An algorithm for quantifying regionalized ore grades

Measured grades rely on the relative positions of measurement locations within the ore site. These measurements at a set of locations give some insight into regional variability. This variability determines the regional behaviour as well as the predictability of the grade. The larger the variability, the more heterogeneous is the geological environment1. One of the tools used to measure regional variability is the semivariogram (variogram), which provides a measure of spatial dependence among a multitude of locations as an alternative to the auto-covariance of a time series2. The classical variogram, although suitable for irregularly spaced data, has practical difficulties. One of the main drawbacks is that it is insufficient to analyse the regional heterogeneous behaviour of the grade. In general, ore deposits have heterogeneous properties rather than homogeneous structures. Heterogeneity means that the properties (grades) observed at different locations do not have the same value, and that different zones are observed in the ore site. In order to quantify the regional behaviours, a cumulative semivariogram (CSV) concept has been proposed by Şen1 as an extension of the classical semivariogram. Şen1 used the CSV in stochastic processes for analysing the regional correlation and concluded that CSV is a better tool than the classical variogram in identifying spatial dependence. Alternatively, a point cumulative semivariogram (PCSV) measure is proposed by Şen3 in identifying the spatial behaviour of a regional variable around a location concerned. The basic principle of the technique is to compute experimental PCSVs for each data location, which leads to the estimation of the radius of influence around each location4. In some recent works5,6, point cumulative semimadogram (PCSM) measure has been proposed instead of PCSV for modelling the regional spatial dependence due to the advantages of absolute difference7. This paper presents a hybrid methodology, which uses the fuzzy clustering based PCSM for identifying the regional dependence. The method proposed in the study uses both soft and probabilistic tools. The algorithm first considers the fuzzy information and then describes the regional variability based on the mean absolute difference measure. In addition, the algorithm allows the regional heterogeneity of the grade to be evaluated at fixed similarity levels. Finally, grade estimations are carried out at different levels using standard regional dependence function (SRDF). An algorithm for quantifying regionalized ore grades