Analysis of potential field data in the wavelet domain

Various Green’s functions occurring in Poisson potential field theory can be used to construct non-orthogonal, non-compact, continuous wavelets. Such a construction leads to relations between the horizontal derivatives of geophysical field measurements at all heights, and the wavelet transform of the zero height field. The resulting theory lends itself to a number of different applications in the processing of potential field data. Some simple, synthetic examples in 2-D illustrate one inversion approach based upon the maxima of the wavelet transform (multiscale edges). These examples are presented to illustrate, by way of explicit demonstration, the information content of the multiscale edges. We do not suggest the methods used in these examples be taken literally as a practical algorithm or inversion technique. Rather, we feel that the real thrust of the method is toward physically based, spatially local filtering of geophysical data images using Green’s function wavelets, or compact approximations thereto. To illustrate our first steps in this direction, we present some preliminary results of a 3-D analysis of an aeromagnetic survey.