electromagnetic survey on the southwest Indian ridge. Six horizontal AgCl electrodes were attached to the transient electromagnetic system to passively record the horizontal electrical-field component (Figure 35). The natural electrical field was extracted from the raw data and was integrated to obtain the self-potential signals. Negative self-potential anomalies (~−27 mV) were observed at the known Yuhuang hydrothermal field. The inversion of these self-potential data reveals localized SMS deposits with a thickness of ~65 m (Figure 36).

The second case study is reported by Kasaya et al. (2020) [116], who conducted a self-potential and marine direct-current-resistivity survey by using two autonomous underwater vehicles (Figures 37 and 38). The self-potential and the apparent resistivity were obtained along a survey line that crossed the known hydrothermal mounds of sulfide ore in the mid-Okinawa Trough. Similar to the previous case study, the raw self-potential data were integrated to obtain a potential field profile. The distribution of the negative self-potential anomalies obtained and the low apparent resistivity (0.2 ohm-m or less) show good agreement with the locations of the known hydrothermal deposits (Figure 39).

Recent studies have demonstrated that self-potential tomography can play an important role in the exploration of SMS deposits. However, the electrical-conductivity distribution of SMS deposits is an important ingredient in the inversion of the recorded self-potential data. Indeed, the self-potential governing equation is given as [111]:

$$ \nabla \cdot (\sigma \nabla \varphi) = \nabla \cdot \mathbf{J}_s \qquad (73) $$

where $\sigma$ denotes the electrical conductivity, $\varphi$ is the self-potential field, and $\mathbf{J}_s$ denotes the source-current density that is associated with the ore body. We can develop the left-hand side to obtain [117]:

$$ \nabla^2 \varphi = \frac{\nabla \cdot \mathbf{J}_s}{\sigma} + \nabla \ln \sigma \cdot \mathbf{E} \qquad (74) $$

where $\mathbf{E} = -\nabla \varphi$ is the electrical field. Equation (74) shows that, in order to obtain the source-current density, knowledge of the conductivity distribution ($\sigma$) below the seafloor is required [111,118]. Future analysis must combine induced-polarization tomography with the inversion of the self-potential data in order to better quantify SMS deposits.

<figure><img src="image_43.png" /><figcaption>Figure 35. Sketch of the deep-towed geophysical instrument that can also be used to measure the self-potential and possibly the resistivity and the induced polarization. The green line denotes the cable-link-control terminal and the time-domain electromagnetic (TEM) coil. The numbers on the cable show the location of 6 Ag/AgCl nonpolarizing electrodes. The data logger is mounted inside of the control terminal (modified from [115]).</figcaption></figure>
<figure><img src="image_44.png" /></figure>

**Figure 36.** Self-potential tomography of self-potential data. The tomography is performed in terms of the causative source-current-density distribution below the seafloor. (a) Inverted source-current-model distribution. The black dots denote the positions of the electrodes in the seawater. (b) Cross-sections along east-west with $y = 0$ m and $y = 70$ m. (c) Tomography of the inverted source-current-density distribution below Profiles SP01 and SP02. (d) Inferred ore body shape from the inverted data (domain where the magnitude of current density is lower than −0.5 mA m⁻²). Note that the lateral extension of the ore body is limited by the self-potential dataset that is acquired only along two parallel lines (modified from [115]).

<figure><img src="image_45.png" /></figure>

**Figure 37.** Sketch of exploration using two autonomous water vehicles (AUVs) and an autonomous surface vehicle (ASV) (see Kasaya et al., 2020 [116], for details). These types of equipment could be revolutionary for the exploration of ore bodies at the seafloor by using a combination of self-potential, resistivity, and induced-polarization data. Since the methods have different sensitivities with respect to the ore bodies, the combined tomograms could provide a highly efficient method to image ore bodies at the seafloor.
<figure><img src="image_44.png" /></figure>

**Figure 36.** Self-potential tomography of self-potential data. The tomography is performed in terms of the causative source-current-density distribution below the seafloor. (a) Inverted source-current-model distribution. The black dots denote the positions of the electrodes in the seawater. (b) Cross-sections along east-west with $y = 0$ m and $y = 70$ m. (c) Tomography of the inverted source-current-density distribution below Profiles SP01 and SP02. (d) Inferred ore body shape from the inverted data (domain where the magnitude of current density is lower than −0.5 mA m⁻²). Note that the lateral extension of the ore body is limited by the self-potential dataset that is acquired only along two parallel lines (modified from [115]).

<figure><img src="image_45.png" /></figure>

**Figure 37.** Sketch of exploration using two autonomous water vehicles (AUVs) and an autonomous surface vehicle (ASV) (see Kasaya et al., 2020 [116], for details). These types of equipment could be revolutionary for the exploration of ore bodies at the seafloor by using a combination of self-potential, resistivity, and induced-polarization data. Since the methods have different sensitivities with respect to the ore bodies, the combined tomograms could provide a highly efficient method to image ore bodies at the seafloor.
<figure><img src="image_46.png" /></figure>

**Figure 38.** Submarine investigation of ore bodies at the seafloor. Left panel: The electrode and towed rod configuration of each AUV. Right panel: photograph of the AUV "JINBEI" before launching with the current rod. Photograph of the instruments on the fore top of AUV "JINBEI" (modified from [116]).

<figure><img src="image_47.png" /></figure>

**Figure 39.** Apparent resistivities and integrated self-potential data with bathymetry on the main survey line. The horizontal position of the calculated apparent resistivity is defined as the midpoint of the two AUVs (adapted from [116]).

## 9. Conclusions

We have reviewed a physics-based model that describes the complex conductivity of porous materials that contain disseminated metallic particles. This model is based on the intrinsic polarization of the metallic grains, in which the charge carriers accumulate at the boundary of the grains. This model can be applied to characterize metallic deposits by using a geophysical technique that is called "induced polarization". The chargeability
<figure><img src="image_46.png" /></figure>

**Figure 38.** Submarine investigation of ore bodies at the seafloor. Left panel: The electrode and towed rod configuration of each AUV. Right panel: photograph of the AUV "JINBEI" before launching with the current rod. Photograph of the instruments on the fore top of AUV "JINBEI" (modified from [116]).

<figure><img src="image_47.png" /></figure>

**Figure 39.** Apparent resistivities and integrated self-potential data with bathymetry on the main survey line. The horizontal position of the calculated apparent resistivity is defined as the midpoint of the two AUVs (adapted from [116]).

**9. Conclusions**

We have reviewed a physics-based model that describes the complex conductivity of porous materials that contain disseminated metallic particles. This model is based on the intrinsic polarization of the metallic grains, in which the charge carriers accumulate at the boundary of the grains. This model can be applied to characterize metallic deposits by using a geophysical technique that is called "induced polarization". The chargeability
depends on the volumetric content of the metallic particles plus the chargeability of the background material. The relaxation time depends on the square of the radius of the metallic grains and it is inversely proportional with respect to the conductivity of the background material, which is weakly dependent on the volume fraction of the metallic particles. The DC conductivity decreases with the increase in the concentration of the metallic particles, while the high-frequency conductivity increases with the concentration of metallic particles. This statement may appear obvious from the fact that the grains act as conductors at high frequencies (absence of polarization) and as insulators at low frequencies (grains totally polarize). With that being said, this point is often forgotten by the practitioners of electromagnetic methods when dealing with the dependence of the electrical conductivity on the fraction of metallic particles. In other words, conduction is not just an electromigration problem, and it cannot be fully understood without its counterpart that corresponds to the grain polarization. We have not discussed the potential effect of redox reactions at the grain/water interface, but such an effect would make the metallic grains leaking capacitors rather than perfect capacitors, as described in this paper.

