Chapter 09
Prospectivity mapping
Mineral prospectivity mapping (MPM) is the flagship supervised-learning task in exploration: given stacked geoscience layers, rank every cell by the chance it hosts a deposit. It is also a textbook case of a problem that looks supervised and is not. Four things to get right, in order of how badly they bite.
1 · Your negatives do not exist
You have a set of known deposits — positives. Everything else is unlabeled: it contains barren ground and undiscovered deposits, mixed, with no way to tell them apart. This is positive-unlabeled (PU) learning, and the fact that MPM is a PU problem rather than a binary classification problem is the single most important modelling statement in this chapter.
The standard theory starts from the SCAR assumption — Selected Completely At Random: labeled positives are a random subset of all positives, with constant label frequency c. Write s = 1 for "is labeled", y = 1 for "is truly a deposit". Then (Elkan & Noto, 2008):
g(x) = P(s = 1 | x) = P(y = 1 | x) · P(s = 1 | y = 1) = f(x) · c
⟹ f(x) = g(x) / c
Train a probabilistic classifier g on labeled-vs-unlabeled. Estimate c as the mean of g(x) over a held-out set of known positives. Divide. You now have a calibrated estimate of the true posterior f(x) rather than a nameless "score".
Un-corrected PU scores are monotone in f, so for pure ranking they can be adequate. The correction matters the moment you need a probability — and you need a probability the moment you compute an expected value in Chapter 10. A model that says "0.8" when it means "0.08" makes every downstream decision wrong while looking fine on AUC.
Practical variants you will meet in the literature: weighted PU learning (differentiated weights for positive and unlabeled instances, which also softens the imbalance), two-step methods that first mine reliable negatives from the unlabeled pool and then train a normal classifier, and one-class approaches that model only the positive support.
- "Sample random negatives." You are labelling undiscovered deposits as barren and teaching the model that their signature means "nothing here."
- "Take negatives far from known deposits." Now your classes are separated by distance-to-known-deposit, and your model learns that. It will score beautifully and generalise nowhere, because at inference time every unexplored cell is far from known deposits.
2 · Your positives encode where humans looked
SCAR is a convenient lie. Discovery is emphatically not random: it concentrates near roads, near historical mining camps, in outcrop rather than under cover, in shallow ground, and in politically stable jurisdictions with good geological surveys. So the labeled set is drawn from p(x | deposit AND someone looked AND they succeeded).
Train on that naively and your model learns exploration history. The tell is a model whose top features are proxies for accessibility, and whose high-scoring cells are all in ground that has already been drilled — a map that is confidently, uselessly correct.
Mitigations, roughly in increasing order of rigour:
- Drop the obvious tells. No distance-to-road, distance-to-mine, or anything downstream of discovery. Audit your features for sneaky ones — data density, survey coverage, and number of samples per cell are all discovery proxies.
- Restrict the unlabeled pool to ground with comparable exploration effort, so labeled and unlabeled cells are exchangeable.
- Model effort explicitly. Treat survey effort as a confounder and separate geological predictors from effort proxies — recent work casts this as a deconfounded point process with propensity-weighted PU learning.
- Borrow from ecology. This is formally the same problem as species distribution modelling from presence-only records, a field that has been fighting sampling bias for twenty years. Their target-group background and bias-layer techniques transfer directly.
3 · Random cross-validation is a lie detector you have disabled
Geological fields are autocorrelated over kilometres (Ch. 8 — that is what the variogram range means). Under a random 80/20 split, a test cell almost always has a training cell a few hundred metres away with nearly identical features and the same label. Your model interpolates and you score it as though it generalised.
The bias is not small — reported hold-out performance routinely collapses when a spatially honest scheme is used. Use one of:
| Scheme | How | When |
|---|---|---|
| Spatial block CV | Partition into contiguous blocks larger than the autocorrelation range; hold out whole blocks | Default choice |
| Buffered / spatial leave-one-out | Hold out one point, exclude everything within a buffer radius from training | Few positives |
| Leave-one-region-out | Train on some belts/provinces, test on an entirely held-out one | The honest test of transfer — and the one that matters, since you deploy on new ground |
Do not guess. Fit a variogram to your residuals (or to the key predictors) and set the block size comfortably beyond the range. This is a nice example of Chapter 8 paying rent in Chapter 9: the same object that parameterises your kernel tells you how far apart folds must be to be independent.
