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PETROG includes patent protected technology.

Sandstone Petrography, Petrology, and Modeling (‘SPPM’)

DOI: 10.2110/sepmcsp.13.06

SEPM Concepts in Sedimentology and Paleontology No. 13, Copyright 2022

SEPM (Society for Sedimentary Geology), ISBN 978-1-56576-374-6, eISBN 978-1-56576-375-3

‘Sandstone Petrography, Petrology, and Modeling’ (‘SPPM’) by Tom Taylor, Linda Bonnell and Rob Lander has become the standard text in its field, which results in many questions for us at PETROG on how to accommodate and implement the book’s principles using our software. We have already answered many questions in isolation and we believe that there is a need to provide some background to those answers. That is the purpose of this note.

PETROG and Conwy Valley Systems Limited recognise the Trademark ‘Touchstone’ of Geocosm limited, acknowledgement of which is omitted in the following text only to promote smooth reading.

The three authors of SPPM have been generous with their time, over many years, sharing their insights as we non-petrographers have tried to understand the topics and background science involved, but PETROG and Conwy Valley Systems Limited are solely responsible for the following content and for the opinions expressed herein.

Where we reproduce here quotes from the text, these are coloured in blue to differentiate them from the main text of this note.

Sandstone Petrography, Petrology, and Modeling  – A note relating to PETROG

Quantitative Grain Coat Analysis

Chapter 1: Petrography, Petrology, and Petrophysics

Page 3 of SPPM states

“Various statistical formulas exist for calculating the number of observations or samples that should be included in a statistical sample set. As a hypothetical example, assume we are asked to study a 100- m-long core cut in a 100-m-thick sandstone bed. Evenly spaced core plug samples are drilled at an interval of three plugs per meter. Before beginning the study, we want to know the minimum number of randomly selected core plugs to analyze in thin section in order to properly represent the total population of 300. Using a standard statistical formula (Cochran 1977, Eq. 1) …”

This is not so much statistics as common sense: what is the point in establishing the statistical confidence in a subset of samples, when the set of samples was created with no known basis? If whoever was in charge had chosen to take plugs at 50cm intervals, the “standard statistical formula” would generate a different answer, a smaller number of plugs to analyze; what does that tell us? The question should be: “how many samples to accurately model the core?”. The 95%, 90% and 99% confidence intervals represent confidence in an intermediate number which is of no relevance.

Chapter 6: Quantitative Textural Analysis, p. 143–160.

6.1.1 Sieve analysis

SPPM has the following to say about sieve analysis on page 143:

“Sieve analysis provides a ‘‘true’’ three dimensional (3D) GSD for the disaggregated sample material.”

“…. the actual grain dimensions reflected in sieve analysis”.

“…. actual grain diameters consistent with sieve analysis”.

The first statement is taken from a full paragraph of:

“Based on decades of study of unconsolidated sands, sieve analysis remains the standard benchmark method of measuring the GSD to which other methods (e.g., thin section measurements, laser particle size analysis) are compared. Sieve analysis provides a ‘‘true’’ three dimensional (3D) GSD for the disaggregated sample material. Attempts to disaggregate lithified sandstone samples by force for the purpose of measuring the sizes of detrital grains via sieve analysis are riddled with pitfalls that lead to serious errors in GSD data.”

This hints at an underlying truth that should be more widely recognised: decades of study have established an expectation (amongst practising petrographers) of a relationship between measured grain size and actual rock properties. For most practical purposes it is less important to have an actual or true measure of grain size than to have an internal picture or expectation of what any measurement tells us about the properties of the rock. This internal picture has been built on “decades of study of unconsolidated sands”, often using sieve analysis. That should not, however, be a justification for the claim that sieve analysis is ‘correct’ or ‘actual’. For example, the amount of energy used in sieving will determine which of the principal planes predominates in what is being measured. Additionally, this paragraph includes one other of the reasons why sieve analysis is not ‘correct’: it requires disaggregation. However, perhaps the most important reason is only introduced later in the chapter, and then tangentially: the material that did not pass through the sieve is weighed, and this measurement is what is plotted. This is therefore not a grain size histogram but a grain mass histogram.