We have discussed five applications and tests of the petrophysical model that use induced-polarization tomography, including conductivity, chargeability, and relaxation-time tomography. Our tests demonstrate that electrical-conductivity tomography is not efficient at imaging disseminated ores. In time-domain induced polarization, the secondary voltage decay can be understood as a transient self-potential problem. The relaxation-time tomography is efficient at imaging massive metallic structures. We also show that the effect of temperature, including the effect of permafrost, is well understood and can be used to interpret field data. An exploration case shows that, on the basis of the spread-spectrum-communication idea and the array SSIP signal acquisition that is based on ZigBee and GPS timing, high-resolution induced-polarization exploration at depths of ~1000 m, even in the presence of strong electromagnetic interferences, can be realized. Further works will need to be conducted to perform the joint inversion of induced-polarization data with self-potential data to further image and localize SMS deposits below the seafloor.

**Author Contributions:** The authors contributed equally to the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** A. Revil thanks the CNRS for its support over the years. We thank Nicolas Florsch for some discussions regarding the transfer functions used in induced polarization. We thank the Editor and two anonymous referees for their very useful reviews.

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Dahlin, T.; Leroux, V. Improvement in time-domain induced polarization data quality with multi-electrode systems by separating current and potential cables. *Near Surf. Geophys.* **2012**, *10*, 545–565. [CrossRef]

2. Schlumberger, C. Etude sur la Prospection Electrique du Sous-Sol, Gauthier-Villars, Paris. The Second Edition without Modification Is Available at https://gallica.bnf.fr/ark:/12148/bpt6k64569898.texteImage. English Version, Translated by Sherwin F. Kelly: "Study of Underground Electrical Prospection". Available online: https://archive.org/details/studyofundergrou00schlrich/page/n37 (accessed on 24 April 2022).

3. Li, J.L. Application of the down-hole IP method to a general survey in the Jinya gold deposit. *Geol. Explor.* **2016**, *2016*, 924–930. (In Chinese)

4. Dakhnov, V.N.; Latyshova, M.G.; Ryapolova, V.A. Investigation of drill holes by the method of induced potentials. *Promysl. Geofiz.* **1952**, *1952*, 46–82.

5. Marshall, D.J.; Madden, T.R. Induced polarization, a study of its causes. *Geophysics* **1959**, *24*, 790–816. [CrossRef]

6. Olhoeft, G.R. Low-frequency electrical properties. *Geophysics* **1985**, *50*, 2492–2503. [CrossRef]

7. Weiss, O. The limitations of geophysical methods and the new possibilities opened up by an electrochemical method for determining geological formations at great depths. *World Pet. Congr. London Proc.* **1933**, *1*, 114–118.

8. Wait, J.R. *Overvoltage Research and Geophysical Applications*; Pergamon: London, UK, 1959; Volume 4.

9. Bleil, D.F. Induced polarization: A method of geophysical prospecting. *Geophysics* **1953**, *18*, 636–661. [CrossRef]

10. Anderson, L.A.; Keller, G.V. A study in induced polarization. *Geophysics* **1964**, *29*, 848–864. [CrossRef]
depends on the volumetric content of the metallic particles plus the chargeability of the background material. The relaxation time depends on the square of the radius of the metallic grains and it is inversely proportional with respect to the conductivity of the background material, which is weakly dependent on the volume fraction of the metallic particles. The DC conductivity decreases with the increase in the concentration of the metallic particles, while the high-frequency conductivity increases with the concentration of metallic particles. This statement may appear obvious from the fact that the grains act as conductors at high frequencies (absence of polarization) and as insulators at low frequencies (grains totally polarize). With that being said, this point is often forgotten by the practitioners of electromagnetic methods when dealing with the dependence of the electrical conductivity on the fraction of metallic particles. In other words, conduction is not just an electromigration problem, and it cannot be fully understood without its counterpart that corresponds to the grain polarization. We have not discussed the potential effect of redox reactions at the grain/water interface, but such an effect would make the metallic grains leaking capacitors rather than perfect capacitors, as described in this paper.

We have discussed five applications and tests of the petrophysical model that use induced-polarization tomography, including conductivity, chargeability, and relaxation-time tomography. Our tests demonstrate that electrical-conductivity tomography is not efficient at imaging disseminated ores. In time-domain induced polarization, the secondary voltage decay can be understood as a transient self-potential problem. The relaxation-time tomography is efficient at imaging massive metallic structures. We also show that the effect of temperature, including the effect of permafrost, is well understood and can be used to interpret field data. An exploration case shows that, on the basis of the spread-spectrum-communication idea and the array SSIP signal acquisition that is based on ZigBee and GPS timing, high-resolution induced-polarization exploration at depths of ~1000 m, even in the presence of strong electromagnetic interferences, can be realized. Further works will need to be conducted to perform the joint inversion of induced-polarization data with self-potential data to further image and localize SMS deposits below the seafloor.

**Author Contributions:** The authors contributed equally to the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** A. Revil thanks the CNRS for its support over the years. We thank Nicolas Florsch for some discussions regarding the transfer functions used in induced polarization. We thank the Editor and two anonymous referees for their very useful reviews.

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Dahlin, T.; Leroux, V. Improvement in time-domain induced polarization data quality with multi-electrode systems by separating current and potential cables. *Near Surf. Geophys.* **2012**, *10*, 545–565. [CrossRef]

2. Schlumberger, C. Etude sur la Prospection Electrique du Sous-Sol, Gauthier-Villars, Paris. The Second Edition without Modification Is Available at https://gallica.bnf.fr/ark:/12148/bpt6k64569898.texteImage. English Version, Translated by Sherwin F. Kelly: "Study of Underground Electrical Prospection". Available online: https://archive.org/details/studyofundergrou00schlrich/page/n37 (accessed on 24 April 2022).

3. Li, J.L. Application of the down-hole IP method to a general survey in the Jinya gold deposit. *Geol. Explor.* **2016**, *2016*, 924–930. (In Chinese)

4. Dakhnov, V.N.; Latyshova, M.G.; Ryapolova, V.A. Investigation of drill holes by the method of induced potentials. *Promysl. Geofiz.* **1952**, *1952*, 46–82.

5. Marshall, D.J.; Madden, T.R. Induced polarization, a study of its causes. *Geophysics* **1959**, *24*, 790–816. [CrossRef]

6. Olhoeft, G.R. Low-frequency electrical properties. *Geophysics* **1985**, *50*, 2492–2503. [CrossRef]

7. Weiss, O. The limitations of geophysical methods and the new possibilities opened up by an electrochemical method for determining geological formations at great depths. *World Pet. Congr. London Proc.* **1933**, *1*, 114–118.

