Explicitly creating an implicit model

There are still those out there that think RBF-based domaining is some sort of magic bullet (or a disaster waiting to happen/waste of time/end of the world as we know it - pick your negative). I have always said RBF is just a wireframing method. It is simply a method of enclosing patches of 3D space with a shell. In that context, there is no difference between wireframing explicitly or wireframing implicitly - they do the same thing. To those that say, "But, RBF will lead to disasters!" I challenge you to prove to me that explicit wireframing has never resulted in disasters!! As a wireframing method, done poorly, you will find RBF shells can become a disaster, just like poorly built explicit wireframes. I have had some queries from people wondering what they should do if their company does not let them get Leapfrog or the implicit modelling modules on their flavour of GMP where they exist. To that, I say just explicitly create an implicit model!

I will try and explain in the following paragraphs. Like all things scientific, building a model starts with data analysis. "You don't say!" might be the response, you would be surprised how often this does not happen (or not...if you do regular reviews of other peoples resource models - Scott Dunham discusses (rants on!!) this rabbit hole here, and here - well worth the read!).

Building robust domains is the basis of building a resource model. To do this correctly, you need to ensure you do it diligently and document what you do. Something as basic as creating a grade domain can cover the complete gamut of geology, and every decision should be discussed and noted. Do we use a grade shell? If so, how do we go about selecting the correct lower cut-off? Should it be geologically or numerically based? If numerically based, there should always be a good geological basis. For example, 0.1% copper shell can be closely related to the first occurrence of chalcopyrite, which may also correlate to the first appearance of actinolite, which in turn describes the outer high-temperature bounds of a porphyry system - with such a strong geological background the 0.1% copper shell becomes a good numerical boundary to constrain the estimate. There is a line of thought that the domains should be geology based (i.e. use the actinolite in the example above). I do not totally agree with this as the "geology" relies on the expert eye of your recent graduate geologist doing his (or her) 10-week induction in the desert (the bets on how long they last are building up back in the office by the day). A grade shell is analytical and generally sampled consistently downhole and can always be related back to geology. Unless you are one of those annoying groups that only sample "the mineralised zone," - please do not do this! The cost of sampling the entire hole is a lot less than having to redrill holes because you missed something or suddenly finding that all that porphyry you thought was waste and is now under a waste dump is actually carrying 2.0 open-pitable grams per tonne. From a practical standpoint, trying to handle non-sampled drill holes that sit in the middle of an ore zone is a nightmare - "Was it not sampled because it is waste and so should get a 0.001 background grade or is it missed ore and if given the background grade will it kill this ore zone??" What do I do???

So back to it, explicitly creating an implicit model. Once we have a background cut-off (or a geology based domain - the same method will apply), we need to assess the data for the true down-plunge direction. Nothing does this better than the ability to use Maximum Intensity Projection (MIP); unfortunately, if you do not have Leapfrog or Micromine, you will not likely have this option. You can rudely emulate the process by creating several percentile indicators and assessing each one, small grey dots for below the percentile cut-off and big red dots for above. This will give you a rough ability to do a similar thing, just nowhere near as elegantly.

• By colouring the composites/drilling as above or below the cut-off or using MIP, we can assess the data's distribution. What is the plunge of the mineralisation? Here we have a thin high-grade trend on the east "hangingwall" at the top, a knot of grade in the middle and a lower-grade western "footwall" trend towards the bottom. This becomes interesting later on. This down plunge view becomes the final wireframing direction so save this view direction so that you can easily come back to it.

• Next, we swap to standard north-looking sections (or on the drill sections if they have a different orientation). Digitise trend lines that follow the grade trends. Less is more here, and these do not need to be closed or snapped; this is best done using the composite files coloured above and below the cut-off. Step through from south to north and try and get an understanding of the geometry. This is often as far as some modellers get - close the strings and wireframe together. In fact, this is step one.

• Look in plan, repeat the process as for the sections. Use a different colour string to the one used for sections, again look for trends and look to follow them - but there is no need to close the strings or snap them to drill holes; again, it is best done using composite point files. As always, as you step through the plans, look at the data, test assumptions and look for anomalies.

• Look at the deposit in long section (parallel to the plunge - not along grid north), repeat as for the other two sections. Use a different colour for the string and start looking for patterns based on the other strings already completed; step from one side to the other. You know the procedure by now!

• Finally, create an oblique-dipping section normal to the grade plunge (the same direction we determined using the MIP/Indicators earlier), load the data as drill strings rather than as point files. It is always good to do this on the composite file, so import this into the drill hole database if need be as I have done here, and only colour by the binary above/below the cut-off. These strings should be closed, and they can be snapped to drilling (according to personal preference/company protocol). You can see that the other strings (pink, cyan and green) all create a loose envelope around the grade. This is your guide to the trend of the grade. Do not go making it up now and undo all the work from earlier. If you see something that does not make sense finish this pass and then review it. You may find something you missed, a fault, lithology change etc.; something might pop up and improve your domain. At this point, we do not care where the high and low grades are; we want to wireframe the envelope that encloses the grade and makes sense.

