1. The Induced Polarisation (IP) Method
ERTH2020 Introduction to Geophysics
The Induced Polarisation (IP) Method

2. “equivalent circuits”
Induced Polarisation
“equivalent circuits” C + - I R
Induced Polarisation
resistance
“capacitance ”
(charge / voltage) I
𝑹= 𝑼 𝑰 + -
DC Resistivity
completely described by Ohm’s law
In the previous lectures we saw that the subsurface reacts as a giant resistor when energised by a steady state-current and the bulk resistance could be described with Ohm’s law.
However when a current is injected into the ground it also acts as a capacitor (or actually a battery), which stores electrical charge. The two phenomena can be depicted in an equivalent circuit as shown here on the right, where R is the earth resistance and C describes the capacitance. Upon turning off the (polarising) DC-current, the ground gradually discharged and returns to equilibrium which is the observed IP effect.
Note that this simple RC circuit is an approximation only and does not fully describe the electrochemical phenomena, but it is useful as a “mental picture”.

3. Induced Polarisation Three main causes
Electrochemical processes at the interface of metallic minerals / pore fluid:  presence of ore deposits.
Exchange reactions in clay and shaly sands:  hydrogeological applications.
Reactions involving organic materials:  hydrocarbon exploration.
IP - Main Applications:
disseminated metallic ores
porphyry coppers,
bedded lead/zinc
sulphide-related gold deposits
environmental related studies
geothermal exploration
Veeken et al., 2009 ; Reynolds, 2011

4. Induced Polarisation
The earliest observation (~1913) of the induced polarization phenomenon associated with sulphide mineralization is attributed to Conrad Schlumberger who observed that if he passed a DC current through rocks containing metallic sulphides and interrupted the current abruptly, the resultant voltages in the Earth decayed slowly rather than instantly.
Today IP is the primary tool used to explore for several important types of mineral deposits—especially porphyry coppers, bedded lead/zinc and sulphide-related gold deposits.
IP is unique among the controlled-source geophysical methods employed in mineral exploration in that it is based on an interface electrochemical phenomenon, rather than on a purely physical property of rocks or minerals.
Seigel et al, 2007

5. Induced Polarisation Seigel et al, 2007
San Manuel porphyry copper deposit, under 330 m of Gila conglomerate.
One of the first IP surveys in the US by Seigel during his PhD study (1948).
Seigel et al, 2007

6. Induced Polarisation
DC & IP over polymetallic deposit in the Altai region (USSR) in the late 1960s
(Schlumberger array with AB = 1200 m and MN = 20 m ).
The results of dual time-domain and frequency-domain IP and resistivity traverses over a known polymetallic deposit in the Altai region (USSR) in the late 1960s. The deposit lies in volcanics and comes within about 30 m of the ground surface. These traverses employed the Schlumberger array with AB = 1200 m and MN = 20 m. For each measurement, charging current flowed for two minutes and the residual transient after 0.5 s was measured. Dual time-domain profiles of apparent polarizability (nk) are shown, for different polarities of the charging current flow. The small differences in nk for the different current polarities are attributed to nonlinear effects. Also shown are the results of the corresponding frequency-domain profile. The IP parameter measured was the phase shift of the measured voltage, using a frequency of 2.44 Hz. The deposit does show as a minor resistivity depression, but is much more clearly indicated by its IP response, both in the time and frequency domains (after Komarov, 1980).
Charging current was 2 minutes and the integration time was 0.5 s. [...] The deposit does show as a minor resistivity depression, but is much more clearly indicated by its IP response, both in the time and frequency domains.
Seigel et al, 2007

7. Principally with the same equipment as Resistivity Measurements:
Induced Polarisation
Principally with the same equipment as Resistivity Measurements: C1 C2 P1 P2
IP measurement principally use the same equipment as the DC resistivity method.
What is observed in IP is that the voltage, which is measured at the potential electrodes, does not immediately drops to zero when the current is switched off.
This means that there is some effect in the ground that stored the energy and then releases that energy after the current is switched off, i.e. there is some kind of capacitor.
In DC resistivity measurements we inject the current and while the current is flowing it builds up a potential field which is measured as a voltage.
In IP the measurement takes place after the current is switched off and we are interested in the decay of the electrical potential, measured as a time-varying (decaying) voltage.