8. Wait, J.R. *Overvoltage Research and Geophysical Applications*; Pergamon: London, UK, 1959; Volume 4.

9. Bleil, D.F. Induced polarization: A method of geophysical prospecting. *Geophysics* **1953**, *18*, 636–661. [CrossRef]

10. Anderson, L.A.; Keller, G.V. A study in induced polarization. *Geophysics* **1964**, *29*, 848–864. [CrossRef]
11. Pelton, W.H.; Ward, S.H.; Hallof, P.G.; Sill, W.R.; Nelson, P.H. Mineral discrimination and removal of inductive coupling with multifrequency IP. *Geophysics* **1978**, *43*, 588–609. [CrossRef]

12. Hallof, P.G.; Klein, J.D. Characterization of electrical properties of metallic mineral deposits. *Ont. Geol. Surv. Open File Rep.* **1983**, *1983*, 5468.

13. Olhoeft, G.R. Electrical properties of rocks and minerals. In *Short Course Notes*; US Geological Survey: Golden, CO, USA, 1983.

14. Vanhala, H.; Peltoniemi, M. Spectral IP studies of Finnish ore prospects. *Geophysics* **1992**, *57*, 1545–1555. [CrossRef]

15. Hallof, P.G.; Yamashita, M.; Fink, J.B.; Sternburg, B.K.; McAlister, E.O.; Wieduwilt, W.G. The use of the IP method to locate gold-bearing sulfide mineralization. In *Applications and Case Histories*; The Society of Exploration Geophysicists: Houston, TX, USA, 1990.

16. Fleet, M.E.; Mumin, A.H. Gold-bearing arsenian pyrite and marcasite and arsenopyrite from Carlin Trend gold deposits and laboratory synthesis. *Am. Mineral.* **1997**, *82*, 182–193. [CrossRef]

17. Florsch, N.; Llubes, M.; Téreygeol, F.; Ghorbani, A.; Roblet, P.J. Quantification of slag heap volumes and masses through the use of induced polarization: Application to the Castel-Minier site. *J. Archaeol. Sci.* **2011**, *38*, 438–451. [CrossRef]

18. Florsch, N.; Camerlynck, C.; Revil, A. Direct estimation of the distribution of relaxation times from induced-polarization spectra using a Fourier transform analysis. *Near Surf. Geophys.* **2012**, *10*, 517–531. [CrossRef]

19. Florsch, N.; Llubes, M.; Téreygeol, F. Induced polarization 3D tomography of an archaeological direct reduction slag heap. *Near Surf. Geophys.* **2012**, *10*, 567–574. [CrossRef]

20. Nordsiek, S.; Weller, A. A new approach to fitting induced-polarization spectra. *Geophysics* **2008**, *73*, F235–F245. [CrossRef]

21. Clavier, C.; Heim, A.; Scala, C. Effect of pyrite on resistivity and other logging measurements. In Proceedings of the SPWLA 17th Annual Logging Symposium, Denver, CO, USA, 9 June 1976.

22. Sternberg, B.K. A review of some experience with the induced-polarization/resistivity method for hydrocarbon surveys: Successes and limitations. *Geophysics* **1991**, *56*, 1522–1532. [CrossRef]

23. Veeken, P.C.; Legeydo, P.J.; Davidenko, Y.A.; Kudryavceva, E.O.; Ivanov, S.A.; Chuvaev, A. Benefits of the induced polarization geoelectric method to hydrocarbon exploration. *Geophysics* **2009**, *74*, B47–B59. [CrossRef]

24. Flekkøy, E.G.; Legeydo, P.; Håland, E.; Drivenes, G.; Kjerstad, J. Hydrocarbon detection through induced polarization: Case study from the Frigg area. In *SEG Technical Program Expanded Abstracts*; The Society of Exploration Geophysicists: Houston, TX, USA, 2013.

25. Okay, G.; Cosenza, P.; Ghorbani, A.; Camerlynck, C.; Cabrera, J.; Florsch, N.; Revil, A. Characterization of macroscopic heterogeneities in clay-rocks using induced polarization: Field tests at the experimental underground research laboratory of Tournemire (Aveyron, France). *Geophys. Prospect.* **2013**, *61*, 134–152. [CrossRef]

26. Hupfer, S.; Martin, T.; Noell, U.; Camerlynck, C.; Chauris, H.; Maineult, A.; Schmutz, M. Laboratory SIP: Investigation on unconsolidated mineral-sand mixtures. In Proceedings of the Third International Workshop on Induced Polarization, ENSEGID Bordeaux, Oléron Island, France, 6–9 April 2014; pp. 12–13.

27. Chen, J.; Hubbard, S.S.; Williams, K.H.; Flores Orozco, A.; Kemna, A. Estimating the spatiotemporal distribution of geochemical parameters associated with biostimulation using spectral induced polarization data and hierarchical Bayesian models. *Water Resour. Res.* **2012**, *48*, W0555. [CrossRef]

28. Orozco, A.F.; Kemna, A.; Oberdörster, C.; Zschornack, L.; Leven, C.; Dietrich, P.; Weiss, H. Delineation of subsurface hydrocarbon contamination at a former hydrogenation plant using spectral induced polarization imaging. *J. Contam. Hydrol.* **2012**, *136*, 131–144. [CrossRef] [PubMed]

29. Mewafy, F.M.; Werkema, D.D., Jr.; Atekwana, E.A.; Slater, L.D.; Aal, G.A.; Revil, A.; Ntarlagiannis, D. Evidence that bio-metallic mineral precipitation enhances the complex conductivity response at a hydrocarbon contaminated site. *J. Appl. Geophys.* **2013**, *98*, 113–123. [CrossRef]

30. Ntarlagiannis, D.; Williams, K.H.; Slater, L.; Hubbard, S. Low-frequency electrical response to microbial induced sulfide precipitation. *J. Geophys. Res. Biogeosci.* **2005**, *110*, G02009. [CrossRef]

31. Weller, A.; Börner, F.D. Measurements of spectral induced polarization for environmental purposes. *Environ. Geol.* **1996**, *27*, 329–334. [CrossRef]

32. Vacquier, V.; Holmes, C.R.; Kintzinger, P.R.; Lavergne, M. Prospecting for ground water by induced electrical polarization. *Geophysics* **1957**, *22*, 660–687. [CrossRef]

33. Martin, T. Complex resistivity measurements on oak. *Eur. J. Wood Prod.* **2012**, *70*, 45–53. [CrossRef]

34. Cole, K.S.; Cole, R.H. Dispersion and absorption in dielectrics I. Alternating current characteristics. *J. Chem. Phys.* **1941**, *9*, 341–351. [CrossRef]

35. Hallof, P.G.; Klein, J.D. Electrical parameters of volcanogenic mineral deposits in Ontario. In *Exploration Technology Development Program of the Board of Industrial Leadership and Development: Ontario Geological Survey, Paper*; Ontario Ministry of Natural Resources: Peterborough, ON, Canada, 1983; Volume 115, pp. 11–26.

