Geological boundary modeling with uncertainty using an indicator interpolated threshold approach

Abstract

ABSTRACT Estimating the quality and quantity of minerals is an important step in evaluating the feasibility of a mining project. Before estimation of resources occurs, the domain extents must be defined. Uncertainty in the placement of boundaries is ubiquitous, and proper evaluation of uncertainty is integral to aiding subsequent engineering decisions. Implicit modeling of boundaries is a popular technique as it is data driven, fast, and automatic. Signed distance functions (SDF) are commonly used in implicit boundary modeling. The SDF in its basic form is the signed-dependent shortest Euclidean distance between data that are not of the same category. However, in the presence of spatial-data asymmetry, the SDF introduces a conservative bias leading to lower global tonnages for estimating resources. Moreover, uncertainty through an additive constant to the SDF results in homogenous and unreasonable uncertainty. A novel approach to implicit boundary modeling with uncertainty is to interpolate a field of probabilities from indicator data and threshold the estimate for boundary extraction. Uncertainty is captured by varying the indicator thresholds, which provides eroded and dilated boundaries. The result is a globally unbiased boundary model that closely follows the structure of the conditioning data and provides a realistic uncertainty bandwidth.