Using observational data to determine the edges of the sources is an important task in the interpretation of potential field data. Extracting the edges of deep and shallow bodies effectively is the key to correctly understanding the underground structure. Based on the good multi-scale decomposition ability of two-dimensional variational mode decomposition (2D-VMD) and the outstanding shape analysis capability of mathematical morphology (MM), a new multi-scale edge detection method for potential

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... field data is proposed. We propose using the variance of this morphological filter as a basis for selecting the optimal structural element (SE) scale. By establishing theoretical models and comparing the results of our method with those of traditional edge detection methods, the proposed method is shown to be effective at detecting edges within potential field data. Taking the Hanmiao area of Chifeng city, Inner Mongolia, China, as an example, 1:50000 aeromagnetic data are processed and analysed by this method. The physical properties of the rocks in the study area are also discussed. The results of theoretical calculations and real data processing show that this method can accurately extract the edges of the sources at different scales. And the real data processing results show that this method is suitable for the identification of structural faults. INDEX TERMS Multi-scale edge detection, potential field data, two-dimensional variational mode decomposition (2D-VMD), mathematical morphology (MM)