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
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 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
“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
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
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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