Understanding imaging methods for potential field data

Abstract

Several noniterative, 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 related or proportional to such distributions. They have been derived in various ways, using generalized linear inversion, Wiener filtering, wavelet and depth from extreme points (DEXP) transformations, crosscorrelation, and migration. We demonstrated 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 appeared most effective in the case of isolated, compact, and depth-limited sources. Because all the approaches were noniterative, computationally fast, and in some cases, produced a fit to the data, they did provide a quick, but approximate picture of physical property distributions. We have found 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, for instance, using the theory of homogeneous fields. A major advantage of these techniques was their speed, efficiently providing a basis for further detailed, follow-up modelling.