[M-GI39] データ駆動地球惑星科学

[MGI39-08] Bayesian modeling of the equation-of-state for liquid iron under high-P and high-T conditions corresponding to the Earth’s outer core

*松村 太郎次郎¹、桑山 靖弘²、上木 賢太³、桑谷 立^3,6、安藤 康伸¹、永田 賢二^4,6、伊藤 伸一⁵、長尾 大道⁵ (1.産業技術総合研究所機能材料コンピュテーショナルデザイン研究センター、2.東京大学地球惑星科学専攻、3.国立研究開発法人海洋研究開発機構、4.国立研究開発法人物質・材料研究機構、5.東京大学地震研究所、6.独立行政法人科学技術振興機構さきがけ )

キーワード：ベイズ推定、状態方程式、液体鉄、地球の外核

We demonstrate Bayesian modeling of the equation-of-state (EoS) by using experimental data sets to constrain the density (ρ) and the P-wave velocity (V_P) of liquid iron under high–pressure (P) and high–temperature (T) conditions corresponding to the Earth’s outer core. As an experiment under the conditions of high–P and high–T is still technically challenging, an optimization of the parameters of EoS is required to be performed efficiently by using small amount of data sets including unobservable data. To analyze such data sets, the parameters and unobservable data were assumed to be random variables in the Bayesian inference, and the Hamiltonian Monte Carlo method successfully calculated the posterior probability density functions of the parameters and unobservable data. These posterior densities enable us to estimate the EoS curves with the credible intervals and the P–ρ and P–V_P relations of liquid iron along the adiabatic P–T paths corresponding to the Earth’s outer core. The P–ρ and P–V_P relations showed that the deviations of ρ and V_P from the preliminary reference Earth model are in the ranges of 8–10% and -3–-5%, respectively, when the temperature at the core-mantle boundary is assumed to be in the range of 3500–4200K.