Imaging polar and dipolar sources of geophysical anomalies by   probability tomography. Part I: theory and synthetic examples
  We develop the theory of a generalized probability tomography method to image source poles and dipoles of a geophysical vector or scalar field dataset. The purpose of the new generalized method is to improve the resolution power of buried geophysical targets, using probability as a suitable paradigm allowing all possible equivalent solution to be included into a unique 3D tomography image. The new method is described by first assuming that any geophysical field dataset can be hypothesized to be caused by a discrete number of source poles and dipoles. Then, the theoretical derivation of the source pole occurrence probability (SPOP) tomography, previously published in detail for single geophysical methods, is symbolically restated in the most general way. Finally, the theoretical derivation of the source dipole occurrence probability (SDOP) tomography is given following a formal development similar to that of the SPOP tomography. The discussion of a few examples allows us to demonstrate that the combined application of the SPOP and SDOP tomographies can provide the best core-and-boundary resolution of the most probable buried sources of the anomalies detected within a datum domain. 
Paolo Mauriello and Domenico Patella