Understanding imaging methods for potential field data

Several non-iterative, imaging methods for potential field data have been proposed that provide an estimate of the 3D magnetization/density distribution within the subsurface or that produce images of quantities proportional or related to such distributions. They have been derived in various ways, using generalized linear inversion, Wiener filtering, wavelet and DEXP transformations, cross-correlation, and migration. We show that the resulting images from each of these approaches are equivalent to an upward continuation of the data, weighted by a (possibly) depth-dependent function. Source distributions or related quantities imaged by all of these methods are smeared, diffuse versions of the true distributions, but owing to the stability of upward continuation, resolution may be substantially increased by coupling derivative and upward continuation operators. These imaging techniques appear most effective in the case of isolated, compact and depth-limited sources. Since all the approaches are non-iterative, computationally fast, and in some cases produce a fit to the data, they do provide a quick picture of physical property distributions. We show that inherent or explicit depth weighting is necessary to image sources at their correct depths, and that the best scaling law or weighting function has to be physically based, using the theory of homogeneous fields, for instance. A major advantage of these techniques is their speed, efficiently providing a basis for further detailed, follow-up modelling.