It is shown how a continuous wavelet technique may be used to locate and characterize homogeneous point sources from the eld they generate measured in a distant hyperplane. For this a class of wavelets is introduced on which the Poisson semi-group essentially acts as a dilation.

The continuous wavelet transform is used to analyze potential fields and to locate their causative sources. A particular class of wavelets is introduced which remains invariant under the action of the upward continuation operator in potential field theory. These wavelets make the corresponding wavelet transforms easy to analyze and the sources' parameters (horizontal location, depth, multipolar nature, and strength) simple to estimate. Practical issues (effects of noise, choice of the analyzing wavelet, etc.) are addressed. A field data example corresponding to a near‐surface magnetic survey is discussed. Applications to the high‐resolution aeromagnetic survey of French Guyana will be discussed in the next paper of the series.

Abstract. A continuous wavelet technique has been recently introduced to analyzepotential fields data. First, we summarize the theory, which primarily consists of interpreting potential fields via the properties of the upward continued derivative field. Using complex wavelets to analyze magnetic data gives an inverse scheme to find the depth and homogeneity degree of local homogeneous sources and the inclination of their magnetization vector. This is analytically applied on several local and extended synthetic magnetic sources. The application to other potential fields is also discussed. Then, profiles crossing dikes and faults are extracted from the recent high-resolution aeromagnetic survey of French Guiana and analyzed using complex one dimensional wavelets. Maps of estimated depth to sources and their magnetization inclination and homogeneity degree are proposed for a region between Cayenne and Kourou.