Sampling and analysis of chemical element concentration distribution in rock units and orebodies
Abstract. Existing sampling techniques applied within known orebodies, such as sampling along mining drifts, yield element concentration values for larger blocks of ore if they are extended into their surroundings. The resulting average concentration values have relatively small "extension variance". These techniques can be used for multifractal modeling as well as ore reserve estimation approaches. Geometric probability theory can aid in local spatial covariance modeling. It provides information about increase of variability of element concentration over short distances exceeding microscopic scale. In general, the local clustering of ore crystals results in small-scale variability known as the "nugget effect". Parameters to characterize spatial covariance estimated from ore samples subjected to chemical analysis for ore reserve estimation may not be valid at local scale because of the nugget effect. The novel method of local singularity mapping applied within orebodies provides new insights into the nature of the nugget effect. Within the Pulacayo orebody, Bolivia, local singularity for zinc is linearly related with logarithmically transformed concentration value. If there is a nugget effect, moving averages resulting from covariance models or estimated by other methods that have a smoothing effect, such as kriging, can be improved by incorporating local singularities indicating local element enrichment or depletion. Although there have been many successful applications of the multifractal binomial/p model, its application within the Pulacayo orebody results in inconsistencies, indicating some shortcomings of this relatively simple approach. Local singularity analysis and universal multifractal modeling are two promising new approaches to improve upon results obtained by commonly used geostatistical techniques and use of the binomial/p model. All methods in this paper are illustrated using a single example (118 Pulacayo zinc values), and several techniques are applied to other orebody datasets (Whalesback copper deposit, Witwatersrand goldfields and Black Cargo titanium deposit). Additionally, it is discussed that nugget effects exist in a binary series of alternating mostly gneiss and metabasite previously derived from KTB borehole velocity and lithology logs, and within a series of 2796 copper concentration values from this same drill-hole.