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

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. Faulting. Seismic waves.

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

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  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. Faulting Seismic waves

  3. Homogeneous Earth

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

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

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

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

  8. 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

  9. Forward Branch Backward Branch

  10. Forward Branch Shadow Zone Forward Branch Backward Branch

  11. 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

  12. PcP Core Reflections

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

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

  15. 1-D Wave Equation Solution T = wave period w = angular frequency LW 3.2.1

  16. 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

  17. Period Wavelength

  18. 3-D Wave Equation with Source source spatial 2nd derivative Near-field Terms (Static Displacements) Solution Far-field Terms (P, S Waves)

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

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

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

  22. Generation of Tsunami from Near-field Term

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

  24. surface waves

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

  26. 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)

  27. A(t) = A0e -ω0t/2Q Amplitude and Intensity Seismic waves loose amplitude with distance traveled - attenuation So the amplitude of the waves depends on distance from the earthquake. Therefore unlike magnitude intensity is not a single number.

  28. Modified Mercalli Intensity I Barely felt II Felt by only few people III Felt noticeably, standing autos rock slightly IV Felt by many, windows and walls creak V Felt by nearly everyone, some dished and windows broken VI Felt by all, damaged plaster and chimneys VII Damage to poorly constructed buildings VIII Collapse of poorly constructed buildings, slight damage to well built structures IX Considerable damage to well constructed buildings, buildings shifted off foundations X Damage to well built wooden structures, some masonary buildings destroyed, train rails bent, landslides XI Few masonary structure remain standing, bridges destroyed, ground fissures XII Damage total

  29. 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

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

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

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

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

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

  35. 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

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