8. Induced Polarisation DC resistivity
direct electrical connection (electrodes)
flow of current
electrical potential in the ground C1 C2 P1 P2
IP methods
direct electrical connection (electrodes)
flow of current switched off
decay of electrical potential
IP measurement principally use the same equipment as the DC resistivity method.
What is observed in IP is that the voltage, which is measured at the potential electrodes, does not immediately drops to zero when the current is switched off.
This means that there is some effect in the ground that stored the energy and then releases that energy after the current is switched off, i.e. there is some kind of capacitor.
In DC resistivity measurements we inject the current and while the current is flowing it builds up a potential field which is measured as a voltage.
In IP the measurement takes place after the current is switched off and we are interested in the decay of the electrical potential, measured as a time-varying (decaying) voltage.

9. Small IP surveys often use porous-pot type electrodes
Induced Polarisation
Reconnaissance or deep IP surveys often use large current electrodes buried in deep, saline-filled holes (Hence the benefit of electrode arrays where the current electrodes do not need to be moved for each reading).
Small IP surveys often use porous-pot type electrodes
Traditionally, special kinds of electrodes were used, so-called porous pot electrodes.
If one were to use metal stakes as SP electrodes, electrochemical contact-potentials would build up at the ground contacts which results in high noise levels.
Therefore non-polarising electrodes are used. These consist of a metal immersed in a saturated solution of its own salt (e.g. Cu in CuSO4) which is contained in a porous pot that allows the solution to leak slowly and make contact with the ground.
(Telford, 1990)

10. Induced Polarisation
We see here some equipment that is used for DC resistivity and IP measurements.
As you can see the receivers and layout resemble those used in seismic.
This kind of equipment is relatively new – measurements are computer controlled and the right pairs of electrodes are automatically selected over the course of measurements.
IP measurements also commonly employ a separate generator as a large current is required to observe the IP effect of buried structures.

11. Induced Polarisation
IP surveys usually use a separate transmitter and receiver
Power requirements are higher than for DC res. surveys
Cables and electrodes must be watched. If a passer-by or animal touched the current electrodes during data acquisition, this could be fatal
We see here some equipment that is used for DC resistivity and IP measurements.
As you can see the receivers and layout resemble those used in seismic.
This kind of equipment is relatively new – measurements are computer controlled and the right pairs of electrodes are automatically selected over the course of measurements.
IP measurements also commonly employ a separate generator as a large current is required to observe the IP effect of buried structures.

12. IP Effect IP-Effect: (below 1kHz or greater than 1 ms)
If a DC current injected into the ground is abruptly switched off, the voltage measured at the potential electrodes does not immediately drop to zero! C1 C2 P1 P2
IP measurement principally use the same equipment as the DC resistivity method.
What is observed in IP is that the voltage, which is measured at the potential electrodes, does not immediately drops to zero when the current is switched off.
This means that there is some effect in the ground that stored the energy and then releases that energy after the current is switched off, i.e. there is some kind of capacitor.
In DC resistivity measurements we inject the current and while the current is flowing it builds up a potential field which is measured as a voltage.
In IP the measurement takes place after the current is switched off and we are interested in the decay of the electrical potential, measured as a time-varying (decaying) voltage.

13. IP Effect Vp Vs IP effect Steady state voltage: Residual voltage:
charge time Vp
Steady state voltage:
(primary voltage)
IP effect Vs
Residual voltage:
(secondary voltage)
The observed IP effect is shown in this figure – a voltage is generated upon injecting a DC current in the subsurface.
The voltage reaches a maximum, Vp, after a certain time, the charge time.
When the current is turned off it can be observed that the voltage decays over a period of time to zero, the residual voltage, Vs, is due to the IP effect.

14. IP Effect
Voltage shows a large initial decrease, then decays slowly over a timescale of seconds (minutes). This is the IP effect
The rate of decay depends on the electrical properties of the ground and the presence of metallic minerals
The decay voltage is the result of storage of energy by the ground during the period when the DC current is on
The effect cannot be explained in terms of the atomic or molecular structure of the material, but depend on the macro- structure.
The observed IP effect is shown in this figure – a voltage is generated upon injecting a DC current in the subsurface.
The voltage reaches a maximum, Vp, after a certain time, the charge time.
When the current is turned off it can be observed that the voltage decays over a period of time to zero, the residual voltage, Vs, is due to the IP effect.

