The probability tomography approach developed for the scalar resistivity method is here extended to the 2D tensorial apparent resistivity acquisition mode. The rotational invariant derived from the trace of the apparent resistivity tensor is considered, since it gives on the datum plane anomalies confined above the buried objects. Firstly, a departure function is introduced as the difference between the tensorial invariant measured over the real structure and that computed for a reference uniform structure. Secondly, a resistivity anomaly occurrence probability (RAOP) function is defined as a normalised crosscorrelation involving the experimental departure function and a scanning function derived analytically using the Frechet derivative of the electric potential for the reference uniform structure. The RAOP function can be calculated in each cell of a 3D grid filling the investigated volume, and the resulting values can then be contoured in order to obtain the 3D tomographic image. Each non-vanishing value of the RAOP function is interpreted as the probability which a resistivity departure from the reference resistivity obtain in a cell as responsible of the observed tensorial apparent resistivity dataset on the datum plane. A synthetic case shows that the highest RAOP values correctly indicate the position of the buried objects and a very high spacial resolution can be obtained even for adjacent objects with opposite resistivity contrasts with respect to the resistivity of the hosting matrix. Finally, an experimental field case dedicated to an archaeological application of the resistivity tensor method is presented as a proof of the high resolution power of the probability tomography imaging, even when the data are collected in noisy open field conditions.
2. Bibby, H. M., "Analysis of multiple-source bipole-quadripole resistivity surveys using the apparent resistivity tensor," Geophysics, Vol. 51, 972-983, 1986.
3. Bibby, H. M. and G.W. Hohmann, "Three-dimensional interpretation of multiple-source bipole-dipole resistivity data using the apparent resistivity tensor," Geophysical Prospecting, Vol. 41, 697-723, 1993.
4. Cammarano, F., P. Mauriello, D. Patella, and S. Piro, "Application of geophysical methods to archaeological prospecting," Science and Technology for Cultural Heritage, Vol. 6, 151-173, 1997.
5. Cammarano, F., P. Mauriello, D. Patella, and S. Piro, "Integrated geophysical methods for archaeological prospecting," Volcanism and Archaeology in Mediterranean Area , M. Cortini and B. De Vivo (eds.), Research Signpost, Trivandrum, 1997.
6. Cammarano, F., P. Mauriello, D. Patella, S. Piro, F. Rosso, and L. Versino, "Integration of high resolution geophysical methods. Detection of shallow depth bodies of archaeological interest ," Annali di Geofisica, Vol. 41, 359-368, 1998.
7. Cammarano, F., B. Di Fiore, D. Patella, and P. Mauriello, "Examples of application of electrical tomographies and radar profiling to cultural heritage," Annali di Geofisica, Vol. 43, 309-324, 2000.
8. Cammarano, F., P. Mauriello, D. Patella, and S. Piro, "Application of the self-potential method to the study of shallow cavities of archaeological interest," Non Destructive Techniques Applied to Landscape Archaeology, M. Pasquinucci and F. Trement (eds.), Oxbow Books, Oxford, 2000.
9. Capineri, L., D. Daniels, P. Falorni, O. Lopera, and C. Windsor, "Ground penetrating radar response from different buried targets," Progress In Electromagnetics Research Letters , Vol. 2, 63-71, 2008.
10. 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," Journal of Volcanology and Geothermal Research, Vol. 82, 219-238, 1998.
11. Gnedenko, B. V., Kurs Teorii Verojatnostej, Mir, Moscow, Published in Italian as Teoria della Probabilita, Editori Riuniti, Rome, 1979.
12. Iuliano, T., P. Mauriello, and D. Patella, "A probability tomography approach to the analysis of potential field data in the Campi Flegrei caldera (Italy)," Annali di Geofisica, Vol. 44, 403-420, 2001.
13. Iuliano, T., P. Mauriello, and D. Patella, "Advanced magnetic visualization of the Mt. Vesuvius shallow plumbing system by probability tomography," Annals of Geophysics, Vol. 45, 431-438, 2002.
14. Iuliano, T., P. Mauriello, and D. Patella, "Looking inside Mount Vesuvius by potential fields integrated geophysical tomographies ," Journal of Volcanology and Geothermal Research, Vol. 113, 363-378, 2002.
15. Lapenna, V., D. Patella, and S. Piscitelli, "Tomographic analysis of self-potential data in a seismic area of southern Italy," Annali di Geofisica, Vol. 43, 361-374, 2000.
16. Loke, M. H. and R. D. Barker, "Least-squares deconvolution of apparent resistivity pseudosections," Geophysics, Vol. 60, 1682-1690, 1995.
