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How well do we know density in the Earth?

How well do we know density in the Earth?. Velocity in the Earth is well known. So far, we have seen how to extrapolate K,G and r using an equation of state K(T f ,P=0) G(T f ,P=0) r (T f ,P=0) K(T,P) G(T,P) r (T,P). What does it all mean? Thermo-chemical Parameterization:

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How well do we know density in the Earth?

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  1. How well do we know density in the Earth?

  2. Velocity in the Earth is well known

  3. So far, we have seen how to extrapolate K,G and r using an equation of state K(Tf,P=0) G(Tf,P=0) r(Tf,P=0) K(T,P) G(T,P) r(T,P)

  4. What does it all mean? • Thermo-chemical • Parameterization: • Temperature • Fraction of Pv • Fraction of total Fe

  5. Inferring the Earth’s interior • If we know density we can link laboratory measurements to models of the Earth interior (temperature and composition) • Vp2=(K+4/3G)/r • Vs2=G/r • Vf2=K/r

  6. Total mass of the Earth Maskelyne (18th) 4.5 g/cm3 Today 5.515 g/cm3

  7. Radius R=6371 km (known since Newton 17th, Kepler) Mass M=5.9739*1024 kg (Kepler) Average density r=5.515 g/cm3 Density of surface rocks 2.5 g/cm3 Density in the centre 13 g/cm3

  8. Moment of inertia about the axis of rotation J2 Full sphere: J2=0.4MR2 Hollow sphere J2=0.66MR2 Astronomical observation (shape and rotation of the Earth) J2=0.33MR2

  9. Density from seismology We can write with T=temperature, P=pressure, F= phase transition and c=chemical variation

  10. Density from seismology In a homogeneous, self-compressed layer, far from phase transitions, dF/dr=0, dc/dr=0 and dP/dr=-rg g is the gravitational acceleration

  11. Density from seismology In a convecting mantle, the temperature gradient is close to adiabatic which gives

  12. Density from seismology We finally get using

  13. Density from seismology This Adams-Williamson’s law Where t describes the deviation from adiabacity

  14. Density from seismology Which can be rewritten as The Earth is abiabatic if the Bullen parameter

  15. Temperature in the Earth

  16. Composition in the Earth Assume that the mantle (core) is adiabatic and homogeneous, make a zero pressure extrapolation Stacey PEPI 2004

  17. Composition in the Earth An approach based on high pressure and high temperature mineral physics data (Deschamps and Trampert, EPSL 2004)

  18. Heating (1-3) Adiabatic compression (4-7)

  19. Method • Pressure is known from PREM for each depth • We vary potential temperature (end temperature is calculated along adiabat) • We vary average composition (Pv, Fe) between certain limits • An adiabatic compression is done for each mineral • VRH average is calculated • Finally, Vp, Vs and r is compared to PREM

  20. We can’t resolve the trade-offs

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