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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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Current distribution
This has an influence on the depth of investigation!
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Current distribution
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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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Constant separation traversing (CST)
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Constant separation traversing (CST)
• 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
Source: Geocarta, Paris
Profile spacing 6m Profile spacing 12m ProfileProfile spacingspacing 24m24m
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Apparent resistivity
10 ohm.m 90 ohm.mSource: Geocarta, Paris
Ecartement 0.5m Ecartement 1m Ecartement 2m
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7510 ohm.m10 ohm.m 60 ohm.m60 ohm.m
Apparent resistivity
Source: Geocarta, Paris
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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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Vertical electrical sounding (VES)
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Vertical electrical sounding (VES)
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Vertical electrical sounding (VES)
• Demo during the lecture
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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
• Demo during the lecture
I t t ti f VES
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Interpretation of VES
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