3DU–TA: A new multifractal model involving surface topography for separation of geochemical anomalies

Abstract

A novel anomaly recognition technique was propounded to help reconcile mineralization-related geochemical patterns with topographic non-stationaries within the study area. The topography variations were characterized by elevation and slope factors of grid cells in a digital elevation model (DEM). In the first step of the technique architecture, the spatial U-statistics formulation was expanded for a 3D framework to integrate elevation-related information into geochemical measurements. Slope angles were then modeled across the cell-based geochemical map using DEM information to modulate planimetric areas into topographic attributes. Three-dimensional spatial U-values and topographic attributes were integrated in a multifractal model called 3DU–TA, providing power-law relations that aid in decomposition of geochemical patterns. The mathematical formulation established for the 3DU–TA model was implemented by programming in MATLAB platform and it was applied to geochemical data pertaining to a deposit-scale porphyry copper system. Core drilling data were used as benchmark to appraise the performance of the 3DU–TA model in the recognition and separation of metal enrichment levels from background and it was compared with the well-established concentration–area (C–A) fractal model. We defined mineralization rate Mr and normalized productivity Np as criteria for judging the integrity of anomalous geochemical patterns derived by the 3DU–TA model in reflecting subsurface mineralization. We also adapted a success-rate plot for deposit-scale experiments and the relevant areas under the curve (AUC) as gauges for quantitative evaluation of model relevance in reflecting subsurface metal enrichment. The derived values of Mr and Np imply that the geochemical populations decomposed with the 3DU–TA model, compared with those decomposed with the C–A model, yielded anomaly patterns that were more consistent with subsurface metallogenic realities. The success-rate curve for topography-enhanced results had an AUC = 0.940, which was higher than that for the C–A model (AUC = 0.867), indicating that the former revealed anomalies with substantially stronger spatial correlations with subsurface metal contents. Intuitive geochemical and quantitative metallogenic assessments suggest that the proposed multifractal modeling technique is capable of providing more practical insights into mineralization realities in geosystems with complex topographic variations.