Interpreting and Modeling the Nugget Effect for Mixed Categorical and Continuous Variables
摘要
This paper introduces mixed variables, a type that combines both continuous and categorical data, such as coal types classified by ash content and volcanic rock series exhibiting a continuum from the mafic (rich in magnesium and iron) to the rhyolite in the felsic end (rich in silica). In the mining industry, modeling and estimates often use samples categorized by visual logging and grade thresholds, such as “High-Arsenene Sulfide rock” or “High-Manganese BIF.” This paper explores the presence of mixed variables in geostatistical problems. It discusses why the nugget effect for this type of variable is the main difference between kriging mixed or purely categorical data. The nugget effect for mixed variables is defined by a combination of three components, and methods to estimate these components are developed, leading to improved variogram modeling and, consequently, better kriging estimates for mixed variables. Two real case studies are presented. The first focuses on optimizing sampling length in a bauxite deposit, while the second refines the relationship between the spacing of blastholes and the mass to be sampled from each one for grade control in an iron ore mine. This paper fills a gap in the geostatistical literature on the understanding and optimization of mixed variables in kriging.