Electrical Surveying

•Exploit the differences of various electrical properties of rock and minerals.

•Resistivity method

•Detects horizontal and vertical discontinuities in the electrical properties of the

ground.

•Detects 3-D bodies of anomalous conductivity.

•Hydrogeology and engineering applications for the shallow subsurface.

•Induced Polarization

•Makes use of the capacitive action of the subsurface to located zones where

conductive materials are disseminated within host rock.

•Self Potential

•Uses natural currents generated by electrochemical processes to locate

shallow bodies of anomalous conductivity.

Resistivity

•Resistivity usually depends on the amount of groundwater present, and on the

amount of salts dissolved in it

•Resistivity is often used for mapping the presence of rocks with different

porosities.

•Hydrogeology – aquifers, contaminant transport, saline pollution

•Mineral prospecting

Artificially generated currents are introduced into the ground and the resulting

potential differences are measured at the surface.

Basic Electrical Quantities

Electrical charges flow around a circuit – current flows from positive to negative

From: Mussett & Khan., 2000

Electrical current is measured in amperes (amp) –

the amount of electric charge that passes any point

in the circuit in 1 second.

The current flows due to a potential difference

(Voltage). A 1.5 volt battery produces a potential

difference of 1.5 volts.

For most materials, the current increases in

proportion to the potential difference – double the

potential difference, the current doubles. Ohm’s Law

The amount of current flowing when the potential

difference is 1 volt is called the resistance of the

piece, and is equal to the slope of the graph to the

right

V

= R (Ω )

I

Basic Electrical Quantities

Resistance depends on the material and its shape:

•A wire of copper has less resistance than one of lead with the same

dimensions.

•A long thin wire has greater resistance than a short, fat one of the same

material

•Doubling the length doubles the resistance

•Doubling the area of cross-section halves the resistance (similarly to

water flow).

From: Mussett & Khan., 2000

Resistivity (the quantity investigated by resistivity surveying) characterizes the

material independent of its shape – it is measure in ohm-m (inverse of resistivity is

conductivity)

length

resistance = resistivity *

cross - sectional area

resistivity = resistance *

cross - sectional area

length

From: Mussett & Khan., 2000

From: Kearey et al., 2002

Rock and Mineral Resistivity

Though some very good conductors (low

resistivity) and insulators (high resistivity) do

occur naturally (silver and quartz respectively)

most rocks fall somewhere between, but with a

wide range of resistivites.

Rock and Mineral Resistivity

Most rock forming minerals, i.e. quartz, feldspar, mica, olivine, are good insulators.

Pores and cracks contain groundwater (fairly low resistivity) – resistivity of rock

is therefore a function of porosity and pore saturation.

Water varies from pure (insulator) to salty (good conductor).

Salts dissociate into positive and negative ions – common salt dissociates

into Na+ and Cl- -- these move through the water forming a current

= Ionic conduction (electronic conduction is due only to electrons –

occurs in metals and some ores).

From: Mussett & Khan., 2000

As the resistivity of a rock is largely due to the pore waters, a single rock can

have a large range of resistivites, making lithological identification problematic.

Rock and Mineral Resistivity

•The resistivity of porous, water bearing sediments (formation resistivity, P p) can be

approximated from the porosity (Ф), the water saturation (Sw) and the resistivity of

the pore water (ρw) – Archie’s Law

ρ t = aρ wφ s

−m −n

w

ρw

=a m n

φ Sw

Where a, m, and n are constants determined from field of lab measurements – used

commonly in the hydrocarbon industry.

•Archie’s law does not hold for clay minerals – the fine particles trap a layer of

electrolyte around them – clay has low resistivity.

•Resistivity decreases as temperature rises – needs to be accounted for in borehole

logging.

Electrical Flow in Rocks

From: Mussett & Khan., 2000

Electrical connections are made through electrodes – metal rods pushed a few cm

into the ground

The current does not travel by the most direct route – as a thin layer has the most

resistance, the current instead spreads out, both downwards and sideways, though

there is a concentration near the electrodes.

In uniform ground only about 30% of the current penetrates below a depth equal to

the separation of the electrodes.

Why

4

Electrodes?

•So far we have only used two electrodes. In this case

•This is not done in resistivity surveys because there is a

large and unknown extra resistance between the

electrode and the ground.

