This article presents a Bayesian framework for manipulating mesh surfaces with the aim of improving the positional integrity of the geological boundaries that they seek to represent. The assumption is that these surfaces, created initially using sparse data, capture the global trend and provide a reasonable approximation of the stratigraphic, mineralization, and other types of boundaries for mining exploration, but they are locally inaccurate at scales typically required for grade estimation. The proposed methodology makes local spatial corrections automatically to maximize the agreement between the modeled surfaces and observed samples. Where possible, vertices on a mesh surface are moved to provide a clear delineation, for instance, between ore and waste material across the boundary based on spatial and compositional analysis using assay measurements collected from densely spaced, geo-registered blast holes. The maximum a posteriori (MAP) solution ultimately considers the chemistry observation likelihood in a given domain. Furthermore, it is guided by an a priori spatial structure that embeds geological domain knowledge and determines the likelihood of a displacement estimate. The results demonstrate that increasing surface fidelity can significantly improve grade estimation performance based on large-scale model validation.

In surface mining, assay measurements taken from production drilling often provide useful information that enables initially inaccurate surfaces (for example, mineralization boundaries) created using sparse exploration data to be revised and subsequently improved. Recently, a Bayesian warping technique was proposed to reshape modeled surfaces using geochemical observations and spatial constraints imposed by newly acquired blasthole data. This paper focuses on incorporating machine learning (ML) into this warping framework to make the likelihood computation generalizable. The technique works by adjusting the position of vertices on the surface to maximize the integrity of modeled geological boundaries with respect to sparse geochemical observations. Its foundation is laid by a Bayesian derivation in which the geological domain likelihood given the chemistry, $$p(g\!\mid \!{\mathbf {c}})$$ , plays a role similar to $$p(y({\mathbf {c}})\!\mid \! g)$$ for certain categorical mappings $$y:{\mathbb {R}}^K\rightarrow {\mathbb {Z}}$$ . This observation allows a manually calibrated process centered on the latter to be automated, since ML techniques may be used to estimate the former in a data-driven way. Machine learning performance is evaluated for gradient boosting, neural network, random forest, and other classifiers in a binary and multi-class context using precision and recall rates. Once ML likelihood estimators are integrated into the surface warping framework, surface shaping performance is evaluated using unseen data by examining the categorical distribution of test samples located above and below the warped surface. Large-scale validation experiments are performed to assess the overall efficacy of ML-assisted surface warping as a fully integrated component within an ore grade estimation system, where the posterior mean is obtained via Gaussian process (GP) inference with a Matérn 3/2 kernel. This article illustrates an application of machine learning within a complex system where grade estimation is accomplished by integrating boundary warping with ML and other components.