Pure and Applied Geophysics

, Volume 176, Issue 8, pp 3607–3628 | Cite as

Self-Potential Data Inversion for Environmental and Hydrogeological Investigations

  • I. OlivetiEmail author
  • E. Cardarelli


In this paper, we present a robust 2-D self-potential (SP) inversion algorithm that has proven to be suitable for both environmental and hydrogeological applications. The work proposed here continues from the recent advances in theoretical and experimental aspects of the self-potential method by detecting the depth and the shape of shallow electrical current density sources using the least square subspace preconditioned (LSQR) method to compute (an approximation to) the standard-form Tikhonov solution. The preconditioner is based on the subspace defined by the columns of the Kernel matrix and the method adopted for choosing the fixed value of the regularization parameter is the generalized cross-validation. The decrease of resolution, due to the fact that the self-potential field decays quickly with the distance, is controlled by a depth weighting matrix. A laboratory experimental setup has been assembled for locating two buried ferro-metallic bodies of any size at different depths using the inversion of self-potential signals associated with the redox process. The inverse problem is solved by accounting for the electrical conductivity distribution and the self-potential data in order to recover the source current density vector field. Both synthetic and real simulations, performed on a sand model with anomalies included, provide low-error inverted models whereas anomalies are well-detected for position and shape. The inversion algorithm has been also applied to a field data set collected in the San Vittorino Plain, located in Central Italy, in order to identify the location of sinkholes and investigate the effects of different resistivity structure assumptions on the streaming potential inversion results.


Numerical modelling inversion algorithm potential field 



The laboratory set-up is part of a PRIN financing (2007–2010). The authors would like to offer their special thanks to Giorgio De Donno (Sapienza University of Rome) for his scientific contribution and his useful suggestions. They wish to acknowledge the help provided by Francesco Pugliese (Sapienza University of Rome) during the laboratory experiences.


