Bayesian Modeling of the Equation of State for Liquid Iron in Earth's Outer Core
Bayesian Modeling of the Equation of State for Liquid Iron in Earth's Outer Core
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DOI：
10.1029/2021jb023062
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发表时间：
2021-12
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通讯作者：
T. Matsumura;Y. Kuwayama;K. Ueki;T. Kuwatani;Y. Ando;K. Nagata;S. Ito;H. Nagao
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作者：
T. Matsumura;Y. Kuwayama;K. Ueki;T. Kuwatani;Y. Ando;K. Nagata;S. Ito;H. Nagao
利用贝叶斯状态方程模型（EoS）对地球外核条件下液态铁的密度（ρ）和P波速度（VP）进行了约束。在如此高的压力（P）和温度（T）下的实验在技术上具有挑战性，因此可用于EoS的参数优化的数据很少。我们的贝叶斯推理模型成功地估计后验概率分布的参数和未观察到的数据，通过使用汉密尔顿蒙特卡罗方法。这些后验概率分布允许计算液态铁沿着绝热P-T分布的P-p和P-VP分布以及相关的可信区间。假设核幔边界的温度为3，500 - 4，200 K，P-ρ和P-VP剖面显示ρ和VP与初步参考地球模型的偏差分别约为8-11%和-3%至-5%。CMB和内核边界的P‐ρ剖面的95%可信区间的偏差分别为6.9-9.7%和6.5- 9.8%。P-VP曲线的等效偏差分别为−4.8%至−1.5%和−6.0%至− 2.3%。EoS的贝叶斯建模能够整合包括未观测数据在内的小数据集，并评估物理特性（如ρ和VP）的不确定性范围，这对于与堆芯的地震学特性进行比较至关重要。
We use Bayesian modeling of the equation of state (EoS) to constrain the density (ρ) and P wave velocity (VP) of liquid iron under conditions of Earth's outer core. Experiments at such high pressures (P) and temperatures (T) are technically challenging, so there are few data available to use in parameter optimization of the EoS. Our Bayesian inference modeling successfully estimates the posterior probability distribution of the parameters and unobserved data by using the Hamiltonian Monte Carlo method. These posterior probability distributions allow calculation of P‐ρ and P‐VP profiles of liquid iron along the adiabatic P‐T profile together with the associated credible intervals. Assuming that the temperature at the core‐mantle boundary (CMB) is 3,500–4,200 K, the P‐ρ and P‐VP profiles show deviations of ρ and VP from the preliminary reference Earth model of about 8–11% and −3% to −5%, respectively. Deviations of the 95% credible intervals of the P‐ρ profile for the CMB and the inner core boundary are 6.9–9.7% and 6.5–9.8%, respectively. Equivalent deviations of the P‐VP profile are −4.8% to −1.5% and −6.0% to −2.3%, respectively. Bayesian modeling of the EoS enables integration of small data sets that include unobserved data and evaluation of uncertainty ranges of physical properties, such as ρ and VP, which are essential for comparison with seismological properties of the core.