“Phase diagrams are the beginning of wisdom…” William Hume-Rothery obe



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“Phase diagrams are the beginning of wisdom…” -- William Hume-Rothery OBE




The Non-Linear Phase Equilibrium Problem



The Non-Linear Phase Equilibrium Problem



The Non-Linear Phase Equilibrium Problem





The Linearized Phase Equilibrium Problem: “Pseudocompound” Approximation



A Problem with Pseudocompounds



Conclusions for Part I



Equation of State, Stixrude & Bukowinski 1990



Computed Pyrolite (CaO-FeO-MgO-Al2O3-SiO2) Phase Relations



“Phase diagrams are the beginning of wisdom not the end of it.” -- William Hume-Rothery



Part II: the beginning of wisdom?



Putting g into geodynamics: What is the geodynamic equation of state (EoS)?



Putting g into geodynamics: What is the geodynamic equation of state (EoS)?



Putting g into geodynamics: What is the geodynamic equation of state (EoS)?



Optimization of exotic free energy functions: example h(s,P)



Optimization of exotic free energy functions: example h(s,P)



How do we put u(s,v) into geodynamic models? The energy (aka temperature) equation as an example



How do we put u(s,v) into geodynamic models? The energy (aka temperature) equation as an example



A morsel of wisdom?



Enter Amir Khan: Geophysical Inversions for Planetary Composition, Temperature and Structure



Inversion Strategy



Searching for the Answer



Bayesian Inversion: Prior Probability, Likelihood and Posterior Probability



Bayesian Inversion: Prior Probability, Likelihood and Posterior Probability



Bayesian Inversion: Prior Probability, Likelihood and Posterior Probability



What’s good about an EM inversion?



The Observations



What’s bad about EM inversion? The forward model.



Parameterization of the Physical Model







Thermal models



mantle composition





Mantle Mineralogy



Mantle Conductivity Profile



Density and Seismic Velocities



Resolution and Stability



Is there any hope of (at least) an inversion consensus?





Mundane Conclusion

  • The EM inversion results suggest a relatively homogeneous, superadiabatic mantle of chondritic composition

  • More generally terrestrial inversions yield low Mg/Si (1.05-1.2) and low bulk CaO and Al2O3



Mars



What is known well: 4 Scalars (Yoder et al. ‘03)



Martian Mantle Composition



Martian Mantle Mineralogy



Core Radius and Density



Areotherms and the Frozen Core Dilemma



Martian Conclusions



“This is not the end, this is not even the beginning of the end, perhaps it is the end of the beginning.” –- Winston Churchill

  • Free energy minimization provides the basis for a general physical model that permits joint inversion of a priori unrelated geophysical data sets (seismic, gravity, electromagnetic)



Martian Temperature Distributions



Seismic Velocities and Thermodynamic Consistency



Core Radius and CMB Temperature



Martian Inversion Resolution (T at 1200 km)



Trade-offs



Mapping Strategy





“Phase diagrams are the beginning of wisdom not the end of it.” -- Sir William Hume-Rothery



Optimize what when? And an Unexpected Virtue of the Linearized Solution



Forward Geodynamic Modelling: Subduction Zone Decarbonation







Slab fluid composition and production



Slab Properties



Some thoughts about cultural differences and data

  • Geophysics/Mineral physics

  • Limited data, lots of theory

  • Individual minerals and phase transitions

  • “A good experiment ****s any computation” D. Yuen, 2005

  • Pro: Amenable to simple parameterization for geodynamic models

  • Con: Ignores strong autocorrelation of thermodynamic parameters





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