Raw Fields → Structural Filters → Model-Ready Features

Geophysical Preprocessing for AI Mineral Prospectivity

Before an AI can rank where to drill, it has to be shown the crust in a language it can learn from. Gravity and magnetic surveys carry that information across whole continents and beneath cover — but the raw fields disguise it. This tutorial builds the bridge: the physics-based filters that turn a smooth potential-field map into sharp layers of faults, contacts and intrusion edges — the exact features a prospectivity model needs. We work it end-to-end on the Arabian Shield, and check every claim against 875 known deposits.

Reduction to Pole Derivatives Tilt & Analytic Signal Upward Continuation Gravity Edges Feature Stacks
Reduction-to-pole magnetic field of the Arabian Shield with known deposits

The destination: the reduction-to-pole magnetic field of the Arabian Shield with 875 known metallic deposits. Gold, copper, chromium and base-metal systems thread along the magnetic grain. By the end of this tutorial you will know exactly which filters reveal that grain — and why it makes the deposits learnable.

What Gravity and Magnetics Actually Measure

Two of the cheapest, most complete datasets in exploration are potential fields: the Earth's gravity and magnetic fields, mapped from satellites, aircraft and ground surveys. They are powerful precisely because they see through cover — but to use them well you must remember what each one responds to.

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Magnetic field

Responds to the magnetic susceptibility of rocks — chiefly magnetite content. It lights up mafic/ultramafic bodies, banded iron, alteration that destroys or creates magnetite, and the faults that offset them. Sensitive to shallow, ore-scale structure.

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Gravity field

Responds to density. The Bouguer anomaly images deep crustal density and thickness; its gradients outline the boundaries between crustal blocks. Sensitive to deep, regional architecture.

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Geology / deposits

The ground truth. Surface maps and known occurrences tell you what the fields mean — and let you test whether a processed layer actually tracks mineralisation.

Why potential fields are a "field"

Both obey Laplace's equation in source-free space, which is what makes the whole filter toolkit possible: a potential field measured on one surface can be mathematically continued, differentiated, or re-pointed to a different magnetisation direction — all as exact operations in the Fourier (wavenumber) domain. Preprocessing is not cosmetic image enhancement; it is the physics of the field, applied.

Why the Raw Field Misleads

If you hand a raw magnetic grid to a machine-learning model, you are handing it the right physics in the wrong frame. Three properties of potential fields make the unprocessed amplitude a poor feature.

1
The anomaly is offset from its source

Because the magnetic field is dipolar and the Earth's field is inclined, a compact magnetic body does not produce a single peak over its centre — it produces a high–low couplet that is shifted and asymmetric. The brightest pixel is not above the rock. A model trained on raw amplitude learns a systematically displaced target.

2
Every wavelength is superimposed

A raw value sums the deep regional field and the shallow local field. The crustal-scale trend (hundreds of km) and the prospect-scale structure (a few km) arrive in the same number. Until you separate scales, the model cannot tell "thick crust" from "buried intrusion".

3
Amplitude hides faint structure

A strong iron-rich body can be a hundred times brighter than a subtle fault that actually controls ore. On a linear colour scale the fault is invisible. The information is there — in the shape of the field, not its magnitude — but raw amplitude buries it.

The preprocessing suite addresses each of these in turn: reduction-to-pole fixes the offset, upward continuation separates the scales, and the derivative/tilt family rescales the field so structure — not magnitude — dominates.

Reduction to Pole — Putting Anomalies Back Over Their Sources

Reduction-to-pole (RTP) mathematically transforms the field into what it would look like if it were measured at the magnetic pole, where the inducing field is vertical. The dipolar couplet collapses to a single anomaly centred on the body. It is the first step in almost every magnetic interpretation.

RTP operator (wavenumber domain)

FRTP(k) = F(k) · |k|² / [ ( m̂·K )( f̂·K ) ]  ,   K = ( i kx, i ky, |k| )

K is the complex 3-D wavevector; = ( cos I sin D, cos I cos D, sin I ) is the ambient-field direction and the magnetisation direction (I = inclination, D = declination). The denominator is a product of two complex factors — it collapses to a single squared factor only for purely induced magnetisation (m̂ = f̂). Equivalently, applied to the total-field anomaly, the per-azimuth factor is [ sin I + i cos I cos(D − θ) ]. The operator divides out the geometry of the inclined inducing field, so it needs the correct I and D for the survey's place and epoch (Baranov & Naudy, 1964; Gunn, 1975; Blakely, 1995).

