1. ERTH2020 Introduction to Geophysics
The self-potential method is a passive geophysical method, like the gravity and magnetic methods.
It involves the measurement of the electric potential at a set of measurement points or self-potential stations.
The sampled electrical potential can be used to determine the causative source of current in the ground.
The SP method used to be an unpopular geophysical exploration tool – even though it is in principal a very simple and inexpensive exploration tool.
However in recent years the technique seems to gain in popularity:
A simple Google-Scholar search of the terms “self potential” and “geophysics” between 1960 and 1990 gave 1,110 results
The same search for the time after 2010 gave 1200 results.
Besides its traditional use in mineral exploration, the SP technique is playing an increasing important exploration tool, especially in environmental and hydrological studies, as well as in reservoir monitoring.
Many of the underlying details are complex and not yet fully understood and interpretation is mostly qualitatively, but more reliable quantitative tools (i.e. geophysical inversion) are emerging.
The Self Potential Method
(or Spontaneous Potential)
“The ugly duckling of environmental geophysics”
Nyquist & Corry, 2002

2. Self Potential Method
Passive geophysical method (like gravity/magnetics)
One of the oldest geophysical methods.
First measurement by Fox (1830) in Cornwell, UK, over sulphide vein mineralisation.
Frequently used since the 1920s as a (secondary) tool for base-metal exploration and also for detecting subsurface fluid-flow.
Involves measurement of electric potentials (voltages) at specific points on the surface or downhole (self-potential stations).
Required: volt-meter, non-polarising electrodes.
Natural potential differences generally exist between any two points on the ground (associated with electrical currents in the subsurface).
Mostly used qualitatively due to lack of quantitative models but this is changing rapidly (complex causative sources of self-potential signal).
c.f. Revil & Jardani, 2013, pp. 14

3. Self Potential Method Applications: for mineral exploration
geothermal applications
groundwater investigation
formation evaluation in the oil and gas industry
to detect fluid flow in fractured rocks and gas reservoirs
engineering applications to detect dam fractures and seepage
and others …
Revil & Jardani, 2013

4. Self Potential Method Revil & Jardani, 2013, p. 2
Piezometer  groundwater pressure
Figure:
Self-potential measurements are performed using non-polarizing electrodes connected to a voltmeter.
The figure shows a multichannel voltmeter used to record the voltage of 80 non-polarizing electrodes at a frequency of one sample per minute.
The difference of the electric potential between two electrodes is measured by using a voltmeter with a high sensitivity (at least 0.1 mV), and high input impedance.
Revil & Jardani, 2013, p. 2

5. Self Potential Method
Development of non-polarising electrodes (porous-pot) in 1865 by M.C. Matteucci, Greenwich Observatory.
Measurements in mV (streaming potential) to several V (mineralisation potential).
An example of non-polarizing electrode, the Petiau Pb/PbCl2 electrode, is shown in this figure.
A non-polarizing electrode is formed by a metal in contact with its own salt (e.g., silver in a silver chloride solution, or copper in a copper sulfate solution) within a porous container.
These pots produce very low electrolytic contact potential, such that the background voltage is as small as possible.
Sealed pots can keep their supersaturated solutions for more than a week, even in arid locales.
Refilling the pot with solution must occur before a day's work due to the possible contact potential change while performing a measurement set.
A useful procedure is to mix remaining fluids from pots in a single container, add new solution to the mixture in the pot, and use the mixed solution to fill the pots. Then all pots contain the same solution mix.
In monitoring, the shallow subsurface is always characterized by diurnal temperature variations in the ground down to 30–50 cm.
Hence, the monitoring electrodes should be installed at a depth of 30–50 cm, or temperature sensors need to be utilized in the vicinity of the electrodes to apply a post-correction of the effect of the temperature.
Other advantages are less sensitive to electromagnetic and other noise.
Revil & Jardani, 2013, p. 2

