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.

International audienceFollowing an earlier study which gives the principles of the method and an example of application to the eastern component of the magnetic field in the European region [Alexandrescu et al., 1995], detection and characterization of geomagnetic jerks using wavelet analysis is generalized to any horizontal component of the field and to a worldwide distribution (involving 97 locations) of observations. This allows for a systematic and global search for such events within the twentieth century and makes it possible to unravel a number of intriguing properties associated with them. Whereas our first study only reveals five such events in Europe, we can now state that seven and only seven events have apparently occurred throughout the world during the present century. Two (1969 and 1978) are unquestionably of global extent, three (1901, 1913, and 1925) being possibly of similar extent, while the remaining two (1932 and 1949) are not seen everywhere at the Earth's surface. We confirm our early result that the events are more singular than previously thought, with a "regularity" systematically closer to 1.5 than to 2, and a common mean value of about 1.6. Furthermore, the 1969 and 1978 events display a two-step spatio-temporal behavior consisting of an "early arrival" in the northern hemisphere, a "late arrival" in the southern hemisphere, and a time lag between the two arrivals of the order of a couple of years. We were also able to show that the 1969 and 1978 events tend to at least partially balance each other. The extent to which this is true remains to be assessed, mainly because our method, although already providing some information about the geometry of the events, does not yet allow the proper recovery of their intensities

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.