Density in the Earth

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Density in the Earth
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So far, we have seen how to extrapolate K,G and r
using an equation of state K(Tf,P0) G(Tf,P0) r(T
f,P0) K(T,P) G(T,P) r(T,P)
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Total mass of the Earth
Maskelyne (18th) 4.5 g/cm3 Today 5.515 g/cm3
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Radius R6371 km (known since Newton 17th,
Kepler) Mass M5.97391024 kg (Kepler) Average
density r5.515 g/cm3 Density of surface rocks
2.5 g/cm3 Density in the centre 13 g/cm3
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Moment of inertia about the axis of rotation J2
Full sphere J20.4MR2 Hollow sphere
J20.66MR2 Astronomical observation (shape and
rotation of the Earth) J20.33MR2
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Density from seismology
We can write
with Ttemperature, Ppressure, F phase
transition and cchemical variation
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Density from seismology
In a homogeneous, self-compressed layer, far from
phase transitions, dF/dr0, dc/dr0 and
dP/dr-rg g is the gravitational acceleration
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Density from seismology
In a convecting mantle, the temperature gradient
is close to adiabatic
which gives
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Density from seismology
We finally get
using
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Density from seismology
This Adams-Williamsons law
Where t describes the deviation from adiabacity
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Density from seismology
Which can be rewritten as
The Earth is abiabatic if the Bullen parameter
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Temperature in the Earth
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Composition in the Earth
Assume that the mantle (core) is adiabatic and
homogeneous, make a zero pressure extrapolation
Stacey PEPI 2004
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Composition in the Earth
An approach based on high pressure and high
temperature mineral physics data (Deschamps and
Trampert, EPSL 2004)
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Heating (1-3)
Adiabatic compression (4-7)
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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

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