Evaluation of the error of analogy and the error of contouring in the calculation of mineral reserves

Abstract

This article examines the issues of determining the error of analogies when calculating the volume of a deposit or the quantity of useful minerals based on drilling results with a regular grid of boreholes. The volume of the deposit or the quantity of ore calculated from drilling results depends on the exploration grid (the distribution of boreholes) or on the position of the starting borehole point. Here, a distinction must be made between the real error and the limiting error of analogy. The real error, like the volume, depends on the position of the starting borehole and therefore cannot be evaluated. The limiting error, however, does not depend on the starting borehole point and is determined both by the variability of the deposit indicator and by the distance between boreholes. For this reason, the limiting error can in principle be assessed from the drilling results. To this end, the article provides a table of limiting error estimates as functions of the exploration indicator. The exploration error is expressed as the ratio of the degree of variability to the relative density of the exploration boreholes. The degree of variability, in turn, can be calculated from the average value of the second differences of the deposit indicators and the arithmetic mean. The article also presents a new formula for calculating the deposit quantity based on the sum of the indicators measured in individual boreholes. The presented formula has a small analogy error compared to other formulas and methods for calculating the quantity of useful minerals. Using this formula and the described method for estimating the limiting error, it is possible to determine the limiting error from exploration results, regardless of the method by which the volume of the deposit or the quantity of minerals was calculated.

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