We present a generalized theory of the probability tomography applied to the gravity method, assuming that any Bouguer anomaly data set can be caused by a discrete number of monopoles, dipoles, quadrupoles and octopoles. These elementary sources are used to characterize, in an as detailed as possible way and without any a priori assumption, the shape and position of the most probable minimum structure of the gravity sources compatible with the observed data set, by picking out the location of their centres and peculiar points of their boundaries related to faces, edges and vertices. A few synthetic examples using simple geometries are discussed in order to demonstrate the notably enhanced resolution power of the new approach, compared with a previous formulation that used only monopoles and dipoles. A field example related to a gravity survey carried out in the volcanic area of Mount Etna (Sicily, Italy) is presented, aimed at imaging the geometry of the minimum gravity structure down to 8 km of depth bsl.
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