Comparative Assessment of Inverse Distance Weighting, Ordinary Kriging, and Simple Kriging for Gold Grade Estimation: Spatial Diagnostics and Grade–Tonnage Responses
Alfred Yeboah
*
Department of Geological and Mining Engineering and Sciences, Michigan Technological University, Houghton, Michigan, USA.
*Author to whom correspondence should be addressed.
Abstract
Gold-grade estimation depends on the interpolation method, the support of the input data, and the way spatial continuity is represented. This study compares inverse-distance-squared weighting (IDW²), ordinary kriging (OK), and simple kriging (SK) using gold-grade modelling outputs prepared in Leapfrog Geo and Leapfrog Edge. The grade dataset contained 9,569 observations, and a nominal 5 m composite dataset contained 2,243 observations. Their respective mean grades were 0.850 and 0.925 in the recorded numerical units. The comparison draws on geological displays, variogram diagnostics, residual distributions, swath plots, grade–tonnage curves, and three-dimensional block models. Residual summaries were reported for 2,243 observations per estimator. Mean residuals were 0.007 for IDW², 0.030 for OK, and −0.895 for SK, with corresponding standard deviations of 2.280, 2.498, and 2.264. Approximate root-mean-square values calculated from these summaries were 2.280, 2.498, and 2.434, respectively. IDW² had the smallest absolute mean residual and calculated root-mean-square value, whereas SK had the lowest residual standard deviation. Differences were also apparent in swath behaviour, grade–tonnage responses, and model-category outputs. These results show that no estimator can be selected confidently on a single measure of performance; evaluation requires complementary statistical, spatial, and geological criteria. The conclusions concern the reported model diagnostics and do not constitute an independently validated Mineral Resource estimate.
Keywords: Gold grade estimation, inverse-distance-squared weighting, ordinary kriging, simple kriging, geostatistics, spatial continuity, grade–tonnage analysis, mineral resource modelling