4 · Evaluate on the decision, not the AUC
From Chapter 7: at prevalence 10⁻⁴, ROC-AUC is nearly uninformative and accuracy is meaningless. What the field uses, and what you should report:
- Capture-efficiency curve. x-axis: cumulative fraction of study area, ordered by descending model score. y-axis: cumulative fraction of known deposits captured. "We capture 70% of known deposits in the top 5% of area" is a sentence a geologist can act on.
- Precision@k for k equal to the number of targets the company can realistically drill.
- Calibration. Reliability diagram plus expected calibration error. Required if the score feeds an expected-value calculation.
- Stability. Refit across bootstrap resamples and spatial folds; map the variance. A target that appears in the top 1% of every fit is a different proposition from one that appears in a third of them.
The only test that fully counts is prospective: make predictions, drill, see what happens. It takes years and costs millions, so almost every published MPM result is retrospective. A weaker but honest proxy is a temporal hold-out — train only on deposits known before some year, test on those discovered after. Very few papers do this. If you do, you will learn more than from another AUC.
The current frontier: self-supervision on unlabeled ground
The defining constraint of MPM is scarce labels alongside enormous quantities of unlabeled geospatial data. That is the exact setting where self-supervised pretraining should win, and it is now being tried.
GFM4MPM (Daruna, Zadorozhnyy, Lukoczki & Chiu, 2024) pretrains a backbone with masked image modelling on unlabeled multi-modal geospatial data alone, then uses it as a feature extractor for downstream prospectivity. Evaluated on Mississippi Valley-type and clastic-dominated lead-zinc deposits across North America and Australia, they report that self-supervision improves robustness of the learned features, and they apply explainable-AI methods to check that individual predictions can be read geologically.
The benchmark those evaluations lean on is the Lawley et al. tri-national dataset: gradient-boosted prospectivity models for sediment-hosted Zn-Pb systems across the US, Canada and Australia, computed on Uber H3 hexagonal cells (~5.16 km² average) and published by the USGS as open GeoTIFF grids. It is the most accessible serious MPM dataset in existence, and Chapter 12 has you build on it.
- PU learning + self-supervision together. Most work does one or the other. The correction and the pretraining address different pathologies.
- Transfer across belts. Does a model trained on Australian MVT systems transfer to North American ones? This is domain adaptation with a physically meaningful covariate shift.
- Uncertainty that separates epistemic from aleatoric. "We don't know because nobody surveyed here" is an entirely different recommendation from "we know, and it's barren." Chapter 10 shows why the distinction has cash value.
- 3-D prospectivity. Nearly all MPM is 2-D map cells. Deposits are 3-D bodies at depth, and depth is where the remaining discoveries are.
A note on explainability
Geologists will not act on a score without a reason, so SHAP and permutation importance are near-universal in this literature. Use them, with one caveat you already know but which bites unusually hard here: geoscience features are strongly correlated (magnetics and gravity both respond to the same intrusion), and attribution methods split credit arbitrarily among correlated features. Read attributions as hypotheses about which layers carried signal, not as causal claims about ore genesis.
Sources for this chapter
- Elkan & Noto, "Learning classifiers from only positive and unlabeled data", KDD 2008. Short, and the origin of the g(x) = c · f(x) correction. Read it in the original.
- Bekker & Davis, "Learning from positive and unlabeled data: a survey", Machine Learning 109 (2020). The modern map of PU methods and, importantly, of when SCAR fails — which in this domain is always.
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Roberts et al., "Cross-validation strategies for data with temporal,
spatial, hierarchical, or phylogenetic structure", Ecography 40
(2017). The standard citation for why random CV is invalid here, and the
practical guide to block designs. See also Valavi et al.'s
blockCV. - Phillips et al., "Sample selection bias and presence-only distribution models", Ecological Applications 19 (2009). Ecology's answer to the sampling-bias problem, including target-group background. Transfers directly.
- Carranza, Geochemical Anomaly and Mineral Prospectivity Mapping in GIS (Elsevier, 2008). The standard domain textbook for MPM — knowledge-driven and data-driven approaches, and the capture-efficiency evaluation used in this chapter.
- Lawley et al. (2022), Ore Geology Reviews 141, 104635 — the tri-national sediment-hosted Zn-Pb benchmark, with open USGS outputs.
- Daruna et al., "GFM4MPM", arXiv:2406.12756 (2024) — self-supervised masked image modelling for prospectivity, and the clearest statement of the foundation-model direction.