15. IP Effect – Sources
Chemical energy is the main source of the IP effect which is stored by subsurface structures in two main ways:
Electrode polarisation (overvoltage) (~below 1kHz)
Related to the transition between electrolytic and electronic conduction at the interfaces between pore fluids and metallic minerals in the rock
Larger than the normal IP effect
Requires presence of metallic minerals (or graphite)
Membrane polarisation (electrolytic) (~below 1Hz)
Due to variations in the mobility of ions contained within pore fluids
Called the “normal” IP effect
May occur in rocks which contain no metallic minerals

16. IP Effect – Electrode Polarisation
Electrode (or grain) polarisation
same process as self-potential.
Metal electrode in an ionic solution:
No voltage applied:
charges with different polarities separate
potential difference between electrode and solution.
With voltage applied:
currents start flowing
change in potential difference
Voltage turned off:
ions diffuse back to equilibrium
The total magnitude of the potential is the Nernst potential and the adsorbed layer gives rise to the Zeta potential
Reynolds, 2011, p.374

17. IP Effect – Electrode Polarisation
Electrolytic conduction only (no IP)
Electrolytic and electronic conduction
Electrode polarisation occurs when electricity is conducted partly electrolytically and partly electronically
When metallic mineral grains block the pore spaces in a rock, an electrochemical barrier must be overcome in order for current to flow across the grain surfaces
Ions accumulate at grain surfaces and the grains become Polarised
When the current flow is interrupted, ions return to their equilibrium positions  voltage decay
Electrode polarisation occurs when electricity is conducted partly electrolytically and partly electronically
The upper figure shows electrolytic conduction only – there is no IP effect.
The lower figure shows a combination of electrolytic and electronic conduction when a metallic mineral grain blocks the pore space.
In this case a chemical reaction takes place at the interface between mineral and solution – an electron exchange takes place between the metal and the solution ions at the interface (overvoltage)
Electrode polarisation takes place in almost all sulphides and also some oxides such as magnetite and – unfortunately – also graphite.

18. IP Effect – Membrane Polarisation
Many minerals (e.g. clays) have a net -ve charge at the interface between mineral surface and pore fluid
+ve ions are attracted to the surface and -ve ions repelled
Build-up of a layer (“cationic cloud”) of +ve ion concn which may extend 1 mm into the pore fluid
(Equilibrium: No applied electrical field)

19. IP Effect – Membrane Polarisation
( Applied electrical field)
Zone of +ve ion concn may extend 1 mm into pore fluid: if the pore has diameter < 1 mm, then, when a voltage is applied, -ve ions will accumulate on one side of the pore and leave the other
When the voltage is removed, the ions return to their equilibrium positions  voltage decay
Membrane polarisation is largest when a rock contains clay materials scattered through the matrix in small (~10%) concentrations and in which the electrolyte has some salinity

20. IP Effect – Electrode Polarisation
IP effect depends on grain size
Large sulphide grain → large amount of current through it, but small surface/volume ratio
IP however is a function of the amount of grain surface exposed to the electrolytic solution
Therefor, as the grain size is reduced, the IP effect increases
However for very small grain sizes, the surface resistance is too large
greatest IP effect for intermediate values of sulphide grain sizes
IP observed in mixtures of pyrite and quartz sand for various pyrite grain sizes
(Keller and Frischknecht, 1966)

21. IP Effect – Sources
In practice, it is not possible to distinguish between membrane and electrode polarisations on the basis of geophysical IP measurements
Membrane polarisation may give rise to a “background” IP effect equivalent to 0.1% - 10% conductive minerals (typically 1% - 2%)
IP is a bulk effect: it does not depend on atomic-scale rock or mineral properties

22. IP Effect – Sources
(P. Kearey et al., 2007)
Chargeability
Apparent resistivity
Time-domain IP profile using a pole–dipole array over the Gortdrum copper–silver body in Ireland
Electrode polarisation depends strongly on the surface area
The IP method is more sensitive to disseminated conductors than to massive ones
This sets the IP method apart from the DC resistivity and EM (electromagnetic) methods, which typically give a weak response over a disseminated target
So electrode polarisation is the dominant effect and it depends strongly on the total surface area.
That means that IP is more sensitive to disseminated material containing mineralisation than to massive ones.
This is a very attractive feature of the method.
The figure shows an example of the resistivity and IP measurement over the Gortdrum copper-silver deposit in Ireland.
Although the deposit is of low grade, containing less than 2% conducting minerals, the chargeability anomaly is well defined and centred over the ore body.
In contrast, the corresponding apparent resistivity profile reflects the large resistivity contrast between the Old Red Sandstone and dolomitic limestone but gives no indication of the presence of the mineralization.

