A new class of space-domain convolution operators permits computation of the components of the horizontal gradient of gridded potential-field data. These so-called gradient-component operators allow one to vary the passband and thus control the frequency content of the resulting horizontal-gradient map. This facilitates computation of gradient maps that accommodate data of widely varying frequency content. Examination of the transfer functions of these operators suggests that this method of numerical differentiation is well suited to potential-field data: in particular, the operators suppress long wavelengths and high-frequency noise bands and amplify signal. Maps of the horizontal gradient of certain potential fields (e.g., gravity, pseudogravity) may be combined with algorithms that locate relative maxima, so-called thresholding, to automate the procedure of source-body edge detection, which is a useful tool in mapping, for example, basement grain, fault patterns, and igneous intrusive bodies. We apply this new operator, together with an existing thresholding algorithm, to a field example from western Canada and demonstrate its potential for improved imaging of the horizontal-gradient magnitude and thus improved edge detection.