What is a histogram? This is both intuitively obvious and not at all clear. ISO (International Standards Organisation) has issued over 50 documents relating to particle sizing, of which 4 are concerned solely with graphical representation. How can it be so complicated? In school we were taught to count the number of times something was seen (frequencies) and put them into groups (‘bins’), then draw rectangles of equal width but with height varying in proportion to frequency. What if we were counting road vehicles and we saw 10 cars and 2 lorries: should the ‘car’ bin be 5 times the height of the ’lorry’ bin? Surely that doesn’t make sense: if a lorry is 10 times the weight of a car, each lorry should be worth 10 cars; so shouldn’t the ‘lorry’ bin be twice the height of the car bin? Considering the problem with doing that (weighting the bin heights based on some attribute of the items being counted) takes us even deeper into understanding what we are doing and why we are doing it. We should always try to capture data at its lowest level of granularity and at its most basic. This is a fundamental principle of database theory.

If our purpose is assessing road damage, then axle weight is critical, because road damage is proportional to the cube of the axle weight. But if we only collect weight data, we cannot use the information for other purposes, such as traffic management, This is second nature to petrographers: if we only collect clay information then the data is not useful to a petrophysicist trying to understand unexplained kicks on logs or, if we only collect information on clay type, without its habit, an engineer will not be able to use it to try to explain porosity-permeability anomalies.

In the case of particle size data, we should collect both size and grain type. If we only collect total weight of particles of a certain size, we have to guess their effective density “in order to estimate the number of particles of that size.  Given the problems associated with conversion of sand GSDs measured in thin section to actual grain diameters consistent with sieve analysis, it is preferable to adopt a single, internally consistent technique for measuring grain size in thin section as a valid standard for sandstone petrology.” (Page 143)

This is true but not always possible, unless we restrict analysis to our own data collected from this moment onward. Conversion is possible (see e.g. ISO 9276) – sieve analysis measures total mass of a size interval so effective density allows conversion to frequency data. This is arguably preferable to ignoring historical data.

PETROG has a ‘Concurrent’ mode of data collection: concurrently describing modal and textural data . Together with the table of typical densities this allows conversion between types of data presentation, by weight or by volume frequency.

6.1.2 Which Grains to Measure

“The recommended procedure for quantitative determination of grain size in sandstones limits the measurement of grain diameter to rigid grains.” (Page 144)

Such limitation is unfortunate, because measuring ductile grains is important for some analyses, such as transport, utilising equant-lath ratio, and is unnecessary, because PETROG allows combined compositional (modal) and textural (grain size) analyses, so that all grains can be measured and then GS analyses conducted on subsets of grains chosen by the petrographer.

N.B. PETROG was designed specifically to overcome the limitations inherent in collecting data for a particular purpose. Collecting grain size data only for rigid grains, because the analyst is, at that moment, only interested in rigid grains, means that the data set is not usable by some other analysts. This limitation can also be seen in collecting data specifically for, for example, Touchstone, which has a data model designed for one purpose and precluding some others. PETROG overcomes this by collecting data, not for any particular purpose but in as general a manner as possible, and then treating e.g. ‘Touchstone-ready data’ as just one possible report, without any loss of generality and without any loss of specificity for Touchstone.

Why is Touchstone not a database? A database is a collection of data that is managed to allow many different applications to use it. Touchstone’s data is for Touchstone only. Obvious examples include:

 Some data cannot be entered/stored, because it is not of interest to the Touchstone model (e.g. absence of heavy minerals observations means that the data cannot be used for investigating unexplained kicks on logs);

 Some data cannot be entered/stored, because it is not observable at sufficient level of detail (PETROG stores such data and, if ‘Touchstone mode’ is switched on, marks this as ‘incomplete for Touchstone’);

 Some items may be entered into more than one location in the Touchstone model, even though they are identical (this is handled internally by Touchstone software, but other applications would not know this).

Construction of a database requires data collection in an application-independent way, allowing each application, such as Touchstone, to receive data as a retrieval or report.

