Inverse radius weighting and its python package “IRWPy”: A new topography-informed interpolation to enhance geological interpretations

The extent and volume of geochemical sampling are inherently constrained by numerous factors, including budgetary limitations, analytical costs, and access restrictions. These constraints result in sampling networks that vary in density and regularity, dividing regions into sampled and unsampled areas. The creation of continuous geochemical maps is essential for geochemical prospectivity, which aims to identify geochemical anomalies, distinguish between background levels and anomalies, and define mineralization patterns. Therefore, it is necessary to interpolate data from sampled areas to estimate values in unsampled regions. Although several interpolation models exist, including Inverse Distance Weighting and various kriging methods, Inverse Distance Weighting is often used in two-dimensional ground modeling because, unlike kriging methods, Inverse Distance Weighting has no smoothing effect on edges. Inverse Distance Weighting’s reliance solely on horizontal Euclidean distances between samples overlooks critical factors such as topography and the ensuing effects on dilution, transportation, and element mobility, rendering it less effective over varied elevations. This study introduces Inverse Radius Weighting, a new interpolation technique that incorporates both Euclidean and elevation fluctuations, therefore Pythagorean distance, to help with better geological interpretations. We assessed the efficacy of Inverse Radius Weighting compared to Inverse Distance Weighting across three elements with varying mobility (Arsenic − highly mobile, Copper − moderately mobile, and Barium − nearly immobile), using different numbers of neighbors and by comparing three different evaluation measures, namely R², Mean Absolute Error and Mean Absolute Percentage Error. By evaluating the spatial uncertainty of the generated maps and selecting the configurations with the least uncertainty as the final maps, our analysis reveals an improvement in correlation between interpolated and actual values with Inverse Haversine Radius Weighting. With this advancement, Inverse Haversine Radius Weighting overcomes the limitations of traditional Inverse Distance Weighting by accounting for elevation and its associated effects, thereby paving the way for more accurate and geochemically meaningful interpolation in geochemical prospectivity mapping.