Abstract 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, ΔT=−δ(ΔV)/δt. 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 δΔT/δx≡−(ΔT′2−ΔT2)/Δx;δΔT/δz≡−(ΔT2−ΔT1)/Δz,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.