

Point Counting in GeologyWhat is Point Counting?Point counting is a means of describing rock in an unbiased and quantitative way. A rock which might be described in the field as “Finegrained Sandstone” has much more information to give up when examined more closely. A thin section viewed under the microscope may show grains of varying sizes, overgrowths on those grains, overgrowths of different clays, each of varying styles and habits, pore spaces between the grains, pores partially filled, grains partly dissolved, and so on, in almost infinite detail. Almost all parts of the detail are of interest to one or other of the specialist geoscientists responsible for making an initial exploration appraisal of a prospect, or for developing a promising prospect, or for exploiting the identified field. It is the job of the petrographer to acquire and document this information and point counting is the principal technique used. Point counting is a statistical technique. It involves looking at a large number of points on the slide, recording exactly what is seen at each point and then assembling a description from all the information recorded. In order to be a statistically valid representation, the number of points described is typically 300 – 500. Moving the slide that number of times, and ensuring the same point is not described more than once, is a significant task. About 40 years ago, Swift Engineering developed a device which moved the slide in equal increments along a line; at the end of a line, the petrographer would reset it to the start and move it up a line, much as typist performed a “carriage return and line feed” operation. Added to this, Swift, and later Prior Scientific Instruments, developed a 20channel device for recording up to 20 different categories of things seen. But 20 is far too few for the large number of minerals, clays, pore types and other materials of interest found in a thin section, even before we try to record the habit and morphology, the combinations, and the diagenetic relationships. Point counting in PETROGPETROG caters for all of this diversity, recording the information in a form suitable for analysis by petrographers, engineers, petrophysicists and other geoscientists, by using comprehensive data dictionaries, hierarchical data structures and relationships, and 3D virtual, adaptive ticklists. The method used by PETROG to simplify control of the slide and ensure statistical validity is in the software used to control the fully automated stepper stage, developed specifically for pointcounting. The myth of step sizeStep size is irrelevant. So why is it that the first question we are asked when we are demonstrating our digital petrography software (PETROG) is “How do I set the step size?”. What we are trying to do in point counting is akin to an exit poll during an election or an opinion poll prior to an election: taking a sample and extrapolating to the whole population. The science of sampling in that context has made huge strides since the USA election of 1948, when the Chicago Tribune went to press with the headline “Dewey Defeats Truman”, based on extrapolation of early results. Nowadays, exit polls are generally very reliable. Petrographers aim to make their extrapolations, from a thin section to the rock from which it was taken, also very reliable, and to do so they need to be able to sample the rock in a representative way. We want to ensure, therefore, that the sample is representative. When we say things about this piece of the rock, we should be able to assume those statements are more generally applicable, to at least a neighbourhood around where this piece of rock was taken (the “population”.) Let’s look at an example. We’ll assume a thin section of 1" x 3" with a 1" margin for the label. If the rock has an average grain size of “fine sand lower” on the Wentworth scale and we pointcount with a step size of 1.5 times the average grain size, then, by counting 400 points we will see roughly 2.5% of the slide; or, if we start at the bottom left (excluding the label) and count the first 400 points, we will look only at the red portion:
Returning to our election / opinion poll analogy, this is equivalent to finding out how the UK will vote at an election by asking every 100^{th} person we meet, starting in Cornwall and continuing across and up the country until we get to Winchester. So where did we go wrong? The answer, obviously, is that step size is not the correct way to control our sampling strategy. Surely, if we want a representative sample of size 400 points, a better way of sampling would be to put a grid over the slide, giving us 34 steps in the horizontal or longaxis direction and 12 steps in the vertical or shortaxis direction. Hence, if we were to approach pointcounting sensibly, step size is a consequence of determining our sampling strategy, not an input to it. In other words, step size is irrelevant. We have temporarily overlooked the original reasoning behind the adage that stepsize should be 1.5 times average grain size; it’s time to look at this as well. Other myths: number of points to count and “1.5 times grain size”By contrast, if we were to take the same thinsection 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 pointcounting. 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 harddoneby 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 301^{st} point is oddson 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 301^{st} 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 301^{st} 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 counterintuitive and we will come back to this point). Number of steps is most frequently determined by accountants rather than geologists. With the predominance of outsourcing, 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 pointcounting 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 readyreckoned 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. ConclusionsIf wireline logging still relied on the data collecting techniques introduced by Schlumberger pere et fils, would petrophysics data feature in a presentday reservoir evaluation? Pointcounting is one of the principle techniques for using firsthand data from the rocks and yet its use declines and its perceived value diminishes. We owe it to the entire E&P process to make information from the rocks more useful to those making decisions on exploration and production. 
