Transformation of magnetic data to the pole and vertical dip and a related apparent susceptibility transform: Exact and approximate approaches

Abstract

The dipolar character of magnetic data means that there is a high and a low associated with each source. The relative positions and sizes of these highs and lows vary depending on the magnetic latitude or the inclination of the earth’s magnetic field. One method for dealing with this complexity is to transform the data to what would be collected if the inclination were vertical (as at the magnetic pole), a process that is unstable at low magnetic latitudes. Unfortunately, remanent magnetization adversely impacts the success of this transformation. A second approach is to calculate the analytic-signal amplitude (ASA) of the data, which creates a single positive feature for each source or edge, with the shape being only weakly dependent on the inclination and the presence of remanent magnetization. The ASA anomalies can appear to be relatively broad, so features sometimes merge together on map views of the ASA. A subsequent transformation of the ASA using an appropriate transforming tilt angle can generate a magnetic field of a body that is at the pole and has a vertical dip. The transformation is exact for contacts when calculated from the first-order ASA, but the sign of the transformed data can be incorrect depending on whether you are over one edge or the other edge of a discrete source body. Another approximate transformation of the zeroth-order ASA does not have this issue and gives good results on synthetic data provided that any noise is handled appropriately. The resulting maps outline the magnetic source bodies and have amplitudes proportional to an apparent magnetic susceptibility. On field data from Black Hill, South Australia, the approximate transformation generates an image that is simple to interpret and enhances some features less obvious on other enhancements of the data.