36. Flekkøy, E.G. A physical basis for the Cole-Cole description of electrical conductivity of mineralized porous media. *Geophysics* **2013**, *78*, D355–D368. [CrossRef]

37. Wong, J. An electrochemical model of the induced-polarization phenomenon in disseminated sulfide ores. *Geophysics* **1979**, *44*, 1245–1265. [CrossRef]
11. Pelton, W.H.; Ward, S.H.; Hallof, P.G.; Sill, W.R.; Nelson, P.H. Mineral discrimination and removal of inductive coupling with multifrequency IP. *Geophysics* **1978**, *43*, 588–609. [CrossRef]

12. Hallof, P.G.; Klein, J.D. Characterization of electrical properties of metallic mineral deposits. *Ont. Geol. Surv. Open File Rep.* **1983**, *1983*, 5468.

13. Olhoeft, G.R. Electrical properties of rocks and minerals. In *Short Course Notes*; US Geological Survey: Golden, CO, USA, 1983.

14. Vanhala, H.; Peltoniemi, M. Spectral IP studies of Finnish ore prospects. *Geophysics* **1992**, *57*, 1545–1555. [CrossRef]

15. Hallof, P.G.; Yamashita, M.; Fink, J.B.; Sternburg, B.K.; McAlister, E.O.; Wieduwilt, W.G. The use of the IP method to locate gold-bearing sulfide mineralization. In *Applications and Case Histories*; The Society of Exploration Geophysicists: Houston, TX, USA, 1990.

16. Fleet, M.E.; Mumin, A.H. Gold-bearing arsenian pyrite and marcasite and arsenopyrite from Carlin Trend gold deposits and laboratory synthesis. *Am. Mineral.* **1997**, *82*, 182–193. [CrossRef]

17. Florsch, N.; Llubes, M.; Téreygeol, F.; Ghorbani, A.; Roblet, P.J. Quantification of slag heap volumes and masses through the use of induced polarization: Application to the Castel-Minier site. *J. Archaeol. Sci.* **2011**, *38*, 438–451. [CrossRef]

18. Florsch, N.; Camerlynck, C.; Revil, A. Direct estimation of the distribution of relaxation times from induced-polarization spectra using a Fourier transform analysis. *Near Surf. Geophys.* **2012**, *10*, 517–531. [CrossRef]

19. Florsch, N.; Llubes, M.; Téreygeol, F. Induced polarization 3D tomography of an archaeological direct reduction slag heap. *Near Surf. Geophys.* **2012**, *10*, 567–574. [CrossRef]

20. Nordsiek, S.; Weller, A. A new approach to fitting induced-polarization spectra. *Geophysics* **2008**, *73*, F235–F245. [CrossRef]

21. Clavier, C.; Heim, A.; Scala, C. Effect of pyrite on resistivity and other logging measurements. In Proceedings of the SPWLA 17th Annual Logging Symposium, Denver, CO, USA, 9 June 1976.

22. Sternberg, B.K. A review of some experience with the induced-polarization/resistivity method for hydrocarbon surveys: Successes and limitations. *Geophysics* **1991**, *56*, 1522–1532. [CrossRef]

23. Veeken, P.C.; Legeydo, P.J.; Davidenko, Y.A.; Kudryavceva, E.O.; Ivanov, S.A.; Chuvaev, A. Benefits of the induced polarization geoelectric method to hydrocarbon exploration. *Geophysics* **2009**, *74*, B47–B59. [CrossRef]

24. Flekkøy, E.G.; Legeydo, P.; Håland, E.; Drivenes, G.; Kjerstad, J. Hydrocarbon detection through induced polarization: Case study from the Frigg area. In *SEG Technical Program Expanded Abstracts*; The Society of Exploration Geophysicists: Houston, TX, USA, 2013.

25. Okay, G.; Cosenza, P.; Ghorbani, A.; Camerlynck, C.; Cabrera, J.; Florsch, N.; Revil, A. Characterization of macroscopic heterogeneities in clay-rocks using induced polarization: Field tests at the experimental underground research laboratory of Tournemire (Aveyron, France). *Geophys. Prospect.* **2013**, *61*, 134–152. [CrossRef]

26. Hupfer, S.; Martin, T.; Noell, U.; Camerlynck, C.; Chauris, H.; Maineult, A.; Schmutz, M. Laboratory SIP: Investigation on unconsolidated mineral-sand mixtures. In Proceedings of the Third International Workshop on Induced Polarization, ENSEGID Bordeaux, Oléron Island, France, 6–9 April 2014; pp. 12–13.

27. Chen, J.; Hubbard, S.S.; Williams, K.H.; Flores Orozco, A.; Kemna, A. Estimating the spatiotemporal distribution of geochemical parameters associated with biostimulation using spectral induced polarization data and hierarchical Bayesian models. *Water Resour. Res.* **2012**, *48*, W0555. [CrossRef]

28. Orozco, A.F.; Kemna, A.; Oberdörster, C.; Zschornack, L.; Leven, C.; Dietrich, P.; Weiss, H. Delineation of subsurface hydrocarbon contamination at a former hydrogenation plant using spectral induced polarization imaging. *J. Contam. Hydrol.* **2012**, *136*, 131–144. [CrossRef] [PubMed]

29. Mewafy, F.M.; Werkema, D.D., Jr.; Atekwana, E.A.; Slater, L.D.; Aal, G.A.; Revil, A.; Ntarlagiannis, D. Evidence that bio-metallic mineral precipitation enhances the complex conductivity response at a hydrocarbon contaminated site. *J. Appl. Geophys.* **2013**, *98*, 113–123. [CrossRef]

30. Ntarlagiannis, D.; Williams, K.H.; Slater, L.; Hubbard, S. Low-frequency electrical response to microbial induced sulfide precipitation. *J. Geophys. Res. Biogeosci.* **2005**, *110*, G02009. [CrossRef]

31. Weller, A.; Börner, F.D. Measurements of spectral induced polarization for environmental purposes. *Environ. Geol.* **1996**, *27*, 329–334. [CrossRef]

32. Vacquier, V.; Holmes, C.R.; Kintzinger, P.R.; Lavergne, M. Prospecting for ground water by induced electrical polarization. *Geophysics* **1957**, *22*, 660–687. [CrossRef]

33. Martin, T. Complex resistivity measurements on oak. *Eur. J. Wood Prod.* **2012**, *70*, 45–53. [CrossRef]

34. Cole, K.S.; Cole, R.H. Dispersion and absorption in dielectrics I. Alternating current characteristics. *J. Chem. Phys.* **1941**, *9*, 341–351. [CrossRef]

35. Hallof, P.G.; Klein, J.D. Electrical parameters of volcanogenic mineral deposits in Ontario. In *Exploration Technology Development Program of the Board of Industrial Leadership and Development: Ontario Geological Survey, Paper*; Ontario Ministry of Natural Resources: Peterborough, ON, Canada, 1983; Volume 115, pp. 11–26.