23. Time-Domain IP Measurements
IP measurements can be made in either the time-domain or frequency-domain (frequency-domain IP won’t be covered today)
An advantage of time-domain systems is that measurements can be made over several transmitter cycles and then averaged (or stacked). This process reduces the effect of random noise.
Current and potential electrodes are arranged as for a normal DC resistivity survey
In time-domain (TD) systems, the transmitter current is abruptly switched off, and the decaying voltage due to the IP effect is measured at a series of delay times

24. Time-Domain IP Measurements
Typical transmitted and received waveforms in time-domain
Charging
time
Off-time
In time-domain IP a square waveform is usually employed for injection of a DC-current.
It consists of a fixed sequence of current-on and –off times and the polarity of the current is changed upon each sequence.
The measured voltages resembles the input current waveform. However the potential field in the subsurface is not setup instantaneously so that there is a small delay in the received signal before the voltage reaches a maximum. This is when DC resistivity is measured.
Upon turning off the transmitter current, the voltages don’t decay to zero immediately which is due to the IP effect.

25. Time-Domain IP Measurements
Effect of chargeable ground
University of British Columbia (UBC-GIF)
In time-domain IP a square waveform is usually employed for injection of a DC-current.
It consists of a fixed sequence of current-on and –off times and the polarity of the current is changed upon each sequence.
The measured voltages resembles the input current waveform. However the potential field in the subsurface is not setup instantaneously so that there is a small delay in the received signal before the voltage reaches a maximum. This is when DC resistivity is measured.
Upon turning off the transmitter current, the voltages don’t decay to zero immediately which is due to the IP effect.

26. Time-Domain IP Measurements
In time-domain IP, the main parameters used to present and interpret data are apparent resistivity (ra) and chargeability (m)
m is a macroscopic physical parameter which represents all of the microscopic phenomena.
The apparent resistivity is calculated as for DC resistivity using the voltage measured before the transmitter is switched off (denoted Vp) 𝜌 𝑎 =𝐾 𝑉 𝑃 𝐼
The measured Vp for a short charging time will be less than that measured for a long charging time - this means that ra calculated for a high frequency Tx waveform will be less than that for a low frequency Tx waveform (the frequency-domain IP effect)
K = geometric factor
(depends on electrode array)
VP depends on the “charging time”

27. Time-Domain IP – Chargeability
The ratio Vs/Vp is called the chargeability (Units: millivolts per volt)
In practice it is impossible to measure Vs (the voltage at current switch-off)
Instead, after an initial delay (500 msec), the decay voltage is measured at a series of (typically four) delay times.
Measured voltages are then used to approximate the area under the decay curve

28. Time-Domain IP – Apparent Chargeability
The apparent chargeability, ma, is defined by
where tn is the time corresponding to the last voltage measurement (on the previous slide, n = 4) and V(t) is the decay voltage at time t
The apparent chargeability is the area under (part of) the voltage decay curve, divided by the “primary” voltage Vp
In practice, the units are milliseconds (ms)
The apparent chargeability depends on the actual values of t1 and tn, and may be different for different field instruments
(Units: milliseconds)

29. Time-Domain IP – Apparent Chargeability
Apparent chargeability also depends on the charging time
(long charging times give larger decay voltages)
A highly polarisable earth will give rise to a longer IP decay and hence a large chargeability
Because of the practical considerations outlined, the apparent chargeability isn’t equal to the actual chargeability of the ground, even in the case of a uniformly polarisable earth.
Note that the DC resistivity measurement made in the course of an IP survey is useful data. Chargeability is usually interpreted together with the resistivity data.