• Once you are done, assess the strings for significant offsets, zig-zags and missing data. Do the strings make sense based on the known geology, do they fit the understanding of mineralisation distribution, are they telling us something we have missed. Try to explain these before simply "smoothing" them, are there faults, rock type changes or fluid dams causing the mineralising fluids to pool by creating a dam wall. Do you need to change the interpretation? I will make the assumption we have tested all this to our best ability and move along.
• Wireframe the resulting strings together to produce a valid wireframe; my effort is presented below. Whilst this looks like a run of the mill standard cross-sectional interpretation, it is not. The shape was constructed using the relationships in the data in multiple different directions. Additionally, it was actually digitised looking some 15 degrees down to the NNE, the plunge direction determined in the data assessment above.

•   Is this a correct interpretation? Who knows, it is but one interpretation of the data; as they say, every geo comes up with a different interpretation. How does it compare with the original domain? As shown below, it is certainly a lot more restricted and does not create the big flat tablet that the original sectional interpretation created. By being more constrained to the drilling we do not create massive zones of unsupported tonnages that are nothing more than geo fantasy. You will note a deep drill hole I have not included - this hole is deep and over 200m away from its nearest neighbour which is far outside the grade continuity. The grade may connect, but it is just as possible that the grade does not! Is it better to say "We have a deep hole with grade that might be worth following up with some drilling!" or "Yeah, I assumed the grade was connected, so I included it into the model but it seems it didn't, going to have to write off around 25% of the Resource.". I know which one I'd prefer!

So, after all this, how does it compare with an implicit model. Have I really explicitly created an implicit model? Below in blue is a very simple implicit model (this one created in Micromine) against the explicit wireframe in orange. This IM shell was created as a gold indicator based on the 0.25g/t cut-off determined in the data analysis. A pretty good match in section given the independent modelling of the IM shell. What about when we look more broadly?

You can see below some difference at the northern end - if you read my earlier posts on implicit mining disasters here and here, you may recognise the shape. A subtle change in geology due to a minor fault here means the fluids no longer precipitate into the host rock. Jun Cowan calls these Perkins Discontinuities; they are very common when you start to look for them, and missing them can mean significant issues for any resource model. There is an uptick in the explicit wireframe base at the same location but certainly not as drastic as implied in the implicit model; the uptick in the explicit wireframe is probably just related to drilling - or lack thereof! One of the issues with explicit wireframing is you habitually step through the model section to section and try to create order from the chaos. Sometimes the chaos is trying to tell you something, but why is it not picked up in the explicit wireframe?

Below I have a section on the left, the location of which is shown on the right, sitting exactly where the implicit model jumps up. As can be seen here, there is grade in the drill hole (including a nice hit), but the grade is spotty due to the aforementioned Perkins discontinuity. As a geologist, you are inclined to wack this hole into the domain and step along to the next slice, let the estimator sort it out. The machine algorithm is a pure black and white beast; the maths doesn't create enough of a solid intersection in 3D space so the shell closes out. While creating the IM shell, I could add a few points and tell the function to wrap this intersection in and include it - which at the end of the day I might, but not before I devote some time to understanding why the grade suddenly drops and makes a sudden shift from the footwall side to the hangingwall side of the domain which we saw earlier in the data analysis. Definitely something we should spend some time on. Should there be a second domain north of the Perkins discontinuity?

So there you have it, explicit wireframing 101 that shows (I hope) that the RBF and implicit modelling is just another wireframing method - one I have used exclusively for 10 years now. Is it possible to create robust domains using explicit wireframes - absolutely! Does it take more time, certainly! Will it create just as many disasters as Implicit modelling, definitely! It is not the software that creates disasters but the seat-keyboard interface. That's where we need to devote the time to improving outcomes. Can we fix this with machine learning and AI - no, relying on these will result in the same number of disasters as everything else. They are great tools for helping us classify rocks, identify patterns, and summarise all the data, but you may also get your two year-old to build the domains - probably just as meaningful. At the end of the day, we can only deal with the data and tools we have available, and we do not always get the most advanced tools or the highest quality data, but sure as heck, we can do the best with what we got!

Happy Modelling!

Ron Reid is the Group Resource Geologist for Harmony Gold in Brisbane, and Adjunct Senior Fellow at the WH Bryan Mining and Geology Research Centre at UQ. Comments contained within are the authors alone and do not represent the opinions of Harmony Gold or UQ.