Multi-Scale Element Interdependency in Mineral Exploration: Integral Transform-Based Cross-Variogram Modeling of Geochemical Data from the Riruwai Complex

Geostatistical methods are fundamental for characterizing the spatial distribution and interdependencies of geochemical elements, providing crucial insights for mineral exploration. This paper investigates the application of integral transform approaches, specifically Normal Score Transformation, Fourier Transform, and Wavelet Transform, to cross-variogram modeling of geochemical data. We delineate the theoretical underpinnings and interpretation of cross-variograms, emphasizing how their parameters directly inform exploration strategies. The advantages and limitations of these integral transforms in addressing common challenges such as highly skewed data distributions, outliers, and multi-scale spatial heterogeneity are thoroughly discussed. Utilizing a conceptual framework applied to Riruwai geochemical dataset, comprising 39 diverse samples across multiple lithological units, we emphasize the critical role of rigorous data preprocessing, geological domaining, and the strategic selection of geologically relevant element pairs. Elemental pairs such as Fe₂O₃–MgO, Sr–Ba, and U–Th demonstrated co-regionalization patterns consistent with magmatic differentiation, hydrothermal alteration, and metallogenic processes. This work demonstrates how these advanced geostatistical techniques can significantly enhance the robustness of variogram models, leading to more accurate resource estimation, improved target generation, and reduced exploration uncertainty, particularly in complex geological settings with irregularly spaced data.