Theta map: Edge detection in magnetic data

The 3D analytic signal amplitude of a total magnetic intensity (TMI) map, introduced by Roest et al. (1992), is widely used in magnetic interpretation as a means of positioning anomalies directly over their sources. This technique is most important at low magnetic latitudes, where reduction to the pole distorts anomalies to the point where they often become uninterpretable: the reduction operator does not converge if the magnetization and regional field are truly horizontal (Baranov, 1957). Methods have been devised to suppress the artifacts appearing in low-latitude reduction to the pole, but no method can reduce such data without distortion (e.g., Silva, 1986; Hansen and Pawlowski, 1989), which becomes severe for inclinations less than 20°. The amplitude of the analytic signal, denoted by | A |, has the added advantage of being independent of the orientation of magnetization of the source bodies. It reaches a maximum over magnetic contacts, and thus, in theory, can be used to trace the outline of magnetic bodies. In practice, especially in the case of aeromagnetic data at high instrument-source separation, | A | is high over magnetic bodies, but is not sufficient to resolve body edges. This appears to be true even with higher-order analytic signal derivatives (Debeglia and Corpel, 1997, their Figure 11).