6.1.3 All grains image

The ‘all grains image’ method described is a biased technique, favouring small grains. SPPM notes that this measures more small grains, but that doesn’t of itself make it biased: it will naturally measure more small grains when there are more small grains present. Bias is, however, introduced because large grains are more likely to span an image (Field of View) boundary and hence be excluded; the statement that 100 grains should be measured is unsupported. The actual number of grains required to achieve a given confidence is dependent on the nature of the variability, and hence will be different for different rock types and locations, but is more significantly dependent on the purpose for which the data will be used. Grain size is not a useful indicator of rock properties; grain size variation, or sorting, is a useful predictor. In general it is necessary to collect many times more measurements in order to achieve the same confidence in sorting as in grain size.

Pages 147 and 148 state

“To obtain a statistically valid estimate of the GSD, the chosen method of grain selection must honor two criteria: (1) the frequencies observed are representative of the overall sample population, and (2) the process of selecting individual grains samples the population randomly (Kelly 1971, Textoris 1971). Methodologies that satisfy these assumptions generate area–frequency data that form a consistent estimate of the volume frequency in the rock sample (Chayes 1956). Thin section point counting (grid sampling) is the most rapid and accurate technique of grain selection that satisfies the above criteria (Kellerhals et al. 1975, Johnson 1994). A sampling grid is set up to cover the entire sample chosen for analysis, either manually or with an automated point count stage and associated software (Fig. 6.11). The density of the grid is established for the desired number of data points.”

“The resulting data can therefore be divided into Wentworth grade scale size fractions as volume percentages, analogous to the results of standard sieve data.”

… except that one is frequency and the other is mass; and

“The two grain selection procedures (“Thin section point counting (grid sampling)”, “all-grains-image”, ) are not equivalent.”

Traditionally, petrographers have used a rule-of-thumb that the step size (in the former) should be larger than a typical grain, making these two techniques closer to being equivalent and hence obviating the need for corrections when comparing results from different methods; this is important, because the actual technique used was not always noted, for historical data, and continues to be missing in many current databases. Note that this is only a ‘rule of thumb’, not a rule based on mathematical statistics.

6.1.4 How many grains?

From page 148: “desired number of data points to be collected, generally, 100 to 250 grains.”

And

“FIG. 6.11.—Grain-size data derived from thin sections of sandstones may be collected using a point count grid consisting of evenly spaced lines and points of intersection. The grid displayed here is 9314, generating 126 intersection points 4 mm apart. A minimum of 100 data points should be collected to adequately estimate the grain-size distribution of most sand samples.”

This glosses over one of the most important aspects of grain size data: sample size needed to obtain any confidence level. As with all sampling in petrography, there is no correct answer, in large part because the number of samples needed to obtain a given confidence level depends on the variability and the purpose to which the data will be put. If we are only interested in size distributions, the number of samples needed is considerably less that if we are interested in sorting, the second moment of the distribution.

6.1.5 Which grains?

Again, from page 148: “Each grain (i.e., undeformed rigid grains) that appears beneath the intersection of grid lines (Fig. 6.11) is measured until the predetermined number of data points is recorded.”

Restricting data collection  to ‘undeformed rigid grains’  is counter to the ethos of building a database (see above, 6.1.2, comment on SSPM page 144)

6.1.6 Graphical methods

This section misses the point, which is that graphical methods exist solely because it was difficult / time-consuming to calculate proper statistics prior to the common availability of electronic calculators, a point made by SPPM earlier in the chapter.

The criticism of Trask (“only evaluates the central portion of the distribution”) is unfair, for two reasons: the central portion (of a distribution) is generally the most reliable (statistically), so this is actually a point in its favour; and, as noted above, GS analysis is in large part a matter of comparison with a mental database of previous cases, and if those were created using Trask, then use of Trask should be continued.

6.1.7 Statistical Error and Measurement Error

“The basic process of collecting grain-size data for lithified sandstone involves two fundamental parts. The first is the measurement of individual grain diameters (large axis a; small axis b; or combination of a and b) in a manner that minimizes measurement error. The second part is the method used to select the grains for measurement.”

