A model study on enhancing the horizontal gradient of potential fields with the vertical derivative

English (OpenAlex)

The total horizontal gradient (THG) and its derivatives are commonly used in interpreting potential fields. Because THG is a nonharmonic function, its vertical derivative (VD) can be consistently computed using, e.g., a finite-difference approximation. The calculation of VD in the wavenumber domain is physically meaningful for harmonic functions, but it provides a pseudovertical derivative (PVD) when applied to nonharmonic fields that can be used in some edge detectors, such as THG. Through experiments with synthetic and field datasets, we evaluated the performance of the PVD of THG in the tilt angle of THG (TAHG) and fast sigmoid-based edge detector (FSED). TAHG and FSED are known as THG-based filters in mapping the edges of causative bodies. The results with synthetic data and magnetic data from the Montresor Belt (Canada) show that maps produced from the PVD of THG are clearer than those from the VD of THG near the source edges. Overall, the PVD of THG significantly enhances the edge detection of potential fields.