地球早期大气氧气上升的分形与多重分形分析
Fractal and Multifractal Analysis of the Rise of Oxygen in Earth's Early Atmosphere
AI总结：
针对早期地球大气模型参数不确定的问题，本文加入不同强度噪声，并用分形与多重分形分析揭示大氧化事件后氧、碳和甲烷时间序列的长程相关及多重分形特征。
摘要：
发生在24亿至22亿年前的地球大气氧气上升被称为地球的“大氧化事件”，其对地球生命发展的影响深远。此后，地球氧气水平的增加持续存在，但速度更为平缓。针对这些过程提出的基础数学模型依赖于物理参数，而由于地质和生物数据的不确定性，这些参数的数值目前尚未得到充分确认。本文对先前开发的一个地球大气模型进行修改，通过加入不同强度的噪声来解释参数的不确定性。文中利用分形和多重分形分析，研究噪声对早期地球氧气、碳和甲烷随时间变化的影响。我们表明，大氧化事件之后的时间变化不能用单一分形维数恰当地描述，因为它们表现出多重分形特征。所得结果证明，所获得的时间序列呈现出由长程时间相关性导致的多重分形性。
英文摘要：
The rise of oxygen in Earth's atmosphere that occurred 2.4 to 2.2 billion years ago is known as the Earth's Great Oxidation, and its impact on the development of life on Earth has been profound. Thereafter, the increase in Earth's oxygen level persisted, though at a more gradual pace. The proposed underlying mathematical models for these processes are based on physical parameters whose values are currently not well-established owing to uncertainties in geological and biological data. In this paper, a previously developed model of Earth's atmosphere is modified by adding different strengths of noise to account for the parameters' uncertainties. The effects of the noise on the time variations of oxygen, carbon and methane for the early Earth are investigated by using fractal and multifractal analysis. We show that the time variations following the Great Oxidation cannot properly be described by a single fractal dimension because they exhibit multifractal characteristics. The obtained results demonstrate that the time series as obtained exhibit multifractality caused by long-range time correlations.
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