6. Self Potential Method High Impedance Potentiometer (Voltmeter).
Impedance (Resistance) has to be at least 10x higher than the ground between the electrodes to avoid current leakage in the voltmeter.
Impedance range from 105Ohm.m to 1012 Ohm.m for very resistive ground (ice, permafrost, crystalline rock)
An inexpensive, high-input-impedance voltmeter is used to read the potential in the millivolt range.
Actual field voltage will be in error when the source potential is within an order of magnitude of the input impedance of the meter.
The input impedance should exceed 50 MΩ. Higher input impedances are desirable due to the impedance reduction of air's moisture. The resolution of the meter should be 0.1 or 1.0 mV.
Revil & Jardani, 2013, p. 2

7. SP-Response associated with an aquifer test.
Self Potential Method
SP-Response associated with an aquifer test.
Water was pumped from one well and injected into another.
Time variation of measured SP data due to ground water flow associated with pumping and injection tests (at one SP station).
The SP response is sensitive to ground water flow triggered through the pumping test
Example – Aquifer Test
The figure shows the time variation of the measured self-potentials (raw data) on one electrode during the test.
An aquifer test (or a pumping test) is conducted to evaluate an aquifer by "stimulating" the aquifer through constant pumping, and observing the aquifer's "response" (drawdown) in observation wells. Aquifer testing is a common tool that hydrogeologists use to characterize a system of aquifers and flow system boundaries.
Most commonly an aquifer test is conducted by pumping water from one well at a steady rate, while carefully measuring the water levels in the monitoring wells. When water is pumped from the pumping well the pressure in the aquifer that feeds that well declines.
Data obtained prior to pumping.
Transient phase during pumping
Steady-state phase
Recovery phase
Steady state phase
thermal drift
Jardani, A. et al., 2008; c.f.

8. Self Potential Method Data acquisition.
Also used is the “star-approach” where first the potential differences between a set of base stations is determined.
Subsequently, each base is used as the local reference of profiles which are radially distributed about this station.
One strategy for self-potential mapping is called the “star network.”
In this approach, we first determine the difference of potential between a set of base stations separated from each other by several hundred meters (up to a kilometer).
Note that, since the wires used to measure a difference of potential between two points of the Earth are usually not shielded, they can be subject to induction effects.
In subsequent steps, each base station is used as the local reference of profiles that are more or less radially distributed about this station.
Figure
Large scale self-potential mapping using a star approach.
(a)
A set of base stations is chosen and prepared with bentonite plug setup in the ground.
The difference of potential between these stations is measured.
(b)
Each of these stations is used as a secondary reference and radial profiles are performed from this station.
The self-potential map is built by using one of the base stations as a reference for the entire survey.
The black plain lines denote the self-potential profiles from the base stations while the grey lines denote the electrical equipotentials obtained from the self-potential data.
Revil & Jardani, 2013, p. 4

9. Self Potential Method Data acquisition.
Large-scale mapping frequently uses a loop network approach
One base station is chosen as the reference and measurements are taken with scanning electrodes at SP stations.
In this approach, a closed-loop mapping is performed – this has the benefit that error checkings can be performed after each closed loop, since the net sum response must be zero.
One approach chooses one base station as the reference and measurements are performed with scanning electrodes at different secondary stations.
To extend the measurement array, the initial base station is removed and the reference electrode is transplanted, or “dropped,” at the position of the last measurement station.
This operation is repeated to close a loop. This approach is called the loop network. The circulation of the electrical field should be zero along a closed loop performed at the ground surface; in other words, the sum of the drop potentials along a closed loop is zero (i.e. he electrostatic field is conservative, assumption that 𝜕 𝑡 𝐵=0→𝛻×𝐸=0 (Faraday)).
It is very important to close the loop when making self-potential measurements, in order to check the closure error (due to the propagation of errors in the changes of the reference electrode) and to correct the selfpotential measurements from this closure error.
If this is not done, there is a risk of accumulating errors toward the end of the profiles (some published self-potential maps in volcanic areas clearly show huge accumulated errors at the end of profiles that were is interpreted as ground water flow pattern).
Figure:
Large-scale self-potential mapping over the ground surface using a close loop approach.
S0 denotes the first base station. Measurements are performed along the self-potential stations characterized by the small black circles.
At some point, a new base station is established at S1 and so on.
The potential distribution can be reconstructed along the loop respecting the fact that the self-potential loop should be closed.
A self-potential map is built by combining the information on several loops and using one of the base stations as reference for the entire map.
The black plain lines denote the selfpotential loops while the gray lines denote the electrical equipotentials obtained via interpolating the self-potential data.
Revil & Jardani, 2013, p. 4

