Curvature of a geometric surface and curvature of gravity and magnetic anomalies

Abstract

Curvature describes how much a line deviates from being straight or a surface from being flat. When curvature is used to interpret gravity and magnetic anomalies, we try to delineate geometric information of subsurface structures from an observed nongeometric quantity. In this work, I evaluated curvature attributes of the equipotential surface as functions of gravity gradients and analyzed the differences between the theoretical derivation and a practical application. I computed curvature of a synthetic model that consisted of representative structures (ridge, valley, basin, dome, and vertical cylinder) and curvature of the equipotential surface, gravity, and vertical gravity gradient (which is equivalent to the magnetic reduction-to-the-pole result) due to the same model. A comparison of curvature of such a geometric surface and curvature of different gravity quantities was then made to help understand these curvature differences and an indirect link between curvature of gravity data and actual structures. Finally, I applied curvature analysis to a magnetic anomaly grid in the Gaspé belt of Quebec, Canada, to illustrate its useful property of enhancing subtle features.