The analytic signal amplitude (As) is commonly used as an edge-detection filter for aeromagnetic data. For profile (2D) data, its shape is independent of the source magnetization vector direction, but this is not the case for map (3D) data. A modified analytic signal amplitude () is introduced here which has a much reduced dependence on this vector for both contact and dike models. When the modified analytic signal amplitude was applied to synthetic data sets, it was more effective in enhancing the edges of the bodies than the standard As. Because it uses second-order derivatives of the magnetic field, the method is sensitive to noise and so an additional formulation was developed for noisy data sets that only use first-order derivatives.