关键词: 马氏距离, 核马氏距离, 主成分得分, 地球化学数据, 多元异常识别

Abstract:

Mahalanobis distance is an effective synthetic index for multivariate geochemical anomaly identification in the situation where geochemical data satisfy multivariate normal distribution. However, complex geological system, multi-stage mineralization, and multiple ore-controlling factors, usually result in the ambiguity and nonlinearity of the critical surface of multivariate geochemical anomaly. This complicated surface can’t be properly represented by the smooth hyper-ellipsoid defined by Mahalanobis distances. Kernel functions can nonlinearly transform the sample set onto a feature space, where the background sample image population constructs a manifold while anomaly sample images distribute the boundary or out space of the manifold. The kernel Mahalanobis distances from a sample image to the sample image population can be computed and used to determine whether the sample is an outlier. The method is applied to the multivariate geochemical anomaly identification of Baishan region, Jilin Province, China. Kernel Mahalanobis distance, Mahalanobis distance, and principal component score serve as the synthetic indexes for identifying the multivariate geochemical anomalies of four combinations of gold-silver, gold-silver-arsenic-bismuth-mercury, gold-silver-copper-lead-zinc-stibnite-cobalt, and gold-silver-copper-lead-zinc-stibnite-cobalt-arsenic-bismuth-mercury. The research shows that the performance of composite kernel Mahalanobis distance is superior to the other indexes in multivariate geochemical anomaly identification.

Key words: Mahalanobis distance, kernel Mahalanobis distance, principal component score, geochemical data, multivariate anomaly recognition