We present the theoretical development of the 3D multipole probability tomography applied to the electric Self-Potential (SP) method of geophysical exploration. We assume that an SP dataset can be thought of as the response of an aggregation of poles, dipoles, quadrupoles and octopoles. These physical sources are used to reconstruct, without a priori assumptions, the most probable position and shape of the true SP buried sources, by determining the location of their centres and critical points of their boundaries, as corners, wedges and vertices. At first, a few synthetic cases with cubic bodies are examined in order to determine the resolution power of the new technique. Then, an experimental SP dataset collected in the Mt. Somma-Vesuvius volcanic district (Naples, Italy) is elaborated in order to define location and shape of the sources of two SP anomalies of opposite sign detected in the northwestern sector of the surveyed area. The modelled sources are interpreted as the polarization state induced by an intense hydrothermal convective flow mechanism within the volcanic apparatus, from the free surface down to about 3 km of depth b.s.l..
2. Patella, D., "Self-potential global tomography including topographic effects," Geophys. Prosp., Vol. 45, 843-863, 1997.
3. Mauriello, P. and D. Patella, "Resistivity anomaly imaging by probability tomography," Geophys. Prosp., Vol. 47, 411-429, 1999.
4. Mauriello, P. and D. Patella, "Principles of probability tomography for natural-source electromagnetic induction fields," Geophysics, Vol. 64, 1403-1417, 1999.
5. Mauriello, P. and D. Patella, "Gravity probability tomography: A new tool for buried mass distribution imaging," Geophys. Prosp., Vol. 49, 1-12, 2001.
6. Mauriello, P. and D. Patella, "Localization of maximum-depth gravity anomaly sources by a distribution of equivalent point masses," Geophysics, Vol. 66, 1431-1437, 2001.
7. Mauriello, P. and D. Patella, "Localization of magnetic sources underground by a probability tomography approach," Progress In Electromagtics Research M, Vol. 3, 27-56, 2008.
8. Mauriello, P. and D. Patella, "Resistivity tensor probability tomography," Progress In Electromagtics Research B, Vol. 8, 129-146, 2008.
9. Mauriello, P. and D. Patella, "Geoelectrical anomalies imaged by polar and dipolar probability tomography," Progress In Electromagtics Research, Vol. 87, 63-88, 2008.
10. Alaia, R., D. Patella, and P. Mauriello, "Application of the geoelectrical 3D probability tomography in a test-site of the archaeological park of Pompei (Naples, Italy)," J. Geophys. Eng., Vol. 5, 67-76, 2008.
11. Alaia, R., D. Patella, and P. Mauriello, "Imaging quadrupolar geophysical anomaly sources by 3D probability tomography. Application to near surface geoelectrical surveys," J. Geophys. Eng., Vol. 5, 359-370, 2008.
12. Landau, L. D. and E. M. Lifsits, Elektrodinamika Splosnych Sred, Nauka, Moscow, 1982.
13. Corwin, R. F., "The self-potential method for environmental and engineering applications," Geotechnical and Environmental, S. H.Ward (ed.), Chap. 1: Review and Tutorial, SEG, 127-146, Tulsa, 1990.
14. Saracco, G., P. Labazuy, and F. Moreau, "Localization of selfpotential sources in volcano-electric effect with complex continuous wavelet transform and electrical tomography methods for an active volcano," Geophys. Res. Lett., Vol. 31, 1-5, 2004.
15. Di Maio, R., P. Mauriello, D. Patella, Z. Petrillo, S. Piscitelli, and A. Siniscalchi, "Electric and electromagnetic outline of the Mount Somma-Vesuvius structural setting," J. Volcanol. Geoth. Res., Vol. 82, 219-238, 1998.
16. Iuliano, T., P. Mauriello, and D. Patella, "Looking inside Mount Vesuvius by potential fields integrated geophysical tomographies," J. Volcanol. Geoth. Res., Vol. 113, 363-378, 2002.
17. Lapenna, V., D. Patella, and S. Piscitelli, "Tomographic analysis of self-potential data in a seismic area of southern Italy," Ann. Geofis., Vol. 43, 361-374, 2000.
18. Soleimani, M., C. N. Mitchell, R. Banasiak, R. Wajman, and A. Adler, "Four-dimensional electrical capacitance tomography imaging using experimental data," Progress In Electromagtics Research, Vol. 90, 171-186, 2009.