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・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves

Delve into the complexities of wave propagation and seismic waves in the Earth's structure, exploring normal modes, faulting, and wave behaviors, such as near-field and far-field terms. Learn about the role of Snell's Law, the Moho discontinuity, and the intricate paths of seismic rays. Discover how Free Oscillations help study the Earth's interior and the nuances of different wave types. Explore the generation of tsunamis and the fascinating world of Earth's natural vibrations.

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・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves

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  1. II.1 Theoretical Seismology 2: Wave Propagation ・ Rays Snell’s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes Free oscillations of the Earth

  2. Magnitude for Local Tsunami (Example) JMA Magnitude (Tsuboi, 1954) M=log 10A + 1.73 log10 Δ －0.83 A : Half of maximum total amplitude [μm] Δ : Epicentral distance [km]

  3. Faulting Seismic waves

  4. Travel Time and Distance

  5. Homogeneous Earth

  6. a1 q1 q2 a２ a1 > a2 Ray Paths in a Layered Medium Faster a1 q1 Ｓlower Slower q2 Faster a２ a1 < a2

  7. 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

  8. Time 1/a3 1/a2 1/a1 Distance Ray Paths in a Layered Medium a1 a2 a3

  9. Structure in the Earth Crust-Mantle Core-Mantle 440 km 660 km

  10. Forward Branch Backward Branch

  11. Forward Branch Shadow Zone Forward Branch Backward Branch

  12. PcP Shadow Zone ・ 1912 Gutenberg observed shadow zone 105o to 143o ・ 1939 Jeffreys fixed depth of core at 2898 km (using PcP) Backward Branch Forward Branch PKP Forward Branch PcP Shadow Zone P Forward Branch Forward Branch Backward Branch

  13. PcP Core Reflections

  14. Why are observed seismograms so complicated ?

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

  16. Surface Wave and Maximum Amplitude Observed in Japan. Δ=57(deg) Max Amp., 40 min after occurrence. (Ms, 20 deg ≦ Δ ≦ 160 deg)

  17. Seismogram of a distant earthquake Fig.16 ( LR: Rayleigh wave, LQ: Love wave )

  18. January 26, 2001 Gujarat, India Earthquake (Mw7.7) vertical Rayleigh Waves radial transverse Love Waves Recorded in Japan at a distance of 57o (6300 km)

  19. Seismic Waves Aspects of Waves not Explained by Ray Theory ・ Different types of waves (P, S) ・ Surface Waves ・ Static Displacements ・ Frequency content

  20. Period Wavelength

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

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

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

  24. Summary Rays Earth structure causes 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

  25. Thank you for your attention

  26. Snell’s Law Fermat’s Principle Rays q1 Air Water q2 sin q1 / sin q2 = n21

  27. Wave Equation 1-D wave equation c = propagation speed Slinky: constant velocity wave propagation, no mass transfer, different from circulation eq.

  28. 1-D Wave Equation Solution T = wave period w = angular frequency LW 3.2.1

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

  30. 3-D Wave Equation with Source source spatial 2nd derivative Near-field Terms (Static Displacements) Solution Far-field Terms (P, S Waves)

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

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

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

  34. Generation of Tsunami from Near-field Term

  35. 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

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

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

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

  39. Natural Vibrations of the Earth Shearer Ch.8.6 Lay and Wallace, Ch. 4.6

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