Geostatistical estimation of mineral resources with soft geological boundaries: a comparative study

Abstract

Mineral resource evaluation requires defining geological domains that differentiate the types of mineralogy, alteration and lithology. Usual practice is to consider the domain boundaries as hard, i.e. data from across the boundaries are disregarded when estimating the grades within a given domain. This practice may hinder the quality of the estimates when a significant spatial correlation of the grades exists across the domain boundaries.

In this paper, several geostatistical methodologies to handle soft geological boundaries are compared through a case study on a copper mine in Chile. The estimation methods considered are: ordinary kriging using hard boundaries between geological domains; ordinary kriging omitting the geological boundaries; traditional and standardized ordinary cokriging of the grades assayed in different domains; ordinary kriging within dilated geological domains, that is, incorporating samples from adjacent domains up to a given radius from the boundary of the domain being considered. The estimations are performed using a set of exploration data (drill hole samples) and are validated using a set of production data (blast hole samples collected for grade control).

Results indicate that kriging with dilated domains performs better than ordinary kriging using hard boundaries or no boundaries and better than the ordinary cokriging approaches. It therefore appears as a simple alternative to global kriging (without considering the geological domains) and allows accounting for changes in the grade average, dispersion and spatial continuity with the geological characteristics of the deposit, via the use of grade variograms proper to each geological domain. The maximal distance for searching samples from adjacent domains should be chosen according to the spatial correlation of the grades across the domain boundaries, or via a cross-validation at an early stage of the mine or a jack-knife if production data are available.