  1. Abbas, M., & Fedi, M. (2015). Fractional-order local wavenumber-an improved source-parameter estimator. In 77th EAGE Conference and Exhibition 2015.Google Scholar
  2. Abdelrahman, E.- S. M., Ammar, A. A. B., Hassanein, H. I., & Hafez, M. A., (1998). Derivative analysis of sp anomalies. Geophysics, 63(3), 890–897.Google Scholar
  3. Abdelrahman, E.- S. M., El-Araby, H. M., Hassaneen, A.- R. G., & Hafez, M. A., (2003). New methods for shape and depth determinations from sp data. Geophysics, 68(4), 202–1210.Google Scholar
  4. Adler, A., & Lionheart, W. R. B. (2006). Uses and abuses of eidors: An extensible software base for eit. Physiological Measurement, 27(5), S25.CrossRefGoogle Scholar
  5. Bastos, J. P. A., & Sadowski, N. (2003). Electromagnetic modeling by finite element methods. London: CRC Press.CrossRefGoogle Scholar
  6. Bear, J. (2013). Dynamics of fluids in porous media. Courier Corporation.Google Scholar
  7. Bigalke, J., & Grabner, E. W. (1997). The geobattery model: A contribution to large scale electrochemistry. Electrochimica Acta, 42(23–24), 3443–3452.CrossRefGoogle Scholar
  8. Birch, F. (1998). Imaging the water table by filtering self-potential profiles. Ground Water, 36(5), 779–782.CrossRefGoogle Scholar
  9. Bolève, A., Revil, A., Janod, F., Mattiuzzo, J., & Jardani, A. (2007). A new formulation to compute self-potential signals associated with ground water flow. Hydrology and Earth System Sciences Discussions, 4(3), 1429–1463.CrossRefGoogle Scholar
  10. Cardarelli, E., Cercato, M., De Donno, G., & Di Filippo, G. (2014). Detection and imaging of piping sinkholes by integrated geophysical methods. Near Surface Geophysics, 12(3), 439–450.CrossRefGoogle Scholar
  11. Cardarelli, E., & Fischanger, F. (2006). 2d data modelling by electrical resistivity tomography for complex subsurface geology. Geophysical Prospecting, 54(2), 121–133.CrossRefGoogle Scholar
  12. Castermant, J., Mendonça, C., Revil, A., Trolard, F., Bourrié, G., & Linde, N. (2008). Redox potential distribution inferred from self-potential measurements associated with the corrosion of a burden metallic body. Geophysical Prospecting, 56(2), 269–282.CrossRefGoogle Scholar
  13. Cella, F., & Fedi, M. (2012). Inversion of potential field data using the structural index as weighting function rate decay. Geophysical Prospecting, 60(2), 313–336.CrossRefGoogle Scholar
  14. Centamore, E., Nisio, S., & Rossi, D. (2009). The san vittorino sinkhole plain: relationships between bedrock structure, sinking processes, seismic events and hydrothermal springs. Italian Journal of Geosciences, 12(8), 629–639.Google Scholar
  15. Corry, C. E. (1985). Spontaneous polarization associated with porphyry sulfide mineralization. Geophysics, 50(6), 1020–1034.CrossRefGoogle Scholar
  16. De Witte, L. (1948). A new method of interpretation of self-potential field data. Geophysics, 13(4), 600–608.CrossRefGoogle Scholar
  17. De Donno, G. (2013). 2d tomographic inversion of complex resistivity data on cylindrical models. Geophysical, Prospecting, 6(1), 586–601.CrossRefGoogle Scholar
  18. De Donno, G., & Cardarelli, E. (2014). 3d complex resistivity tomography on cylindrical models using eidors. Near Surface, Geophysics, 12(5), 587–598.CrossRefGoogle Scholar
  19. De Donno, G., & Cardarelli, E. (2017). Vemi: A flexible interface for 3d tomographic inversion of time-and frequency-domain electrical data in eidors. Near Surface Geophysics, 15.Google Scholar
  20. Fedi, M., & Abbas, M. A. (2013). A fast interpretation of self-potential data using the depth from extreme points method. Geophysics, 78(2), E107–E116.CrossRefGoogle Scholar
  21. Fedi, M., Cella, F., Quarta, T., & Villani, A. (2010). 2d continuous wavelet transform of potential fields due to extended source distributions. Applied and Computational Harmonic Analysis, 28(3), 320–337.CrossRefGoogle Scholar
  22. Fedi, M., Hansen, P. C., & Paoletti, V. (2005). Analysis of depth resolution in potential-field inversion. Geophysics, 70(6), A1–A11.CrossRefGoogle Scholar
  23. Fournier, C. (1989). ne des Puys (Puy-de-Dôme, France) Spontaneous potentials and resistivity surveys applied to hydrogeology in a volcanic area: Case history of the chaîne des puys (puy-de-dôme, france). Geophysical Prospecting, 37(6), 647–668.CrossRefGoogle Scholar
  24. Gibert, D., & Sailhac, P. (2008). Comment on “Self-potential signals associated with preferential groundwater flow pathways in sinkholes”. Journal of Geophysical Research, 113(B3), B03210.CrossRefGoogle Scholar
