Electrical Surveying Part I: Resistivity method Lecture A · 2019. 7. 14. · • Electromagnetic...

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Electrical SurveyingPart I: Resistivity method

Lecture ADr. Laurent Marescot

[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 methodThe resistivity method is used in the study of horizontal and vertical discontinuities in the electrical properties (resistivity) of the subsurface

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Application

• Exploration of bulk mineral deposit (sand, gravel)• Exploration of underground water supplies• Engineering/construction site investigation• Waste sites and pollutant investigations• Cavity, karst detection• Glaciology, permafrost• Geology• Archaeological investigations

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Structure of the lecture

The next two lectures…

1. Resistivity of rocks2. Equations in resistivity surveying3. Survey strategies and interpretation4. Summary of resistivity methods: case histories5. Conclusions

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1. Resistivity of rocks

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Resistivity and units

LRAARL

δδ ρδδρ δδ

=

=

• 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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Electronic conductibility

The current flows by displacement of electrons. Known as electronic conductibility or metallic because it is a similar conductibility to that of metals. This solid conductibility is really significant only for certain massive mineral deposits.

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Electrolytic conductibilityThe 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 conductibilityThe resistivity of a rock will depend :

• on the resistivity of the natural pore water and consequently the quantity of dissolved salts in the electrolyte

1g/liter=1000 ppm

• on the quantity of electrolyte contained in the unit of rock volume (saturation)

• on the mode of electrolyte distribution, porosity

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Effect of temperature

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

( )18025.0118

−+=

ttρρ

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Archie´s Law

nmw Sa −−= φρρ

• ρ resistivity of the rock• ρw resistivity of the fluid (water)• Φ porosity• S saturation in water• a factor which depends of the lithology (varies between

0.6 and 2)• m cementation factor (depends of the pores shape, of the

compaction and varies between 1.3 for unconsolidated sands to 2.2 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

nw

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 direct relationship between resistivity and permeability.

This table shows also the problem in identifying rocks due to overlapping resistivity values (no contrast)

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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 (<10 ohm.m)

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Effect of clay and graphite

• 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!

• Graphite, often associated with pyrite, makes the resistivity decrease

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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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Maxwell equations

0

or

MaxwellAmpère

inductionFaraday0

=⋅∇∂∂

=⋅∇=⋅∇

−=∂∂

−×∇

=∂∂

+×∇

BtpjpD

jtDH

tBE

)(C/mdensitycharge)(A/mdensitycurrent

)(C/mfieldntdisplaceme

(A/m)fieldmagnetic

)(Wb/mfieldinductionmagnetic

(V/m)fieldelectrical

3

2

2

2

pjD

H

B

E

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Static approximation

0

0MaxwellAmpère

inductionFaraday0

=⋅∇

=⋅∇

−=×∇

=×∇

B

jjH

E

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Current flow in the ground

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Equations for DC approximation

jE ρ=

0=⋅∇ j

011 2 =∇−=⋅∇=⋅∇ VEjρρ

VE −∇=

Ohm´s Law

Definition of electrical field E

Divergence is null except at the current source

Laplace´s equation

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Potential from a single electrode

02 =⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

rVr

r 12 C

rVr =∂∂

21 C

rCV +−=

0sin1sin

sin1

2

2

2222 =

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

ψθθθ

θθV

rV

rrVr

r

In polar coordinates, Laplace´s equation rewrites:

In polar coordinates, the current flow is symmetrical with respect of θ and ψ directions

Direct integration can then be performed…

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ρπ

ρρ1

21 2 Cdsr

CdsEdsjIsS s

−===⋅= ∫∫ ∫

Determination of C1 using the definition of current I…

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Remember...Vr Cr

∂=

∂

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rIVπρ2

=

21 C

rCV +−= 12 CI π

ρ= −

C2 tends to 0, if D tends to infinity…

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Two current electrodes

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Potential field betweentwo current electrodesA and B

A B

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Potential difference

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−=−+=

2121

112/2/2/1 rr

IrIrIVP πρπρπρ

Vp1 is the sum of the potential contributionfrom the current electrodes C1 and C2

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Two potential electrodes

111112

11112

112

112

−

⎟⎠⎞

⎜⎝⎛ +−−

Δ=

⎟⎠⎞

⎜⎝⎛ +−−=−=Δ

⎟⎠⎞

⎜⎝⎛ −=

⎟⎠⎞

⎜⎝⎛ −=

NBANMBAMIV

NBANMBAMIVVV

NBANIV

MBAMIV

MNa

NMMN

N

M

πρ

πρ

πρπρ

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Apparent resistivity

• In a heterogeneous medium, the measured resistivity is an apparent resistivity, which is a function of the form of the inhomogeneity and of the electrode spacing and surface location.

• K is named the geometric factor.

