On the reflectance map and the generalised derivative operator

The reflectance map is a widely used algorithm in the imaging process to determine the shape of objects. In geophysics, it is also used as a filter to improve the delineation of the edges of buried bodies causing gravimetric or magnetic anomalies. In this paper we recall the theory behind the formulation of the reflectance index and we show that the generalised derivative operator is the result of the reflectance algorithm implementation when applied to a three-dimensional function f(x,y,z). Moreover, we highlight that, in a representation on a horizontal plane, the two are equivalent. We discuss applications of the two filters, introducing the directional derivative, to gravity and magnetic field data and to onshore and offshore total magnetic field anomaly data for Italy.