10. Self Potential Method Data processing. Revil & Jardani, 2013, p. 6
The potential of the electrodes is always temperature dependent.
For example having a reference electrode in the cold ground and scanning the potential at the ground surface with a warmer electrode (e.g., one held in a hand) can easily generate a difference of potential higher than 10 mV.
Therefore, several corrections can be made using the closed-loop apprach:
The first correction is naturally to reestablish the continuity of the electrical potential using the first base station of the profile as a global base station for the entire loop.
And the final step is to correct for the closure error along the loop as the net response must be zero.
Revil & Jardani, 2013, p. 6

11. Geophysical Exploration
Self Potential Method
Mechanisms governing the occurrence of SP signals can be classified as follows:
Diffusion potentials (liquid-junction potential)
Shale Potentials (Nernst potential)
Bioelectric potentials
Mineral potentials
Streaming potentials (zeta potential)
Background/ Noise
Geophysical Exploration
All mechanisms are fundamentally electrochemical in nature
Telford et al, 1991, pp. 283

12. Self Potential Method Diffusion potentials (liquid-junction potential)
associated with gradients in concentrations of ionic species in the ground that set up diffusion potentials.
Shale Potential (Nernst potential)
(special case of diffusion potential) electrodes are immersed in a homogeneous solution but with different concentrations at the electrodes.
Bioelectric potentials
ion selectivity and water pumping action of plant roots can create SP anomalies.
Mineral potentials
(apparently) arise from geochemical oxidation-reduction (redox) reactions, equivalent to the galvanic cell defined in electrochemistry.
Streaming potentials (zeta potential)
arise when water or other fluids flow through sand, porous rock, moraines, basalts, etc.
Most self-potentials are of electrochemical origin.
For example, if the ionic concentration in an electrolyte varies with location, the ions tend to diffuse through the electrolyte so as to equalise the concentration.
The diffusion is driven by the diffusion potential, which depends on the temperature as well as the differences in ionic concentrations.
When a metallic electrode is inserted in the ground, the metal reacts electrochemically with the groundwater (or any other electrolyte), causing therefore a contact potential.
If two identical electrodes are inserted in the ground, variations in concentration of the electrolyte cause different electrochemical reactions at each electrode.
A potential difference arise, called the Nernst Potential.
The combined diffusion and Nernst potential are called the electrochemical self-potential.
These potentials are small as compared to those associated with ore bodies which give rise to mineral potentials.
These potentials are invariably negative and commonly asssociated with sulfide ores (pyrite, pyrrhotite, chalcopyrite and metallic oxides)
Nyquist and Corry, 2002; Telford et al, 1991, pp. 283

13. → via Nernst-Planck equation
Self Potential Method
Diffusion potentials
associated with gradients in concentrations of ionic species in the ground that set up diffusion potentials.
Anions & Cations with different mobilities result in different diffusion rates
𝑉 𝑒 + > 𝑉 𝑒 − ⟶ electric potential (faster moving ions of one charge will begin to outpace the ions of the opposite charge. The resultant electric field is just what is required to speed up the slower moving ions and maintain electro-neutrality).
In equilibrium, the diffusion potential, 𝐸 𝑑 , is given by:
SP anomalies are associated with gradients in concentrations of ionic species in the ground that set up diffusion potentials.
If the anions and cations involved have different mobilities, then the resulting difference in diffusion rates will create an electric potential, because the faster moving ions of one charge will begin to outpace the ions of the opposite charge.
The resultant electric field is just what is required to speed up the slower moving ions and maintain electro-neutrality.
Notice that magnitude of both the diffusion and membrane potentials is directly proportional to temperature, so geo- thermal activity will enhance these SP anomalies.
(the gas constant is the constant of proportionality that relates the energy scale to the temperature scale)
(the Faraday constant denotes the magnitude of electric charge per mole of electrons)
→ via Nernst-Planck equation
𝐟 𝑖 =− 𝐷 𝑖 𝛻 𝑐 𝑖 + 𝐹 𝑅𝑇 𝑛 𝑖 𝑐 𝑖 𝐄
𝐟 𝑖 : flux density, 𝐷 𝑖 : diffusion coefficient, 𝑖: ionic species and electric field 𝐄.
𝐸 𝑑 =− 𝑅𝑇 𝑛𝐹 𝐼 𝑎 − 𝐼 𝑐 𝐼 𝑎 + 𝐼 𝑐 ln 𝑐 1 𝑐 2
𝐼 𝑎 , 𝐼 𝑐 anion/cation mobilities; 𝑛 electric charge/ion, 𝑅 universal gas constant;
𝑇 is the temperature; 𝐹 is the Faraday constant; 𝐶 1 , 𝐶 2 solution concentrations
Nyquist and Corry, 2002; Telford et al, 1991, pp. 283