MNa

V KI

ρ Δ=

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Geometric factor

41 1 1 1 1 1 1 1K

AM AN BM BN A M A N B M B N

π=

− − + + − − +′ ′ ′ ′

For a half-space, a general definition for the geometric factor can be written:

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Electrode spreads

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Electrode spreads

IVaa

Δ= πρ 2

( 1)aVn n aI

ρ π Δ= +

IVannna

Δ++= )2)(1(πρ

Wenner array

Schlumberger array

dipole-dipole array

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Current penetration

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛= −

ABzI f

2tan2 1

π

• z depth• AB distance between current electrodes• If fraction of current penetrating between the

surface and z

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⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛= −

ABzI f

2tan2 1

π

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Principle of reciprocity

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Heterogeneous Earth

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Modified Snell´s Law

1221 /tan/tan ρρθθ =

2121

22

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/tan/tan/tan/tan

zz

xz

xz

LLLLLL

=⇒==

θθθθ

122121

2211

/tan/tan//1,/1

/

ρρθθρρ

ρρ

==⇒∝∝⇒

=⇒=

zz

zz

LLLL

jVLLjV

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1

2

2

1

tantan

ρρ

θθ

=

21 ρρ <

21 ρρ >

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Current distribution

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This has an influence on the depth of investigation!

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Reflection and transmission

( )( )21

12

ρρρρ

+−

=⇒= kVV NMFor r1=r2=r3

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟⎠

⎞⎜⎜⎝

⎛=

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2

2

1

1

1

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4

rk

rIV

rkI

rIV

N

M

πρ

πρ

πρ

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Anisotropy

l

n

i i

in

HhSSSS

ρρ==+++= ∑

=121 ...

t

n

iiin HhTTTT ρρ ==+++= ∑

=121 ...

t

l

ρλρ

=

• ρl longitudinal resistivity• ρt transverse resistivity• λ coefficient of anisotropy

e.g.λ ≅1 for alluviumλ >2 for graphitic slates

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Effect of topography

Equipotential: dashed lines

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3. Survey strategies and interpretation

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Resistivity survey equipment

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Device

• Current source: batteries in series• Voltmeter and ammeter (resistivimeter)• Electrodes: metallic stakes

current electrodes: stainless steelpotential electrodes: stainless steel or nonpolarizing electrodes

Polarization occurs at the contact electrode/ground: this creates an additional potential difference.

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Polarization and skin depth

Skin depth: depth δ at which the amplitude of the field reaches 1/e of its original value a the source

• Use an alternating current to avoid polarization• Very low frequency (<10 Hz)

fρδ 503≈

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Contact resistance

22 LdL

sdLdR

πρρ ==

⎟⎠⎞

⎜⎝⎛ −=

LrR 11

2πρ

L = distance to the centre of the electrode [m]r = radius of the electrode [m]R = resistance [ohm]ρ = resistivity of the surrounding ground [ohm.m]

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To decrease the contact resistance…

• Add electrodes in parallel• Increase the current intensity• Increase the diameter of the current electrodes• Put electrode deeper into the ground• Add water (with salt) near the electrodes

About 90% of the contact resistance contribution comes from a portion of the ground around the electrode that is equal to 10 times the diameter of the electrode

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Equivalent circuit

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Origine of noise

• Telluric currents• Man-made currents• Metallic conductors in the ground (short-circuits)

Solutions:• Use of alternating current• Stacking operations• Rejection filters (16-20 Hz, 50-60 Hz)

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Survey strategies• Resistivity mapping, constant separation traversing (CST):

used to determine lateral variations of resistivity. The current and potential electrodes are maintained at a fixed separation and moved along profiles

• Vertical electrical sounding (VES):used in the study of near-horizontal interfaces. The electrode spread is progressively expanded about a central point

• Resistivity tomography (ERT):is a mix between CST and VES. Also named electrical imaging

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Constant separation traversing (CST)

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• Demo during the lecture

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Interpretation of CST

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UnstableUnstableareaarea

PontisPontis NappeNappe

SiviezSiviez--MischabelMischabel

NappeNappe

WaterWaterinfiltrationinfiltration

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Small scale resistivity map (archaeology)

AB=4m

wallwall

fountainfountain??

70Source: Geocarta, Paris

100 data points/seconde100 data points/seconde1 data point 1 data point eacheach 20cm20cm

Mobile arrays

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Mobile arrays

Source: Geocarta, Paris VineyardsVineyards investigationsinvestigations

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

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

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AA BB

M1M1 N1N1

M2M2 N2N2

M3M3 N3N3

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


15 ohm.m 150 ohm.mSource: Geocarta, Paris

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


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

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Ecartement 0.5m Ecartement 1m Ecartement 2m

10 ohm.m10 ohm.m 60 ohm.m60 ohm.m


Source: Geocarta, Paris

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Vertical electrical sounding (VES)

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One layer and two layers

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Three layers and more…

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Equivalence

R hρ= hRρ

=

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Parametric sounding

A parametric sounding is a VES carried out on an outcrop or near a borehole to precisely determine the resistivity of a geological formation.

A precise determination of resistivity reduce the problem of equivalence

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Suppression

90• Demo during the lecture

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Interpretation of VES

• Demo during the lecture

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Interpretation of VES

Electrical Surveying Part I: Resistivity method Lecture A · 2019. 7. 14. · • Electromagnetic...

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