Chapter 05
The data
Six modalities, wildly different physics, resolutions spanning eight orders of magnitude, and none of them measure the thing you want. Here is what each one actually is, and the two structural facts that govern how you can combine them.
Nothing measures grade
Start here, because it reframes everything: no remote measurement detects copper. Geophysics measures density, magnetic susceptibility, electrical conductivity, chargeability. Spectroscopy measures photon absorption by crystal lattices. These respond to rock properties correlated with the processes that concentrate metal — not to metal.
Only two things measure grade: an assay of physical material, and nothing else. Every other layer is a proxy, and the strength of that proxy relationship is itself uncertain and deposit-type dependent.
The modality zoo
| Method | Physical property | Typical resolution | Data shape |
|---|---|---|---|
| Magnetics | Magnetic susceptibility (mostly magnetite) | 25–400 m line spacing, airborne | 2-D raster, continent-scale coverage |
| Gravity / gradiometry | Density contrast | 0.5–5 km ground; finer airborne | 2-D raster, sparse ground stations |
| Electromagnetics (EM) | Electrical conductivity | Airborne, ground, and downhole variants | Time- or frequency-series per station |
| Induced polarization (IP) | Chargeability — disseminated sulphides | Ground lines, 10s–100s m dipoles | 2-D pseudo-section per line |
| Radiometrics | K, U, Th gamma emission | Airborne; only the top ~30 cm | 3-channel raster |
| Magnetotellurics | Deep conductivity structure | Sparse stations, km depth | Impedance tensor vs frequency |
| Geochemistry | Element concentrations in soil, stream sediment, till, rock | Point samples, 10s m–km spacing | Compositional vector per point (30–60 elements) |
| Multi/hyperspectral | Mineral absorption features (VNIR–SWIR) | 10–30 m satellite; mm on core scanners | Hyperspectral cube (x, y, λ) |
| Drilling | Everything, directly | cm downhole; 25–200 m between holes | 1-D transects in 3-D — see Ch. 4 |
You have a multi-modal fusion problem where the modalities are not independent channels of the same image. They are different nonlinear functionals of one shared latent state — the 3-D distribution of rock properties. Concatenating them as raster bands and feeding a CNN throws away that structure. It also works surprisingly well, which is why almost everyone starts there. Knowing why it is wrong tells you where the headroom is.
Structural fact 1: inversion is ill-posed
Turning a surface measurement into a subsurface model is an inverse problem:
d = G(m) + ε
d = observed data (e.g. gravity readings at the surface); m = the subsurface property model (e.g. density in every voxel); G = the forward operator given by physics; ε = noise.
For potential fields — gravity and magnetics — G has a non-trivial null space. There are infinitely many density distributions producing exactly the same surface gravity field, and the ambiguity is not marginal: you cannot separate "shallow and small" from "deep and large" from the data alone. This is a theorem, not a data-quality problem. No amount of additional surface gravity fixes it.
So inversion is always regularised — which is to say, it is always MAP estimation under a prior you chose:
m̂ = argminm ‖ Wd ( G(m) − d ) ‖² + λ · R(m)
W_d weights by data uncertainty; R(m) is the regulariser — smoothness, closeness to a reference model, sparsity, or petrophysical plausibility. λ trades data fit against prior belief.
When a geophysicist shows you an inversion, you are looking at a posterior mode under an unstated prior, rendered as if it were a measurement. Ask what regularisation was used and what reference model it was pulled toward. Smoothness regularisation, the default, systematically produces blurry blobs and will not give you sharp contacts — which is exactly the geometry that matters for drilling.
Joint inversion
The escape from non-uniqueness is to invert several physics together, coupled either structurally (penalise models whose gradients point in different directions — the cross-gradient constraint) or petrophysically (tie density, susceptibility and conductivity through known rock-property relationships). This is a multi-task learning problem with a shared latent geometry, and it is a live research area — as well as a capability KoBold cites in its own stack (Ch. 11).
Structural fact 2: support mismatch
A satellite pixel integrates 30 × 30 m of ground surface. An airborne magnetic reading integrates a large subsurface volume with a depth-dependent kernel. A core assay integrates roughly a 1 m × 5 cm cylinder. These are measurements of different random variables, and their statistics differ systematically: as support increases, variance decreases and the distribution shifts.
This is why you cannot validate a prospectivity raster against drill assays by simply sampling the raster at collar locations and correlating. You are comparing a km-scale integral to a cm-scale point. The correlation will be weak for reasons that have nothing to do with whether your model is any good. Aggregate to a common support first, and state which one you chose.
