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作为非线性、复杂性理论的重要领域之一,多重分形理论所提供的奇异性、广义自相似性、分形谱系等概念和相关模型,不仅能够客观的描述成矿系统、成矿过程、成矿富集规律,还提供了定量模拟和识别成矿异常的有效模型。本文从小波系数的角度出发,与目前惯用的盒子测度法对比,进行多重分形分析,从原理上来看前者是基于复杂系统中的概率测度值的积分,而后者是基于信号测度域的差分。验证数据分别来自经典矿物分割模型deWijs模型。结果表明,基于盒子测度法在小尺度的数据方面表现出了比WLs(Wavelet leaders,WLs)更高的稳定性以及优越性,但是对于大尺度的数据,两者的分析结果相同,基于WLs的多重分形分析手段对于严重依赖方法和数据本身的多重分析手段来说,可以作为一种选择。
As one of the important fields of nonlinear and complexity theory, concepts and related models such as singularity, generalized self-similarity and fractal pedigree provided by multi-fractal theory can not only objectively describe metallogenic systems, metallogenic processes, mineralization Enrichment law, but also provides an effective model for quantitative simulation and identification of metallogenic anomalies. In this paper, from the perspective of wavelet coefficients, compared with the conventional box measure method, the multifractal analysis is carried out. The former is based on the integral of the probability measure value in a complex system and the latter is based on the difference of the signal measure range. The validation data are from the deWijs model of the classical mineral partition model. The results show that the box-based measure method has higher stability and superiority than WLs (Wavelets leaders, WLs) in small-scale data, but the analysis results of the two are the same for the large-scale data. Based on the WLs Multifractal analysis can be an option for multiple analyzes that rely heavily on methods and data themselves.