Transformative geophysics: Alternatives to the reduction-to-pole transformation of magnetic data

Magnetic data is difficult to interpret due to the bipolar nature of the field and the fact that the amplitude and phase of the response varies depending on the inclination of the Earth's field and the dip of magnetic bodies. The reduction to the pole transform gives a less complicated anomaly independent of many of these issues. However, this transformation can be problematic to compute and assumes no remanent magnetization. If there is remanence, then the resulting field can be just as difficult to interpret, in fact more so, as the direction of the remanence has to be taken into account. Another approach is to transform the data to the analytic-signal amplitude (ASA), which removes the dipolar character, creating a single positive anomaly for each body or edge. Further, the ASA is independent of remanent magnetization. However, ASA anomalies are broader than total-field anomalies. I introduce a transformation of the ASA to the total field of a body that is at the pole and the edge of the body has a vertical dip. This transformation uses an appropriate local phase or tilt angle. An exact transformation that starts from the firstorder ASA and gives the vertical derivative can have an incorrect sign in the result. However, an approximate transformation that starts from the zeroth-order ASA does not have this sign issue and gives reasonable results. A field example of the approximate transform outlines the magnetic source bodies and has amplitudes proportional to the magnetic susceptibility.