Geochemistry is compositional data
Geochemical analyses are vectors of concentrations that sum to a constant (100%, or 10⁶ ppm). This closure makes the space a simplex, not Euclidean, with real consequences:
- Correlations are spurious by construction — if one element rises, others must fall, whether or not they are geologically related.
- Euclidean distance, PCA and k-means on raw concentrations are not valid operations on the simplex.
- The standard fix is a log-ratio transform — centred log-ratio (CLR) or isometric log-ratio (ILR) — before any multivariate method. Aitchison's compositional data analysis is the reference framework.
clr(x) = [ ln(x₁ / g(x)), … , ln(xD / g(x)) ], g(x) = (Π xᵢ)1/D
g(x) is the geometric mean. Note this needs strictly positive values — hence the censored-data problem below is not optional to solve.
Two more geochemistry-specific wrinkles. Censoring: a
meaningful fraction of values are below detection limit and arrive as
<0.005; substituting zero breaks the log, and substituting
DL/2 is a convention with known bias. Method heterogeneity:
the same element measured by a partial-digestion technique and by a
total-digestion technique are different quantities, and merging them across
decades of a database without normalising is a classic silent corruption.
Hyperspectral: mineralogy at a distance
Minerals have diagnostic absorption features in the short-wave infrared (~2.0–2.5 µm) driven by molecular vibrations in OH, H₂O and CO₃ bonds. Clays, micas, chlorite, carbonates — precisely the alteration minerals that form the large halo around a deposit — are separable this way.
Practically this gives you two very different products. From orbit (ASTER, EnMAP, PRISMA, EMIT) you get regional alteration mapping — powerful in arid, well-exposed terrain, and largely useless under vegetation or transported cover. On a core scanner you get continuous, objective, millimetre-scale mineralogy down the entire hole, which is transformative because it replaces subjective visual logging with a reproducible measurement.
Spectral unmixing is non-negative matrix factorisation with a physics constraint: each pixel spectrum is a mixture of endmember spectra with non-negative abundances that sum to one. Linear unmixing is the classic approach; real mixing at the grain scale is nonlinear (intimate mixing), which is where learned unmixing models earn their place. Core-scan hyperspectral plus assay gives you an unusually clean supervised setup — dense cheap features, sparse expensive labels, perfectly co-registered in depth.
The layer everyone underestimates: documents
A mature project's most valuable asset is often forty years of prior work — scanned assay certificates, logging sheets, government reports, old company memos, maps as raster images. Much of it never made it into a database. Some of it contradicts the database.
This is genuinely well-suited to modern tooling: OCR plus a document-grounded retrieval layer over the historical corpus, with every extracted number carrying a pointer back to the page it came from. The pointer is the important part. An extracted grade with no provenance is worse than no grade, because it looks authoritative.
Every layer above has coverage holes, and the holes are informative. Ground IP exists where someone already thought a target was worth the expense. Dense drilling exists where mineralisation was found. If you impute missing data without modelling why it is missing, you leak the outcome into the features — a target-leakage pathway that is very hard to see in a cross-validation score.
Sources for this chapter
- Telford, Geldart & Sheriff, Applied Geophysics (Cambridge, 2nd ed. 1990). The standard reference for what each geophysical method measures and why. Dense but definitive.
- Blakely, Potential Theory in Gravity and Magnetic Applications (Cambridge, 1996). Where the non-uniqueness of potential-field inversion is established properly — worth reading the relevant chapter rather than taking my word for it.
- Oldenburg & Li, "Inversion for Applied Geophysics: A Tutorial", in Near-Surface Geophysics (SEG, 2005). The clearest introduction to regularised inversion as MAP estimation, by the group behind the UBC-GIF codes.
- SimPEG — Cockett et al., Computers & Geosciences 85 (2015). Open-source framework for geophysical forward modelling and inversion; the fastest way to experience non-uniqueness rather than read about it.
- Aitchison, The Statistical Analysis of Compositional Data (Chapman & Hall, 1986), and Pawlowsky-Glahn & Egozcue for the modern treatment. Why log-ratio transforms are mandatory for geochemistry.
- Hunt, "Spectral signatures of particulate minerals in the visible and near infrared", Geophysics 42 (1977) — the foundational paper for why SWIR maps alteration minerals. Paired with the USGS Spectroscopy Lab spectral libraries, which are free and are what unmixing algorithms are matched against.