Earth's Outer Core Properties Estimated Using Bayesian Inversion of Normal Mode Eigenfrequencies

The outer core is arguably Earth's most dynamic region, and consists of an iron-nickel liquid with an unknown combination of lighter alloying elements. Frequencies of Earth's normal modes provide the strongest constraints on the radial profiles of compressional wavespeed, VΦ, and density, ρ, in the outer core. Recent great earthquakes have yielded new normal mode measurements; however, mineral physics experiments and calculations are often compared to the Preliminary reference Earth model (PREM), which is 35 years old and does not provide uncertainties. Here we investigate the thermo-elastic properties of the outer core using Earth's free oscillations and a Bayesian framework. To estimate radial structure of the outer core and its uncertainties, we choose to exploit recent datasets of normal mode centre frequencies. Under the self-coupling approximation, centre frequencies are unaffected by lateral heterogeneities in the Earth, for example in the mantle. Normal modes are sensitive to both VΦ and ρ in the outer core, with each mode's specific sensitivity depending on its eigenfunctions. We include a priori bounds on outer core models that ensure compatibility with measurements of mass and moment of inertia. We use Bayesian Monte Carlo Markov Chain techniques to explore different choices in parameterizing the outer core, each of which represents different a priori constraints. We test how results vary (1) assuming a smooth polynomial parametrization, (2) allowing for structure close to the outer core's boundaries, (3) assuming an Equation-of-State and adiabaticity and inverting directly for thermo-elastic parameters. In the second approach we recognize that the outer core may have distinct regions close to the core-mantle and inner core boundaries and investigate models which parameterize the well mixed outer core separately from these two layers. In the last approach we seek to map the uncertainties directly into thermo-elastic parameters including the bulk modulus, its pressure derivative, and molar mass and volume, with particular attention paid to the (inherent) trade-offs between the different coefficients. We discuss our results in terms of added uncertainty to the light element composition of the outer core and the potential existence of anomalous structure near the outer core's boundaries.