30. 1% Volume concentration
Chargeabilities of rocks
mineral
m (ms)
material
1% Volume concentration
Charging time 3 seconds
Integration 1 second
Charging time 1 minute
Integration 1 minute
Charging time 3 seconds
Integration 0.02 to 1 second
(from Telford et al., 1990)

31. Electrode arrays: Gradient
Any of the common DC resistivity electrode arrays may be used for IP surveys - the two most commonly used are the dipole-dipole and gradient arrays.
For mineral exploration, the gradient array is similar to the Schlumberger array, except that the potential electrodes do not have to be kept in-line with the current electrodes
Plan View
A,B current electrodes (fixed)
M,N potential electrodes (roving)
Because the current electrodes are not moved, the gradient array is useful for reconnaissance surveying of relatively large areas

32. Electrode arrays: Dipole-dipole
With the dipole-dipole array, measurements of apparent resistivity and apparent chargeability are made at several “n-spacings” for each current electrode setup
n = 1, 2, 3, etc.

33. Rocky’s Reward, WA (NiS), 1986, dipole-dipole
2D electrical imaging surveys
Dipole-dipole IP data are commonly displayed as separate pseudosections of apparent resistivity and apparent chargeability
15 ohm-m
24 msec (n=4)
n-spacing
Rocky’s Reward, WA (NiS), 1986, dipole-dipole
(Mutton and Williams, 1994)

34. 2D electrical imaging surveys
Combine vertical (sounding) and lateral (profiling) survey method
This provides a 2D geoelectrical model of the subsurface:
vertical and horizontal changes in electrical properties
assumption: no changes perpendicular to survey line
Typical 1D sounding surveys involve 10 – 20 readings
Typical 2D imaging surveys involve 100 – 1000 readings
In comparison, 3D would involve several 1000’s of readings

35. 2D electrical imaging surveys
Pseudosections are a convenient means of plotting data acquired using a variety of current and potential electrode separations in a single plot
They do not represent true cross-sections of ra and ma, except in the sense that the depth of penetration increases as the “n- spacing” increases
As a rough rule-of-thumb, the depth of investigation is ( na / 2 ) for the dipole-dipole array
Although pseudosections are useful for displaying data and for assessing data quality, the resistivity and chargeability pseudosections do not provide a realistic portrayal of the true subsurface distributions of these parameters

36. Dipole-Dipole – combine Sounding and Profiling
2D electrical imaging surveys
Dipole-Dipole – combine Sounding and Profiling
45°
Data acquisition proceeds by combining Depth Sounding and Lateral Profiling to obtain data from a 2D section of the subsurface.
The horizontal location of a data point is at the mid-point of a set of electrodes used.
The vertical position (pseudo-depth) of a data point is at a depth proportional to the electrode spacings.

37. 2D electrical imaging surveys
Horizontal location of data point at mid-point of set of electrodes used
Vertical position (pseudo-depth) of data point at a depth proportional to electrode spacings
The measured parameter is plotted at the intersection of 45° lines extending from the mid-points of the transmitter and receiver pairs
Note that this is a convention only and does not constitute the depth of investigation

38. Centenary gold deposit, WA (disc. 1996)
2D electrical imaging surveys
The Centenary gold deposit is a concealed ore body located 110 km north of Leonora, Western Australia
The ore body is associated with sulphides and is hosted in the magnetic portion of the Mount Pickering Dolerite.
Due to its sulphidic nature, both gravity and induced polarization (IP) were trialled soon after discovery.
A dipole–dipole IP and resistivity survey detected a significant chargeability anomaly over Centenary.
Centenary gold deposit, WA (disc. 1996)
survey line
ore body
drill holes
high chargeability (ore body)
conductive overburden
low resistivity (ore body)
Pittard and Bourne, Exploration Geophysics, 2007, 38, 200–207

39. Centenary gold deposit, WA (disc. 1996)
2D electrical imaging surveys
Centenary gold deposit, WA (disc. 1996)
Example electrode polarisation
survey line
ore body
drill holes
high chargeability (ore body)
conductive overburden
low resistivity (ore body)
Pittard and Bourne, Exploration Geophysics, 2007, 38, 200–207

40. IP Data Interpretation
The most common method of interpretation of IP data is via automatic two-dimensional inversion
Inversion of IP data results in cross-sections of resistivity and chargeability vs depth, which are similar to geological cross sections
Inversion of the data is performed in “real time” by some instruments, and inverted sections are now a standard product delivered by geophysical contractors
NB Remember resolution, suppression of features and model equivalence apply to any best-fit geophysical model, so be prepared to supply the relevant modelling information (or ask your contractor to do so)

