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. ¿ 1999 American Geophysical Union