14. Self Potential Method Shale Potential (Nernst potential)
when two identical electrodes are immersed in a homogeneous solution but with different concentrations at the electrodes.
Sandstone and Shale, marlimillerphoto.com  
Shale potential develops at the boundary between shale and sandstone because shale is more permeable to Na+ ions than Cl- ions.
The net effect is that voltages recorded adjacent to shale are higher than voltages recorded adjacent to sandstone.
In general, this mechanism can create anomalies in the tens of millivolts, and is just a source of noise in most SP surveys.
𝐸 𝑛 =− 𝑅𝑇 𝑛𝐹 ln 𝑐 1 𝑐 2
(Nernst potential)
In general, Diffusion/Nernst potentials can create anomalies in the tens of millivolts, and is just a source of noise in most SP surveys.
Nyquist and Corry, 2002; Telford et al, 1991, pp. 283

15. Self Potential Method Bioelectric potentials
ion selectivity and water pumping action of plant roots can create SP anomalies.
Bioelectric anomalies can reach hundreds of millivolts.
Abrupt changes in SP have been noted in the field when the vegetation changes (commonly associated with changes in soil composition).
Background/Noise in conventional geophysics, but useful to map electrical potential gradients which governs water and nutrients uptake by plants.
Roots are ion-selective membranes, so it isn’t surprising that they generate SP-anomalies.
Bioelectric anomalies can reach hundreds of millivolts.
Abrupt changes in SP have been noted in the field when the vegetation changes, which are, of course, commonly associated with changes in soil composition or the underlying rocks.
landviser.net
landviser.net
Nyquist and Corry, 2002

16. Self Potential Method Mineral potentials
arise from geochemical oxidation-reduction (redox) reactions, equivalent to a ‘battery’.
Mineral potentials arise above ore bodies and depend on variations in oxidation (redox) potential with depth.
The ground above the water table is more accessible to oxygen than the submersed part, so moisture above the water table contains more oxidised ions than below it.
An electrochemical reaction takes place at the surface between the ore body and the host rock above the water table.
It results in reduction of the oxidised ions in the adjacent solution. An excess of negative ions appears above the water table.
Simultaneously, the submersed part of the ore body reacts with the groundwater producing excess positive ions in the solution.
The ore body acts as a conductor of these excess charges where electrons flow from the deep part to the shallow part.
(Lowrie, 1997, p. 209)
Lowrie, 1997, p. 209

17. Self Potential Method Mineral potentials After Sato & Mooney (1960):
arise from geochemical oxidation-reduction (redox) reactions, equivalent to a ‘battery’.
After Sato & Mooney (1960):
Cathodic reaction above the water table
Chemical reduction  electron gain
Anodic reaction at depth below water table
Chemical oxidation  electron loss
The ore body itself functions only to transport electrons from anode to cathode
SP anomaly associated with ore bodies can be in the order of a few hundreds of millivolts to over 1 V
Sketch of the classical Sato and Mooney geobattery model proposed for ore bodies.
Far from the ore body, the redox potential decreases with depth mainly because of the decrease with depth of the concentration of dissolved oxygen in the pore water.
In the vicinity of the ore body, a redox potential disturbance is created because of the redox reactions at the surface of the ore body.
Typically, a self-potential anomaly associated with an ore body can amount to a few hundreds of millivolts at the ground surface but cannot be higher than the difference of the redox potential between the terminal points (anode and cathode) of the system.
Nyquist and Corry, 2002; Revil & Jardani, 2013, p.72

