Several power-law relationships of geophysical potential fields have been discussed recently with renewed interests, including field value–distance (Symbol) and power spectrum–wavenumber (Symbol) models. The singularity mapping technique based on the density/concentration–area (C–A) power-law model is applied to act as a high-pass filter for extracting gravity and magnetic anomalies regardless of the background value and to detect the edges of gravity or magnetic sources with the advantage of scale invariance. This is demonstrated on a synthetic example and a case study from the Nanling mineral district, Southern China. Compared with the analytic signal amplitude and total horizontal gradient methods, the singularity mapping technique provides more distinct and less noisy boundaries of granites than traditional methods. Additionally, it is efficient for enhancing and outlining weak anomalies caused by concealed granitic intrusions, indicating that the singularity method based on multifractal analysis is a potential tool to process gravity and magnetic data.