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## Geological Sampling Theory (9 replies and 1 comment)

Any lot (to be sampled) usually is larger and more complex (heterogeneous) than what a haphazardly extracted little "sample" will be able to reveal to scientific satisfaction. This type of 'grab sampling' will never do!But let's begin by stressing that a "sample" (to be defined in due course) is not "selected" ... The lot is NOT a collection of units that only differ with respect to one important feature (the concentration of a specific analysis f.ex.); the lot is NOT a statistical population (of analytical results).

The nasty word 'representative' raises its head again. A representative sample is one that is fit for the purpose to which the assay of sample will be put. As Kim said, you cannot 'select' a sample; you have to take the sample in a mechanically correct manner that will ensure that it has no bias between the true assay of the lot and itself. The entire lot of material about which you wish to have information must be available to the sampling tool. After that, a sufficient number of increments must be taken from the lot to form the sample - this is to overcome the distributional heterogeneity of the lot. Then, at each stage of the sampler preparation, a sufficient mass of material must be retained to ensure that the sampling variance due to intrinsic heterogeneity of the material at a particular state of comminution does not bring the total sampling variance to a value that will make the result unfit for the purpose of the sampling. The first step in sampling is to determine how accurate that sampling must be for your purpose. That is all there is to it.

This is a great question. Reading much description from NI 43-101 or other technical literature on the sampling completed to develop a representative understanding of ore-bodies reveals great range of apparent beliefs with limited linkage to how well this 3D volume comprised of 3, 4, 5 billion tons. I say beliefs because the analysis after moving on from assay values and perhaps core logging gets extremely sparse. To say a single 'representative' sample represents this much volume / mass is misleading.

An elephant in the photo can be described by the blind men as the elephant is a solid (not fragmented) volume. With enough blind men to ensure all the parts are can be sampled to estimated the shape, volume, and limits of each part. Variography will give a measure as to whether the samples you have are correlated and hopefully give confidence that the volume is being defined in other than a random manner. The sample histogram will also give an idea whether the ranges are representative and combining this with de-clustering methods will give a reasonable estimate of the shape of the histogram. Geo-statistical estimation methods (in theory) over come the problem of single sample to block volume representation. The representation of the samples can then be quantified through bootstrapping and or conditional simulation. However I expect your question is about fragmented lots which is an entirely different measurement problem to the blind men and the elephant.

Designing, extracting, and preparing a mass of material to represent the lot is a multi-foe battle where heterogeneity, physics,mass reduction, and cost conspire to inflict the maximum possible bias upon the sample result. This is before the material is submitted to the analytical device or extending the analytical result to a larger volume (change of support). The flawed proxy of a sample is the best we can do, and one must do his best to address in advance the sources or sampling error so they can be minimized. If you are already touching the elephant without preparing, you have already introduced enormous bias.

It is possible to go further in the search for 'fit for purpose' quantification. When sampling in situ with the objective of estimating the mineral content of a block in a mine plan, the sampling must include a sufficient number of samples to estimate the spatial covariance of grade in the region of interest and then use that information and the assay data to estimate the grade of the block. The estimation variance for that block is a measure of the 'sampling variance' to which the estimate is subject. There is also an independent component of uncertainty that adds to the estimation variance that comes from the preparation and analysis variance for your samples. Your sampling will be 'fit for purpose' when the sum of the block estimation variance and the variance due to S & P is small enough to limit your risk to an acceptable level.

I see that the Kruskal and Mosteller list of meanings of the term representative sample given in my last post was scrambled. Let me try again.

- General acclaim for data.
- Absence of selective forces.
- Typical or ideal case.
- Coverage of the population.
- Vague term, to be made precise.
- Representative sampling as a specific sampling method.
- Representative as permitting good estimation.
- Representative as good enough for a particular purpose.

The question should be rephrased in the context of "what is the sample supposed to represent?" From rephrasing this question in the context of the objective of the sampling you then define the criteria on how determine if sample is representative of the question you seek answered. In many cases you may be looking at more descriptive qualitative characteristics needed for interpretation and exploration. The problem I find is that often the objective behind an individual sample is lost by the time the office receives the results of the analysis. Other than for grade control, all sample descriptions should include the question why the sample is being collected and the methodologies used. On a typical exploration program several different sampling methodologies may be used by a geologist to answer several different questions in a given day.

Great add. Objective of a sample is often left unspecified & it is assumed all are seeing the answer similarly.

Tony, yes we should by all means know the purpose of the sample. Further, the sample should ideally be collected (and assayed) in such a manner that we have a good estimate of the bias and precision of the sample result. How well does it represent the sampled lot of material? This is where all is falling apart. To have an understanding of the precision and bias of a sample is thought unimportant, perhaps because the general population of minerals folk lack an understanding of minerals sampling. We fall back on standards, rules of thumb and opinions of "experts". Too much money changes hands on the results of samples that lack proper providence. Too bad.

As a follow-up to http://www.911metallurgist.com/geology-prospecting/representative-sample-selection

What Does Selecting A Geologically Representative Sample Mean?

Sampling theories yes, but what do it mean in practice.

To a millman, representative means = what will go into the metallurgical concentrator/mill day to day.

If the "stuff" named Mill Feed is uniform, the answer is easy I suppose. Otherwise... Too many times, 'ore' is blended by or for grade instead of tonnage or metallurgical performance.

After the design metallurgical testwork is done if the results are 'not good enough', the Geo is asked how/where he got his 'representative' samples? Most often, he cannot answer or replicate.

I have seen so many "oh, metallurgy results are bad = it must not have been a representative sample", while if results are good, the integrity of the sample is never put in question.

This forces a going back to the core shack for forms a piece-meal variability or now called geometallurgy program.

All very interesting. We are scientists but yet... I do not think Pierre Gy' theory or Kruskal and Mosteller have been reviewed nor understood by too many.

I have yet to see a step-by-step to GeoMet sampling anywhere.