Abstarct: Using Geophysical methods to find rock physical properties of the underground is the best way to find buried deposits. Because of the simplicity and cost efficiency of Gravity and Magnetic methods, these methods are considered as useful methods and have been used for pre-exploration methods. A lots of methods have been improved for auto-interpretation of the acquired data with these two methods. One of the targets potentioal field methods is to identify subsurface structures in terms of horizontal, vertical and their extension (anomalies edges). Detecting of the edges in potential field methods can produce the suitable models and prepare the results. In this thesis, the edges of anomalies have been detected by using local amplitude and phase of the scale-space monogenic signals and then the results have been compared with analytical signal amplitude (ASA) and tilt angle (TILT) methods. In order to, the first some MATLAB codes have been written and the results of each code for synthetic and real data have been compared. By applying the methods on magnetic and gravity synthetic data, it has been demonstrated that the local amplitude and phase of the scale-space monogenic signals can work better than both ASA and TILT methods. At the end these methods have been applied to some real data from Qom Basin, Mobron massive sulfide copper mine and OjetAbad Iron deposit, and the results haave been evaluated and compared with the results of analytical signal methods and Tilt angle methods.