archeo2007 electrical surveying resistivity a

8/18/2019 Archeo2007 Electrical Surveying Resistivity A

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Electrical Surveying (part A)

Dr. Laurent Marescot

Contact:[email protected]


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Introduction

Electrical surveying…

• Resistivity method

• Induced polarization method (IP)• Self-potential (SP) method

Higher frequency methods (electromagnetic surveys):

• Electromagnetic induction methods

• Ground penetrating radar (GPR)


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Resistivity method

The resistivity method is used in the study of horizontal

and vertical discontinuities in the electrical properties

(resistivity) of the subsurface


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Structure of the lecture

• Resistivity of rocks

• Equations in resistivity surveying

• Survey strategies and interpretation

• Conclusions


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1. Resistivity of rocks


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Resistivity and units

L R

A

A R L

δ δ ρ

δ

δ ρ δ δ

=

=

• ρ resistivity in ohm.m (Ωm)• σ =1/ ρ conductivity in Siemens per meter (S/m)

Resistivity is the physical property which determines the aptitude of

this material to be opposed to the passage of the electrical current


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Electrolytic conductibility

The current is carried by ions. The electrical resistivity of

rocks bearing water is controlled mainly by the water which

they contain.


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Electrolytic conductibility

The resistivity of a rock will depend :

• on quality of the electrolyte, i.e., on the resistivity of the natural pore

water and consequently the quantity of dissolved salts in the electrolyte

1g/liter=1000 ppm

• on the mode of electrolyte distribution, porosity

• on the quantity of electrolyte contained in the unit of rock volume

(saturation)

• on the temperature


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Quality of electrolyte

The water resistivity ρ w

depends on the quantity of

dissolved salts:

( )1 1 2 2 3 3 ...w n n f c v c v c v c v= + + + +

With C n concentration in ion n

V n mobility of ion n


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Porosity

Total volume of communicating voids

Total volume of rock e

Φ =

Total volume of voids

Total volume of rock

t Φ =

Effective porosity:

Total porosity:


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Saturation

Volume of saturated voids

Total volume of voidswS =


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Effect of temperature

A rock totally frozen is infinitely resistant and it isimpossible to implement resitivity methods (use EM

methods)

( )18025.0118

−+=

t t

ρ ρ


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Archie´s Law

nmw S a −−= φ ρ ρ

• ρ resistivity of the rock

• ρ w resistivity of the fluid (water)• Φ porosity

• S saturation in water

• a factor which depends of the lithology (varies between0.6 and 2)

• m cementation factor (depends of the pores shape, of thecompaction and varies between 1.3 for unconsolidated sands to2.2 for cimented limestone

• n about 2 for majority of the formations with normal porosities

containing water between 20 and 100 %.


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Formation factor F

m nw

n

w

a S

F S

ρ ρ φ

ρ ρ

− −

−

==

• For sand and sandstones: F ≈ 0.62/φ2.15

• For well cemented rocks: F ≈ 1/φ2


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Permeability

There is no directrelationship betweenresistivity and

permeability.

This table shows also the problem in identifyingrocks due to overlapping

resistivity values (nocontrast)


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Resistivity of rocks and minerals

Air, gas or oil: infinite or very high resistivity!Liquid materials from landfills are generally conductive (


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Effect of clay

Clay has a high ionic exchange capacity, therefore the

conductivity of the pore fluid largely increases

Archie´s Law is not valid if clay is present!


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Summary…

The conductivity of a rock increases if…

• The quantity of water increases

• The salinity increases (quantity of ions)• The quantity of clay increases

• The temperature increases


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2. Equations in resistivity surveying


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Current flow in the ground

r


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Potential from a single electrode

r

I

V π

ρ

2=

r


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Two current electrodes


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Potential difference

( ) ( ) ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −=−+=

21

21

112/2/2/1 r r I r I r I V

P π ρ π ρ π ρ

V p1 is the sum of the

potential contribution

from the current

electrodes C 1 and C 2


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Potential field betweentwo current electrodes

A and B

Note the fast decreasenear A and B (contact

resistance)

A B


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Current penetration

⎟ ⎠ ⎞⎜

⎝ ⎛ ⎟

⎠ ⎞⎜

⎝ ⎛ = −

AB

z I f

2tan

2 1

π

• z depth• AB distance between current electrodes

• I f fraction of current penetrating below a depth z


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⎞

⎜⎝

⎛

⎟ ⎠

⎞

⎜⎝

⎛

=

−

AB

z

I f

2

tan

2 1

π


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Principle of reciprocity


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Current distribution


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This has an influence on the depth of investigation!


