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Seismic Waves & Earth Structure: Theory and Application

Explore wave propagation, near-field and far-field terms, normal modes, and structures of the Earth crust-mantle-core in seismology. Understand Ray theory, wave equations, and the complexities of seismic waves.

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Seismic Waves & Earth Structure: Theory and Application

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

  25. 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)

  26. 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

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

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

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

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

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

  32. 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

  33. Why are observed seismograms so messy ?

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

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