36. Flekkøy, E.G. A physical basis for the Cole-Cole description of electrical conductivity of mineralized porous media. *Geophysics* **2013**, *78*, D355–D368. [CrossRef]

37. Wong, J. An electrochemical model of the induced-polarization phenomenon in disseminated sulfide ores. *Geophysics* **1979**, *44*, 1245–1265. [CrossRef]
38. Wong, J.; Strangway, D.W. Induced polarization in disseminated sulfide ores containing elongated mineralization. *Geophysics* **1981**, *46*, 1258–1268. [CrossRef]

39. Bücker, M.; Orozco, A.F.; Kemna, A. Electrochemical polarization around metallic particles—Part 1: The role of diffuse-layer and volume-diffusion relaxation. *Geophysics* **2018**, *83*, E203–E217. [CrossRef]

40. Bücker, M.; Undorf, S.; Flores Orozco, A.; Kemna, A. Electrochemical polarization around metallic particles—Part 2: The role of diffuse surface charge. *Geophysics* **2019**, *84*, E57–E73. [CrossRef]

41. Abdulsamad, F.; Florsch, N.; Camerlynck, C. Spectral induced polarization in a sandy medium containing semiconductor materials: Experimental results and numerical modelling of the polarization mechanism. *Near Surf. Geophys.* **2017**, *15*, 669–683. [CrossRef]

42. Hupfer, S.; Martin, T.; Weller, A.; Günther, T.; Kuhn, K.; Ngninjio, V.D.N.; Noell, U. Polarization effects of unconsolidated sulphide-sand-mixtures. *J. Appl. Geophys.* **2016**, *135*, 456–465. [CrossRef]

43. Abdulsamad, F.; Revil, A.; Ghorbani, A.; Toy, V.; Kirilova, M.; Coperey, A.; Duvillard, P.; Ménard, G.; Ravanel, L. Complex conductivity of graphitic schists and sandstones. *J. Geophys. Res. Solid Earth* **2019**, *124*, 8223–8249. [CrossRef]

44. Revil, A.; Tartrat, T.; Abdulsamad, F.; Ghorbani, A.; Coperey, A. Chargeability of Porous Rocks With or Without Metallic Particles. *Petrophysics-SPWLA J. Form. Eval. Reserv. Descr.* **2018**, *59*, 544–553. [CrossRef]

45. Revil, A.; Coperey, A.; Mao, D.; Abdulsamad, F.; Ghorbani, A.; Rossi, M.; Gasquet, D. Induced polarization response of porous media with metallic particles—Part 8: Influence of temperature and salinity. *Geophysics* **2018**, *83*, E435–E456. [CrossRef]

46. Revil, A.; Binley, A.; Mejus, L.; Kessouri, P. Predicting permeability from the characteristic relaxation time and intrinsic formation factor of complex conductivity spectra. *Water Resour. Res.* **2015**, *51*, 6672–6700. [CrossRef]

47. Revil, A.; Abdel Aal, G.Z.; Atekwana, E.A.; Mao, D.; Florsch, N. Induced polarization response of porous media with metallic particles—Part 2: Comparison with a broad database of experimental data. *Geophysics* **2015**, *80*, D539–D552. [CrossRef]

48. Niu, Q.; Revil, A. Connecting complex conductivity spectra to mercury porosimetry of sedimentary rocks. *Geophysics* **2016**, *81*, E17–E32. [CrossRef]

49. Hall, S.; Olhoeft, G. Nonlinear complex resistivity of some nickel sulphides from western australia. *Geophys. Prospect.* **1986**, *34*, 1255–1276. [CrossRef]

50. Chu, K.T.; Bazant, M.Z. Nonlinear electrochemical relaxation around conductors. *Phys. Rev. E* **2006**, *74*, 011501. [CrossRef] [PubMed]

51. Zonge, K.; Sauck, W.A.; Sumner, J.S. Comparison of time, frequency, and phase measurements in induced polarization. *Geophys. Prospect.* **1972**, *20*, 626–648. [CrossRef]

52. Orozco, A.F.; Kemna, A.; Zimmermann, E. Data error quantification in spectral induced polarization imaging. *Geophysics* **2012**, *77*, E227–E237. [CrossRef]

53. Günther, T.; Martin, T. Spectral two-dimensional inversion of frequency-domain induced polarization data from a mining slag heap. *J. Appl. Geophys.* **2016**, *135*, 436–448. [CrossRef]

54. Kemna, A.; Huisman, J.A.; Zimmermann, E.; Martin, R.; Zhao, Y.; Treichel, A.; Flores Orozco, A.; Fechner, T. Broadband Electrical Impedance Tomography for Subsurface Characterization Using Improved Corrections of Electromagnetic Coupling and Spectral Regularization. In *Tomography of the Earth's Crust: From Geophysical Sounding to Real-Time Monitoring*; Springer: Cham, Switzerland, 2014; pp. 1–20.

55. Revil, A.; Schmutz, M.; Abdulsamad, F.; Balde, A.; Beck, C.; Ghorbani, A.; Hubbard, S.S. Field-scale estimation of soil properties from spectral induced polarization tomography. *Geoderma.* **2021**, *403*, 115380. [CrossRef]

56. Van Voorhis, G.D.; Nelson, P.H.; Drake, T.L. Complex resistivity spectra of porphyry copper mineralization. *Geophysics.* **1973**, *38*, 49–60. [CrossRef]

57. Revil, A.; Coperey, A.; Shao, Z.; Florsch, N.; Fabricius, I.L.; Deng, Y.; Delsman, J.; Pauw, P.; Karaoulis, M.; De Louw, P. Complex conductivity of soils. *Water Resour. Res.* **2017**, *53*, 7121–7147. [CrossRef]

58. Dias, C.A. Developments in a model to describe low-frequency electrical polarization of rocks. *Geophysics* **2000**, *65*, 437–451. [CrossRef]

59. Winsauer, W.; McCardell, W.M. Ionic double-layer conductivity in reservoir rock. *J. Pet. Technol.* **1953**, *5*, 129–134. [CrossRef]

60. Waxman, M.H.; Smits, L.J.M. Electrical conductivities in oil-bearing shaly sands. *Soc. Pet. Eng. J.* **1968**, *8*, 107–122. [CrossRef]

61. Vinegar, H.J.; Waxman, M.H. Induced polarization of shaly sands. *Geophysics* **1984**, *49*, 1267–1287. [CrossRef]

62. Batchelor, G.K.; O'Brien, R.W. Thermal or electrical conduction through a granular material. *Proc. R. Soc. London A Math. Phys. Sci.* **1977**, *355*, 313–333.

63. Stroud, D.; Milton, G.W.; De, B.R. Analytical model for the dielectric response of brine-saturated rocks. *Phys. Rev. E* **1986**, *34*, 5145. [CrossRef]

64. Revil, A.; Florsch, N.; Mao, D. Induced polarization response of porous media with metallic particles—Part 1: A theory for disseminated semiconductors. *Geophysics* **2015**, *80*, D525–D538. [CrossRef]

65. Mahan, M.K.; Redman, J.D.; Strangway, D.W. Complex resistivity of synthetic sulphide bearing rocks. *Geophys. Prospect.* **1986**, *34*, 743–768. [CrossRef]

66. Pridmore, D.F.; Shuey, R.T. The electrical resistivity of galena, pyrite, and chalcopyrite. *Am. Mineral.* **1976**, *61*, 248–259.

