The Earth in three dimensions

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The Earth in three dimensions

• From seismology to composition and temperature

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Is this the only model compatible with the data?
If we project some chosen model onto the null
space of the forward operator
Then add it to original model. The same data fit
is guaranteed!
Deal et al. JGR 1999
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Seismic tomography (Masters et al., 2000)
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Radial variation of dlnVs/dlnVp most popular
diagnostic
Robertson and Woodhouse, 1996
The observations of RW96 and SD97 reinforce the
conclusion that we should seek a compositional
interpretation of tomographically observed
velocity anomalies in the lower mantle Stacey,
1998.
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Interpretation ratios
Vp?(K4/3G)/r Vs?G/r The ratio
dlnVs/dlnVp2.25 if the only variation is in G
for a Poisson solid. This is also observed in
laboratory experiments for thermal variations.
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Average ratios of dlnVs/dlnVp are not useful if
more than one cause is at play. It can best give
a qualitative indication. The full histogram
gives statistical evidence of compositional
anomalies, but they can not be located in the
Earth
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Direct inversion
Example of a descending slab
Using ?lnVp/?T-1.9x10-5, ?lnVs/?T-3.0x10-5 ?lnVp
/?X 0.056 and ?lnVs/?X-0.025, X is the
perovskite content Taking dlnVp0.003 and
dlnVs0.006, we find dT-190K and dX 0.011 which
is -1.1 perovskite variation, as expected
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Probabilistic tomography
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• Averaged and gravity filtered models over 15x15
  degree equal area caps
• Likelihoods in each cap are nearly Gaussian
• Most likely model (above one standard deviation)
• Uniform uncertainties
• dlnVs0.12
• dlnVF0.26
• dln?0.48

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Likelihood of correlation between seismic paramete
rs
Evidence for chemical heterogeneity Vs-VF
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Incompressibility KS-V(?P/?V)S Thermal
expansivity a-1/r(?r/?T)P Grüneisen parameter
(?P/?T)VgCV/V Anderson-Grüneisen
d-1/aKs(?Ks/?T)P Anderson-Grüneisen
e-1/aKs(?G/?T)P d Ks-1-gq Ks4, q1, g1,
egt6 dlnr/dlnVs0.2
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Likelihood of rms-amplitude of seismic parameters
Evidence for chemical heterogeneity RMS density
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Likelihood of correlation between seismic and
thermo-chemical parameters in the lowermost mantle
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• Ricard et al. JGR 1993
• Lithgow-Bertelloni and Richards Reviews of
  Geophys. 1998
• Superplumes

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How good is
tomography