The 3D probability tomography theory is developed to image polar and dipolar sources of a geophysical field dataset. The purpose of the method is to improve resolution power of buried geophysical targets, using probability as a suitable paradigm allowing all possible equivalent solutions to be included within a single 3D image. The new approach is described by assuming a geophysical field dataset as caused by a discrete number of source poles and dipoles. A few tests are given to show how the combined polar and dipolar tomography can provide a reliable core-and-boundary resolution of the most probable sources of anomalies. An application to the Vesuvius volcano (Naples, Italy) is finally illustrated by analyzing self-potential and geoelectrical datasets collected within the whole volcanic area. A gravity dataset is also analyzed for completeness. The purpose is to get new insights into the Vesuvius shallow structure and hydrothermal system and to outline the features of the deep tectonic depression within which the volcano grew
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