Bayesian Surface Warping Approach for Rectifying Geological Boundaries Using Displacement Likelihood and Evidence from Geochemical Assays

Abstract

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.