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.A novel spatial estimation method is needed to consider the characteristics of geo-data.In this study, we proposed the application of Gaussian Mixture Model (GMM) among machine learning algorithms with multivariate data for robust spatial predictions.The performance of the proposed approach was tested through soil chemical concentration data from a former smelting area.The concentrations of As and Pb determined by ex-situ ICP-AES were the primary variables to be interpolated, while the other metal concentrations by ICP-AES and all data determined by in-situ portable X-ray fluorescence (PXRF) were used as auxiliary variables in GMM and ordinary cokriging (OCK).Among the multidimensional auxiliary variables, important variables were selected using a variable selection method based on the random forest.The results of GMM with important multivariate auxiliary data decreased the root 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 for Pb compared to those from ordinary kriging and OCK using univariate or bivariate data.The use of GMM improved the performance of spatial interpretation of anthropogenic metals in soil.The multivariate spatial approach can be applied to understand complex and heterogeneous geological and geochemical features.