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  using an equation of state K(T f,P=0) G(T f,P=0)  (T f,P=0) K(T,P) G(T,P)  (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) Vp 2 =(K+4/3G)/  Vs 2 =G/  V  2 =K/ 

6. Total mass of the Earth Maskelyne (18 th ) 4.5 g/cm 3 Today 5.515 g/cm 3

7. Radius R=6371 km (known since Newton 17 th, Kepler) Mass M=5.9739*10 24 kg (Kepler) Average density  =5.515 g/cm 3 Density of surface rocks 2.5 g/cm 3 Density in the centre 13 g/cm 3

8. Moment of inertia about the axis of rotation J 2 Full sphere: J 2 =0.4MR 2 Hollow sphere J 2 =0.66MR 2 Astronomical observation (shape and rotation of the Earth) J 2 =0.33MR 2

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

10. Density from seismology In a homogeneous, self-compressed layer, far from phase transitions, d  /dr=0, dc/dr=0 and dP/dr=-  g 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  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)

20. 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  is compared to PREM

23. We can’t resolve the trade-offs