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.

20 points and their Voronoi cells (larger version below).

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.

Advantages

• Easy to understand
• Easy to calculate manually
• Easy to use as a repeatable standard
• When automated, reasonably fast in 2D

Disadvantages

• Local discontinuities are unrealistic
• 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.

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.^[1]

${\displaystyle w_{i}=\left[{\frac {1}{d_{i}}}\right]^{p}}$

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.

Inverse distance interpolation for different power parameters p, from scattered points on the surface ${\displaystyle z=\exp(-x^{2}-y^{2})}$.

Advantages

• Computationally simple
• Exponent gives flexibility. The same estimation procedure can be used to create very smooth estimates (like a moving average) or very variable estimates (like nearest neighbor)

Disadvantages

• Preferential sampling makes estimates unreliable
• Requires decision on which sample to use
• Extremes create large halos of great estimates
• Choice of exponent introduces arbitrariness

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.^[2] 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.

Example of one-dimensional data interpolation by Kriging, with confidence intervals. Squares indicate the location of the data. The Kriging interpolation, shown in red, runs along the means of the normally distributed confidence intervals shown in gray. The dashed curve shows a spline that while smooth nevertheless departs significantly from the expected intermediate values given by those means.

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".

Advantages

• Very good in local and global estimates.
• Geological knowledge is captured in variogram.
• Statistical approach allows uncertainty to be quantified.

Disadvantages

• Not easy to comprehend.
• Computationally intensive: hardware, software.
• Flexibility and power created by many parameters also create arbitrariness and more possibilities for error.

Mineral resources

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.^[3]

Inferred Mineral Resource

An inferred mineral resource is that part of a Mineral Resource for which quantity and grade or quality can be estimated on the basis of geological evidence and limited sampling and reasonably assumed, but not verified, geological and grade continuity. The estimate is based on limited information and sampling gathered through appropriate techniques from locations such as outcrops, trenches, pits, workings and drill holes.

Indicated Mineral Resource

An indicated mineral resource is that part of a Mineral Resource for which quantity, grade or quality, densities, shape and physical characteristics, can be estimated with a level of confidence sufficient to allow the appropriate application of technical and economic parameters, to support mine planning and evaluation of the economic viability of the deposit. The estimate is based on detailed and reliable exploration and testing information gathered through appropriate techniques from locations such as outcrops, trenches, pits, workings and drill holes that are spaced closely enough for geological and grade continuity to be reasonably assumed.

Measured Mineral Resource

A measured mineral resource is that part of a Mineral Resource for which quantity, grade or quality, densities, shape, and physical characteristics are so well established that they can be estimated with confidence sufficient to allow the appropriate application of technical and economic parameters, to support production planning and evaluation of the economic viability of the deposit. The estimate is based on detailed and reliable exploration, sampling and testing information gathered through appropriate techniques from locations such as outcrops, trenches, pits, workings and drill holes that are spaced closely enough to confirm both geological and grade continuity.

Mineral reserves

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.^[3]

Probable Mineral Reserve

A probable mineral reserve is the economically mineable part of an Indicated and, in some circumstances, a Measured 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.

Proven Mineral Reserve

A proven mineral reserve is the economically mineable part of a Measured 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 is justified.

Bre-X

Bre-X was a group of companies in Canada. A major part of the group, Bre-X Minerals Ltd. based in Calgary, was involved in a major gold mining scandal when it reported it was sitting on an enormous gold deposit at Busang, Indonesia (in Borneo). Bre-X bought the Busang site in March 1993 and in October 1995 announced significant amounts of gold had been discovered, sending its stock price soaring. Originally a penny stock, its stock price reached a peak at CAD $286.50 (split adjusted) in May 1996 on the Toronto Stock Exchange (TSE), with a total capitalization of over CAD $6 billion. Bre-X Minerals collapsed in 1997 after the gold samples were found to be a fraud.^[4]

Emergence of reporting standards

Plainly put, the purpose of the National Instrument 43-101 is to ensure that misleading, erroneous or fraudulent information relating to mineral properties is not published and promoted to investors on the stock exchanges overseen by the Canadian Securities Authority.^[5]

The NI 43–101 was created after the Bre-X scandal to protect investors from unsubstantiated mineral project disclosures.

"The gold reserves at (Bre-X's) Busang were alleged to be 200 million ounces (6,200 t), or up to 8% of the entire world's gold reserves at that time. However, it was a massive fraud and there was no gold. The core samples had been faked by salting them with outside gold. An independent lab later claimed that the faking had been poorly done, including the use of shavings from gold jewelry. In 1997, Bre-X collapsed and its shares became worthless in one of the biggest stock scandals in Canadian history."^[6]

The promulgation of a codified reporting scheme makes it more difficult for fraud to occur and reassures investors that the projects have been assessed in a scientific and professional manner. However, even properly and professionally investigated mineral deposits are not necessarily economic, nor does the presence of a NI 43-101-, JORC- or SAMREC and SAMVAL-compliant CPR or QPR necessarily mean that it is a good investment.

Similarly, the publication of a complex technical report with all the inherent jargon, technical wording and abstract geological, metallurgical and economic information may not actually significantly advantage an investor who is not able to fully nor properly understand the content or importance of this information. In this way the NI 43–101 may not serve the interests of those it is designed to protect— the retail investors who may easily misinterpret such information.

Two main regulatory documents exist depending on the national jurisdiction the company is filed with. In Canada, the National Instrument 43-101 report details requirements of reporting mineralized findings. In Australia, the Joint Ore Reserves Committee Code (JORC Code), and South Africa mandates the South African Code for the Reporting of Mineral Resources and Mineral Reserves (SAMREC). All 3 codes are similar but not identical on requirements, definitions, and terminology. Regardless of the technicalities of each document, all exist to:

• Set criteria for approval of assay labs and methods
• Regulate ways of making sure samples are not tampered with
• Ensure periodic, independent reporting of reserves and review and approval of reserve reports
• Standardize for the disclosure of assay and drill results and procedures so that all data is clear to investors
• Standardize definitions of reserve types and reserve calculations
• Assign accountability to an individual deemed to be a competent person/ professional in the industry

The establishment and subsequent revisions of the NI 43 101 document by the Ontario Securities Commission provides a framework to adhere to when writing the report. By establishing these standards, investors are able to have a more reliable and honest review of potential mineralized zones.