For the Arabian Shield we evaluate the International Geomagnetic Reference Field (IGRF-14) at the grid centre for the survey epoch: inclination ≈ 39°, declination ≈ +3° (grid-centre values — the inclination falls toward the lower-latitude south-western shield, e.g. ≈ 33° in the west-central shield; Abdelrahman et al., 2024). Use the wrong angles and every anomaly shifts — and so does every "structure" a downstream model would key on.

TMI versus RTP

Figure 3.1 — (a) Raw total magnetic intensity (TMI): anomalies are skewed and sit off their sources. (b) After RTP, peaks recentre over the bodies that cause them and align with mapped geology. Identical data — only the frame has changed.

Key Insight

RTP is unstable at low magnetic latitudes (small |I|), where the operator blows up along one wavenumber direction. Near the magnetic equator you reduce-to-equator or apply a stabilised kernel instead. On the Arabian Shield, I ≈ 39° — comfortably stable — but the principle matters anywhere you process magnetics: always check the inclination before you trust an RTP.

Derivatives — Sharpening Structure

Differentiation is the workhorse of potential-field interpretation. Taking a derivative suppresses long-wavelength regional content and amplifies short-wavelength, shallow structure — exactly where ore-controlling faults and contacts live. In the Fourier domain it is a one-line operation.

Directional & vertical derivatives (order n)

nf/∂zn ⇌ |k|n · F(k)    ∂f/∂x ⇌ i kx · F(k)    ∂f/∂y ⇌ i ky · F(k)

The first vertical derivative (1VD) is the most-used: it acts as a high-pass filter that crisps up the edges of shallow sources and resolves anomalies that merge in the raw field. The horizontal derivatives ∂f/∂x and ∂f/∂y are the raw material for the gradient and tilt transforms that follow.

The catch — and why padding and detrending matter

Multiplying by |k|n amplifies high wavenumbers, which also amplifies noise and edge artefacts. Robust derivatives require the grid to be gap-free, evenly sampled, detrended and tapered before the FFT. The Kalpa plugin handles this automatically — it infills data gaps, removes a planar trend, and pads the grid — so the derivative reflects geology, not the survey boundary.

Total Gradient & Analytic Signal — Mapping Edges Directly

Derivatives sharpen structure but still depend on magnetisation direction. The gradient transforms combine them into quantities whose maxima sit directly over the edges of bodies — turning interpretation into edge-finding.

Total horizontal gradient (THG) & analytic signal (AS)

THG = √( (∂f/∂x)² + (∂f/∂y)² )     |AS| = √( (∂f/∂x)² + (∂f/∂y)² + (∂f/∂z)² )

The total horizontal gradient peaks over near-vertical contacts and faults — it is the classic boundary-mapper (though, like the derivatives, it remains magnetisation-direction dependent for magnetic data). The analytic signal adds the vertical derivative, giving a positive quantity that sits over source edges largely independently of the magnetisation direction — strictly so only in 2-D, and approximately in 3-D (Li, 2006) — which is why it is comparatively robust at low latitudes or where remanence is present. Both convert the field into a clean "where are the boundaries?" image.

Magnetic enhancement suite

Figure 5.1 — The same magnetic field seen four ways. (a) RTP, (b) first vertical derivative, (c) tilt angle, (d) analytic signal. Moving left to right, amplitude gives way to structure: by panel (d), the image is essentially a map of magnetic boundaries — exactly the kind of layer a model can split on.

The Tilt Angle — Equalising Strong and Weak

The single most useful display transform for structure is the tilt angle. It normalises the vertical derivative by the horizontal gradient, so it depends on the shape of the field rather than its amplitude — faint anomalies over deep or weakly magnetic rocks read just as clearly as strong ones.

Tilt angle

θ = arctan( (∂f/∂z) / √( (∂f/∂x)² + (∂f/∂y)² ) )

Bounded to ±90°. Positive over sources, negative off them, and θ = 0 over the edge (strictly, above a vertical contact; Salem et al., 2007) — so the zero contour is a near-automatic structure map.

Because arctan compresses the dynamic range, the tilt angle is the great equaliser: it makes the subtle structural fabric of a whole terrane visible at once. Drag the slider below to watch the raw field dissolve into pure structure.

Raw total magnetic intensity
Tilt angle of the RTP field
Raw TMI Tilt of RTP

Figure 6.1 (interactive) — Drag across the image. Left of the handle: the raw magnetic intensity, dominated by a few bright bodies. Right: the tilt angle, where the entire structural grain of the shield — faults, contacts, fold trends — emerges at uniform contrast.

Why this matters for AI

A model splits on whatever separates deposits from background. On raw amplitude, a deep ore-controlling fault and barren bedrock can have nearly identical values — there is nothing to split on. On the tilt angle, the fault is a sharp zero-crossing and the bedrock is not. The transform doesn't add information; it moves the existing information into a form the model can act on.

