Phase Transformation of the Analytic Signal for Enhancing the Resolution of Potential Field Data ^†

Enhancement methods based on first-order derivatives are well established tools for gravity and magnetic data processing. Higher-resolution filters have been developed using high-order derivatives, but they are generally more sensitive to noise. Based on a transformation that sharpens the instantaneous phase of the complex analytic signal, which corresponds to the tilt angle map, we obtain an enhancement filter that improves the resolution of the total horizontal gradient (THG) without the need for additional derivative calculations. The steps of the proposed method are as follows: (1) compute the horizontal and vertical derivatives of the data; (2) compute the tilt angle and the analytic signal amplitude; (3) apply a sigmoidal-type transformation to the tilt angle; and (4) reconstruct the THG from the analytic signal amplitude and the transformed tilt angle. The reconstructed THG provides sharper boundary estimates than the true THG, as qualitatively shown with noise-corrupted synthetic data and aeromagnetic data from the Seival copper mining area in Caçapava do Sul, Brazil.