18. Self Potential Method Mineral potentials ( 𝑬 𝒉 )
arise from geochemical oxidation-reduction (redox) reactions, equivalent to a ‘battery’.
Calculated via the Nernst Potential
Used very successfully in base metal exploration.
Note: the Sato & Mooney (SM) “battery” model cannot fully explain all observed phenomena:
Large amplitudes > 800 mV
(Max SM model ~ 800 mV)
Large measured voltage gradients
(SM model predicts smooth gradients)
Anomalies of ore bodies completely below the water table
Lack of positive pole
Measured data always negative for completely drilled body
Nyquist and Corry, 2002;

19. Self Potential Method Mineral potentials ( 𝑬 𝒉 )
Typical contour map and profile over an ore body producing a large SP anomaly
The negative maximum lies directly over the sulphide mass
Over steep topography, the centre will usually be displaced
Telford et al, 1991, pp. 298

20. Self Potential Method Mineral potentials ( 𝑬 𝒉 )
SP anomaly across a sulfide ore- body at Sariyer, Turkey.
Pyrite & chalcopyrite occur in varying concentrations within a massive deposit, hosted in Andesite and below Devonian schist.
The area shows steep topography, shifting the SP anomaly downhill
Sulphide orebody at Sariyer, Turkey.
An often cited example of a self-potential anomaly over a sulphide ore body is the one given by Yungul (1954) for a complex ore body at Sariyer in Turkey.
Chalcopyrite and pyrite occur in varying concentrations within a massive deposit within andesite and below Devonian schist.
The area is characterised by a steep surface gradient which displaces the SP minimum downhill.
The orebody comprises four regions, of which the one furthest downhill is pyritised and the three remaining zones have decreasing concentrations of copper from 14% on the downhill side to 1–2% on the upslope side.
Each of these zones may be represented by a sphere whose SP anomaly contributes to the total anomaly observed.
(Reynolds, 2011, pp. 363)
Reynolds, 2011, pp. 363

21. Self Potential Method Mineral potentials ( 𝑬 𝒉 )
Each of the various mineralisation zones may be represented by a sphere whose SP anomaly contributes to the total anomaly observed
Reynolds, 2011, pp. 363

22. Self Potential Method 𝐸 𝑠 =− 𝜁𝜀𝜌 4𝜋 𝜂 ∆𝑃
Streaming potentials (electrokinetic or zeta potential)
arise when water or other fluids flow through sand, porous rock, moraines, basalts, etc.
This is observed when a solution of electrical resistivity 𝜌 and viscosity 𝜂 is forced through a capillary or porous medium.
The resultant potential difference between the ends of the passage is
Some potentials have a mechanical origin – when an electrolyte is forced through a narrow pipe, a potential difference (voltage) may arise between the ends of the pipe.
The amplitude depends on the electrical resistivity and the viscosity of the electrolyte as well as the pressure difference that causes the flow.
The voltage arises due to differences in the electrokinetic or streaming potential, which in turn is influenced by the interaction between the liquid and the surface of the solid (zeta potential).
Streaming potentials may be positive or negative and can be observed in conjunction with seepage from dams or groundwater flow through different lithological units.
(Lowrie, 2009, p. 208)
Zeta potential is a value determined by the material of the capillary wall and electrolyte.
Es is in the same direction as the pressure gradient (opposite to the direction of electrolyte flow).
𝜁: adsorption (zeta) potential
∆𝑃: pressure difference
𝜀: solution dielectric constant
𝐸 𝑠 =− 𝜁𝜀𝜌 4𝜋 𝜂 ∆𝑃
In areas of high rainfall, steep topography and porous rock, streaming potentials can be of large amplitude.
E.g. A 2693-mV SP anomaly on Agadak Volcano (Adak Island, Alaska) is attributed to streaming potentials
Telford et al, 1991, pp. 283

