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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)
3
Resistivity methodThe resistivity method is used in the study of horizontal and vertical discontinuities in the electrical properties (resistivity) of the subsurface
4
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
5
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
8
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.
10
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
11
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 %.
13
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
14
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)
15
Resistivity of rocks and minerals
Air, gas or oil: infinite or very high resistivity!Liquid materials from landfills are generally conductive (<10 ohm.m)
16
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
17
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
18
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
20
Static approximation
0
0MaxwellAmpère
inductionFaraday0
=⋅∇
=⋅∇
−=×∇
=×∇
B
jjH
E
21
Current flow in the ground
22
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
23
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…
24
Potential from a single electrode
ρπ
ρρ1
21 2 Cdsr
CdsEdsjIsS s
−===⋅= ∫∫ ∫
Determination of C1 using the definition of current I…
21
Remember...Vr Cr
∂=
∂
25
Potential from a single electrode
rIVπρ2
=
21 C
rCV +−= 12 CI π
ρ= −
C2 tends to 0, if D tends to infinity…
26
Two current electrodes
27
Potential field betweentwo current electrodesA and B
A B
28
Potential difference
( ) ( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛−=−+=
2121
112/2/2/1 rr
IrIrIVP πρπρπρ
Vp1 is the sum of the potential contributionfrom the current electrodes C1 and C2
29
Two potential electrodes
111112
11112
112
112
−
⎟⎠⎞
⎜⎝⎛ +−−
Δ=
⎟⎠⎞
⎜⎝⎛ +−−=−=Δ
⎟⎠⎞
⎜⎝⎛ −=
⎟⎠⎞
⎜⎝⎛ −=
NBANMBAMIV
NBANMBAMIVVV
NBANIV
MBAMIV
MNa
NMMN
N
M
πρ
πρ
πρπρ
30
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=
31
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:
32
Electrode spreads
33
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
34
Current penetration
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛= −
ABzI f
2tan2 1
π
• z depth• AB distance between current electrodes• If fraction of current penetrating between the
surface and z
35
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛= −
ABzI f
2tan2 1
π
36
Principle of reciprocity
37
Heterogeneous Earth
38
Modified Snell´s Law
1221 /tan/tan ρρθθ =
2121
22
11
/tan/tan/tan/tan
zz
xz
xz
LLLLLL
=⇒==
θθθθ
122121
2211
/tan/tan//1,/1
/
ρρθθρρ
ρρ
==⇒∝∝⇒
=⇒=
zz
zz
LLLL
jVLLjV
39
1
2
2
1
tantan
ρρ
θθ
=
21 ρρ <
21 ρρ >
40
Current distribution
41
Current distribution
This has an influence on the depth of investigation!
42
Current distribution
43
Reflection and transmission
( )( )21
12
ρρρρ
+−
=⇒= kVV NMFor r1=r2=r3
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟⎠
⎞⎜⎜⎝
⎛=
33
2
2
1
1
1
14
41
4
rk
rIV
rkI
rIV
N
M
πρ
πρ
πρ
44
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
45
Effect of topography
Equipotential: dashed lines
46
3. Survey strategies and interpretation
47
Resistivity survey equipment
48
49
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.
50
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≈
51
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]
52
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
53
Equivalent circuit
54
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)
55
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
56
Constant separation traversing (CST)
57
Constant separation traversing (CST)
58
Constant separation traversing (CST)
59
Constant separation traversing (CST)
60
Constant separation traversing (CST)
• Demo during the lecture
61
Interpretation of CST
62
63
64
65
66
67
68
UnstableUnstableareaarea
PontisPontis NappeNappe
SiviezSiviez--MischabelMischabel
NappeNappe
WaterWaterinfiltrationinfiltration
69
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
71
Mobile arrays
Source: Geocarta, Paris VineyardsVineyards investigationsinvestigations
72
AA BB
M1M1 N1N1
M2M2 N2N2
M3M3 N3N3
Mobile arrays
Current injection
Resistivity measurement (three investigation depths)
Source: Geocarta, Paris
73
Mapping example with mobile array(spacing 2m)Surface: 140 hectares
Apparent resistivity
15 ohm.m 150 ohm.mSource: Geocarta, Paris
74
Profile spacing 6m Profile spacing 12m Profile Profile spacingspacing 24m24m
Apparent resistivity
10 ohm.m 90 ohm.mSource: Geocarta, Paris
75
Ecartement 0.5m Ecartement 1m Ecartement 2m
10 ohm.m10 ohm.m 60 ohm.m60 ohm.m
Apparent resistivity
Source: Geocarta, Paris
76
Vertical electrical sounding (VES)
77
Vertical electrical sounding (VES)
78
Vertical electrical sounding (VES)
79
Vertical electrical sounding (VES)
80
81
One layer and two layers
82
83
84
Three layers and more…
85
86
Equivalence
R hρ= hRρ
=
87
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
88
Suppression
89
90• Demo during the lecture
91
Interpretation of VES
• Demo during the lecture
92
Interpretation of VES
93
94
95
96
97
98