## 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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