23. Self Potential Method Streaming potentials.
C i = ζ i
Streaming potentials.
A vertical boundary with upwelling from the right
Pumping from a well.
Horizontal boundary flow along different interfaces .
Idealised SP profiles and maps of streaming potentials for various models.
Interfaces are marked by a contrast in streaming potential coefficients (zeta potential).
The potentials tend to increase in positiveness with the direction of water flow as the electric charge flows in the opposite direction. Consequently, negative charge flows uphill and can result in large SP anomalies on topographic highs.
A vertical boundary with upwelling on the right
Pumping from a well
Horizontal boundary flow.
Reynolds, pp. 351

24. (geothermal activity)
Self Potential Method
Thermal gradient and SP profiles over the Dome Fault Zone, Roosevelt Hot Springs (Utah) associated with Mineral, Streaming and Diffusion Potentials.
Streaming potentials.
Pos. anomaly
(geothermal activity)
Neg. anomaly
(Alunite & Pyrite)
Correspondence of broad SP anomaly and thermal gradient profile suggest a thermal origin for the SP anomaly.
Roosevelt Hot Springs, Utah, USA
A self-potential profile carried out across the Dome Fault Zone, Roosevelt Hot Springs, Utah(Corwin and Hoover, 1979).
Alunite and pyrite occur in the zone, both of which normally produce negative polarity anomalies that may be evident on the profile within 1 km west of the reference electrode position.
The area within 1 km to the east of the reference electrode has a positive anomaly of about +80 mV, which is thought to be due to the geothermal activity.
Comparison of the thermal gradient profile with the SP transect indicates that the axis of the thermal gradient anomaly is coincident with the position of the reference electrode.
The negative potentials associated with the mineralised areas within the zone may be degrading the anomaly due to the geothermal activity.
The geothermal SP anomaly results from streaming potentials being driven by the convective cells within such a zone, and also from elevated diffusion potentials due to the higher temperatures.
The geothermal SP anomaly results from Streaming Potentials driven by convection cells, but also due to Diffusion Potentials due to temperature gradient.
Arrows denote points at which faults cross the SP survey line.
Reynolds, 2011, pp. 359

25. The Electric Double layer
The Zeta potential is the potential drop across the mobile part of the double layer:
i.e. it is the electric potential in the interfacial double layer (DL) at the location of the slipping plane versus a point in the bulk fluid away from the interface.
The double layer is formed in order to neutralize the charged surface and, in turn, causes an electrokinetic potential between the surface and any point in the mass of the suspending liquid.
This voltage difference is on the order of millivolts and is referred to as the surface potential.
The magnitude of the surface potential is related to the surface charge and the thickness of the double layer.
As we leave the surface, the potential drops off roughly linearly in the Stern layer and then exponentially through the diffuse layer, approaching zero at the imaginary boundary of the double layer.
A charged particle’s movement through this potential field is related to the dielectric constant and viscosity of the suspending liquid and to the electrical potential at the boundary between the moving particle and the liquid. This boundary is called the slip plane.
Charges in the Stern layer are more rigidly attached to the colloid, while in the diffuse layer charges can move.
As a result, the electrical potential at this junction is related to the mobility of the particle and is called the zeta potential. ( (
ζ is positive if the potential increases from the bulk of the liquid phase towards the interface.

26. The Electric Double layer
The 𝜁-potential develops across boundaries between a fluid electrolyte and mineral grains in fractured rock and porous media.
The more negative the 𝜁 -potential the more positive ions are transported with the flow and thus the greater the net transport of negative charge ions.
Aggregation of excess charge on each side of the interface  electrical double layer.
The mobile part of the electrical double layer is dragged along with the fluid-flow  transport of electric charge with the flow.
The amount of charge transported is directly related to the 𝜁 -Potential.
Costar et al., 2008, pp. 15