The distinction between two parts of the process is important because they have different error characteristics.

6.1.8 Poroperm

“Porosity and permeability, key factors in determining the flow capacity of aquifers and reservoirs, are influenced by grain size and sorting because they affect flow path tortuosity and the wetted surface area.” (page 149)

It is useful to separate out porosity and permeability: theoretically, porosity, being defined purely geometrically, is far less dependent on size than it is on sorting (for any given configuration, scaling up or down changes the size but not the porosity). The same applies for surface area.

“we recommend creating a mosaic of registered (‘‘stitched’’) higher-resolution images to use as the basis for the measurements.”

PETROG is ideal for this because its stitched mosaics are spatially referenced, so the points at which compositional analysis have been undertaken are known.

Chapter 7: Quantitative Modal Analysis of Sandstone

We have PETROG users working with the Gazzi-Dickinson technique, implemented via bespoke changes to dictionaries and the internal rulebase.  We would be pleased to hear from PETROG users as to whether making this more readily available would be of interest i.e. so that a selection could be made under Data Entry Methodology as to whether standard point counting or Gazzi-Dickinson should be applied, and then the relevant dictionaries and rules would be applied automatically.  We note the reference in SPPM to the Garzanti ternary scheme that is designed to be used with Gazzi-Dickinson.  This scheme could be easily implemented in PETROG v6, along with adding an option to plot both present-day and reconstructed compositions on the ternary diagram.   We would very much appreciate input from users as to the importance of these features, and how they should be implemented for your workflows.

“Quality control is important. Recount several samples during an extended modal analysis study and compare the results statistically. “

In PETROG, the starting point (origin of area of interest) can be offset by an amount, the count repeated, and results compared. Researchers at University of Liverpool have used this method to find practical estimates of variability in textural measurements.

Chapter 8: Quantitative Grain Coat Analysis

8.1 General Observations

“As discussed in Chapter 11, grain coats on detrital quartz grains can inhibit quartz cementation by blocking or impeding cement growth (Heald and Larese 1974, Pittman et al. 1992). The most effective types of grain coats observed in sandstones are authigenic clay minerals and microcrystalline quartz. Less effective types of grain coats include detrital clay rims (Wilson and Pittman 1977), iron oxide, solid hydrocarbon, and fine crystalline carbonates such as siderite.”

This is increasingly important for petrographers preparing data for input to the Touchstone system. The chapter is the shortest in the book and is light on detail, possibly because recognition of this importance is relatively new. Previous work had been largely qualitative. The observation (C. MacCaulay, pers comm – we are assuming that this is common knowledge amongst petrographers and was news only to us) that porosity preservation is not in general linearly related to coating percentage, obviously limited any desire for a fully quantitative approach.

Aysen Ozkan (Ph.D., U. Texas Austin) developed a comparator-based approach to grain coat categorisation that was initially adopted by many petrographers preparing data for Touchstone. Fully qualitative approaches rely on technologies only recently made available to petrographers. PETROG now offers alternatives ranging from qualitative visual estimation through to fully quantitative digitising and measurement. It is useful to compare these options with those in chapter 8 of SPPM, but first an observation on data granularity and the building of a database.

8.2 What is a Grain Coat?

“three categories—coated, uncoated, and unavailable (Table 8.1). The ‘‘coated’’ category includes surfaces where quartz could grow if not for the occurrence of thin, grain-rimming materials (Fig. 8.2). ‘‘Uncoated’’ surfaces consist of two types, (1) the contacts between the uncoated surfaces of detrital quartz and open pore space, and (2) the contacts between detrital quartz and authigenic quartz overgrowths”

TABLE 8.1.—Categories for petrographic measurement of grain coats on quartz sand grains in thin section.

Coated

Detrital quartz surfaces that are lined with a thin layer of authigenic clay minerals.

Detrital quartz surfaces that are lined with thin rimming detrital clay minerals

Detrital quartz surfaces that are lined with a thin layer of microcrystalline quartz crystals.

Detrital quartz grain surfaces that are coated with a thin layer of siderite or micritic calcite.

Detrital quartz surfaces that are coated with a thin layer of solid hydrocarbon.

