1. The Earth in three dimensions From seismology to composition and temperature

4. Is this the only model compatible with the data? Deal et al. JGR 1999 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!

6. Seismic tomography (Masters et al., 2000)

7. 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. Radial variation of dlnVs/dlnVp most popular diagnostic

8. Interpretation: ratios Vp=  [(K+4/3G)/  ] Vs=  [G/  ] The ratio dlnVs/dlnVp=2.25 if the only variation is in G for a Poisson solid. This is also observed in laboratory experiments for thermal variations.

12. 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

13. 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 dlnVp=0.003 and dlnVs=0.006, we find dT=-190K and dX –0.011 which is -1.1% perovskite variation, as expected

14. Probabilistic tomography

15.  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  dlnVs=0.12 %  dlnVΦ=0.26 %  dlnρ=0.48 %

16. Likelihood of correlation between seismic parameters Evidence for chemical heterogeneity Vs-V 

17. Incompressibility: K S =-V(  P/  V) S Thermal expansivity  =-1/  (  /  T) P Grüneisen parameter (  P/  T) V =  C V /V Anderson-Grüneisen :  =-1/  Ks(  Ks/  T) P Anderson-Grüneisen :  =-1/  Ks(  G/  T) P  = Ks’-1-  +q Ks’~4, q~1,  ~1,  >6 dln  /dlnVs~0.2

18. Likelihood of rms-amplitude of seismic parameters Evidence for chemical heterogeneity RMS density

21. Likelihood of correlation between seismic and thermo- chemical parameters in the lowermost mantle

22. oRicard et al. JGR 1993 oLithgow-Bertelloni and Richards Reviews of Geophys. 1998 oSuperplumes