Modelling geological trends of categorical variables under proportion uncertainty

Categorical data, such as mineralization zones and depositional lithofacies, often exhibit large-scale deterministic trends controlled by the depositional or alteration environment. Accurately capturing these trends is significant in geological modeling, as trend characterization directly influences the reliability of resource estimation. However, the traditional approach of trend modeling for categorical variables is based on indicator kriging, which has the limitation of overfitting. In this research, the radius-optimized moving average approach is introduced to improve the trend modeling of categorical variables. This approach involves optimization of the smoothing parameters and demonstrates notable improvement in accuracy metrics compared with the traditional indicator kriging approach. Furthermore, a practical framework is proposed to model categorical variable trends under proportion uncertainty. The proposed methodology includes: (i) generating a base case trend model using the radius-optimized approach; (ii) quantifying categorical proportion uncertainty by performing unconditional sequential indicator simulation at well locations; and (iii) selecting representative models in the presence of proportion uncertainty. Lastly, the proposed workflow is illustrated in an example of facies trend modeling. The results indicate that the workflow not only effectively reduces the overfitting commonly observed in indicator-kriging–based trend modeling, but also enables quantitative characterization of proportion uncertainty, thereby substantially enhancing the reliability of reservoir models. This approach offers significant potential for applications in both the mining and petroleum industries.