves • ・ No net displacement • in an elastic medium • ・ P waves • ・ S waves

33. Other aspects of wave propagation • Diffracted Waves • ・ Surface Waves • ・ Static Displacements • ・ Frequency content • Normal Modes

34. Surface Waves GroupVelocity (km/sec) Love Rayleigh Period (sec) S Shearer, Fig. 8.1

35. January 26, 2001 Gujarat, India Earthquake (Mw7.7) Body waves vertical Rayleigh Waves P PP S SS radial transverse Love Waves Recorded in Japan at a distance of 57o (6300 km)

36. Other aspects of wave propagation • Diffracted Waves • ・ Surface Waves • ・ Static Displacements • ・ Frequency content • Normal Modes

37. Few minutes after the earthquake Constructive interferences  free oscillations (or stationary waves) Free Oscillations of the Earth (Normal Modes) Few hours after the earthquake (0S20)  Standing Waves with Periods < 54 min, amplitudes < 1 mm  Observable months after great earthquakes (e.g. Sumatra, Dec 2004) From Michel van Camp, Royal Obs. of Belgium

38. Normal Modes (Stein and Gellar 1978) Free Oscillations of the Earth 1960 Chile Earthquake (Daishinji, Fukui Prefecture) Useful for studies of ・ Interior of the Earth ・ Largest earthquakes

39. Toroidal and Spheroidal Modes Toroidal Spheroidal Dahlen and Tromp Fig. 8.5, 8.17

40. Natural Vibrations of the Earth Indexes describe spherical harmonics Shearer Ch.8.6 Lay and Wallace, Ch. 4.6

41. Free Oscillations l=1 m=1 Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

42. Free Oscillations l=1 m=2 Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

43. Free Oscillations l=1 m=3 Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

44. Structure: Free Surface Earth is a not homogenous whole-space Free surface causes many complications - surface waves - reflections (pP, sP, sS)

45. Summary Rays Velocity structure includes gradients, discontinuities and LVZ’s, causing complicated ray paths through the Earth (P, PKP, PcP) Wave theory explains ・ P and S waves ・ Static displacements ・ Surface waves Normal Modes The Earth rings like a bell at long periods

47. Why are observed seismograms so messy ?