Accurate grade estimation in heterogeneous porphyry copper deposits is frequently constrained by spatial non-stationarity and the excessive smoothing inherent in traditional geostatistical methods. This study introduces the Geological Distance Field-Machine Learning (GDF-ML) framework, which transforms raw spatial coordinates into a geological coordinate system defined by the structural architecture. By mapping grade distribution within this geologically informed space, the framework enables machine learning models to discern non-linear mineralizing patterns that are typically obscured in traditional Euclidean 3D space. Functioning as an expert-constrained regression architecture rather than a purely data-driven interpolator, the framework estimates grade distributions conditional upon established metallogenic controls. In this context, the achieved spatial separation cross-validation R2 of 0.851 quantifies the proportion of grade variance structurally explainable by the geological architecture, highlighting the workflow’s capacity to distinguish continuous structural trends from localized random variability. Industrial reconciliation against high-density production data confirms this performance, demonstrating an average grade bias of only 0.79%, compared to 9.68% achieved by Ordinary Kriging. Furthermore, SHAP analysis verifies that these predictions are systematically driven by the non-linear relationship between structural proximity and mineralization. Consequently, this study suggests that incorporating structural distance metrics into regression workflows offers an alternative approach to evaluate the geometric constraints of geological features alongside the localized variability of porphyry mineralization.
Liwei Yan (2026) studied this question.