Application of continuous restricted Boltzmann machine to identify multivariate geochemical anomaly

Abstract

In multivariate geochemical anomaly identification, geochemical background sample population is usually supposed to satisfy a known multivariate probability distribution, such as multivariate Gaussian distribution, so that a simple predefined function can describe the general features of the multivariate geochemical background. However, complex geological settings often result in an unknown complex multivariate probability distribution of the geochemical background sample population. In this case, the predefined simple function can't effectively describe the characteristics of the complex multivariate geochemical background. Continuous restricted Boltzmann machine can be trained to encode and reconstruct statistical samples from an unknown complex multivariate probability distribution. Large probability samples can be encoded and reconstructed better than small ones. Therefore, the trained continuous restricted Boltzmann machine can differentiate the small probability samples from the training sample population. In geochemical exploration, the overwhelming majority of geochemical samples are the background samples from the geochemical background sample population. Comparing with the background samples, geochemical anomaly samples are the small probability samples that can be identified by the trained continuous restricted Boltzmann machine from the training geochemical sample population. Two anomaly indicators, ASC and ASE, are defined on the basis of the trained continuous restricted Boltzmann machine for the multivariate geochemical anomaly identification. The Baishan district in northeastern China linked with a complex geological background is chosen as a case study area. Continuous restricted Boltzmann machines with 14 visible units and differing hidden units are constructed and trained on all the 6607 geochemical samples in the study area. The ASCs and ASEs are used to identify the multivariate geochemical anomaly samples from the training geochemical sample population. Likelihood ratio is used to test the performance of these two types of anomaly indicators. The results show that ASC and ASE have similar good performance in the multivariate geochemical anomaly identification. The identified multivariate geochemical anomalies are spatially consistent with the known mineral deposits and extend along the direction of the regional tectonics in the study area.