It was pointed out some time ago (Bhattacharyya, 1965) that the total intensity anomaly of a magnetic field ΔT in the direction of the normal magnetic field of earth is expressed by the equation,
Here ΔV denotes the anomaly of the magnetic potential and t the unit vector in the direction of earth's undisturbed total field.
Horizontal and vertical gradients observed along the tracks of airborne magnetic surveys were discussed by several authors (Wickerham, 1954; Glicken, 1955; Hood, 1965; Langan, 1966). These gradients are obtained from the formulas
where the magnetic intensity differences are observed over horizontal and vertical intervals Δx and Δz between two sensors. However, this approach is only valid when the depth h of the causative body or structure is relatively large compared to Δx and Δz; thus in cases of shallow anomalies, the nonlinear characteristics of the anomalous magnetic field would distort the observed gradients and render interpretation of data very difficult.