多元地球化学异常识别的核马氏距离方法

地球化学数据满足多元正态分布时，马氏距离是一种有效识别多元地球化学异常的综合指标。然而，由于地质系统的复杂性、成矿作用的多期多阶段性以及控矿因素的多重性常常导致多元地球化异常临界面是非线性的和模糊的，用马氏距离定义的平滑超椭球面不能准确表示这种复杂曲面。核函数能够将地球化学样品集非线性变换至特征空间，背景样品的映像集合在特征空间中构成一种流型，异常样品的映像则零散分布于流型的边缘及外围。计算和比较样品映像到样品映像总体的核马氏距离，可以识别异常样品。把该方法应用于白山地区多元地球化学异常识别，用核马氏距离、马氏距离和主成分得分识别金-银、金-银-砷-铋-汞、金-银-铜-铅-锌-锑-钴、金-银-铜-铅-锌-砷-锑-铋-汞-钴4种组合模式的多元地球化学异常。研究结果表明：复合核函数马氏距离的多元地球化学异常识别效果优于其他方法。

Kernel Mahalanobis Distance for Multivariate Geochemical Anomaly Recognition

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.