•The potential difference is instead measured between

two other two potential electrodes – the voltmeter draws

negligible current, therefore the contact potential

difference is negligible.

•Power supply usually run from batteries.

•Wires have small resistances.

•Applied voltage ~100 volts, current ~mA

•Potential difference typically volts to mV.

•As ions accumulate on the electrodes, they are

dispersed by reversing the current flow a few times a

second.

From: Mussett & Khan., 2000

the potential difference is measured between the ends of

the resistance.

Vertical Electric Sounding

Vertical electric sounding is used when the subsurface approximates to a series of

horizontal layers.

•The electrode array is expanded from a fixed center.

•If the electrode spacing is much less than the thickness of the top layer, nearly

all will remain in that layer.

From: Mussett & Khan., 2000

•As the electrode spacing is expanded beyond the thickness of the top layer, a

significant amount of the current will be flowing through the lower layer.

In a uniform layer the current paths are smooth

The current paths refract towards the normal as they

cross into a rock of higher resistivity, and away when

they cross into a rock of lower resistivity. The angles

are related by:

ρ1 tan θ1 = ρ 2 tan θ 2

From: Mussett & Khan., 2000

As refraction changes the distribution of current in a layered subsurface,

compared to uniform ground, the ratio of the potential difference to the current

changes, making it possible to measure the change of resistivity with depth.

From: Mussett & Khan., 2000

Refraction of Current Paths

Apparent Resistivity

In a VES survey the ratio of current to potential difference changes because:

•Change of resistivity with depth

•Because electrodes are moving further apart

The second effect has to be removed

•As current travels through the ground the current paths diverge from one

current electrode before converging on the other.

From: Mussett & Khan., 2000

•Resistance of “bundle of paths” is proportional to length, but inversely

proportional to cross-sectional area

From: Mussett & Khan., 2000

Apparent Resistivity

•If the current electrode separation is doubled, the cross-sectional area quadruples,

so the resistance halves.

•The ratio of potential difference to current, ΔV/I has to be multiplied by a

geometrical factor that depends on the electrode separation:

ρ a = geometrical factor *

∆V

I

The factor is such that, for a uniform subsurface, ρa remains constant as the

separation is changed and equals the resistivity of the ground

a

ρ

I

j=

2

4πl

j =−

1

ρ

gradU = −

1 δU l

ρ δr l

ρI dl

⇒ dU = −

4π∞ l 2

U (∞ ) − U (l ) = ∫ dU =

l

U (l ) =

Iρ

4πl

Iρ

4πl

UM =

Iρ 1

1

(

−

)

2π AM BM

∆U

ρ =k

I

Iρ 1

1

(

−

)

2π AN BN

Iρ 1

1

1

1

⇒ ∆U =

(

−

−

+

)

2π AM BM AN BN

UN =

K = 2π

1

1

1

1

1

−

−

+

AM

BM

AN

BN

Wenner Array

In a Wenner array, the electrodes are equally spaced (spacing = a).

•Geometrical factor = 2πa, therefore ρa = 2πa ΔV/I

•In uniform ground doubling a halves ΔV/I , with ρa remaining constant.

From: Mussett & Khan., 2000

•If the subsurface is layered, the value of ρa depends on the resistivities of the

layers – the value calculated is the apparent resistivity. As the electrode

separation is expanded ρa changes as more current flows into deeper layers.

Wenner VES Survey

•Four electrodes pushed into the

ground symmetrically about the

junction of the tapes.

•Electrode separation

progressively increased – not

incrementally as the same

increment at a wide spacing

would produce little or no change

in reading – ie 1, 1.5, 2, 3, 4, 6,

8.

•Stopped when current is deep

enough.

From: Mussett & Khan., 2000

•Two measuring tapes laid end to

end.

Wenner VES Survey

•Apparent resistivity is calculated for each spacing, using ρa = 2πa ΔV/I

From: Mussett & Khan., 2000

•Graph is plotted of log10ρ vs log10a.

•The curves are both for two

layer cases – same resistivities

but different thickness upper

layer.

•At small electrode spacing the

current only penetrates the

upper layer. The apparent

resistivity at small spacing is

therefore the resistivity of the

upper layer.

•At the largest spacing the curve flatten – here most of the current is spending most

of its time in the lower layer. Therefore the resistivity of the lower layer

approximates the apparent resistivity at large spacing.

