1. Electrical Properties of Rocks and Electrical Resistivity Methods

2. R = Resistance Definition of an OHM
An ohm is a resistance in a conductor that produces a potential difference of one volt when a current of one ampere is flowing through it.
                     
R =

3. Ohm’s Law

4. Resistance vs. Resistivity
Resistance is relevant only to a particular measurement circuit. Units: ohms
Resistivity is an intrinsic property of all physical materials Units: ohm-meters
Apparent Resistivity is a resistivity estimate based on a assuming a half-space geometry. Units: ohm-meters

5. Electrical Resistivity vs Electrical Conductivity
Resistivity = ρ (ohm-meter)
Conductivity = σ = 1/ρ (mho/meter)
(siemens/meter, S/m)

6. Calculating Resistance from Resistivity

7. Factors Influencing Electrical Conductivity in Rocks
Porosity (connected/effective - fractures or pores)
Pore saturation (% air or gas)
Hydrocarbon Fluid Saturation
Water salinity (TDS)
Clay Content
Metallic Sulfide Mineral Content
Fluid temperature
Rock Matrix intrinsic resistivity

8. Archie’s Law

9. Formation Factor

10. The conductivity of most geological formations can be fit to Archie’s Law

11. Influence of Permeability
A rock with a non-conducting matrix must be permeable (connected pores) as well as porous to conduct electricity.
Darcy's Law:
                                                                                                                          
Ohm's Law:
                                                                                                                                     
where
                                                                                     
Despite the similarity between Darcy’s and Ohm’s Laws, electric currents have zero
viscosity so even a narrow crack can provide an effective electrical connection between pores that not contribute to hydraulic permeability.

12. Comparison of electric and hydraulic properties.
Electrical
Hydraulic
Transverse resistance: 
  T = S hiri = Hrl
Transmissivity:  
Th = Shiki= KlH
Longitudinal conductance:
S= Shi/ri = H/rl
Leakance:
Lh=Ski/hi = Kt/H
Average aquifer resistivities:
rl, rt
Avg. hydraulic conductivities:
Kl, Kt

13. Metallic Sulfide Mineral Content
Electrical resistivity of rocks with various wt % of sulfide. 

14. Effect of Water Temperature

15. Conductivity Ranges of Various Materials

19. Resistance vs Resistivity
Resistance is relevant only to a particular measurement circuit. Units: ohms or Ω
Resistivity is an intrinsic property of all physical materials Units: ohm-meters or Ω-m
Apparent Resistivity is a resistivity estimate based on a assuming a half-space geometry. Units: ohm-meters or Ω-m

20. Calculating Resistance from Resistivity

21. Four Electrode Resistivity Measurement on rock sample
… are used to avoid electrode contact resistance effects
seen in two-electrode measurements. C1 C2
current I P1 P2

22. Four-electrode resistivity arrays

23. The Basic Concept of an Earth Resistivity Measurement

24. Electrode Contact Resistance is typically much higher than the intrinsic earth resistivity

25. Electrode Contact Resistance is concentrated around each electrode

26. If a standard two electrode resistivity meter were used to measure the earth’s “resistance” we only obtain information on the quality of the electrode contacts – not the earth’s resistivity

27. Pole-Pole Array

28. Pole-Dipole Array

29. Pole-Dipole Array

30. Wenner Array

31. Schlumberger

32. Dipole-Dipole Array

33. Fig. 5.4g
The electric potential varies as 1/r around a single current electrode on a homogeneous half-space

34. Fig. 5.5g

35. Fig. 5.9g

36. Fig. 5.6g
Equal potential voltage surfaces between the electrodes

37. Depth of current flow between two current electrodes

38. Fig. 5.14g

39. Fig. 5.13g (a)

40. Fig. 5.13g (b)

41. Fig. 5.13g (c)

42. Fig. 5.12g (a)

43. Fig. 5.12g (b)

44. Fig. 5.12g (c)

45. Fig. 5.14g

46. Fig. 5.15g (a)

47. Fig. 5.15g (b)

48. Fig. 5.13g (b)

49. Fig. 5.13g (c)

50. Fig. 5.18g (a)

51. Fig. 5.18g (b)

52. Fig. 5.18g (c)

53. Fig. 5.19g

54. Fig. 5.21g (a)

55. Fig. 5.20g

56. Fig. 5.21g (b)

57. Fig. 5.21g (c)

58. Fig. 5.22g

59. Fig. 5.23g (a)

60. Fig. 5.23g (c)

61. Fig. 5.24g (a)

62. Fig. 5.24g (c)

63. Fig. 5.25g (a)

64. Fig. 5.25g (b)

65. Fig. 5.26g

66. Fig. 5.27g (a)

67. Fig. 5.27g (b)

68. Fig. 5.28g

69. Fig. 5.29g

70. Fig. 5.30g (a,b)

71. Fig. 5.30g (c,d)

72. Fig. 5.31g

73. Fig. 5.33g (a)

74. Fig. 5.33g (b)

75. Fig. 5.33g (c)

76. Fig. 5.39g

78. One point removed

80. C:\Shortcut to Geo-CD-ROM.exe

81. Airborne EM Resistivity

82. Airborne EM Resistivity