Uncoated

Contact between detrital quartz surfaces and open pore space.

Contact between detrital quartz surfaces and authigenic quartz overgrowths.

Unavailable

Detrital quartz surfaces in contact with neighboring grains.

Detrital quartz surfaces in contact with detrital matrix

Detrital quartz surfaces in contact with pore-filling cement that predates quartz cementation

In PETROG, the “Revisit Logged Points” option allows users to sub-select the compositional data points that have been identified in a first pass of the slide, for instance by selecting Quartz from the list of Compound Items.  All points logged as Quartz grains are then highlighted in a different colour, and there are controls to step through just these points, based on a selection strategy – so this can be the first n points, the last n points, or a random subset of n points, where n is the required number of textural measurements (set under Data Entry Methodology).  At any point, the user can grab the image, digitise the perimeter of the quartz grain, and then use node tagging to enter grain coat information.  

For Touchstone, the tagging options include more detailed information than just “coated” or “uncoated” – for instance, “Detrital quartz surfaces that are lined with a thin layer of authigenic clay minerals” and other entries as shown in the above table.  

 

Based on the selected tagging option, the proportion of the tagged section of the overall grain perimeter will be assigned to the relevant category when reporting the data for the sample i.e. % of Coated, % of ‘Coated - Detrital quartz surfaces that are lined with a thin layer of authigenic clay minerals’, etc. are all automatically calculated and reported by the software.

PETROG has implemented this for Touchstone but it could be extended to general selection of the material forming the grain coat, i.e. to make it generic.

8.2 Databases

SSPM states (page 189):

“The reason that surfaces associated with grain contacts, pore-filling matrix, and pore-filling cement are not considered grain coatings is that quartz cementation algorithms already account for their impact on the reduction of nucleation surface area available for overgrowths.”

If this is adopted as a data-entry procedure, then the data are useful for a specific application (i.e. ‘quartz cementation algorithms’) but not necessarily for other applications.

8.3 Methods for Calculating a Mean

8.3.1 Overall Mean, or Mean of Grain Means?

SPPM page 189 states

“Three techniques have been employed to estimate grain coat coverage of sandstones: image digitizing, angular proportion, and visual estimation.’”

The measure of grain coat coverage arrived at by image digitizing is described as

“The segment lengths are summed, and a sample mean grain coat coverage is calculated”.  

This presumably means that the lengths of all segments (of grain coating) on all grains are summed, and the perimeter lengths of every grain are summed, and the former divided by the latter. It is not clear whether perimeters are required for grains with no coating; one would presume so, so every grain must be digitised, regardless of whether or not they have any coating.

However, there is a later statement:

“The data are reported as the mean grain coat coverage of all analyzed grains in the sample.’”

This implies a different interpretation of the required calculation. This would suggest that a mean is calculated for each grain and then these means are averaged (in an arithmetical mean sense).

Another statement:

“The grain coat coverage is an area percentage that is calculated from sums of the lengths of 2D line segments for the coated and uncoated categories for each analyzed quartz grain.”

supports this latter interpretation (mean of means for each grain), since here sums are specified for each grain.

“rather than the sum of coated and uncoated segments for the entire sample”

implies that the statement on page 189,

“The data are reported as the mean grain coat coverage of all analyzed grains in the sample”

is being interpreted as the sums being done first and then averaged, as opposed to the average for each grain. But

“The grain coat coverage is an area percentage that is calculated from sums of the lengths of 2D line segments for the coated and uncoated categories for each analyzed quartz grain”

implies to us, with the wording

“for each analyzed quartz grain”,

that the coating is calculated for each grain using the formula (1) and then the mean of those coatings is what is reported. But the end-note (2) on page 190 implies the other interpretation.

PETROG provides both interpretations as options.

8.3.2 Possible Consequences

At the start of this chapter (page 188) SSPM observes:

“Mean grain coat coverage does not generally correlate with total chlorite cement volume determined by modal analysis (point counting).…… (Fig. 8.1).”

The first graph in 8.1 shows an apparent, if maybe weak, non-linear correlation. The non-linearity could be due to the choice of method used to calculate the means (which is stated here as being individual grain means).