•The fact that the upper layer is thicker in the right-hand plot is apparent from the

longer time spent at low apparent resistivity.

From: Mussett & Khan., 2000

Modeling the Data

Modeling the Data

•Electrode spacing is plotted as a ratio to

the thickness of the top layer, a/h1, and

the apparent resistivity as a ration to the

resistivity if the top layer ρa / ρ1, with

different curves labeled by the value of

the ratio of the resistivities.

•The master curve and

apparent resistivity

curves must be on the

same scale.

From: Mussett & Khan., 2000

•In practice the thickness of the layers

and the resistivities are found by

comparing the actual plot with master

curves calculated for different values of

thickness and resistivity.

Modeling the Data

•The apparent resistivity plot

is slid over the master curve

until a match is found.

•The horizontal part of the

curve cuts the y-axis at 1.27,

giving a value of 18.9 ohmm for layer 1 (ρ1).

•The value for layer 2 is thus

6 * 18.9 = 113 ohm-m (ρ2).

•The thickness of the top

layer is found from where

the a/h1 curve of the master

curve cuts the x –axis on the

apparent resistivity curve –

in this case 0.2 m.

From: Mussett & Khan., 2000

•In this case it would be the

ρa / ρ1 = 6.

Multiple Layers

•The number of layers

can be determined by

the number of changes

from concave to convex,

or vice versa – kinks.

•This is the minimum

number of layers.

•In reality, modeling for

multiple layers is usually

done on a computer,

where a theoretical

master curve can be

compared actual data

and a depth vs.

resistivity curve created.

From: Mussett & Khan., 2000

In the case of multiple layers, the curve never reaches the resistivity of layer 2 as the

current is penetrating into yet deeper layers.

Limitation of VES

•Thin layers, or layers with negligible resistivity contrast are said to be suppressed.

•No hard guidelines on the limits of thickness of a detectable layer – usually

estimated by modeling.

•Anisotropic layers have resistivities that vary perpendicular to lamination (shale).

From: Mussett & Khan., 2000

•The method assumes that layers are horizontal – if they are dipping, are series of

VES profiles should be carried out.

•Ambiguity

•Exploit the differences of various electrical properties of rock and minerals.

•Resistivity method

•Detects horizontal and vertical discontinuities in the electrical properties of the

ground.

•Detects 3-D bodies of anomalous conductivity.

•Hydrogeology and engineering applications for the shallow subsurface.

•Induced Polarization

•Makes use of the capacitive action of the subsurface to located zones where

conductive materials are disseminated within host rock.

•Self Potential

•Uses natural currents generated by electrochemical processes to locate

shallow bodies of anomalous conductivity.

Resistivity

•Resistivity usually depends on the amount of groundwater present, and on the

amount of salts dissolved in it

•Resistivity is often used for mapping the presence of rocks with different

porosities.

•Hydrogeology – aquifers, contaminant transport, saline pollution

•Mineral prospecting

Artificially generated currents are introduced into the ground and the resulting

potential differences are measured at the surface.

Basic Electrical Quantities

Electrical charges flow around a circuit – current flows from positive to negative

From: Mussett & Khan., 2000

Electrical current is measured in amperes (amp) –

the amount of electric charge that passes any point

in the circuit in 1 second.

The current flows due to a potential difference

(Voltage). A 1.5 volt battery produces a potential

difference of 1.5 volts.

For most materials, the current increases in

proportion to the potential difference – double the

potential difference, the current doubles. Ohm’s Law

The amount of current flowing when the potential

difference is 1 volt is called the resistance of the

piece, and is equal to the slope of the graph to the

right

V

= R (Ω )

I

Basic Electrical Quantities

Resistance depends on the material and its shape:

•A wire of copper has less resistance than one of lead with the same

dimensions.

•A long thin wire has greater resistance than a short, fat one of the same

material

•Doubling the length doubles the resistance

•Doubling the area of cross-section halves the resistance (similarly to

water flow).

From: Mussett & Khan., 2000

Resistivity (the quantity investigated by resistivity surveying) characterizes the

material independent of its shape – it is measure in ohm-m (inverse of resistivity is

conductivity)

length

resistance = resistivity *

cross - sectional area

resistivity = resistance *

cross - sectional area

length

From: Mussett & Khan., 2000

From: Kearey et al., 2002

Rock and Mineral Resistivity

Though some very good conductors (low

resistivity) and insulators (high resistivity) do

occur naturally (silver and quartz respectively)

most rocks fall somewhere between, but with a

wide range of resistivites.

