VẬT lý địa CHẤN geoelectric

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 = R I... In un

•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

Basic Electrical Quantities

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

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

)(

= R 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)

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

areasectional-

cross

*resistance

y resistivit

areasectional-

cross

length

*

y resistivitresistance

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

= Ionic conduction (electronic conduction is due only to electrons – occurs in metals and some ores)

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

n w m

w

n w

m w

t

S

a s

a

φ

ρ φ

ρ

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

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

the potential difference is measured between the ends of

the resistance

•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

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

•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

Refraction of Current Paths

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:

2 2

1

1 tan θ ρ tan θ

ρ =

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

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

•Resistance of “bundle of paths” is proportional to length, but inversely proportional to cross-sectional area

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:

separation is changed and equals the resistivity of the ground

a

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U gradU

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1 1

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π

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1 1

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Wenner Array

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

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

Wenner VES Survey

•Two measuring tapes laid end to

end

•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

Wenner VES Survey

Modeling the Data

•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

Modeling the Data

•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

•Electrode spacing is plotted as a ratio to

the apparent resistivity as a ration to the

different curves labeled by the value of

the ratio of the resistivities

•The master curve and

Modeling the Data

•The apparent resistivity plot

is slid over the master curve

until a match is found

•In this case it would be the

ρ a / ρ 1 = 6.

•The horizontal part of the

curve cuts the y-axis at 1.27,

giving a value of 18.9

•The value for layer 2 is thus

•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 –

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

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)

•The method assumes that layers are horizontal – if they are dipping, are series of VES profiles should be carried out

Other Electrode Arrays

•Schlumberger array:

Only the current

electrodes are moved

Resistivity Profiling

•Resistivity profiling investigates lateral changes

•In VES an array is expanded symmetrically about a single point

•In profiling some or all of the electrodes are moved laterally with fixed spacing

•Targets usually include things like faults, intrusions, or ore veins

•Far to each side of the boundary the resistivity is constant

•The transition becomes complicated as different combinations of the electrodes

are in each rock

•The Wenner array is

particularly complicated, and

varies depending on the

electrode spacing

•The array can also be arranged

broadside to the feature

•In the case of the gradient array

the current electrodes are fixed,

and the potential electrodes

Mise-à-la-Masse Method

•If an ore reserve has be proven in a

borehole, one current electrode can be

put in the borehole in contact with the

ore

•Another current electrode is put on the

surface beyond the extent of the ore

•One potential electrode is fixed on the

surface above the body

•The second potential electrode is

moved around (over the surface an/or

down the borehole)

•The apparent resistivity is measured

and contoured to indicate the extent of

Electrical Imaging

Resistivity may vary both vertically and horizontally, so to create a complete image

of the subsurface arrays have to be expanded and moved laterally

•If the body is very elongated horizontally (veins, faults, layers), a pseudosection can be used

•Repeated profiles along the same traverse crossing the body with a range of electrode separations

•In (a) the electrodes are first moved across the area with a constant separation

• The value of resistivity is plotted between the electrodes at the point of

•The spacing is changed, and the process repeated

•Values are plotted and contoured to create a pseudosection

Electrical Imaging

A common distortion is a small area of low resistivity such as a massive

sulphide giving rise to an inverted V, or ‘pant legs’

A Wenner array can also be used, with the values plotted below the midpoint of the array at a depth equal to the electrode spacing

Electrical Imaging

It is now possible to

convert a pseudosection

into to ‘true’ resistivity

section using tomographic

theory

In the example to the right

the ‘pant legs’ have been

replaced by an oval area

much closer to the size of