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几乎所有的地球化学数据都是成分数据,其特征为各个元素含量的总和为一定值(e.g.,1 000 000 mg/kg or 100%)。成分数据的几何空间为Aitchison空间,其观测点的距离也属于Aitchison距离,它有别于欧式空间和欧式距离。因此,在地球化学数据处理前,需要打开成分数据,使基于欧式空间发展的地球化学处理方法可用来提取地球化学异常。此外,主成分分析是目前使用最广泛的多元统计方法之一。然而,它的第一主成分极易受到异常值的影响。因此,当数据中有异常值时,普通的主成分分析的结果可能有误差。稳健的主成分分析可以克服普通主成分分析方法的不足,其用MCD(reweighed minimum covariance determinant)来代替协方差,以减少异常值的影响。该文首先使用ILR变换(isometric logratio transformation)打开数据,再利用稳健的主成分综合多个元素的异常。结果显示该组合方法可有效识别研究区的地球化学异常。
Almost all of the geochemical data is compositional data and is characterized by a certain value for each elemental content (e.g., 1 000 000 mg / kg or 100%). The geometric space of the component data is Aitchison space, the distance between the observation points also belongs to Aitchison distance, which is different from the European space and the European distance. Therefore, before geochemical data processing, the composition data needs to be opened so that geochemical treatment methods based on the development of European space can be used to extract geochemical anomalies. In addition, PCA is one of the most widely used multivariate statistical methods. However, its first principal component is highly susceptible to outliers. Therefore, when there are outliers in the data, the result of ordinary principal component analysis may be inaccurate. Robust principal component analysis can overcome the deficiencies of the common principal component analysis method, which uses the MCD (reweighed minimum covariance determinant) instead of covariance to reduce the impact of outliers. The paper first uses the isometric logratio transformation to open the data and then uses the robust principal component to synthesize the anomalies of multiple elements. The results show that this method can effectively identify the geochemical anomalies in the study area.