Obtaining the equation of state for multiphase iron under Earth's core conditions using Bayesian statistics

Abstract

Iron is the primary constituent element of Earth's core, and its equation of state plays a pivotal role in understanding the thermodynamic properties of the core. However, uncertainties in experimental data have significant effects on the parameters within the iron equation of state. Using Bayesian statistical analysis coupled with Markov chain Monte Carlo simulation methods, we quantified the uncertainties in the equation of state parameters. During the simulation process, we proposed a simple yet efficient computational method for determining the probability of phase boundary data. The equation of state we obtained accurately reproduces various experimental data, including phase boundary experiments, static pressure data under different conditions, shock wave data, and sound velocity data at different states. With 100 posterior parameter samples, we predict that the density deficit of Earth's outer core falls within a range of approximately 9.5%–10.7%.