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The analytic signal amplitude (As) is a commonly used edge detection filter for aeromagnetic data. For profile data its response is independent of the source magnetisation vector direction, but this is not the case for map data. A modified As is inroduced here which has a much reduced dependance on the source magnetisation vector direction. Because it uses second order derivatives the method is sensitive to noise. The modified As is demonstrated on synthetic datasets and on an aeromagnetic dataset from South Africa.