The analytic signal method, known also as the total gradient method, as defined here produces a particular type of calculated gravity or magnetic anomaly enhancement map used for defining in a map sense the edges (boundaries) of geologically anomalous density or magnetization distributions. In exploration potential field applications, the term analytic signal loosely refers to the calculated modulus of the gravity or magnetic anomaly field's three mutually orthogonal spatial (x, y, z) derivative terms. Mapped maxima (ridges and peaks) in the calculated analytic signal of a gravity or magnetic anomaly map locate the anomalous source body edges and corners (e.g., basement fault block boundaries, basement lithology contacts, fault/shear zones, igneous and salt diapirs, etc.). Analytic signal maxima have the useful property that they occur directly over faults and contacts, regardless of structural dip which may be present, and independent of the direction of the induced and/or remanent body magnetizations. Various extensions to the analytic signal method (as defined here) exist. For example, some extensions to the method include as an additional solved parameter the anomalous source body depth(s).