<p>Seeking peaks of transformed gravity anomalies provides an effective map to detect abrupt lateral changes in density. Thus, filters that determine the horizontal boundaries of gravity sources are a useful tool in geological research. These filters are based on expressions using derivatives of the field. Recently, many phase filters using derivative ratios of the field to outline source edges have been developed. The limitation of most phase filters is their low resolution or inability to identify all boundaries. In this study, we propose to use second-order derivatives in the arctan function to improve the edge resolution. We also consider other phase filters in comparison with the proposed filter. To attenuate the noise effect, vertical derivatives are calculated by using the stable finite difference method. Synthetic examples and real applications in the northwestern region (Vietnam) and Vredefort dome area (South Africa) show that the proposed filter can identify the boundaries more precisely and clearly.</p>