Upward Continuation — Choosing Your Depth of View

Upward continuation recomputes the field as if it were measured at a higher altitude. Raising the observation level attenuates short wavelengths faster than long ones, so the continued field is a smoothed, deep-source-dominated version of the original. It is the cleanest way to separate the regional from the residual.

Upward continuation by height h

Fh(k) = F(k) · e−|k| h     residual = f − fh

Continue the field up by, say, 20 km and you isolate the regional field of deep crustal sources. Subtract that from the observed field and you isolate the residual — the shallow structure where ore systems live. Feeding a model both the regional and several residual bands lets it reason about depth without ever being told what depth is.

Upward continuation regional-residual separation

Figure 7.1 — (a) Observed field. (b) Upward-continued 20 km — the deep regional trend. (c) Residual — shallow, local structure. Each becomes a separate feature band; together they encode a crude depth dimension.

The Gravity Family — Bouguer, Free-Air, Isostatic, Disturbance

Gravity tells a different and complementary story: density, not magnetism. The same derivative, gradient and tilt operators apply — but there is no reduction-to-pole, because gravity's source is mass: a scalar, monopolar density distribution with no magnetisation or inducing-field direction to correct (unlike the dipolar magnetic field). Instead, the choice is which gravity anomaly to start from, each having removed a different reference effect.

Free-air

Corrected for the height variation of normal gravity (not for the rock mass below the station). Strongly tracks topography — useful, but dominated by terrain.

Bouguer

Also removes the gravitational pull of the rock above sea level. The workhorse for crustal density and thickness.

Isostatic

Further removes the deep root that compensates topography — sharpens mid-crustal density contrasts.

Disturbance

Observed minus normal gravity at the true station — a cleaner reference for many crustal studies.

Gravity preprocessing suite

Figure 8.1 — Gravity preprocessing on the western Arabian Shield. (a) Bouguer anomaly and (b) isostatic anomaly with gold deposits overlaid — deep crustal density and thickness. (c) The Bouguer total horizontal gradient traces the boundaries between crustal blocks. The same operators as the magnetics, now applied to density.

Gravity Reads the Deep Crust — and a Lesson in Not Over-Reading It

Gravity's Bouguer and isostatic fields are a statement about density kilometres down — genuinely useful as a regional context layer. They also make a perfect teaching case for the most important discipline in this whole subject: telling a real signal from a confounded one.

Apparent association of gold with Bouguer lows and isostatic highs

Figure 9.1 — Gold deposits (orange) vs shield background (blue) on the Bouguer and isostatic anomalies. Gold appears to concentrate on Bouguer lows (71% below the background median) and isostatic highs (76% above). A tempting "deep-crustal gold signature" — but look closer before believing it.

Why this is mostly an artefact — and how to catch it

Two checks deflate the story. (1) A confounder: the Bouguer anomaly is −0.94 correlated with elevation, and the gold belts sit in the higher western shield (median 949 m vs 805 m for background). So "gold on Bouguer lows" is largely "gold at altitude" — isostasy, not ore-bearing crust. (2) Pseudo-replication: the 718 gold points are not independent — they cluster into ~15 belts (tens of effective cells), so a naive AUC or percentage is badly over-confident. The honest verdict: gravity is a sound deep-crustal context feature, but its apparent gold association is not demonstrated — it must be tested with elevation-controlled, spatially-blocked validation.

Geology of the Arabian Shield with deposits

Figure 9.2 — Surface geology with the deposits by commodity. The gold and VMS belts sit inside the Precambrian juvenile-arc terranes — useful ground truth, and a reminder that the deposits are clustered by geology, which is exactly why per-point geophysical statistics must be declustered before they are trusted.

Building the Feature Stack

A prospectivity model never sees a "map". It sees, at every grid cell, a vector of numbers — the feature stack. The preprocessing suite is precisely how that vector is built: each filter contributes one or more bands, each with a one-line physical meaning.

Raw open datasets Preprocessing → feature bands Model input Magnetic field (EMAG2) Gravity field (WGM2012) Geology / deposits RTP · 1VD · tilt · analytic signal upward-continued + residual bands Bouguer · THG · tilt (crustal frame) free-air · isostatic · disturbance lithology · distance-to-contact 50 km neighbourhood statistics Prospectivity model

Figure 10.1 — From three open datasets to one feature vector per cell. Magnetics contributes shallow-structure bands; gravity the crustal frame; geology the lithological context. Neighbourhood statistics add regional context. This stack — not the raw maps — is what the model in Tutorial 2 learns from.

