Applied Earth Science: Transactions of the Institutions of Mining and Metallurgy

Geostatistical modelling of grades in mineral deposits often requires the simulation of multiple related variables that have sum and fraction constraints. Sum constraints occur when the sum of some variables may not exceed or must equal a given constant. Fraction constraints occur when a variable may not exceed another variable. In this case, the geostatistical simulations should reproduce the histograms, variograms, multivariate relationships and honour the constraints. We present a methodology for the geostatistical simulation of multiple related variables that considers sum and fraction constraints. The methodology is illustrated in a case study. The data were obtained from a bauxite deposit. First, the original variables were re-expressed as ratios. Second, the variables were transformed using the Projection Pursuit Multivariate Transform (PPMT). Then the PPMT transformed variables were simulated independently using sequential Gaussian simulation and back-transformed. The simulations reproduced the histograms, variograms and bivariate relationships and honoured the sum and fraction constraints.

Surface and borehole sampling along a ∼80 km section of the lower Tista river, northwestern Bangladesh, indicated that the river sands offer significant potential as a heavy mineral (HM) resource. Characterisation of sediments from the surface to 15 m depth showed that the sand-sized component was dominated by quartz, feldspar, mica, lithic fragments, amphibole and pyroxene group minerals. The most common particle size was between +125–500 μm with 84 wt-% of all material reporting to this size range. Laterally spaced sampling indicated slight grain size coarsening upstream. Heavy liquid separation studies revealed that HMs such as amphiboles, micas, garnets, aluminosilicate (Al2SiO5) phases, ilmenite and zircon made up ∼10.99% (on average). The percentage of valuable HMs (ilmenite, rutile, zircon, monazite, garnet) was 2.47% (average). Detailed borehole sampling and resource mapping of a large, mid-channel sand bar showed that placer-style HM accumulations occur upstream and along the margins of the bar.

Large geochemical datasets are commonly composed of several subgroups of measurements with a diverse level of uncertainty. Ignoring data quality and heterogeneity by pooling all data together leads to information loss and suboptimal analysis. Therefore, we propose a novel approach to define the measurement uncertainty attached to each sample by defining subgroups which have the same relationship between concentration and its measurement uncertainty and use this equation to estimate the uncertainty of measurements made on the original samples. The proposed approach is not only based on available information such as rock type or in the used sampling protocols, but also by the extraction of information gained from duplicates in successive steps of graphical analysis to define subgroup candidates and test their statistical significance. The illustrative example defined subgroups very close to the simulated ones and estimates of each original concentration measurement were at least 30% better than other evaluated methods.