Interpreting the Paleomagnetic Field Using Stochastic Models

地球磁场是地球宜居性的一个重要方面，但人们对磁场的长期行为知之甚少。历史观察提供了宝贵的信息来源，但这一记录的持续时间太短，无法得出有意义的结论。相反，我们必须依靠古地磁观测来建立更完整的理解。不幸的是，古地磁观测和潜在动力学之间的联系既不简单也不直接。一种很有前途的新策略将被开发出来，它使用随机模型来量化偶极场的时间依赖性。这种方法非常适合于这项任务，因为它侧重于磁场的可观测部分(即偶极)，同时以统计方式处理未观测到的磁场部分。这项工作的预期结果是双重的。首先，随机模型将使研究人员能够对磁场的许多属性做出定量预测，包括偶极极性的反转速率以及磁场的短期中断持续时间(通常称为漂移)。其次，随机模型可以接受物理解释，这意味着该团队可以在将古地磁观测与地球深处的物理过程联系起来方面取得重要进展。让研究生和大四的本科生参与该项目将促进物理建模、数据分析、统计和高性能计算方面的技能。第一步是使用过去两百万年来对偶极场的观测来构建随机模型。对偶极涨落功率谱的预测可能与物理性质有关，如核心的电导率或对流的翻转时间。第二个任务将解决观测到的偶极涨落的自协方差问题。地核中的湍流运动驱动偶极子场的随机波动，因此对自协方差的详细估计为偶极产生的机制提供了独特的见解。第三项任务涉及极性转变的持续时间，目的是确定在逆转期间起作用的时间尺度和过程。最后，研究人员将在初始状态没有完全建立在稳定的极性下，在假设它们代表极性转变的情况下，定量评估短克莱恩的相对出现情况。在每个阶段，他们将通过与现有观察结果进行详细比较来评估模型的成功或失败。

Earth's magnetic field is an important aspect of our planet's habitability, yet the long-term behavior of the magnetic field is poorly understood. Historical observations provide a valuable source of information, but the duration of this record is just too short to draw meaningful conclusions. Instead, we must rely on paleomagnetic observations to build a more complete understanding. Unfortunately, the link between paleomagnetic observations and the underlying dynamics is neither simple nor direct. A promising new strategy will be developed using stochastic models to quantify the time dependence of the dipole field. This approach is ideally suited for the task because it focuses on the observed part of the field (i.e. the dipole), while treating the unobserved part of the magnetic field in a statistical fashion. The expected outcome of this work is two-fold. First, the stochastic models will enable the investigators to make quantitative predictions for many properties of the magnetic field, including the rates of reversal in the dipole polarity as well as the duration of short disruptions in the magnetic field (often called excursions). Second, the stochastic models are amenable to physical interpretation, which means that the team can make important advances in connecting paleomagnetic observations to physical processes deep inside the planet. Engagement of graduate and senior undergraduate students in the project will promote skills in physical modeling, data analysis, statistics, and high-performance computing.The proposed work identifies four main tasks. The first step is to construct stochastic models using observations of the dipole field over the past two million years. Predictions for the power spectrum of dipole fluctuations can be related to physical properties, like the electrical conductivity of the core or the overturn time for convection. The second task will address the autocovariance of the observed dipole fluctuations. Turbulent motions in Earth's core drive random fluctuations in the dipole field, so detailed estimates of the autocovariance offer unique insights into the mechanisms of dipole generation. The third task deals with the duration of polarity transitions with the aim of identifying timescales and processes at work during reversals. Finally, the investigators will quantitatively assess the relative occurrence of short chrons under the hypothesis that they represent polarity transitions when the initial state is not fully established in a stable polarity. At each stage they will assess the success or failure of the models by making detailed comparisons with available observations.