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Multiplicative Cascade Simulations of Geochemical Distribution Patterns in Relatively Open Systems

机译:相对开放系统中地球化学分布模式的级联模拟

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As we all know, it's of great significance to study geochemical element distribution patterns by using fractal and multifractal methods in recent years. Although many authors have proved through computer simulations from different aspects that various geochemical fields follow some kinds of multifractal properties, the forming mechanism of one multifractal geochemical field is still vexing. Especially, many simulations based on De Wijs model supposed that the systems of interest is closed. That is to say, there is not any kind of materials adding or removing and the system is balanced during the simulation processes. In essence, any process is not absolutely conserved and it has experienced some kinds of interactions with surroundings to different degrees. However, little attention has been paid to the fractal and multifractal simulations of open systems. In this paper, we applied one typical multifractal model, called Moran cascade process, and one famous calculation method, the method of moments, to investigate the relationship between different multifractal spectrum curve shapes and the enrichment and depletion extents of geochemical fields. Three Monte Carlo Simulation experiments based on Moran Cascade Process are being presented to generate some random data, individually drawn from multifractal data sets with different similarity ratios. By analyzing their corresponding shapes of their multifractal spectra, the experiments are indicative of the possible formation mechanisms of elements in geochemical fields. It's found mat the multifractal spectrum curve shapes are completely dependent on the similarity ratios of the geochemical field of interest, which means, the multifractal spectrum shapes are closely associated with the enrichment and depletion mechanisms of the field in study.
机译:众所周知,近年来利用分形和多重分形方法研究地球化学元素的分布格局具有重要意义。尽管许多作者从不同方面通过计算机模拟证明了各种地球化学场都具有某种多重分形特性,但一个多重分形地球化学场的形成机理仍然令人困惑。尤其是,许多基于De Wijs模型的模拟都假定目标系统是封闭的。也就是说,在仿真过程中没有添加或删除任何材料,并且系统处于平衡状态。从本质上讲,任何过程都不是绝对守恒的,它与周围环境发生了不同程度的某种相互作用。但是,很少关注开放系统的分形和多重分形模拟。在本文中,我们应用了一种典型的多重分形模型,称为Moran级联过程,以及一种著名的计算方法,即矩量法,研究了不同的多重分形谱曲线形状与地球化学场的富集和枯竭程度之间的关系。提出了三个基于Moran级联过程的蒙特卡罗模拟实验,以生成一些随机数据,这些数据是分别从具有不同相似率的多重分形数据集中得出的。通过分析其相应的多重分形光谱形状,实验表明了地球化学领域中元素的可能形成机理。已经发现,多重分形谱曲线的形状完全取决于感兴趣的地球化学场的相似率,这意味着多重分形谱的形状与研究场的富集和耗尽机制密切相关。

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