Estimation of Spatial Distribution Using the Gaussian Mixture Model with Multivariate Geoscience Data

Spatial estimation of geoscience data (geo-data) is challenging due to spatial heterogeneity, data scarcity, and high dimensionality. Anovel spatial estimation method is needed to consider the characteristics of geo-data. In this study, we proposed the application ofGaussian Mixture Model (GMM) among machine learning algorithms with multivariate data for robust spatial predictions. Theperformance of the proposed approach was tested through soil chemical concentration data from a former smelting area. Theconcentrations of As and Pb determined by ex-situ ICP-AES were the primary variables to be interpolated, while the other metalconcentrations by ICP-AES and all data determined by in-situ portable X-ray fluorescence (PXRF) were used as auxiliary variables inGMM and ordinary cokriging (OCK). Among the multidimensional auxiliary variables, important variables were selected using avariable selection method based on the random forest. The results of GMM with important multivariate auxiliary data decreased theroot mean-squared error (RMSE) down to 0.11 for As and 0.33 for Pb and increased the correlations (r) up to 0.31 for As and 0.46 forPb compared to those from ordinary kriging and OCK using univariate or bivariate data. The use of GMM improved the performanceof spatial interpretation of anthropogenic metals in soil. The multivariate spatial approach can be applied to understand complex andheterogeneous geological and geochemical features.