AI 中文总结
该研究针对观测噪声扭曲有序模式概率分布的问题，利用优化理论表征其影响，提出无需拟合的噪声量化与校正策略，并通过古地磁记录分析验证方法，以探究地球偶极子演化的动力学属性。
AI 中文摘要
Bandt-Pompe排列熵框架与复杂度-熵因果平面已成为表征时间序列动力学特性的标准工具。然而，观测噪声会扭曲有序模式概率分布，可能系统性地将时间序列误置于因果平面内，损害动力学分类。该效应对地球物理信号尤为关键，这类信号通常采样质量差、不规则且信噪比低。本研究利用优化（majorization）形式主义表征有序模式统计的扭曲，给出理论结果并提出校正策略，可在实际测量条件下恢复可区分性。为此，我们引入的方法可表征含噪动力学序列，还能无需拟合程序即可量化观测噪声。最后，我们通过分析古地磁记录说明该方法，以确定地球偶极子的地质演化更适合用随机系统还是混沌系统描述。
英文摘要
The Bandt-Pompe permutation entropy framework, alongside the complexity-entropy causality plane, has become a standard tool for characterizing the dynamical properties of time series. However, observational noise distorts ordinal pattern probability distributions in ways that can systematically misplace time series within the causality plane, compromising dynamical classification. This effect is particularly relevant for geophysical signals, which are typically poorly and irregularly sampled, and have a low signal-to-noise level. In this work, we characterize the distortions on ordinal pattern statistics using the formalism of majorization. We provide theoretical results and propose corrective strategies that restore discriminability under realistic measurement conditions. To achieve this, we introduce methodology that allows the characterization of noisy dynamical series and further allows the quantification of observational noise without the need of a fitting procedure. Finally, we illustrate our methodology by analyzing paleomagnetic records to determine if the geological evolution of the Earth dipole is better described by a stochastic or chaotic system.
