Geostatistics / Field notes / 31 July 2026 / 4 min
The math was never the bottleneck
Geologists and machine-learning researchers spent forty years inventing the same equations without noticing. That is a good story. The useful part is what it implies: if the mathematics has been settled since the 1960s, then the reason a prospectivity map still takes weeks is not the mathematics.
01Two fields, one equation
Here is the problem every exploration geologist has: you have grades at a few hundred points, and you need a number everywhere else. Not a guess — a number you can defend, with an honest statement of how confident you are.
In the 1950s a South African mining engineer, Danie Krige, worked out how to do it on the Witwatersrand goldfields, and a French mathematician, Georges Matheron, later gave the method its theory and its name.[1] The idea is simple enough to state in a sentence: measure how quickly similarity falls off with distance, then use that to weight the samples near any point you want to estimate. Two holes ten metres apart tell you almost the same thing. Two holes a kilometre apart barely tell you about each other at all. The curve describing that falloff is called a variogram, and fitting it is the central craft of the discipline.
Four decades later, machine-learning researchers built something called a Gaussian process. It also measures how quickly similarity falls off with distance, using a curve they call a kernel. It also uses that to weight nearby observations.
They are the same method. Not analogous — the same. The variogram is the kernel turned upside down, and the equations you get from either starting point are identical, term for term.[2] One field derived it to estimate ore reserves; the other derived it to do statistics. Neither noticed the other for years.
02So why does a map still take weeks?
This is the part worth sitting with. The equations are sixty years old. The software has been free and open since the 1990s.[3] And a prospectivity map still takes a specialist weeks.
Almost none of that time is spent computing anything. Solving the system is a machine cost, and it is the small term. The weeks go into the work wrapped around it:
Pulling assays out of four systems and reconciling them against the collar survey. Deciding which historical campaigns are trustworthy. Choosing a search direction and defending it. Re-running everything when a batch comes back from the lab. Rebuilding the figures for the board pack.
That has a real cost, and it is not the salary. It is that when a model takes three weeks, you build one. A geologist who could test twenty search orientations tests two, picks the more defensible, and moves on — not from laziness, but because there is a board meeting. The map that guides the drill programme is the map someone had time to make.
03What changes when the cost goes away
Agents are good at exactly the part that is slow. Not the judgement — the assembly, the bookkeeping, the hundred variants nobody has time to try.
Pull the assays together and flag what does not reconcile. Fit every plausible model rather than the two you can defend in a meeting, and score them against held-out ground so the winner has to earn it. Rebuild the whole thing the morning new results land, instead of the next time someone is free. None of that is a new discovery in geostatistics. It is the same sixty-year-old mathematics, run at a cadence a person could never sustain.
What the geologist gets back is not an answer. It is a shortlist with its working attached — this ranking, under these assumptions, and here is what changes if you disagree with any of them. That is a far more useful object than a single map handed over with a shrug.
A ranked target is a model output, not a resource estimate, and no amount of compute makes it one. Aethermine flags and prepares; it never verifies, certifies or clears anything. A Qualified Person signs off — and the reason to write the reasoning down in plain language is so they can take it apart.
04The part worth remembering
Two fields spent forty years building the same thing and did not notice, because they were reading different journals. It is a good reminder that the hard problem is rarely the one everyone is looking at.
The equations under exploration targeting are settled. What is not settled is how much of a company's own record ever reaches them — and that is a plumbing problem, not a mathematics one. Which is a much better problem to have, because plumbing is fixable.
If you want the technical version
- Matheron, G. (1963). Principles of geostatistics. Economic Geology, 58(8), 1246–1266. doi:10.2113/gsecongeo.58.8.1246 — the paper that named the field, building on Krige's work on the Witwatersrand.
- Rasmussen, C.E., Williams, C.K.I. (2006). Gaussian Processes for Machine Learning. MIT Press. free online — §2.2 and §B.1 state the equivalence directly, from the machine-learning side.
- Deutsch, C.V., Journel, A.G. (1998). GSLIB: Geostatistical Software Library and User's Guide, 2nd ed. Oxford University Press. ISBN 978-0195100150 — the reference implementations, open since the nineties.
- Chilès, J.-P., Delfiner, P. (2012). Geostatistics: Modeling Spatial Uncertainty, 2nd ed. Wiley. doi:10.1002/9781118136188 — the standard modern treatment if you want the derivations in full.
- Rossi, M.E., Deutsch, C.V. (2014). Mineral Resource Estimation. Springer. doi:10.1007/978-1-4020-5717-5 — on why a smoothed estimate misleads at a cutoff, and what to do instead.
- Roberts, D.R., et al. (2017). Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. Ecography, 40(8), 913–929. doi:10.1111/ecog.02881 — why holding out random points overstates how well a spatial model generalises.
Figures are original diagrams drawn for this post; Fig 2 is schematic and is not measured from a specific project. This is the short version of a longer piece — if you want the equations, the references above are where they live, and we are happy to argue about any of it at founders@aethermine.net.