41. IP Data Interpretation
Example electrode polarisation
The Century deposit, approximately 250 km north-northwest of Mt. Isa in northwest Queensland, Australia, is hosted by relatively flat-lying middle Proterozoic siltstone and shale units. Mineralization occurs preferentially within black shale units as fine-grained sphalerite and galena with minor pyrite.
The recovered model after inversion shows the superposed geologic section. The inversion nicely delineates the resistive overburden of limestones on the right.
The resistivity at depth is not correlated with mineralization, however.
2D inversion
observed data

42. IP Data Interpretation
Example electrode polarisation
2D inversion
observed data

43. IP Data Interpretation
Example membrane polarisation
Induced-polarization detection and mapping of contaminant plumes
monitoring wells
survey line
EDB (0.02)
EDB (10)
EDB (100)
2D time-domain IP & DC Resistivity mapping of a contaminant plume at the Massachusetts Military Reservation.
The plume consists of approximately m3 of fuel that erupted from a broken underground pipeline in the early 1970s.
Benzene and ethylene dibromide (EDB) are the primary contaminants exceeding the allowed maximum concentration levels.
Plan view of the plume site, indicating existing wells; geologic section line CC', IP survey line, as well as the ethylene dibromide (EDB) concentration plot
Sogade et al, 2006

44. Geological Cross-Section
IP Data Interpretation
Example membrane polarisation
EDB (0.02)
EDB (10)
EDB (100)
Geological Cross-Section
Sogade et al, 2006

45. Dipole-dipole pseudosection, electrode separation a = 24.38
IP Data Interpretation
Example membrane polarisation
EDB (100)
Dipole-dipole pseudosection, electrode separation a = 24.38
Extrapolated plume concentration data for benzene and EDB based on ground-monitoring wells
Sogade et al, 2006

46. Chargeability Anomalies (Contaminants ?)
IP Data Interpretation
Example membrane polarisation
Conductive zone ~1000 𝛺∙𝑚 (Groundwater?)
Conductive zone ~300 𝛺∙𝑚 (Clays?)
Log Resistivity (𝛺∙𝑚)
EDB (100)
2D resistivity Section
Chargeability Anomalies (Contaminants ?)
Chargeability (mV/V)
EDB (100)
2D IP Section
Sogade et al, 2006

47. Summary
The IP effect, voltage decay after switching off a DC voltage and membrane polarisation and electrode polarisation mechanisms a sources of this effect.
Time-domain IP measurements, Tx and Rx waveforms
Determination of apparent chargeability
Display of IP data, pseudosections and depth of investigation
Inversion and interpretation of resistivity and chargeability results

48. References
Veeken P.C.H., Legeydo P.J., Davidenko Y.A, Kudryavceva E.O, Ivanov S.A., Chuvaev A.: “Case History: Benefits of the induced polarization geoelectric method to hydrocarbon exploration”, 2009, Geophysics, V74, p. B47–B59
Telford, W.M, Geldart, L.P., Sheriff, R.E.: “Applied Geophysics”, 1991, Cambridge University Press
Reynolds, J.M., "An Introduction to Applied and Environmental Geophysics", 2011, John Wiley & Sons
Seigel H., Nabighian M., Parasnis D., Vozoff K., “The early history of the induced polarization method”, March 2007, The Leading Edge, pp. 312
Sogade, J.A, Scira-Scappuzzo F., Vichabian Y., “Induced-polarization detection and mapping of contaminant plumes”, 2006, Geophysics, V71, p. B75–B84

49. Supplementary slides

50. IP Data Interpretation
Assumption: the ultimate effect of chargeability is to alter the effective conductivity (resistivity) when current is applied (Seigel, 1959).
This assumption permits the IP responses to be numerically modelled by carrying out two forward modellings using a DC resistivity algorithm
measured potential in the absence of chargeability effects
the apparent chargeability can be computed by carrying out two DC resistivity forward modellings with conductivities 𝜎 1−𝜂 and 𝜎
potential including chargeability effects
D.W. Oldenburg and Y. Li, 1994, "Inversion of induced polarization data", Geophysics, 59, P

51. IP Data Interpretation
DC / IP data are gathered together
Invert potentials for conductivity (background) model
Use 𝜎-model for forward mapping of chargeability
Invert for chargeability models DC IP
Least-Squares Inversion