COMPARATIVE STUDY OF LINEAR AND NON-LINEAR KRIGING APPROACHES FOR GEOSTATISTICAL MODELING OF GOLD GRADE IN MINE TAILINGS.

Abstract

The modern mining industry, particularly resource estimation and mine planning, progressively initiates the software development and their application as a part of technology that concentrates its focus on estimating the high-precision models. These models concern the estimation of reserves, the planning of overall slope angle, and many other aspects of mine design, which take into account many different factors. In this regard, different geological units, complexity of ground water level, or shortage of borehole information pose difficulties in estimating the correct model that will be financially feasible and will be approved for exploitation. Thus, geostatistics was evolved for resolving the uncertainties, or raising the confidence of prediction, over the resource estimation to a larger extent. In terms of functionality, the geostatistical tools might be divided into two categories: deterministic and stochastic. The deterministic geostatistical tools are based on modeling single-prediction maps using mathematical equations on well-known datasets. The most common representatives of this category are IDW, trend surface analysis, and spline interpolation. The IDW stands for inverse distance weighting and works on assigning the value based on the inverse of distance from the known dataset, such as grade value or percentage. Trend surface analysis is based on predicting the value at an unknown region by fitting the polynomial function of low-order into a dataset that provides already collected information. Likewise, the spline interpolation is based on fitting the mathematical equation for creating the smooth surface along which the unknown points along the spatial continuity will be predicted. However, the major limitation of the deterministic approach is that methods do not consider spatial uncertainty using a single-prediction map. Thus, the application of this type of geostatistical tool is only applicable for creating a preliminary review of resource allocation and modeling high-prediction maps exclusively for well-sampled regions. The other category of geostatistical modeling stands for stochastic tools, which constitute simulation techniques. The simulation is commonly represented by SGS, SIS, and turning bands simulation. The SGS is described as a sequential Gaussian simulation and is based on creating numerous prediction maps for delivering the optimal unbiased linearly dependent estimate. The SIS is denoted as sequential indicator simulation and works on the same principle as the above-mentioned techniques except for dividing the dataset on several domains. The turning band simulation also works by the principle of creating several maps but is used for predicting spatial variability for continuous datasets. Another deterministic method with stochastic elements is kriging, which uses various models for predicting local error maps with partially unknown regions or poorly sampled datasets. As geostatistical tools have been thoroughly discussed, the focus of this paper will be centralized on assessing the kriging techniques, which will be elaborated further and compared for creating higher precision maps based on a univariate dataset.