Midterm results Average mark 73.7% (29.5 / 40) Median mark 30 / 40.

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”