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Elastic moduli Young’s modulus, E –Shortening || stress Bulk modulus, k –Volume change / pressure Shear modulus,  –Rotation plane stress Poisson’s ratio,

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Presentation on theme: "Elastic moduli Young’s modulus, E –Shortening || stress Bulk modulus, k –Volume change / pressure Shear modulus,  –Rotation plane stress Poisson’s ratio,"— Presentation transcript:

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  11 =E(  L/L) LL

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

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

4 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 Elastic moduli

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

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

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

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

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

11 Harold Jeffreys The core is fluid (1926)

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

13 Inge Lehmann Discovery of the Earth’s inner core (1936) P-wave pathsS-waves

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

15 Don Anderson Adam Dziewonski Preliminary Reference Earth Model (1981)

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17 PREM radially symmetric earth model Best fit to following data: P and S wave travel times versus  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)

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

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23 # great circles = l -1 Zero crossings

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


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