17. Makki, S. V., T. Z. Ershadi, and M. S. Abrishamian, "Determining the specific ground conductivity aided by the horizontal electric dipole antenna near the ground surface ," Progress In Electromagnetics Research B, Vol. 1, 43-65, 2008.
18. Mauriello, P. and D. Patella, "Resistivity anomaly imaging by probability tomography," Geophysical Prospecting, Vol. 47, 411-429, 1999.
19. Mauriello, P. and D. Patella, "Principles of ground surface physical tomography for natural source electromagnetic induction fields," Geophysics, Vol. 64, 1403-1417, 1999.
20. Mauriello, P. and D. Patella, "A physical pattern recognition approach for 2D electromagnetic induction studies," Annali di Geofisica, Vol. 43, 343-360, 2000.
21. Mauriello, P. and D. Patella, "Gravity probability tomography: a new tool for buried mass distribution imaging," Geophysical Prospecting, Vol. 49, 1-20, 2001.
22. 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.
23. Mauriello, P. and D. Patella, "Localization of magnetic sources underground by a data adaptive tomographic scanner,", arXiv:physics/0511192v2, 2005.
24. Mauriello, P. and D. Patella, "Introduction to tensorial resistivity probability tomography,", arXiv:physics/0512147v1, 2005.
25. Mauriello, P. and D. Patella, "Localization of magnetic sources underground by a probability tomography approach," Progress In Electromagnetics Research M, Vol. 3, 27-56, 2008.
26. Mauriello, P., D. Monna, and D. Patella, "3D geoelectric tomography and archaeological applications," Geophysical Prospecting, Vol. 46, 543-570, 1998.
27. Mauriello, P., D. Patella, Z. Petrillo, A. Siniscalchi, T. Iuliano, and C. Del Negro, "A geophysical study of the Mount Etna volcanic area,", Mt.Etna: Volcano Laboratory, A. Bonaccorso, S. Calvari, M. Coltelli, C. Del Negro, and S. Falsaperla (eds.), American Geophysical Union, Geophysical Monograph Series, 143, 2004.
28. Nishimoto, M., S. Ueno, and Y. Kimura, "Feature extraction from GPR data for identification of landmine-like objects under rough ground surface ," J. of Electromagn. Waves and Appl., Vol. 20, No. 12, 1577-1586, 2006.
29. Park, S. K. and G. P. Van, "Inversion of pole-pole data for 3D resistivity structure beneath arrays of electrodes," Geophysics, Vol. 56, 951-960, 1991.
30. Patella, D., "Introduction to ground surface self-potential tomography," Geophysical Prospecting, Vol. 45, 653-681, 1997.
31. Patella, D., "Self-potential global tomography including topographic effects," Geophysical Prospecting, Vol. 45, 843-863, 1997.
32. Patella, D. and P. Mauriello, "The geophysical contribution to the safeguard of historical sites in active volcanic areas. The Vesuvius case-history," Journal of Applied Geophysics, Vol. 41, 241-258, 1999.
33. Ra, J.-W., H.-K. Choi, and J.-S. Kim, "Two-and-half dimensional reconstruction of buried tunnel and pipes from cross-borehole and reflection measurements by using a genetic and Levenburg-Marquardt hybrid algorithm," J. of Electrom. Waves and Appl., Vol. 17, No. 2, 233-251, 2003.
34. Santoro, P., "Colle del Forno, loc. Montelibretti (Roma). Relazione di scavo sulle campagne 1971–1974 nella necropoli," Atti dell'Accademia Nazionale dei Lincei, Vol. 31, 211-298, 1977.
35. Uduwawala, D., "Modeling and investigation of planar parabolic dipoles for GPR applications: A comparison with bow-tie using FDTD," J. of Electrom. Waves and Appl., Vol. 20, No. 2, 227-236, 2006.
36. Uduwawala, D., M. Norgren, P. Fuks, and A. Gunawardena, "A complete FDTD simulation of a real GPR antenna system operating above lossy and dispersive grounds," Progress In Electromagnetics Research, Vol. 50, 209-229, 2005.
37. Van den Bosch, I., S. Lambot, M. Acheroy, I. Huynen, and P. Druyts, "Accurate and efficient modeling of monostatic GPR signal of dielectric targets buried in stratified media," J. of Electrom. Waves and Appl., Vol. 20, No. 3, 283-290, 2006.
38. Verma, S. K. and S. P. Sharma, "Resolution of thin layers using joint-inversion of electromagnetic and direct current resistivity sounding data," J. of Electrom. Waves and Appl., Vol. 7, No. 3, 443-479, 1993.
39. Wait, J. R., "Electromagnetic response of an anisotropic halfspace model when the medium striations are tilted relative to the vertical ," J. of Electrom. Waves and Appl., Vol. 10, No. 6, 871-881, 1996.