8.3.3 End Notes: Which IA Method?

Page 190 states

“2. The IA technique used for this analysis differs from the approach described above. The grain coat percentage is determined from line segments for each grain (rather than the sum of coated and uncoated segments for the entire sample), thereby providing a grain-to-grain comparison with the visual estimate technique.”

So both ways of estimating mean are used by SSPM, at different times. Whilst an individual lab or organisation can standardise on one or the other, it is not clear to us which is expected by Touchstone but, as both are reported by PETROG, the Touchstone modeller can choose, and hence provide consistency with their other models.

8.4 Statistical Analysis

“The third technique requires an experienced petrologist to make a careful visual estimate of grain coat coverage on a minimum of 50 randomly chosen quartz grains. Application of this method requires much practice and routine checking of accuracy by comparison with IA results in order to develop sufficient expertise. If done properly, the visual estimate technique provides a practical, time-effective alternative for generating data for studies that include numerous samples.

In order to evaluate the variability between the two methods when performed by a single operator, visual estimate and IA techniques were applied in parallel to the same 50 quartz grains in four sandstone samples2. For each individual grain, a visual estimate of grain coat coverage was made and recorded, followed by quantitative IA analysis as described above. This procedure was strictly followed, and the results are shown in Figure 8.7. A strong linear correlation exists between estimates obtained from the two methods for all four samples. Although the estimated grain coat coverage differs by 10% or more for some individual quartz grains, the sample means and standard deviations are remarkably similar. The results of this comparison demonstrate that the visual estimate technique applied by an experienced operator is a viable method for approximating grain coat coverage.”

a) Unfortunately there is no scientific or repeatable meaning to the term “experienced petrologist”. We would expect the correlation to depend more on the experience level of the petrographer than on other factors, such as the difference between the two methods, the number of grains analysed in each sample, etc.

b) SSPM makes no attempt to justify or explain geologically the differences in R2 between the four samples. Statistically one might question whether the higher correlations being associated with the greater control at low percentages is relevant or significant, or, similarly, whether the in-sample variance is related to the correlation coefficient. A key question over the technique should then be: “Why might this be the case?”. In other words, is the accuracy of the technique affected by the range of values of grain coat percent?

c) Does SSPM mean 50 samples each of 50 grains per sample or, as seems more likely, just 50 grains per geological setting?

d) “At least 50 quartz grains selected at random and distributed in a representative manner throughout the thin section are analyzed.”

The reason for petrographers to have traditionally used 50 as the target has arguably had as much to do with time constraints, when all available methods were tedious, as with any other consideration. There is no theoretical justification available and practical work is context-dependent. Work undertaken at University of Liverpool (Hinds et al, 2014; Duller et al, 2014; Wells et al 2016) shows that the number of grain measurements required to achieve any pre-defined level of confidence is highly dependent on the purpose for which data will be used.

8.5 Erratum

“FIG. 8.5.—Grain coat coverage measurement techniques. A) Angular proportion technique. Yellow lines—coated; red lines—uncoated.

B) Image analysis–perimeter measurement. Yellow lines—coated; red lines—uncoated; black dashed lines—unavailable. Measured grain coat coverage = 42%.”

The images for parts A and B of this figure are labelled the wrong way round.

8.6 Conclusions

A key feature of PETROG is its ability to collect data for input to the Touchstone forward modelling package (‘Touchstone-ready data’) whilst also building a database of more general value. PETROG was designed to be the complete petrographic data collection, management, analysis and reporting package. Achievement of this goal was evidenced by the ease with which PETROG was able to support data collection meeting the specific demands of Touchstone. Its use by both Geocosm and major consortium members, either directly or through sub-contracted data collection, has contributed to further development, accommodating demands for more quantitative data for, for example, grain coat analysis (SPPM ch. 8).

PETROG has a user-switchable ‘Touchstone input’ mode that allows the petrographer to see, during data collection, whether data conform to Touchstone’s rules, without waiting for completion of data collection. The checks are repeated when the data are exported to a Touchstone-ready file.