67. Revil, A.; Florsch, N. Determination of permeability from spectral induced polarization in granular media. *Geophys. J. Int.* **2010**, *181*, 1480–1498. [CrossRef]
38. Wong, J.; Strangway, D.W. Induced polarization in disseminated sulfide ores containing elongated mineralization. *Geophysics* **1981**, *46*, 1258–1268. [CrossRef]

39. Bücker, M.; Orozco, A.F.; Kemna, A. Electrochemical polarization around metallic particles—Part 1: The role of diffuse-layer and volume-diffusion relaxation. *Geophysics* **2018**, *83*, E203–E217. [CrossRef]

40. Bücker, M.; Undorf, S.; Flores Orozco, A.; Kemna, A. Electrochemical polarization around metallic particles—Part 2: The role of diffuse surface charge. *Geophysics* **2019**, *84*, E57–E73. [CrossRef]

41. Abdulsamad, F.; Florsch, N.; Camerlynck, C. Spectral induced polarization in a sandy medium containing semiconductor materials: Experimental results and numerical modelling of the polarization mechanism. *Near Surf. Geophys.* **2017**, *15*, 669–683. [CrossRef]

42. Hupfer, S.; Martin, T.; Weller, A.; Günther, T.; Kuhn, K.; Ngninjio, V.D.N.; Noell, U. Polarization effects of unconsolidated sulphide-sand-mixtures. *J. Appl. Geophys.* **2016**, *135*, 456–465. [CrossRef]

43. Abdulsamad, F.; Revil, A.; Ghorbani, A.; Toy, V.; Kirilova, M.; Coperey, A.; Duvillard, P.; Ménard, G.; Ravanel, L. Complex conductivity of graphitic schists and sandstones. *J. Geophys. Res. Solid Earth* **2019**, *124*, 8223–8249. [CrossRef]

44. Revil, A.; Tartrat, T.; Abdulsamad, F.; Ghorbani, A.; Coperey, A. Chargeability of Porous Rocks With or Without Metallic Particles. *Petrophysics-SPWLA J. Form. Eval. Reserv. Descr.* **2018**, *59*, 544–553. [CrossRef]

45. Revil, A.; Coperey, A.; Mao, D.; Abdulsamad, F.; Ghorbani, A.; Rossi, M.; Gasquet, D. Induced polarization response of porous media with metallic particles—Part 8: Influence of temperature and salinity. *Geophysics* **2018**, *83*, E435–E456. [CrossRef]

46. Revil, A.; Binley, A.; Mejus, L.; Kessouri, P. Predicting permeability from the characteristic relaxation time and intrinsic formation factor of complex conductivity spectra. *Water Resour. Res.* **2015**, *51*, 6672–6700. [CrossRef]

47. Revil, A.; Abdel Aal, G.Z.; Atekwana, E.A.; Mao, D.; Florsch, N. Induced polarization response of porous media with metallic particles—Part 2: Comparison with a broad database of experimental data. *Geophysics* **2015**, *80*, D539–D552. [CrossRef]

48. Niu, Q.; Revil, A. Connecting complex conductivity spectra to mercury porosimetry of sedimentary rocks. *Geophysics* **2016**, *81*, E17–E32. [CrossRef]

49. Hall, S.; Olhoeft, G. Nonlinear complex resistivity of some nickel sulphides from western australia. *Geophys. Prospect.* **1986**, *34*, 1255–1276. [CrossRef]

50. Chu, K.T.; Bazant, M.Z. Nonlinear electrochemical relaxation around conductors. *Phys. Rev. E* **2006**, *74*, 011501. [CrossRef] [PubMed]

51. Zonge, K.; Sauck, W.A.; Sumner, J.S. Comparison of time, frequency, and phase measurements in induced polarization. *Geophys. Prospect.* **1972**, *20*, 626–648. [CrossRef]

52. Orozco, A.F.; Kemna, A.; Zimmermann, E. Data error quantification in spectral induced polarization imaging. *Geophysics* **2012**, *77*, E227–E237. [CrossRef]

53. Günther, T.; Martin, T. Spectral two-dimensional inversion of frequency-domain induced polarization data from a mining slag heap. *J. Appl. Geophys.* **2016**, *135*, 436–448. [CrossRef]

54. Kemna, A.; Huisman, J.A.; Zimmermann, E.; Martin, R.; Zhao, Y.; Treichel, A.; Flores Orozco, A.; Fechner, T. Broadband Electrical Impedance Tomography for Subsurface Characterization Using Improved Corrections of Electromagnetic Coupling and Spectral Regularization. In *Tomography of the Earth's Crust: From Geophysical Sounding to Real-Time Monitoring*; Springer: Cham, Switzerland, 2014; pp. 1–20.

55. Revil, A.; Schmutz, M.; Abdulsamad, F.; Balde, A.; Beck, C.; Ghorbani, A.; Hubbard, S.S. Field-scale estimation of soil properties from spectral induced polarization tomography. *Geoderma.* **2021**, *403*, 115380. [CrossRef]

56. Van Voorhis, G.D.; Nelson, P.H.; Drake, T.L. Complex resistivity spectra of porphyry copper mineralization. *Geophysics.* **1973**, *38*, 49–60. [CrossRef]

57. Revil, A.; Coperey, A.; Shao, Z.; Florsch, N.; Fabricius, I.L.; Deng, Y.; Delsman, J.; Pauw, P.; Karaoulis, M.; De Louw, P. Complex conductivity of soils. *Water Resour. Res.* **2017**, *53*, 7121–7147. [CrossRef]

58. Dias, C.A. Developments in a model to describe low-frequency electrical polarization of rocks. *Geophysics* **2000**, *65*, 437–451. [CrossRef]

59. Winsauer, W.; McCardell, W.M. Ionic double-layer conductivity in reservoir rock. *J. Pet. Technol.* **1953**, *5*, 129–134. [CrossRef]

60. Waxman, M.H.; Smits, L.J.M. Electrical conductivities in oil-bearing shaly sands. *Soc. Pet. Eng. J.* **1968**, *8*, 107–122. [CrossRef]

61. Vinegar, H.J.; Waxman, M.H. Induced polarization of shaly sands. *Geophysics* **1984**, *49*, 1267–1287. [CrossRef]

62. Batchelor, G.K.; O'Brien, R.W. Thermal or electrical conduction through a granular material. *Proc. R. Soc. London A Math. Phys. Sci.* **1977**, *355*, 313–333.

63. Stroud, D.; Milton, G.W.; De, B.R. Analytical model for the dielectric response of brine-saturated rocks. *Phys. Rev. E* **1986**, *34*, 5145. [CrossRef]

64. Revil, A.; Florsch, N.; Mao, D. Induced polarization response of porous media with metallic particles—Part 1: A theory for disseminated semiconductors. *Geophysics* **2015**, *80*, D525–D538. [CrossRef]

65. Mahan, M.K.; Redman, J.D.; Strangway, D.W. Complex resistivity of synthetic sulphide bearing rocks. *Geophys. Prospect.* **1986**, *34*, 743–768. [CrossRef]

66. Pridmore, D.F.; Shuey, R.T. The electrical resistivity of galena, pyrite, and chalcopyrite. *Am. Mineral.* **1976**, *61*, 248–259.

