Method and validation
Detectability answers one question before fieldwork: will this method see this target? It models the response of the target along a profile across it, compares the result with the noise you can expect, and states every assumption behind the answer.
From target to verdict
- Forward model. The anomaly of the target is computed along a profile through its centre, from closed-form solutions (table below).
- Noise. Effective noise is the instrument noise and the field noise added in quadrature: σ = √(σinstrument² + σfield²).
- Signal-to-noise ratio. S/N = peak anomaly ÷ σ (for a step, the step amplitude).
- Verdict. S/N ≥ 5: clearly detectable; 2–5: marginal; below 2: not detectable. These are conventions, not physics, and are printed with every result.
- Station spacing. At least five stations across the anomaly width (full width at half maximum, or the 25–75 % width of a step), rounded down to 1, 2 or 5 × 10ⁿ m.
- Profile length. At least six times the depth to the top of the target and four times the anomaly width, so that the background on both sides is measured.
Main field and properties
Main field. The magnetic response depends on the direction and strength of the Earth's field at the survey site. Detectability computes it from the location and date with the 14th-generation International Geomagnetic Reference Field (IGRF-14), using the official IAGA coefficients.
Total-field anomaly. Magnetometers measure the total field; its anomaly is the projection of the anomalous field on the main-field direction, valid while the anomaly is much smaller than the main field. Magnetisation is induced (χF/μ₀) plus optional remanence; self-demagnetisation is neglected (χ ≪ 1).
Physical properties. Typical densities and magnetic susceptibilities, with their ranges, come from Telford, Geldart & Sheriff (1990), Tables 6.1 and 3.3. Natural values vary widely; enter measured contrasts when you have them.
Models
| Target | Gravity | Magnetic |
|---|---|---|
| Sphere: cavity, boulder, buried object | Point mass (exact outside the sphere) | Point dipole |
| Horizontal cylinder: tunnel, pipe, gallery | Line mass (2D) | Line dipole (2D) |
| Rectangular prism: room, foundation, tank | Nagy (1966); Plouff (1976) | Gravity gradient tensor (Nagy, Papp & Benedek 2000) and Poisson's relation |
| Vertical cylinder: shaft, well | Square prism of equal cross-section | Same |
| Dyke, wall, trench (any dip) | Two vertical steps; dipping: 2D polygon (Talwani et al. 1959; Won & Bevis 1987) | 2D polygon, surface magnetic charge (Blakely 1996, ch. 9) |
| Vertical contact: fault, edge of a fill | Faulted slab (Telford et al. 1990, §2.6) | 2D polygon |
Instrument presets
Instrument noise is one standard deviation of a reading, taken from the manufacturer's data sheet (checked 4 November 2026). It is added in quadrature to the field noise, which usually dominates: the defaults are 10 µGal for gravity and 2 nT for magnetics, and both can be changed for your site.
| Preset | Noise | Figure in the data sheet | Source |
|---|---|---|---|
| Scintrex CG-6 | 5 µGal | repeatability, standard deviation < 5 µGal | Scintrex CG-6 Autograv |
| Scintrex CG-5 | 5 µGal | standard deviation < 5 µGal (1 µGal resolution) | Scintrex CG-5 Autograv |
| LaCoste & Romberg G | 20 µGal | manufacturer's repeatability 10-20 µGal; the upper value is used | LaCoste & Romberg Model G |
| proton precession | 0.1 nT | resolution and sensitivity 0.1 nT | Geometrics G-856AX |
| Overhauser | 0.022 nT | sensitivity 0.022 nT/√Hz, i.e. at 1 Hz | GEM Systems GSM-19 v7 |
| caesium vapour | 0.008 nT | noise < 0.008 nT/√Hz RMS, i.e. at 1 Hz | Geometrics G-858 |
Fluxgate gradiometers measure a vertical gradient rather than the total-field anomaly modelled here, so they are not offered yet.
Validation
The Validation page shows each comparison as a figure with its error. Every model is checked against a result computed in a different way. The library's automated test suite covers, among others:
- Analytical limits: point-mass peak, Bouguer slab, half-width rules for the sphere and the cylinder, far-field behaviour of the prism.
- Numerical integration: the 2D line dipole against 3D dipoles integrated along strike; the magnetic prism against Gauss–Legendre sums of point dipoles.
- Poisson's relation: the gravity and magnetic codes are independent, yet at the pole the magnetic anomaly must equal the vertical derivative of the gravity anomaly scaled by M/(4πGΔρ). Checked for the sphere, the vertical and the dipping dyke, and the contact.
- Gradient tensor: traceless and symmetric, and equal to finite differences of the prism's gravity.
- Main field: IGRF-14 values match the British Geological Survey's IGRF-14 service at five sites on four continents, to 1 nT and 0.002°.
Limitations
- Flat topography, a homogeneous host and no regional trend. Terrain, regional fields and heterogeneous cover reduce the margin.
- 2D targets are infinitely long along strike and cross the profile at right angles.
- The profile passes over the centre of the target.
- Results are expectations under these assumptions, not guarantees. Resistivity and ground-penetrating radar are planned for a later version.
References
- Blakely, R. J. (1996). Potential Theory in Gravity and Magnetic Applications. Cambridge University Press.
- Nagy, D. (1966). The gravitational attraction of a right rectangular prism. Geophysics 31, 362–371.
- Nagy, D., Papp, G., Benedek, J. (2000). The gravitational potential and its derivatives for the prism. Journal of Geodesy 74, 552–560.
- Plouff, D. (1976). Gravity and magnetic fields of polygonal prisms and application to magnetic terrain corrections. Geophysics 41, 727–741.
- Talwani, M., Worzel, J. L., Landisman, M. (1959). Rapid gravity computations for two-dimensional bodies. Journal of Geophysical Research 64, 49–59.
- Telford, W. M., Geldart, L. P., Sheriff, R. E. (1990). Applied Geophysics, 2nd ed. Cambridge University Press.
- Won, I. J., Bevis, M. (1987). Computing the gravitational and magnetic anomalies due to a polygon. Geophysics 52, 232–238.
- IAGA Working Group V-MOD. International Geomagnetic Reference Field, 14th generation, coefficients.