Electrical Methods • Resistivity is a rock property – quantifies resistance to current flow • Range of rock resistivities is very large • Widely used in mineral exploration, and in geoenvironmental applications • Widely used in boreholes in the oil and gas industry
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Electrical Methods • Resistivity is a rock property – quantifies resistance to current flow• Range of rock resistivities is very large• Widely used in mineral exploration, and in geoenvironmental
applications• Widely used in boreholes in the oil and gas industry
Resistivity method
• Is an example of a “controlled source” method• Requires direct electrical contact with the ground
(electrodes, spools of wire, …)• Labour intensive, but better resolution than
gravity or magnetics
Resistivity method
Resistance and resistivity
Resistance: Simply a ratio between voltage drop and current flow in an electric circuit (i.e., across a rock sample):
Resistivity: An inherent rock property, controls resistance to current flow
Solving for resistivity:
Resistance depends on geometrical factors, as well as resistivity:
I
_V
A
_l
Resistivity and conductivity
Resistivity: An inherent rock property, controls resistance to current flow – measures resistance for a unit cube.
Conductivity: The inverse of resistivity (i.e., the ease with which current flows)
Ohm’s law
The current, I distributes itself across the cross-sectional area, A of the sample. We define the current density,
Ohm’s law states , thus
Ohm’s law in “continuous media”
Ohm’s law states
From calculus:
In 3-D:
Injecting current at a single electrode
Earlier, for a sample:
Geometrical term
How do we do this from the surface, for ground measurements?
Start with a single current electrode …
Injecting current at a single electrode
Current, I is distributed over a half-sphere, hence
Using Ohm’s law
or
Injecting current at a single electrode
Integrating
Solving for resistivity:
Geometrical term
Current flow in the ground
Field electrode arrays
Apply the single electrode formula for each of the four electrode combinations:
Geometrical term
Geometrical term
Field electrode arrays
Geometrical term
Field electrode arrays
(for the gradient array, we usually require L – x > 3l )
The Gradient array is often used for “lateral profiling” (see later)
In the next array, the Schlumberger array we use x = 0
Geometrical term
Field electrode arrays
The Schlumberger array is commonly used for “depth sounding” (see later)
Geometrical term
Field electrode arrays
The dipole-dipole array is commonly when both the lateral position, and spacing are varied (see later)
Next lecture: Types of resistivity surveys
There are several variations on resistivity surveys:
1. A “lateral profile” aims to locate anomalies, along a line or on a map
2. A “depth profile” aims to construct a vertical profile of subsurface resistivities and depths
3. A combination of the above, which aims to construct a “pseudo-section” or a “real section”