基于遗传算法的多母体正态分离及其地质应用

摘要

In the very long geological evolution history,earth surface has undergone multi-period and multistage geological processes,and the distribution of the same element in the same stratum differs or its material source might have come from different matrixes,which results in data histogram presenting a multimodal morphology.Multimodal separation is the basis of differentiating material sources,and helps improve geological interpretation level.The fact that geological data mostly obey the normal distribution (or logarithmic normal distribution) provides mathematical basis for multimodal separation.This paper explains the math principles of multiple matrix sample data separation and uses genetic algorithm as implementation approach to theoretically prove that genetic algorithm has a better effect on multiple matrix sample data separation,and its goodness of fit can be up to 95％.An analysis of practical examples shows that the genetic algorithm can correctly distinguish 2 kinds of lithology of the stratum,which suggests that it has practical significance in geological research.%在漫长的地质演化史中,地球表面经历了多期多阶段的地质作用,同一地层同一元素其分布状态存在差异,或其物质来源可能来自不同的母体,致使数据直方图呈现多峰形态.多峰分离是区分物质来源的基础,有利于提高地质解释质量.而地学数据大多服从正态分布(或对数正态分布),这就为多峰分离提供了数学依据.文章阐述了多母体样本数据分离的数学原理,并以遗传算法作为实现手段,从理论上证明了遗传算法对多母体样本数据的分离具有较好效果,其拟合优度可达95％.通过实例分析,遗传算法能正确区分白垩系大凤组第一段(Kd1)地层的两种岩性,说明其在地质研究中具有实际意义.