Block model estimation To determine and define the ore tonnage and grade of a geological deposit, from the developed
block model, a
mineral resource estimation is used. There are different estimation methods used for different scenarios dependent upon the ore boundaries, geological deposit geometry, grade variability and the amount of time and money available. A typical resource estimation involves the construction of a geological and resource model with data from various sources. Once the geological modeling is completed, the geological envelopes are divided into block models. Subsequently, the estimation of these blocks is done from "composites" that are point measures of the
grade of ore in the rock. Several different mathematical methods can be used to do the estimation depending on the desired degree of precision, quality and quantity of data and of their nature.
Nearest neighbor method The
nearest neighbor method assigns grade values to blocks from the nearest sample point to the block. Closest sample gets a weight of one; all others get a weight of zero. In two dimensions, this method generates a
Voronoi diagram composed of
polygons each with a unique grade; in three dimensions this method generates a
Voronoi diagram composed of
polyhedra each with a unique grade. ). In mathematics, a
Voronoi diagram is a
partitioning of a
plane into regions based on distance to points in a specific subset of the plane. That set of points (called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points
closer to that seed than to any other. These regions are called Voronoi cells. The Voronoi diagram of a set of points is
dual to its
Delaunay triangulation. Put simply, it's a diagram created by taking pairs of points that are close together and drawing a line that is equidistant between them and perpendicular to the line connecting them. That is, all points on the lines in the diagram are equidistant to the nearest two (or more) source points. This method is easy to understand calculate manually, but it produces biased estimates of grade and tonnage above an ore waste cut-off. Which is called the volume variance relationship i.e. the variability of the grade distribution depends on the volume of samples. Large volume samples mean small variability whereas small volume samples mean large variability.
Inverse distance weighting method The name "
inverse distance weighting method" was motivated by the
weighted average applied, since it resorts to the inverse of the distance to each known point ("amount of proximity") when assigning weights. This method is computationally simple and flexible, but the preferential sampling makes estimates unreliable. The simplest weighting function in common usage is based upon the inverse of the distance of the sample from the point to be estimated, usually raised to the second power, although higher or lower powers may be useful. : w_i = \left[\frac{1}{d_i}\right]^p Samples closer to the point of interest get a higher weighting than samples farther away. Samples closer to the point of estimation are more likely to be similar in grade. Such inverse distance techniques introduce issues such as sample search and declustering decisions, and cater for the estimation of blocks of a defined size, in addition to point estimates.
Kriging In
statistics, originally in
geostatistics, Kriging or Gaussian process regression is a method of
interpolation for which the interpolated values are modeled by a
Gaussian process governed by prior
covariances, as opposed to a piecewise-polynomial
spline chosen to optimize smoothness of the fitted values. Under suitable assumptions on the priors, Kriging gives the
best linear unbiased prediction of the intermediate values. Interpolating methods based on other criteria such as smoothness need not yield the most likely intermediate values. The method is widely used in the domain of
spatial analysis and
computer experiments. The technique is also known as Wiener–Kolmogorov prediction, after
Norbert Wiener and
Andrey Kolmogorov. The theoretical basis for the method was developed by the French mathematician
Georges Matheron based on the Master's thesis of
Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the
Witwatersrand reef complex in
South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes. The English verb is
to krige and the most common noun is
Kriging; both are often pronounced with a
hard "g", following the pronunciation of the name "Krige". This method is good in local and global estimates, but hard to comprehend, computationally intensive, and the flexibility and power created by many parameters also create arbitrariness and more possibilities for error.
Resource block model The block model is created using geostatistics and the geological data gathered through drilling of the prospective ore zone. The block model is essentially a set of specifically sized "blocks" in the shape of the mineralized orebody. Although the blocks all have the same size, the characteristics of each block differ. The grade, density, rock type and confidence are all unique to each block within the entire block model. An example of a block model is shown on the right. Once the block model has been developed and analyzed, it is used to determine the ore resources and reserves (with project economics considerations) of the mineralized orebody. Mineral resources and reserves can be further classified depending on their geological confidence. A mineral resource can be explained as a concentration or occurrence of diamonds, natural solid inorganic material, or natural solid fossilized organic material including base and precious metals, coal, and industrial minerals in or on the Earth's crust in such form and quantity and of such a grade or quality that it has reasonable prospects for economic extraction. The location, quantity, grade, geological characteristics and continuity of a mineral resource are known, estimated or interpreted from specific geological evidence and knowledge. A Mineral Reserve is the economically mineable part of a Measured or Indicated Mineral Resource demonstrated by at least a Preliminary Feasibility Study. This Study must include adequate information on mining, processing, metallurgical, economic and other relevant factors that demonstrate, at the time of reporting, that economic extraction can be justified. A Mineral Reserve includes diluting materials and allowances for losses that may occur when the material is mined. == Bre-X scandal ==