Sensitivity analysis of Kriging to variogram model selection and spatial continuity direction in support of sustainable mineral resoursce management (SDGs 9 and 12)

¹ Mining Engineering Study Program, Faculty of Engineering, State University of Surabaya, Surabaya, 60231, Indonesia
² Mechanical Engineering Study Program, Faculty of Engineering, State University of Surabaya, Surabaya, 60231, Indonesia
³ Cooperative Program of Resources Engineering, Faculty of Engineering, Kyushu University, 744 Motooka, Nishi-Ku, Fukuoka 919-0395, Japan

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract

The research examines how ordinary kriging reponds to changes in both the theoretical variogram model-Spherical, Exponential, and Gaussian-and the direction of spatial continuity. The analysis was carried out using 80 borehole samples containing galena (PbS) grades. Empirical variograms were built and fitted, and their influence on kriging estimation was examined through cross-validation using the correlation coefficien (r), coefficient of determination (r²), standard error (SE), and root mean square error (RMSE). The results show that different variogram models and anisotropy directions can noticeably shift the kriging output. Among all combinations, the Exponential model at 45° produced the most stable and convincing performance, with the highest correlation (r = 0.825, r² = 0.680) and the lowest RMSE (0.510). This pattern suggests that PbS mineralization in the study area demonstrates a moderate level of spatial continuity aligned with the main geological trend. The Gaussian model produced smoother surfaces but tended to reduce local variability, while the Spherical model showed comparatively higher residual errors. Overall, selecting an appropriate variogram model and anisotropy direction is essential for producing kriging estimates that are both geologically reasonable and statistically reliable.