IntegralGP: Volumetric estimation of subterranean geochemical properties in mineral deposits by fusing assay data with different spatial supports

This article presents an Integral Gaussian Process (IntegralGP) framework for volumetric estimation of subterranean properties in mineral deposits. It provides a unified representation for data with different spatial supports, which enables blasthole geochemical assays to be properly modelled as interval observations rather than points. This approach is shown to improve regression performance and boundary delineation. A core contribution is a description of the mathematical changes to the covariance expressions which allow these benefits to be realised. The gradient and anti-derivatives are obtained to facilitate learning of the kernel hyperparameters. Numerical stability issues are also discussed. To illustrate its application, an IntegralGP data fusion algorithm is described. The objective is to assimilate line-based blasthole assays and update a block model that provides long-range prediction of Fe concentration beneath the drilled bench. Heteroscedastic GP is used to fuse chemically compatible but spatially incongruous data with different resolutions and sample spacings. Domain knowledge embodied in the structure and empirical distribution of the block model must be generally preserved while local inaccuracies are corrected. Using validation measurements within the predicted bench, our experiments demonstrate an improvement in bench-below grade prediction performance. For material classification, IntegralGP fusion reduces the absolute error and model bias in categorical prediction, especially instances where waste blocks are mistakenly classified as high-grade.