I'm not from the industry, but sometimes, quantitative approaches are helpful.

Such would be Constrained Optimization, Unitary Associations or Ranking and Scaling. These methods with their pros and cons are well-explained in:

Hammer & Harper (2005) Palaeontological data analysis.

Hi Christian (sorry for the late reply - I've been on holiday) and thanks for your comments. Yes quantitative approaches will be certainly be useful. In commercial datasets however CONOP and its allies may not be easy to apply unless the data has been rigorously "cleaned", particularly with respect to fossil base ranges which can be artificially extended by various drilling factors - mainly "caving". The vast majority of datasets do not do this and most commercial interpretations are therefore based on "tops" only. Commercial companies (contractors and operators alike) often have their own particular practices on how biostratigraphic interpretations are made and also how they are displayed. There appears to be no "standard" methodology. The machine learning age is already upon us (i.e. biostratigraphy) and biostratigraphers have to ensure that data scientists "know how we think" as they construct their ML algorithms. Therefore we need to agree a common set of "standards" in our practice.

I think I understand what you're asking, let me know if I'm answering a question you didn't ask. The boundaries of biozones are generally based on defined events, for example in Raffi et al. (2016) the boundary between CNM5 and CNM6 is the base of common Sphenolithus heteromorphus. The bottom of CNM5 is identical to the top of CNM6.

The way boundaries are drawn with respect to sample depths depends on the sampling. For core sampling, if you treat sample depths as point values rather than sampling ranges (i.e., the sample is at 500 meters below sea floor (mbsf) vs the sample was taken between 490-510 mbsf), the events are treated differently. Commonly in academic studies of cores the sample depths are treated as points and events like LADs are estimated to be halfway between the sample depth and the next highest sample. For example, if you observe an LAD that defines a biozone at, say, 500 mbsf, and the sample immediately above the sample with the LAD is at 450 mbsf, the event is really at some point in between those depths, so the best place to draw the biozone boundary is at 475 mbsf, assuming a normal probabilistic distribution. The opposite applies for things like FADs; if the FAD is observed at 700 mbsf, and the next deepest sample is 800 mbsf, the true stratigraphic FAD should be estimated at 750 mbsf. For events like acmes which are not directional the event is best placed at the sample where it is observed.

In industrial biostratigraphy the samples are often well cuttings spaced into 30 foot intervals, and the fossils are assumed to represent a mix of depths between the intervals. For example, lets say there's a sample at 600-630 feet, with the sample above it at 570-600 feet. If an LAD is observed at the 600-630 sample, it seems to me the best depth for the event is the average depth at 615 feet. All we really know is that it is in between 600 and 630 feet. It shouldn't be above 600 feet because it wasn't observed in the 570-600 foot range.

It's interesting to consider samples which are given as depth ranges but which are not continuous, for example a sample at 490-510 mbsf and the next sample at 590-610 mbsf, with the LAD observed in the 590-610 mbsf sample. It seems to me that the true LAD can be at any depth between 510-610 mbsf, so the true stratigraphic LAD should be estimated at 560 mbsf. I don't think I've ever seen this applied in practice in academia or industry, even though in reality core samples which are generally considered to be at a single stratigraphic level are in reality samples taken with some measurable depth range. Usually this range is negligible in comparison with the spacing between samples and they are just treated as point samples.

Quantitative biostratigraphic techniques such as CONOP/RASC are used to rank and scale biostratigraphic events, but are not really relevant to Mike's question as I understand it. Mike's question assumes the existence of an already developed biozonation, whether it is based on CONOP/RASC/etc. or not doesn't really matter.

Article A Cenozoic calcareous nannofossil biozonation from low and m...

Hi Vann, sorry for the delayed reply - I seem to be doing a lot of travelling around lately. Many thanks for your comments. Yes, although it seems like a fairly unimportant point, I am looking (among other common practices) at how biostratigraphers draw their zonal boundaries in a hypothetical well situation. There are, as far as I can see, two approaches. One where the top of a biozone (in well material normally picked on a "top" or extinction event) automatically defines the base of the overlying zone (I call this the "top defines base" principle), or the other approach where the base of the overling zone is placed in the sample immediately above that in which the top-defining event of the zone below is seen (the "sample defines base" principle).

You make a good point too when data is from a series of "discontinuous" samples. At some point, depending on where the intervening samples have been "composited into" the nominal, analysed, sample or not (in most cases where such selecttive sampling occurs I think they probably have not been) we will need to treat each sample as a "point" sample rather than as part of a contiguous set, with all the caveats that that implies.

In the commercial sector it is usually the base depth of a (composite) cuttings sample (i.e. for 600'-630', it is 630' would normally be assigned as the "nominal" depth). However, I have seen some companies use the top depth and some use (like you do) the mid-point.

At the moment I am trying to determine which combination of methods is the "best" one. Although I appreciate that there can be advantages and disadvantages to all.

It may seem rather a small thing to worry about in the grand scheme of things but I'm coming at this from the viewpoint of Data Science. Companies (including myself and Halliburton Exploration Insights whom I contract to) are very interested in developing AI/Machine Learning algorithms to run on their historical biostratigraphic data sets and Data Scientists will need a comprehensive set of paleontologic/biostratigraphic "rules" to follow if they are to produce meaningful and successful algorithms. Dealing with cuttings sample depths and the drawing of biozonal boundaries are components of a much larger picture where there seems to be few agreed "best practice" procedures - it's in biostratigraphers'/paleontologists' natures to debate and argue I guess! :)

Mike,

It is important I think to honour the sample spacing and therefore follow your sample defines base approach. This means there will be unzoned intervals where there are no studied samples; this is fine as it means if additional samples become available in the gap that the zonal boundaries can be adjusted to fit any new data which may be in the new sample.

There is also another approach whereby regional knowledge allows you to know that a formation boundary, which may fall between biostratigraphic sample points allows you to say that the overlying biozone definitely has to fall above that formational (and associated wireline log) boundary. So to take the top defines base principle in these circumstances is something you may know has to be wrong.

I hope this helps.

Phil