Complex attributes of the magnetic signal are computed using a multiple source approach. Polygonal bodies are considered and the attributes of each corner are summed to produce the overall response; that is a decomposition of the polygonal body into magnetized steps to simulate the vertices. The method is tested on synthetic examples of buried ditches, as well as on real magnetic data. This type of target was selected because it comprises a common objective in ‘archaeological geophysics’. The resolution of the method in detecting the edges of the buried ditches depends on their lateral dimensions with respect to the sampling interval used. In general, the signal of the shallowest edges of the buried targets obscures the signal from the deeper corners, thus prohibiting their detection. In some extreme cases, the signals from the deeper corners posed a recognizable signature. The analytic signal may be seen as an anomaly rectification technique. In this context, it is suitable for the presentation of ‘archaeological prospection’ data since it provides an image that resembles the plane view of the buried antiquities better than the total field anomaly itself. Copyright © 2010 John Wiley & Sons, Ltd.