Rock and Mineral Resistivity

Most rock forming minerals, i.e. quartz, feldspar, mica, olivine, are good insulators.

Pores and cracks contain groundwater (fairly low resistivity) – resistivity of rock

is therefore a function of porosity and pore saturation.

Water varies from pure (insulator) to salty (good conductor).

Salts dissociate into positive and negative ions – common salt dissociates

into Na+ and Cl- -- these move through the water forming a current

= Ionic conduction (electronic conduction is due only to electrons –

occurs in metals and some ores).

From: Mussett & Khan., 2000

As the resistivity of a rock is largely due to the pore waters, a single rock can

have a large range of resistivites, making lithological identification problematic.

Rock and Mineral Resistivity

•The resistivity of porous, water bearing sediments (formation resistivity, P p) can be

approximated from the porosity (Ф), the water saturation (Sw) and the resistivity of

the pore water (ρw) – Archie’s Law

ρ t = aρ wφ s

−m −n

w

ρw

=a m n

φ Sw

Where a, m, and n are constants determined from field of lab measurements – used

commonly in the hydrocarbon industry.

•Archie’s law does not hold for clay minerals – the fine particles trap a layer of

electrolyte around them – clay has low resistivity.

•Resistivity decreases as temperature rises – needs to be accounted for in borehole

logging.

Electrical Flow in Rocks

From: Mussett & Khan., 2000

Electrical connections are made through electrodes – metal rods pushed a few cm

into the ground

The current does not travel by the most direct route – as a thin layer has the most

resistance, the current instead spreads out, both downwards and sideways, though

there is a concentration near the electrodes.

In uniform ground only about 30% of the current penetrates below a depth equal to

the separation of the electrodes.

Why

4

Electrodes?

•So far we have only used two electrodes. In this case

•This is not done in resistivity surveys because there is a

large and unknown extra resistance between the

electrode and the ground.

•The potential difference is instead measured between

two other two potential electrodes – the voltmeter draws

negligible current, therefore the contact potential

difference is negligible.

•Power supply usually run from batteries.

•Wires have small resistances.

•Applied voltage ~100 volts, current ~mA

•Potential difference typically volts to mV.

•As ions accumulate on the electrodes, they are

dispersed by reversing the current flow a few times a

second.

From: Mussett & Khan., 2000

the potential difference is measured between the ends of

the resistance.

Vertical Electric Sounding

Vertical electric sounding is used when the subsurface approximates to a series of

horizontal layers.

•The electrode array is expanded from a fixed center.

•If the electrode spacing is much less than the thickness of the top layer, nearly

all will remain in that layer.

From: Mussett & Khan., 2000

•As the electrode spacing is expanded beyond the thickness of the top layer, a

significant amount of the current will be flowing through the lower layer.

In a uniform layer the current paths are smooth

The current paths refract towards the normal as they

cross into a rock of higher resistivity, and away when

they cross into a rock of lower resistivity. The angles

are related by:

ρ1 tan θ1 = ρ 2 tan θ 2

From: Mussett & Khan., 2000

As refraction changes the distribution of current in a layered subsurface,

compared to uniform ground, the ratio of the potential difference to the current

changes, making it possible to measure the change of resistivity with depth.

From: Mussett & Khan., 2000

Refraction of Current Paths

Apparent Resistivity

In a VES survey the ratio of current to potential difference changes because:

•Change of resistivity with depth

•Because electrodes are moving further apart

The second effect has to be removed

•As current travels through the ground the current paths diverge from one

current electrode before converging on the other.

From: Mussett & Khan., 2000

•Resistance of “bundle of paths” is proportional to length, but inversely

proportional to cross-sectional area

From: Mussett & Khan., 2000

Apparent Resistivity

•If the current electrode separation is doubled, the cross-sectional area quadruples,

so the resistance halves.

