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

2025-12-09

AI Summary

In 3D grade modeling of underground orebodies, estimation bias arises from spatial scale mismatch between drill-hole assay data (interval observations) and block models (volumetric support). To address this, we propose IntegralGP: the first Gaussian process framework rigorously generalizing covariance functions to integral observations, enabling probabilistic modeling of interval data. We introduce a joint computation strategy for antiderivatives and gradients to enhance kernel hyperparameter learning stability. The framework further integrates heteroscedastic noise modeling, numerically stable differentiation/integration, and multi-source spatial data fusion. In iron ore grade prediction, IntegralGP significantly improves block-grade estimation accuracy. In classification tasks—distinguishing ore from waste—it reduces absolute error and systematic bias, substantially decreasing boundary misclassifications (e.g., high-grade blocks erroneously labeled as waste or vice versa).

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Relational Probabilistic ModelsData Mining & Knowledge Management: Intelligent Query Processing

Application Category

Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsWeb Mining and Content Analysis: Web data integration and cleaningGraph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

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.

Problem

• Estimates subterranean geochemical properties volumetrically in mineral deposits
• Fuses assay data with different spatial supports and resolutions
• Improves regression performance and boundary delineation for material classification

Innovation

• IntegralGP framework for volumetric estimation
• Fuses blasthole assays as interval observations
• Uses heteroscedastic GP for multi-resolution data fusion