  25. Jacobsen, M., Hansen, P. C., & Saunders, M. A. (2003). Subspace preconditioned lsqr for discrete ill-posed problems. BIT Numerical Mathematics, 43(5), 975–989.CrossRefGoogle Scholar
  26. Jardani, A. , Dupont, J. , & Revil, A. (2006). Self-potential signals associated with preferential groundwater flow pathways in sinkholes. Journal of Geophysical Research: Solid Earth, 111(B9).Google Scholar
  27. Jardani, A., Revil, A., Bolève, A., Dupont, J.- P., & Jardani, C. (2008, 09). 3d inversion of self-potential data used to constrain the pattern of ground water flow in geothermal fields. Journal of Geophysical Research 113.Google Scholar
  28. Jardani, A., Revil, A., Santos, F., Fauchard, C., & Dupont, J. (2007). Detection of preferential infiltration pathways in sinkholes using joint inversion of self-potential and em-34 conductivity data. Geophysical Prospecting, 55(5), 749–760.CrossRefGoogle Scholar
  29. Li, Y., & Oldenburg, D. W. (1998). 3-d inversion of gravity data. Geophysics, 63(1), 109–119.CrossRefGoogle Scholar
  30. Marshall, D. J., & Madden T. K. (1959). Induced polarization, a study of its causes. Geophysics, 24(1), 790–816.CrossRefGoogle Scholar
  31. Meiser, P. (1962). A method for quantitative interpretation of selfpotential measurements*. Geophysical Prospecting, 10(2), 203–218.CrossRefGoogle Scholar
  32. Minsley, B. J., Sogade, J., & Morgan, F. D. (2007). Three-dimensional self-potential inversion for subsurface dnapl contaminant detection at the savannah river site, south carolina. Water Resources Research, 43(4).Google Scholar
  33. Naudet, V. , & Revil, A. (2005). A sandbox experiment to investigate bacteria-mediated redox processes on self-potential signals. Geophysical Research Letters, 32(11).Google Scholar
  34. Naudet, V., Revil, A., Rizzo, E., Bottero, J.- Y., & Bégassat, P. (2004). Groundwater redox conditions and conductivity in a contaminant plume from geoelectrical investigations. Hydrology and Earth System Sciences Discussions, 818–22.Google Scholar
  35. Nourbehecht, B. (1963). Irreversible Thermodynamic Effects in Inhomogeneous Media and their Applications in Certain Geoelectric boblems, Ph.D. thesis, M.I.T.Google Scholar
  36. Oliveti, I., & Cardarelli, E. (2017). 2D approach for modelling self-potential anomalies: application to synthetic and real data. Bollettino di Geofisica Teorica ed Applicata, 58(4), 415–430.Google Scholar
  37. Paige, C. C., & Saunders, M. A. (1982). Lsqr: An algorithm for sparse linear equations and sparse least squares. ACM Transactions on Mathematical Software (TOMS), 8(1), 43–71.CrossRefGoogle Scholar
  38. Pascual-Marqui, R. D., Esslen, M., Kochi, K., Lehmann, D. (2002). Functional imaging with low-resolution brain electromagnetic tomography (loreta): A review. Methods and findings in experimental and clinical pharmacology, 24(Suppl C), 91–95.Google Scholar
  39. Patella, D. (1997). Self-potential global tomography including topographic effects. Geophysical Prospecting, 45(5), 843–863.CrossRefGoogle Scholar
  40. Paul, M. (1965). Direct interpretation of self-potential anomalies caused by inclined sheets of infinite horizontal extensions. Geophysics, 30(3), 418–423.CrossRefGoogle Scholar
  41. Petitta, M. (2009). Hydrogeology of the middle valley of the velino river and of the s. vittorino plain (rieti, central italy). Italian Journal of Engineering Geology and Environment, 1, 157–181.Google Scholar
  42. Rao, D. A., Babu, H. R., & Sinha, G. S. (1982). A fourier transform method for the interpretation of self-potential anomalies due to two-dimensional inclined sheets of finite depth extent. Pure and Applied Geophysics, 120(2), 365–374.CrossRefGoogle Scholar
  43. Rittgers, J. B., Revil, A., Karaoulis, M., Mooney, M. A., Slater, L. D., & Atekwana, E. A. (2013). Self-potential signals generated by the corrosion of buried metallic objects with application to contaminant plumes. Geophysics, 78(5), EN65–EN82.CrossRefGoogle Scholar
  44. Sato, M., & Mooney, H. M. (1960). The electrochemical mechanism of sulfide self potentials. Geophysics, 25(1), 226–249.CrossRefGoogle Scholar
  45. Stoll, J., Bigalke, J., & Grabner, E. (1995). Electrochemical modelling of self-potential anomalies. Surveys in Geophysics, 16(1), 107–120.CrossRefGoogle Scholar
  46. Tikhonov, A. N., & Arsenin, V. I. (1977). Solutions of ill-posed problems Solutions of ill-posed problems. Hoboken: Wiley.Google Scholar
  47. Wahba, G. (1990). Spline models for observational data Spline models for observational data (59). Siam.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil, Constructional and Environmental Engineering“Sapienza” University of RomeRomeItaly

Personalised recommendations