The enhancement of horizontal boundaries of potential field sources is of great significance for the study of geological structures. Most of the existing filters for horizontal edges enhancement are presented based on the derivatives of potential field data, but these filters often show some shortcomings, for example, the output edges are divergent, strong and weak anomalies cannot be balanced, or some extra false edges appear in the results. In this paper, the edges enhancement filter MMA based on mathematical morphology is first defined by the combination of the basic operators of mathematical morphology. In order to make the filter have the ability to balance different amplitude anomalies, MMAZ and MMAT are proposed, and both of them can be used to delineate the horizontal edges of the field sources by their maxima. The experimental results of synthetic data show that MMAZ and MMAT have good equalization and anti-noise performances. Compared with several traditional filters, the horizontal edges of geological bodies obtained by these two filters are clearer and more convergent, and there are no extra edges in the output results for the complex situations that positive and negative anomalies exist simultaneously. Finally, the two new equalization filters are applied to gravity anomaly data in a potash mine area in Vientiane basin of Laos and the aeromagnetic anomaly of a metal mine in northwest China, the obtained positions of the structures are more accurate and clearer, which further illustrates the effectiveness of the two filtering techniques.