# The Earth is Electric: Resistivity Geophysics

The earth is electric.

From the telluric currents constantly zipping through the oceans and the subsurface to the electric arc we behold in the form of lightning strikes, the earth is spinning with electrical power.

But the Earth (or the crust of the Earth) is generally not a great conductor. That doesn’t mean that electricity can’t move through it, it just means it is very inefficient to try. A fictional (and/or apocryphal) example of currents in the ground from the life of Nikola Tesla that probably wouldn’t work in real life is shown in the movie The Prestige. (A totally real-life example of a similar mad-scientist-type tower to convey electricity through the air that Tesla tried to build that probably would have worked in real life is pictured below; wikipedia article here, image below. It was called the Wardenclyffe Tower, because it definitely had to have a mad-scientist-type name).

The ability of electric potential to be conveyed through a variably resistive earth is important to much of the near-surface geophysics we do at the Illinois State Geological Survey, and is a very effective way of differentiating between materials in the subsurface, especially in the unconsolidated glacial drift we have in most of Illinois. The development of this technique nearly a century ago was also vital to the founding of what is currently the largest oilfield services corporation in the world–Schlumberger Limited.

## Two Brothers to the World

The first people to tap the potential electricity to understand the subsurface were Conrad Schlumberger and his brother Marcel in the 1910s. Conrad especially was interested in knowing whether electricity could be used to find metallic ores in the subsurface. Starting with experiments in a converted bathtub in his basement, within a decade he and his brother had scaled up the experiments for field use (both to use at the surface and in wells). The ability of this method to find ore bodies in mining applications helped their business grow exponentially. In the next decades, several variations would be introuduced (e.g., Wenner, Dipole-dipole, pole-dipole, etc.), and it would gain wide use globally.

A decade after the Schlumberger brothers published their first findings using this novel method, electric resistivity measurements made their way to the plains of Illinois via a geophysics lecturer named Marion Hubbert. Hubbert–better known as M. King Hubbert–was the first geophysicist to listen to the subsurface speaking in Illinois in this way. He became famous for his controversial-at-the-time “Peak Oil” theory (also called the Hubbert Peak Theory), and his contributions to the burgeoning field of geophysics. I will get into his work and the early ERT days in Illinois in a later post (with historic pictures too!).

## The Electric Resistivity Method

Without getting into the gritty details, electric resistivity surveys works like this:

Materials:

• Electric source (e.g., battery)
• Voltmeter (to measure electric potential)
• Ammeter (to measure electric current)
• 4x metal “stakes” (to pound into the ground; also called “electrodes”)
• 4x cables (to connect to those ^ stakes)

Instructions (if this gets too confusing, just look at the diagrams below):

• Hammer two stakes (the “A” and “B” stakes) into the ground at a specified distance from a point of interest (this distance is called the s-distance*). Connect these stakes to the battery and the ammeter using two cables (one positive, one negative). These are going to be used to “pump” electric current into the ground.
• Hammer the other two stakes (the “M” and “N” stakes) in between and in-line with the previous two at a specified distance from the same point (this distance is α/2, or α for the total distance from M to N). Connect these stakes to the ohmmeter using the other two cables. These are going to be used to measure the electric potential created in the ground by the other stakes.

And that’s it! (Well, nowadays there may be dozens of these electrodes all measuring at once in a computer-controlled sequence–but that’s basically it). See the diagrams below for what this looks like.

The A and B stakes (or, rather, electrodes) “pump” current into the ground. The M and N electrodes are used to measure the potential as the current “flows” through the ground, which is then used to caclulate resistivity.

The further away the outside electrodes are, the deeper the effect they have on the electric potential in the subsurface. This is probably the most difficult aspect of the method to explain–it may be easier just to look at the diagram on the right above. The curved lines show the current passing through the subsurface, and they get deeper as the electrodes get further out.