67. Revil, A.; Florsch, N. Determination of permeability from spectral induced polarization in granular media. *Geophys. J. Int.* **2010**, *181*, 1480–1498. [CrossRef]
68. Tarasov, A.; Titov, K. Relaxation time distribution from time domain induced polarization measurements. *Geophys. J. Int.* **2007**, *170*, 31–43. [CrossRef]

69. Tarasov, A.; Titov, K. On the use of the Cole–Cole equations in spectral induced polarization. *Geophys. J. Int.* **2013**, *195*, 352–356. [CrossRef]

70. Gurin, G.; Tarasov, A.; Ilyin, Y.; Titov, K. Time domain spectral induced polarization of disseminated electronic conductors: Laboratory data analysis through the Debye decomposition approach. *J. Appl. Geophys.* **2013**, *98*, 44–53. [CrossRef]

71. De Witt, G.W. Parameter Studies of Induced Polarization Spectra. Master's Thesis, University of Utah, Salt Lake City, UT, USA, 1979.

72. Abdel Aal, G.Z.; Atekwana, E.A.; Revil, A. Geophysical signatures of disseminated iron minerals: A proxy for understanding subsurface biophysicochemical processes. *J. Geophys. Res. Biogeosci.* **2014**, *119*, 1831–1849. [CrossRef]

73. Schwarz, G. A theory of the low-frequency dielectric dispersion of colloidal particles in electrolyte solution1. *J. Phys. Chem.* **1962**, *66*, 2636–2642. [CrossRef]

74. Nernst, W. Zur kinetik der in lösung befindlichen körper. *Z. Phys. Chem.* **1888**, *2*, 613–637. [CrossRef]

75. Nernst, W. Die elektromotorische wirksamkeit der jonen. *Z. Phys. Chem.* **1889**, *4*, 129–181. [CrossRef]

76. Planck, M. Ueber die erregung von electricität und wärme in electrolyten. *Ann. Phys.* **1890**, *275*, 161–186. [CrossRef]

77. Maxwell, J.C. *A Treatise on Electricity and Magnetism*; Clarendon Press; Oxford, UK, 1873; Volume 1.

78. Misra, S.; Torres-Verdín, C.; Revil, A.; Rasmus, J.; Homan, D. Interfacial polarization of disseminated conductive minerals in absence of redox-active species—Part 1: Mechanistic model and validation. *Geophysics* **2016**, *81*, E139–E157. [CrossRef]

79. Misra, S.; Torres-Verdín, C.; Revil, A.; Rasmus, J.; Homan, D. Interfacial polarization of disseminated conductive minerals in absence of redox-active species—Part 2: Effective electrical conductivity and dielectric permittivity. *Geophysics* **2016**, *81*, E159–E176. [CrossRef]

80. Shuey, R.T. *Semiconducting Ore Minerals*; Elsevier Publishing Co.: Amsterdam, The Netherlands, 1975; Volume 4.

81. Seigel, H.O. Mathematical formulation and type curves for induced polarization. *Geophysics* **1959**, *24*, 547–565. [CrossRef]

82. Phillips, C.R. Experimental Study of the Induced Polarization Effect Using Cole-Cole and GEMTIP Models. Ph.D. Dissertation, The University of Utah, Salt Lake City, UT, USA, 2010.

83. Sen, P.N.; Scala, C.; Cohen, M.H. A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. *Geophysics* **1981**, *46*, 781–795. [CrossRef]

84. Revil, A. Thermal conductivity of unconsolidated sediments with geophysical applications. *J. Geophys. Res. Solid Earth* **2000**, *105*, 16749–16768. [CrossRef]

85. Revil, A. On charge accumulation in heterogeneous porous rocks under the influence of an external electric field. *Geophysics* **2013**, *78*, D271–D291. [CrossRef]

86. Archie, G.E. The electrical resistivity log as an aid in determining some reservoir characteristics. *Trans. AIME* **1942**, *146*, 54–62. [CrossRef]

87. Revil, A.; Sleevi, M.F.; Mao, D. Induced polarization response of porous media with metallic particles—Part 5: Influence of the background polarization. *Geophysics* **2017**, *82*, E77–E96. [CrossRef]

88. Ghorbani, A.; Revil, A.; Coperey, A.; Ahmed, A.S.; Roque, S.; Heap, M.; Grandis, H.; Viveiros, F. Complex conductivity of volcanic rocks and the geophysical mapping of alteration in volcanoes. *J. Volcanol. Geotherm. Res.* **2018**, *357*, 106–127. [CrossRef]

89. Revil, A.; Karaoulis, M.; Johnson, T.; Kemna, A. Some low-frequency electrical methods for subsurface characterization and monitoring in hydrogeology. *Hydrogeol. J.* **2012**, *20*, 617–658. [CrossRef]

90. Ostrander, A.G.; Zonge, K.L. Complex resistivity measurements of sulfide-bearing synthetic rocks. In *48th Annual SEG Meeting, SEG, Abstract*; SEG: Houston, TX, USA, 1978; Volume 44, p. 409.

91. Vanhala, H. Laboratory and field studies of environmental and exploitation applications of the spectral induced-polarization. *Geol. Tutk.* **1997**, 1997.

92. Collett, L.S.; Brant, A.A.; Bell, W.E.; Ruddock, K.A.; Seigel, H.O.; Wait, J.R. Laboratory investigation of overvoltage. In *Overvoltage Research and Geophysical Applications*; Pergamon Press: Oxford, UK, 1959; pp. 50–69.

93. Grissemann, C. Examination of the frequency-dependent conductivity of ore-containing rock on artificial models. In *Scientific Report No. 2, University of Innsbruck Electronics Laboratory*; University of Innsbruck: Innsbruck, Austria, 1971.

94. Grissemann, C.; Rammlmair, D.; Siegwart, C.; Fouillet, N.; Mederer, J.; Oberthür, T.; Heimann, R.; Pentinghaus, H. Spectral induced polarization linked to image analyses: A new approach. *Appl. Mineral. Balkema* **2000**, *2000*, 561–564.

