Review of magnetic functions for geophysical prospecting

In magnetic methods, the magnetic anomaly vector C is defined as the difference between the measured magnetic field vector B and the calculated reference field R i.e. C = B - R. Vector C is characteristic of the magnetic source object. However in continuous magnetic surveys, there are no sensors enabling accurate measurements of the three magnetic field components with respect to a reference coordinate system. In practice, only the norm B is measured. Thus it is possible to define and assess the magnitude of total-field anomaly: F = B - R. Assuming that C is very small compared to the reference field, the limited development of F can be calculated. Typically, only the first order F1 of the development is kept and considered to be equal to F. The first problem is to assess precisely F1 and evaluate the error in the approximation F ≈ F1 for synthetic anomalies and real magnetic data. A solution is proposed to reduce this error by updating and proving the formula intuited by Lourenço and Morrison in 1973. By making this relation iterative, it is applied to different synthetic anomalies. In all cases, from the first iteration, the gap between F1 and F is reduced by a factor of 100. Finally, this method is applied to aeromagnetic data. Now that F1 is correctly calculated, it becomes possible to assess potential functions. Broadening the Baranov classical relationship of 1957 between F1 and U the magnetic potential, a new potential function, equivalent of the gravimetric potential, is introduced for magnetic methods: the magnetic superpotential Φ easily linked to F1. This function is very interesting as a new way to assess the magnetic anomaly tensor for data processing. The foregoing figure summarizes the six magnetic functions. Relationships between these, show how to assess one from another. In orange are presented the new functions, in blue the classical ones.