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Elastic moduli

Elastic moduli. Young’s modulus, E Shortening || stress Bulk modulus, k Volume change / pressure Shear modulus,  Rotation plane stress Poisson’s ratio,  Ratio perp/parallel strains.  L.  11 =E(  L/L). Elastic moduli. Young’s modulus, E Shortening || stress Bulk modulus, k

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Elastic moduli

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  1. Elastic moduli • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains L 11=E(L/L)

  2. Elastic moduli • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains K=-V dP/dV =  dP/d

  3. Elastic moduli • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains  = xy/xy/2

  4. Elastic moduli • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains =-22/11

  5. Elastic moduli Auxetic material • Young’s modulus, E • Shortening || stress • Bulk modulus, k • Volume change / pressure • Shear modulus,  • Rotation plane stress • Poisson’s ratio,  • Ratio perp/parallel strains =-22/11

  6. Richard Oldham Discovery of the Earth’s (outer) core (1906)

  7. Richard Oldham Discovery of the Earth’s (outer) core (1906)

  8. Andrija Mohorovicic Discovery of the MOHO discontinuity (1909 or 1910?)

  9. Beno Gutenberg Accurate measure of the core-mantle boundary--or “Gutenberg discontinuity”--radius (1912)

  10. Harold Jeffreys The core is fluid (1926)

  11. Inge Lehmann Discovery of the Earth’s inner core (1936)

  12. Inge Lehmann P-wave paths S-waves Discovery of the Earth’s inner core (1936)

  13. “Travel time” of seismic phases vs. epicentral distance (Jeffreys-Bullen)

  14. Adam Dziewonski Don Anderson Preliminary Reference Earth Model (1981)

  15. Preliminary Reference Earth Model (1981)

  16. PREM radially symmetric earth model • Best fit to following data: • P and S wave travel times versus D • Body wave evidence for boundaries • crust-mantle • transition zone (410 km, 660 km jumps) • core-mantle boundary • outer-inner core boundary • Surface wave phase velocities as a function of wave period • Rayleigh waves (SV and P) • Love waves (SH) • Periods of free oscillations • Spheroidal (Standing Rayleigh waves + gravity) • Torsional (Standing Love waves)

  17. Fowler, page 106 Phases: freq dec. as distance inc. Groups: constant frequency/period

  18. # great circles = l-1 Zero crossings

  19. Varies w/ depth, too! Diff. modes sense different depths. “Sensitivity kernel”

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