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The complex analytic signal is a theoretical concept that is useful to geophysical data processing. The analytic signal of a seismic trace can provide information on the reflection strength and the instantaneous phase. For gravity and magnetic data, the complex analytic signal is usually defined from horizontal derivatives of the anomalous field. Its amplitude and phase, which are known as the analytic signal amplitude and the tilt angle, respectively, are well-known enhancement filters. Recently, a transformation that sharpens the instantaneous phase of the analytic signal has been proposed, improving the temporal and spatial resolution of reflections in seismic traces. We noted that this transformation is effective for potential field maps as well. In fact, the transformed instantaneous phase turns out to enhance the tilt angle filter. Enhancements of the tilt angle can also be obtained, e.g., by multiplicative factors or by combining it with the horizontal tilt angle, but the improvements of our approach apply not only to the tilt angle, but to all components of the complex analytic signal. This is illustrated with aeromagnetic data from the Jinchuan Cu-Ni sulfide deposit (China).