## “Electrical fire loves water”: Hydraulics, Electricity, and American History

You might notice, I’ve been using a lot of water-based analogies (“flow,” “pump,” etc.). There is a simple reason for this: the concepts (and mathematics) for the two are quite similar. In many physics courses, the more tangible water-flow analogy is used to help introduce new electrical concepts to students. In fact, when Benjamin Franklin reported upon his electrical experiments with a kite in a lightning storm in Experiments and Observations on Electricity, he used the idea of a fluid. After listing off fifty-six “Obsevations and Suppositions” about electricity, he moves on to what he thinks electricity is:

• Electricity is a fluid of sorts, with smaller particles than water and perhaps similar in particle-size to fire (he went back and forth between calling it “electric fluid” and “electric fire” because of its effects; but he thought in its essence, it is a fluid). He noted that water is also a conductor–that “electric fire loves water.”
• Matter is like a sponge. These “sponges” can contain an electric charge to varying degress, just like sponges can hold water to a varying degree. (Remember, he was pretty much only dealing with static electricity). Matter (i.e., “sponges”) with large “pores” and repellent surfaces are what we would call conductors (“electrical fluid” can move through them quickly).
• “Electrical fluid” is inherent within common matter and can be pumped out like a juice

He wasn’t exactly right, but this fluid way of understanding electricity was pretty close to correct at a conceptual level.** More importantly, it helped formed the foundations of the way we understand electricity today, and helped lead James Maxwell’s formulations of the fundamental equations for electromagnetism about a century later.

And a short historical aside: for those of you who may think this is just more boring science, consider the following. In 1751, Benjamin Franklin wrote his Experiments and Observations on Electricity. This scientific success is what brought him to prominence both in America and allowed him access to the halls of power in Europe. Some of his experiences in Europe drove him to be an American Patriot and informed him as he edited the Declaration of Independence in 1776. His prominence in Europe enabled him to negotiate an alliance between the France and U.S. in 1778 in the middle of the Revolutionary War that is considered by many to be the point at which American victory became possible. It wouldn’t be a stretch to say that electricity bred freedom in America. (For more on this history, check out the book Simply Electrifying.)

This is an introduction to electric resistivitiy tomography (ERT), also called Electric Earth Resistivity (EER) measurements, or electric resistivity imaging (ERI). This is not the only way that electromagnetism is used in geophysics. In future posts, I will be going into the historical development of ERT at the Illinois State Geological Survey I mentioned above. I will also get into some of the other fun geophysical methods we use here at ISGS (and maybe even some we don’t!)–utilizing scientific phenomena from the nuclear level to the planetary level.

Stay tuned.

* There are a number of variations on this method, and various terminology used to talk about the distance between the electrodes. I am just going to use one, simple method of nomenclature to explain this.

**Beyond forming the the conceptual basis for the understanding of electricity, the mathematics describing hydrology (or hydraulics) and electricity are also very closely related.

If you’ll allow, I’m going to put a (scary) equation in this footnotes:

$I=\frac {1}{R}*V$ (basic electric equation)

Ok, I lied, there’s actually two (scary) equations:

$Q=-K*\nabla p$ (basic hydraulic equation)

In the first equation I = electrical current, V = the voltage (also called electric potential), and R = resistance. These are terms most people have probably heard of…but what do they mean?

Current (or I) is the measure of the flow of electric charge. That’s pretty simple.

Resistance (or R) is also pretty intuitive. It is the measure of how difficult it is to pass an electric current through something (measured in ohm-meters, or Ωm). So, metals are called conductors because they have extremely low resistance. Like, the resistance of copper is about 0.000 000 017 Ωm.

Voltage (or V) is a bit harder to explain, but it is a measure of the difference in electrical potential between two points. It is formally denoted as V (the triangle essentially means “the difference in…”). We more often simply use V. It is actually probably easier to explain V using water – we’ll come back to that.

So, the second equation:

Discharge (or Q) is the measure of how much water is flowing through a specific area at a given time (commonly measured in gallons per second). That’s pretty simple.

Hydraulic conductivity (or K) is the measure of how difficult it is for water to pass through a piece of ground. An aquifer is called such more or less just because it can store and pass water through with relative ease.

The pressure gradient ($\nabla p$) is the difference in the hydraulic pressure between two points. Sound familiar?

I’ve simplified this a little, but the basic idea is that the equations are analogies of one another. This actually happens with a number of seemingly unrelated properties in physics.

† (a footnote within a footnote?! Footnote-ception?!) I’ve actually simplified this a little. Hydraulic conductivity takes into account the properties of the object through which the fluid is passing, as well as properties of the fluid itself (such as viscosity and density). Since this is always the same for water, I’m just using K to represent the variation between the different objects water passes through (just like R represents the variations between the different objects electricity passes through).