how well do we know density in the earth?
DESCRIPTION
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: - PowerPoint PPT PresentationTRANSCRIPT
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How well do we know density in the Earth?
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Velocity in the Earth is well known
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So far, we have seen how to extrapolate K,G and using an equation of state
K(Tf,P=0)
G(Tf,P=0)
(Tf,P=0)
K(T,P)
G(T,P)
(T,P)
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What does it all mean?
Thermo-chemicalParameterization:•Temperature•Fraction of Pv•Fraction of total Fe
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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)/• Vs2=G/• V2=K/
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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 R=6371 km (known since Newton 17th, Kepler)
Mass M=5.9739*1024 kg (Kepler)
Average density =5.515 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: J2=0.4MR2
Hollow sphere J2=0.66MR2
Astronomical observation (shape and rotation of the Earth) J2=0.33MR2
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Density from seismology
dr
dc
cdr
d
dr
dT
Tdr
dP
Pdr
d
We can write
with T=temperature, P=pressure, phase transition and c=chemical variation
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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
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Density from seismology
In a convecting mantle, the temperature gradient is close to adiabatic
CKP
TPs
S
TT
dP
dT
which gives
dr
dPT
dr
dT
CP
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Density from seismology
We finally get
CP
gTg
dr
d
using
KVV
PK
TS
SP
S
S
P
22
3
4,,
1
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Density from seismology
This Adams-Williamson’s law
g
dr
d
Where describes the deviation from adiabacity
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Density from seismology
Which can be rewritten as
gdr
d
gdP
dK S
11
The Earth is abiabatic if the Bullen parameter
11
dr
d
gdP
dK S
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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 is compared to PREM
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We can’tresolve the trade-offs