The feature-engineering principle

The choice of algorithm matters far less than the choice of representation. A good feature already encodes the geology; a bad one forces the model to rediscover physics from pixels. Geophysical preprocessing is the highest-leverage feature engineering available in exploration — it injects a century of potential-field theory directly into the model's inputs.

Do Deposits Sit on the Edges? (And How Would We Know?)

A feature is only worth its place in the stack if it separates deposits from background. So we test it directly: sample each processed layer at the gold deposits and at 8,000 random shield-interior background points, and compare — then ask hard questions of the result.

Gold enrichment on magnetic gradients

Figure 11.1 — Distribution of the magnetic analytic signal and |1VD| at gold-deposit sites (orange) vs shield background (blue). About two-thirds of deposits exceed the background median. The association is real in this dataset and far stronger than for the raw field — but read it as a promising, testable feature, not a proven control.

That separation is a good start — on raw magnetic amplitude, deposits and background overlap almost completely; after preprocessing, the gradient layers pull them apart. But the same cautions from §9 apply to the magnetics too: the gold points cluster into ~15 belts, so the effective sample is tens, not 718, and the analytic signal is also elevated over basement-versus-cover generally. The filters didn't invent the separation, and they didn't prove a control either — they produced a candidate feature whose predictiveness must be earned through spatially-blocked cross-validation, not declared from a histogram.

Tilt angle with deposits and gold belts

Figure 11.2 — Map view: deposits strung along the tilt-angle discontinuities. The named mineralised corridors (the Nabitah suture, the Wadi Bidah VMS belt and the Wadi Tathlith gold belt) follow magnetic edges that are often interpreted as crustal sutures and shear corridors — a plausible association to test, not a settled one.

Best Practice & Pitfalls

FFT-based filters are exact in theory and fragile in practice. The difference between a feature stack that helps and one that injects artefacts comes down to a few disciplines.

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Don't over-interpret — correlation is not control

The biggest trap is not a bad filter; it is a good-looking correlation. Before claiming a layer "predicts" deposits, rule out the obvious: spatial clustering (deposits in belts are pseudo-replicates — decluster, and validate with spatially-blocked folds, never random ones), confounders (here, Bouguer ≈ −0.94 with elevation, so an apparent density signal was mostly topography), and sampling bias (basement-vs-cover, AOI extent). A feature being associated with known deposits earns it a place as a candidate; only honest validation earns it the word "predictive".

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Fill gaps before the FFT

The Fourier transform cannot accept missing values — a single NaN poisons the whole grid. Infill data gaps (and re-mask them afterwards if you want honest coverage) before any filter. Global compilations like EMAG2 have real holes; ignore them and every output is empty.

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Detrend and pad

Remove a low-order trend and taper/pad the grid edges, or the periodic FFT will wrap the field around and stamp a false high-gradient frame around your area of interest — which a model will happily mistake for structure.

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Project to metres, correctly

Derivatives and continuation are defined in metres, not degrees. Reproject to an equal-area or conformal grid before filtering. A naive single-UTM-zone shortcut can mis-register a continental grid by tens of kilometres — moving every feature off its geology.

!
Get the RTP angles right; respect low latitudes

Use the IGRF inclination/declination for the survey's location and epoch. Below |I| ≈ 15°, switch to reduction-to-equator or the analytic signal, which is direction-independent.

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Match resolution to the question

A 3.7 km global grid resolves belts, not drill targets. Use it for regional permissivity; bring in airborne surveys for prospect-scale features. Don't over-claim what a coarse layer can predict.

Takeaway

Geophysical preprocessing is not a beautification step that happens before the "real" modelling. It is the modelling's foundation — the point at which raw physics becomes learnable structure.

The one-paragraph version

Gravity and magnetics carry the crust's structure across continents, but the raw fields disguise it: anomalies are offset, scales are mixed, and amplitude hides faint faults. A small suite of exact, physics-based filters — reduction-to-pole, derivatives, tilt, analytic signal, upward continuation — re-expresses the field as sharp, depth-aware, structure-revealing layers, and that is their real job: turning physics into candidate features. On the Arabian Shield, known gold deposits are measurably enriched on the magnetic gradients those filters reveal, and gravity adds deep-crustal context. We are careful not to call any of it a proven control — apparent associations can be clustering or topography in disguise — but as features, honestly built and honestly validated, they are exactly what an AI needs to read the geology the eye cannot.

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See it applied

The short case study distils this workflow into a four-figure exploration narrative.

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Where the features go next

Tutorial 2 takes a stack just like this one and builds the spatial–temporal AI that ranks drill targets.

References

Primary and authoritative sources for the methods, datasets and geology above. Every entry was checked against a resolving DOI or the issuing agency; links go to the publisher of record.

Show full reference list
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