27. Application: Sinkhole Detection
The self-potential method has been used successfully in the past for mineral exploration, related to the large mineral potential anomalies over sulphide ore bodies.
However, the SP method finds increasing use for example in environmental-geophysics as well as in reservoir monitoring which utilise the streaming potential in the absence of mineral potential anomalies.
Here is an example to qualitatively detect the position of sinkholes because they form vertical preferential pathways for the flow of the ground water so that we can expect a streaming potential anomaly.
A test site was located in Normandy (France) in the Upper Cretaceous chalk karst of the Western Paris basin.
In this region of extensive agricultural areas, sinkholes are frequently clustered in a thick chalk substratum.
The cover of this substratum is composed of Pliocene clay-with-flint and loess materials resulting from the alteration of the chalk substratum
The thickness of this cover ranges between a few meters to ten meters outside sinkholes. It can reach ~15 m over some sinkholes.
The SP survey used non-polarizing electrodes consisting of a bare copper cylinder immersed in a supersaturated copper sulfate solution in a porous ceramic cup.
The distance between two measurement stations was 10 m and 5 m in the outer and central parts of the investigated areas.
A total of 225 measurements were performed over a surface area of m2 .
The self-potentials between the reference station and the scanning electrode were measured with a calibrated Metrix MX-20 voltmeter with a sensitivity of 0.1 mV and an internal impedance of 100 MOhm.
The standard deviation of the self-potential measurements at this specific site was 1 mV. This means a very high signal-to-noise ratio and a high reproducibility of the measurements.
Picture of Sinkhole A1, which has a diameter of 10 meters. The depth of the depression is about 2 m
Revil & Jardani, 2013, p.161

28. Application: Sinkhole Detection
Between the loess and the clay-with-flint covers, a shallow perched aquifer exists above the clay-with-flint formation in spring.
Water flow is predominantly lateral in this upper flow system until a sinkhole is encountered.
Sinkholes act as local vertical pathways through the clay, connecting the shallow upper flow system to the main aquifer located in the chalk formation at a depth of about 30 m.
Revil & Jardani, 2013, p.162

29. Application: Sinkhole Detection
SP Stations (+)
DC Resistivity Survey
Visible Sinkholes
Self-potential map of the test site.
The symbols correspond to the stations where the self-potential was measured
“Ref” indicates the position of the self-potential reference station.
The self-potential data were obtained
in spring during the rainy season and
in summer during the dry season.
W1 and W2 denote two boreholes.
AB is a multi-electrode resistivity profile termed P1.
The self-potential anomalies A1 and A2 are associated with the presence of two sinkholes visible from the ground surface.
They are located on the depression of the clay-with-flint/loess interface.
Anomalies B1, B2 and B3 denote crypto-sinkholes
(Interpreted) “Crypto “Sinkholes
Revil & Jardani, 2013, p.164

30. Application: Sinkhole Detection
SP Contour Map & DC Resistivity Section
Comparison between the self-potential map and the d.c.-electrical resistivity imaging.
Self-potential map. Electrical resistivity tomography along profile P1 (spacing of 3 m, Wenner)
Revil & Jardani, 2013, p.165

31. References
Revil, A., Jardani, A.: “The Self-Potential Method", 2013, Cambridge.
Nyquist, J. E., Corry, E. C., “Self-potential: The ugly duckling of environmental geophysics”, , The Leading Edge, pp. 446.
Jardani, A. et al., “Reconstruction of the Water Table from Self-Potential Data: A Bayesian Approach”, 2008, Ground Water, pp. 213
Telford, W.M, Geldart, L.P., Sheriff, R.E.: “Applied Geophysics”, 1991, Cambridge University Press
Lowrie, W. “Fundamentals of Geophysics”, 1997, Cambridge University Press
Reynolds, J.M., "An Introduction to Applied and Environmental Geophysics", 2011, John Wiley & Sons
Costar A., Heinson G., Wilson T., Smit, Z.,: “Hydrogeophysical mapping of fracture orientation and groundwater flow in the Eastern Mount Lofty Ranges, South Australia”, 2009, DWLBC Report, Gov. South Australia
Fagerlund F., Heinson G., “Detecting subsurface groundwater flow in fractured rock using self-potential (SP) methods”, 2003, Environmental Geology, 43, pp. 782