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Heterogeneous Earth


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Effect of topography


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3. Survey strategies and interpretation


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Two potential electrodes

111112

1111

2

11

2

11

2

−

⎟ ⎠

⎞⎜⎝

⎛ +−−Δ

=

⎟ ⎠

⎞⎜⎝

⎛ +−−=−=Δ

⎟ ⎠ ⎞⎜

⎝ ⎛ −=

⎟ ⎠

⎞⎜⎝

⎛ −=

NB AN MB AM I

V

NB AN MB AM

I V V V

NB AN

I V

MB AM

I V

MN a

N M MN

N

M

π ρ

π

ρ

π

ρ

π

ρ


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Apparent resistivityIn a heterogeneous medium, the measured resistivity is an

apparent resistivity, which is a function of the form of theinhomogeneity and of the electrode spacing and surface

location.


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Constant separation traversing (CST)


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• Demo during the lecture


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Electrode spreads


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Electrode spreads

I

V

aaΔ

= π ρ 2

( 1)a V n n a I

ρ π Δ= +

I

V annna

Δ++= )2)(1(π ρ

Wenner array

Schlumberger array

dipole-dipole array


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Penetration depth


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Sensitivity


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Cylindrical structure


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Vertical plane structure


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PontisPontis NappeNappe


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UnstableUnstable

areaarea

SiviezSiviez--MischabelMischabel

NappeNappe

WaterWater

infiltrationinfiltration


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Multiple “twin probes”

RM15RM15 resistanceresistance meter meter withwith

multiplexer multiplexer

Sanctuary of Poseidon (island of Poros, Greece)


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63Papadopoulos et al., 2006. Archeological Prospection, 13, 75-90

Ancient Royal Site of Rathcroghan, Ireland


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64Barton & Fenwick, 2005. Archeological Prospection, 12, 3-18

Peristyle villa Gallo-romaine Yvonand (Vaud)


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AB=4m

wallwall

fountainfountain??


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Manually dragged systems

Dabas et al., 2000, Archeological Prospection, 7, 107-118

Roman city, Wroxester (UK)


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67Dabas et al., 2000, Archeological Prospection, 7, 107-118


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68Source: Geocarta, Paris

100 data points/seconde100 data points/seconde1 data point1 data point eacheach 20cm20cm

Mobile arrays with vehicle


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Mobile arrays

Source: Geocarta, Paris VineyardsVineyards investigationsinvestigations

http://geocarta.sa.free.fr/fr/technologie/arp.htmhttp://geocarta.sa.free.fr/fr/technologie/arp.htm


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AA BB

M1M1 N1 N1

M2M2 N2 N2

M3M3 N3 N3

Mobile arrays

Current injection

Resistivity measurement

(three investigation depths)

Source: Geocarta, Paris


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Mapping example with mobile array

(spacing 2m)

Surface: 140 hectares


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Apparent resistivity

15 ohm.m 150 ohm.m


Profile spacing 6m Profile spacing 12m ProfileProfile spacingspacing 24m24m


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10 ohm.m 90 ohm.mSource: Geocarta, Paris

Ecartement 0.5m Ecartement 1m Ecartement 2m


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Inaccuracy in location


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Electrostatic mobile arrays

XVII and XVIII centuries structures (La Rochelle, France)


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78Panissod et al., 1998, Archeological Prospection, 5, 239-251


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Vertical electrical sounding (VES)


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One layer and two layers


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h l d


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Three layers and more…

E i l


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Equivalence

R h ρ = h

R ρ =

P i di


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Parametric soundingA parametric sounding is a VES carried out on an outcrop

or near a borehole to precisely determine the resistivity ofa geological formation.

A precise determination of resistivity reduce the problemof equivalence

S i


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Suppression

I t t ti


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InterpretationField data Model Calculated data (response of model B)

Comparison between dataA and C and modification

of model B

I t t ti f VES


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Interpretation of VES


I t t ti f VES


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Interpretation of VES


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archeo2007 electrical surveying resistivity a

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