## What is point counting?

Point investigation may suggests that of describing rock in an unbiased and quantitative means.

A rock which could be represented within the field as “Fine-grained Sandstone” has additional way more data to relinquish up once examined more closely. a skinny section viewed underneath the magnifier could show grains of variable sizes, overgrowths on those grains, overgrowths of various clays, every of variable designs and habits, pore areas between the grains, pores part crammed, grains part dissolved, and so on, in nearly infinite detail. most components of the detail area unit of interest to 1 or alternative of the specialist geoscientists answerable for creating an initial exploration appraisal of an opportunity, or for developing a promising prospect, or for exploiting the known field. it's the task of the petrographer to amass and document this data and purpose investigation is that the principal technique used.

Point investigation may be a applied mathematics technique. It involves watching an outsized range of points on the slide, recording precisely what's seen at every purpose and so collecting an outline from all the knowledge recorded. so as to be a statistically valid illustration, the amount of points represented is usually three hundred – five hundred.

Moving the slide that range of times, and guaranteeing constant purpose isn't represented quite once, may be a important task. concerning forty years agone, Swift Engineering developed a tool that enraptured the slide in equal increments on a line; at the tip of a line, the petrographer would re-set it to the beginning and move it up a line, very much like employee performed a “carriage come back and line feed” operation.

Added to the current, Swift, and later previous Scientific Instruments, developed a 20-channel device for recording up to twenty completely different classes of things seen. however twenty is way too few for the big range of minerals, clays, pore varieties and alternative materials of interest found in an exceedingly skinny section, even before we tend to try and record the habit and morphology, the combos, and therefore the diagenetic relationships.

Number of points to count and “1.5 times grain size”

By contrast, if we were to take the same thin-section dimensions as previously but now with a rock which has an average grain size of “Very Coarse Sand Upper”, we would find that the “step size (at least) 1.5 times grain size” adage means we run out of rock to look at when we have stepped about 130 times. We simply cannot get enough material to look at. What has gone wrong this time?

We have to look again at why we are point-counting. The reason is to collect data from a representative sample of the rock, and hence to be able to make predictions or deductions about the rock as a whole. Where did “400 points” come from? And why “1.5 times grain size”? What do they contribute to the determination of a strategy for finding a representative sample of rock?

If you are an oil company sedimentologist feeling hard-done-by because you have to describe 400 points on your slides, think of coal petrologists working to the ICCP recommendation of 900 points. But even they are getting off lightly: ASTMS recommend 2000 – 4000 for clinker. Where do these numbers come from? Felix Chayes is frequently referred to as the father of mathematical geology and in 1953 he published a discussion of how variability in the rock should determine the target point count. This should be obvious: if we have counted 300 points already and they were all quartz, the 301st point is odds-on not to add any new information, the relative percentages will almost certainly remain unchanged; if we have counted 300 points already and 100 were quartz, 100 feldspar and 100 microcline, then the 301st pint is bound to change the relative percentages, but only slightly; but if, at the other extreme, every one of those 300 points was a different mineral, then the 301st is going to effect a large percentage change, no matter what we see there. Logically, if we want a statistically representative (or, to put it another way, accurate) description of the rock, we should keep counting until the changes effected by further counting are negligible.

The “magic number” approach to setting point count targets is a hangover from a bygone age. If one has no simple way to place a grid over a slide, then step size is a simple, if crude and inefficient, means of determining a sampling strategy. The dictum “1.5 times average grain size” comes from a desire not to count a grain twice. This itself is dubious thinking (if we were sampling the electorate in Britain, would we only ask one person in London, because we don’t want to ask Londoners twice? I appreciate that this is different in kind and in principle, but should at least serve to provoke thought) but is worse if it leads us to count the wrong number of points. It is surely obvious that, if there are fewer but larger grains, we shouldn’t be counting less points. (It may be less obvious that there is an implication that we should, on the contrary, be counting more points; statistical theory is occasionally counter-intuitive and we will come back to this point).

Number of steps is most frequently determined by accountants rather than geologists. With the predominance of out-sourcing, number of points to count will usually be determined by available budget. More correctly it should be determined by our degree of tolerance for errors taken with our expectation (based on background knowledge and experience) for spatial and statistical variation in the rock.

If we start with a knowledge of what the data will be used for, and hence how much we can tolerate errors, we can devise a point-counting strategy to suit. For example, if the petrophysicists wish to know whether certain trace minerals are present, we should count until we have a reasonable confidence that, were they present, we would have seen them. Statistics is very good at measuring and determining this kind of confidence: tests exist which, if applied correctly, will give us a numerical measure of confidence. We can ask the petrophysicist: “How sure do you want us to be – 90% confident? 95% confident? 99% confident?” and, based on her/his answer, determine how many points we should count.

The additional input to this calculation of confidence is the geologists expectation of variation in the rock. We can, however, refine this as we go along, by determining the actual degree of variation in this particular thin section. This would add inordinately to the effort if tallying manually, even using one of the ready-reckoned graphs as published by, for instance, xyz; but, if using a computer to do the tallying of counts, it is trivial to ask the computer to tell us when to stop counting, based on our target for percentage confidence.

Different answers might come from the engineers, who are only going to average our data into blocks hundreds or thousands of times the size of our thin sections, or from specialist geologists, who may be using the data as input to models for determining diagenetic history, basin development, etc. In each case, we can determine a strategy from the requirements – are we trying to catch odd occurrences of extreme events (trace minerals) or quantify relative abundances of significant occurrences (e.g. clay habit)? – and, if necessary, take the worst case from each to allow the data to be of maximum use to all parties. The down side is that someone has to think: this becomes a genuine test of skill, using a large amount of background information on the specific rocks or on rocks from similar environments, instead of a simplistic application of a universal formula handed down through the generations and having little or no relevance. It is therefore a task for the geologist, not for the company accountant.

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