95. Revil, A.; Razdan, M.; Julien, S.; Coperey, A.; Abdulsamad, F.; Ghorbani, A.; Gasquet, D.; Sharma, R.; Rossi, M. Induced polarization response of porous media with metallic particles—Part 9: Influence of permafrost. *Geophysics* **2019**, *84*, E337–E355. [CrossRef]

96. Gurin, G.; Titov, K.; Ilyin, Y.; Tarasov, A. Induced polarization of disseminated electronically conductive minerals: A semi-empirical model. *Geophys. J. Int.* **2015**, *200*, 1555–1565. [CrossRef]

97. Oldenburg, D.W.; Li, Y. Inversion of induced polarization data. *Geophysics* **1994**, *59*, 1327–1341. [CrossRef]

98. Qi, Y.; Soueid Ahmed, A.; Revil, A.; Ghorbani, A.; Abdulsamad, F.; Florsch, N.; Bonnenfant, J. Induced polarization response of porous media with metallic particles—Part 7: Detection and quantification of buried slag heaps. *Geophysics* **2018**, *83*, E277–E291. [CrossRef]
68. Tarasov, A.; Titov, K. Relaxation time distribution from time domain induced polarization measurements. *Geophys. J. Int.* **2007**, *170*, 31–43. [CrossRef]

69. Tarasov, A.; Titov, K. On the use of the Cole–Cole equations in spectral induced polarization. *Geophys. J. Int.* **2013**, *195*, 352–356. [CrossRef]

70. Gurin, G.; Tarasov, A.; Ilyin, Y.; Titov, K. Time domain spectral induced polarization of disseminated electronic conductors: Laboratory data analysis through the Debye decomposition approach. *J. Appl. Geophys.* **2013**, *98*, 44–53. [CrossRef]

71. De Witt, G.W. Parameter Studies of Induced Polarization Spectra. Master’s Thesis, University of Utah, Salt Lake City, UT, USA, 1979.

72. Abdel Aal, G.Z.; Atekwana, E.A.; Revil, A. Geophysical signatures of disseminated iron minerals: A proxy for understanding subsurface biophysicochemical processes. *J. Geophys. Res. Biogeosci.* **2014**, *119*, 1831–1849. [CrossRef]

73. Schwarz, G. A theory of the low-frequency dielectric dispersion of colloidal particles in electrolyte solution1. *J. Phys. Chem.* **1962**, *66*, 2636–2642. [CrossRef]

74. Nernst, W. Zur kinetik der in lösung befindlichen körper. *Z. Phys. Chem.* **1888**, *2*, 613–637. [CrossRef]

75. Nernst, W. Die elektromotorische wirksamkeit der jonen. *Z. Phys. Chem.* **1889**, *4*, 129–181. [CrossRef]

76. Planck, M. Ueber die erregung von electricität und wärme in electrolyten. *Ann. Phys.* **1890**, *275*, 161–186. [CrossRef]

77. Maxwell, J.C. *A Treatise on Electricity and Magnetism*; Clarendon Press; Oxford, UK, 1873; Volume 1.

78. Misra, S.; Torres-Verdín, C.; Revil, A.; Rasmus, J.; Homan, D. Interfacial polarization of disseminated conductive minerals in absence of redox-active species—Part 1: Mechanistic model and validation. *Geophysics* **2016**, *81*, E139–E157. [CrossRef]

79. Misra, S.; Torres-Verdín, C.; Revil, A.; Rasmus, J.; Homan, D. Interfacial polarization of disseminated conductive minerals in absence of redox-active species—Part 2: Effective electrical conductivity and dielectric permittivity. *Geophysics* **2016**, *81*, E159–E176. [CrossRef]

80. Shuey, R.T. *Semiconducting Ore Minerals*; Elsevier Publishing Co.: Amsterdam, The Netherlands, 1975; Volume 4.

81. Seigel, H.O. Mathematical formulation and type curves for induced polarization. *Geophysics* **1959**, *24*, 547–565. [CrossRef]

82. Phillips, C.R. Experimental Study of the Induced Polarization Effect Using Cole-Cole and GEMTIP Models. Ph.D. Dissertation, The University of Utah, Salt Lake City, UT, USA, 2010.

83. Sen, P.N.; Scala, C.; Cohen, M.H. A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. *Geophysics* **1981**, *46*, 781–795. [CrossRef]

84. Revil, A. Thermal conductivity of unconsolidated sediments with geophysical applications. *J. Geophys. Res. Solid Earth* **2000**, *105*, 16749–16768. [CrossRef]

85. Revil, A. On charge accumulation in heterogeneous porous rocks under the influence of an external electric field. *Geophysics* **2013**, *78*, D271–D291. [CrossRef]

86. Archie, G.E. The electrical resistivity log as an aid in determining some reservoir characteristics. *Trans. AIME* **1942**, *146*, 54–62. [CrossRef]

87. Revil, A.; Sleevi, M.F.; Mao, D. Induced polarization response of porous media with metallic particles—Part 5: Influence of the background polarization. *Geophysics* **2017**, *82*, E77–E96. [CrossRef]

88. Ghorbani, A.; Revil, A.; Coperey, A.; Ahmed, A.S.; Roque, S.; Heap, M.; Grandis, H.; Viveiros, F. Complex conductivity of volcanic rocks and the geophysical mapping of alteration in volcanoes. *J. Volcanol. Geotherm. Res.* **2018**, *357*, 106–127. [CrossRef]

89. Revil, A.; Karaoulis, M.; Johnson, T.; Kemna, A. Some low-frequency electrical methods for subsurface characterization and monitoring in hydrogeology. *Hydrogeol. J.* **2012**, *20*, 617–658. [CrossRef]

90. Ostrander, A.G.; Zonge, K.L. Complex resistivity measurements of sulfide-bearing synthetic rocks. In *48th Annual SEG Meeting, SEG, Abstract*; SEG: Houston, TX, USA, 1978; Volume 44, p. 409.

91. Vanhala, H. Laboratory and field studies of environmental and exploitation applications of the spectral induced-polarization. *Geol. Tutk.* **1997**, 1997.

92. Collett, L.S.; Brant, A.A.; Bell, W.E.; Ruddock, K.A.; Seigel, H.O.; Wait, J.R. Laboratory investigation of overvoltage. In *Overvoltage Research and Geophysical Applications*; Pergamon Press: Oxford, UK, 1959; pp. 50–69.

93. Grissemann, C. Examination of the frequency-dependent conductivity of ore-containing rock on artificial models. In *Scientific Report No. 2, University of Innsbruck Electronics Laboratory*; University of Innsbruck: Innsbruck, Austria, 1971.

94. Grissemann, C.; Rammlmair, D.; Siegwart, C.; Fouillet, N.; Mederer, J.; Oberthür, T.; Heimann, R.; Pentinghaus, H. Spectral induced polarization linked to image analyses: A new approach. *Appl. Mineral. Balkema* **2000**, *2000*, 561–564.

95. Revil, A.; Razdan, M.; Julien, S.; Coperey, A.; Abdulsamad, F.; Ghorbani, A.; Gasquet, D.; Sharma, R.; Rossi, M. Induced polarization response of porous media with metallic particles—Part 9: Influence of permafrost. *Geophysics* **2019**, *84*, E337–E355. [CrossRef]

96. Gurin, G.; Titov, K.; Ilyin, Y.; Tarasov, A. Induced polarization of disseminated electronically conductive minerals: A semi-empirical model. *Geophys. J. Int.* **2015**, *200*, 1555–1565. [CrossRef]

97. Oldenburg, D.W.; Li, Y. Inversion of induced polarization data. *Geophysics* **1994**, *59*, 1327–1341. [CrossRef]

98. Qi, Y.; Soueid Ahmed, A.; Revil, A.; Ghorbani, A.; Abdulsamad, F.; Florsch, N.; Bonnenfant, J. Induced polarization response of porous media with metallic particles—Part 7: Detection and quantification of buried slag heaps. *Geophysics* **2018**, *83*, E277–E291. [CrossRef]
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