•The ratio of potential difference to current, ΔV/I has to be multiplied by a

geometrical factor that depends on the electrode separation:

ρ a = geometrical factor *

∆V

I

The factor is such that, for a uniform subsurface, ρa remains constant as the

separation is changed and equals the resistivity of the ground

a

ρ

I

j=

2

4πl

j =−

1

ρ

gradU = −

1 δU l

ρ δr l

ρI dl

⇒ dU = −

4π∞ l 2

U (∞ ) − U (l ) = ∫ dU =

l

U (l ) =

Iρ

4πl

Iρ

4πl

UM =

Iρ 1

1

(

−

)

2π AM BM

∆U

ρ =k

I

Iρ 1

1

(

−

)

2π AN BN

Iρ 1

1

1

1

⇒ ∆U =

(

−

−

+

)

2π AM BM AN BN

UN =

K = 2π

1

1

1

1

1

−

−

+

AM

BM

AN

BN

Wenner Array

In a Wenner array, the electrodes are equally spaced (spacing = a).

•Geometrical factor = 2πa, therefore ρa = 2πa ΔV/I

•In uniform ground doubling a halves ΔV/I , with ρa remaining constant.

From: Mussett & Khan., 2000

•If the subsurface is layered, the value of ρa depends on the resistivities of the

layers – the value calculated is the apparent resistivity. As the electrode

separation is expanded ρa changes as more current flows into deeper layers.

Wenner VES Survey

•Four electrodes pushed into the

ground symmetrically about the

junction of the tapes.

•Electrode separation

progressively increased – not

incrementally as the same

increment at a wide spacing

would produce little or no change

in reading – ie 1, 1.5, 2, 3, 4, 6,

8.

•Stopped when current is deep

enough.

From: Mussett & Khan., 2000

•Two measuring tapes laid end to

end.

Wenner VES Survey

•Apparent resistivity is calculated for each spacing, using ρa = 2πa ΔV/I

From: Mussett & Khan., 2000

•Graph is plotted of log10ρ vs log10a.

•The curves are both for two

layer cases – same resistivities

but different thickness upper

layer.

•At small electrode spacing the

current only penetrates the

upper layer. The apparent

resistivity at small spacing is

therefore the resistivity of the

upper layer.

•At the largest spacing the curve flatten – here most of the current is spending most

of its time in the lower layer. Therefore the resistivity of the lower layer

approximates the apparent resistivity at large spacing.

•The fact that the upper layer is thicker in the right-hand plot is apparent from the

longer time spent at low apparent resistivity.

From: Mussett & Khan., 2000

Modeling the Data

Modeling the Data

•Electrode spacing is plotted as a ratio to

the thickness of the top layer, a/h1, and

the apparent resistivity as a ration to the

resistivity if the top layer ρa / ρ1, with

different curves labeled by the value of

the ratio of the resistivities.

•The master curve and

apparent resistivity

curves must be on the

same scale.

From: Mussett & Khan., 2000

•In practice the thickness of the layers

and the resistivities are found by

comparing the actual plot with master

curves calculated for different values of

thickness and resistivity.

Modeling the Data

•The apparent resistivity plot

is slid over the master curve

until a match is found.

•The horizontal part of the

curve cuts the y-axis at 1.27,

giving a value of 18.9 ohmm for layer 1 (ρ1).

•The value for layer 2 is thus

6 * 18.9 = 113 ohm-m (ρ2).

•The thickness of the top

layer is found from where

the a/h1 curve of the master

curve cuts the x –axis on the

apparent resistivity curve –

in this case 0.2 m.

From: Mussett & Khan., 2000

•In this case it would be the

ρa / ρ1 = 6.

Multiple Layers

•The number of layers

can be determined by

the number of changes

from concave to convex,

or vice versa – kinks.

•This is the minimum

number of layers.

•In reality, modeling for

multiple layers is usually

done on a computer,

where a theoretical

master curve can be

compared actual data

and a depth vs.

resistivity curve created.

From: Mussett & Khan., 2000

In the case of multiple layers, the curve never reaches the resistivity of layer 2 as the

current is penetrating into yet deeper layers.

Limitation of VES

•Thin layers, or layers with negligible resistivity contrast are said to be suppressed.

•No hard guidelines on the limits of thickness of a detectable layer – usually

estimated by modeling.

•Anisotropic layers have resistivities that vary perpendicular to lamination (shale).

From: Mussett & Khan., 2000

•The method assumes that layers are horizontal – if they are dipping, are series of

VES profiles should be carried out.

•Ambiguity

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