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MULTIVARIATE METHOD FOR DISTINGUISHING GEOCHEMICAL BACKGROUND FROM GEOCHEMICAL ANOMALIES

Ji Hongjin  
Distinguishing between geochemical backgrounds and anomalies is still limitted by univariate method at present which is un-suitable to geochemical data usually multivariated and there are so many other defects. A multivariate method for distinguishing backgrounds from geochemical anomalies is developed in this paper by intruducing the principle of multivariate robust statistics. This method is based on the theory of multivariate normal distribution, and anomaly samples are recognized by testing Mahalanobis distance D2 - (X - X)'S-1(X -X).A sample X1 will be recognized as an anomaly if D2; is greater than the critical value D2a for given significance a. The hyperellipsoidal surface (X-X)'S-1(X-X) =D2a containing no anomaly sample is defined as critical surface, the cente X of the hyperellipsoidal body is defined as background vector;samples outside the dcmain are recognized as anomalies. By supposing X to be one-dimensional in D2=(X-X)' S(X-X), we can obtain the traditional formula xa = x±tas which defines the threshold value; so this method is an expanding of univariate method.The particular advantages are shown in respect to recognising anomaly samples and mapping anomalies integratively because of the informations abstracted by multivariate method are more than the informations abstracted by univariate method and the multivarites arc integrated into a single index Mahalanobis distance D2. The basic principle, the calculation method and application of the method are elaborated in simple case,while in complex situations the solution is not discussed.
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