Stories of the Lithosphere

How Do We Know: Part 1

Discovering Things We Can't See--The Earth's Interior

Earth Science Essentials

by Russ Colson

 

Lecture Recap

 To be scientific, any belief must be based on observation (not on theory!).   From the lecture, how do we make observations of the Earth's core?

 

 

 

Measuring Distances and Depths

Every time a seismic wave encounters a surface, some of the energy of the wave is reflected back and some of the energy continues on through the surface.

  

Suppose we know the velocity of a seismic wave through rock. We might determine this by measuring seismic velocities in a laboratory, using rock of known compositions under known temperatures and pressures.

Or we might time how long it takes for a seismic wave to travel through a known distance of rock, such as a wave that travels from an earthquake in San Francisco to a seismograph in a nearby city.

 

If we know the velocity of a seismic wave, then we can determine the thickness of different layers of the Earth by measuring how long a seismic wave takes to travel down to the bottom of that layer and then back.

 

 

This is analogous to determining the distance to St. Paul from Moorhead, MN if you know travel time and velocity. Suppose that my average velocity is 60 miles per hour.

It takes me 8 hours to travel to St. Paul and then back to Moorhead. How far is it to St. Paul from Moorhead?

 

Well, if we traveled at 60 mph for 8 hours, we traveled 480 miles.

Thus, the distance to St. Paul is half of this, or 240 miles.

 

You try one. Suppose that the average velocity for a P-wave in Earth's upper crust is 5.6 km per second. You explode a stick of dynamite to generate seismic waves starting at 4:05:02 in the afternoon.

At 4:05:08 the wave returns to your seismograph. How thick is the upper crust at your location?

 

Let's try a two-layer problem.   Suppose that you measure the velocity of the P-wave in the upper crust as 5.6 km per second and the velocity in the deeper crust at 6.5 km per second.   You expect a return signal from both the bottom of the upper crust and a second return signal from the bottom of the deeper layer, as shown in the diagram below.   Again, with waves starting at 4:05:02 pm, you get the first return signal at 4:05:08 and the second return signal at 4:05:25.   What is the thickness of the lower layer of crust?

 

 

 

Inferring Internal Structures—Refraction of Waves

 

Seismic waves are different from electromagnetic waves like light, however, both share certain properties such as refraction. Refraction is the bending of the wave when it passes between different materials in which the wave has different velocities.

It's easier to measure refraction with light than with seismic waves, so we're going to do an experiment using light as a proxy for seismic waves.

 

To start, let's shoot a red laser across a sheet of graph paper to a meter stick. Since the laser does not pass through materials with different velocities, it travels in a straight line.

 

  

We can mark that straight line so we remember its path, as shown below.

 

 

Now, let's put a bottle of water in the path of the light, with the edges of the bottle at an angle to the light beam.   Because the velocity of light is lower in the glass and water than in air, the light beam refracts both when it enters the bottle and again when it emerges from the bottle, as shown below.

 

We can understand the direction that the light refracts by considering imaginary lines drawn normal (perpendicular) to the interface between the two kinds of materials as shown below.

 

We can infer a model for diffraction of light waves (which in this property behave like seismic waves) as the following:   a wave will refract toward the normal to the boundary between two materials if the velocity decreases when the wave crosses the boundary.   A wave will refract away from the normal to the boundary between two materials if the velocity increases when the wave crosses the boundary.   This is illustrated below.

This gives us a way to see inside the Earth with waves; we can reconstruct how the waves are bending based on measurement made at the Earth's surface. This process involves a complex 'CAT scan' into the Earth because we can't travel into the Earth to 'watch' the waves bending.

We can only figure out the bending based on how long the waves take to travel from one place to another as measured at the Earth's surface. What's more, many things inside the Earth cause the waves to bend and to bend again, over and over.

To figure out all this complexity, we need measurements of travel times at many locations and a computer to calculate what those travel times tell us about refraction inside the Earth. Using this technique, we can study non-layered structures within the Earth, like plumes rising from deep in the mantle, chunks of ancient crust now subducted into the mantle, or strange topographic features that form at the boundary between the core and mantle.

 

Remember when I drew arrows in the lecture to show the path of seismic waves through the Earth and I drew the arrows curved?

I suspect that you were desperately wanting to ask me "wait, why are you drawing the arrows in a curve instead of a straight line?" But you couldn't ask your question because this is an online course (curses to online courses, you were thinking!).

 

But now, you get the answer anyway!

The waves curve because they refract as they go into deeper layers with different wave velocities. As the waves travel deeper into the Earth, the rock is generally denser and seismic velocities higher.

This causes the waves to bend away from the normal. Below is a screen shot from the lecture in case you didn't get this into your notes.

 

 

As the wave curves and begins traveling back toward the surface, it travels into material with lower velocity and the wave bends toward the normal. This causes the wave to travel through the Earth in an arc, as shown below.

 

 

You may have also noticed in the lecture that I drew the wave with a kink where it entered Earth's outer core.   I drew the kink such that the P-wave refracted toward the normal.   Where the wave re-emerged from the outer core, the kink bent away from the normal, as shown below.

 

 

 

A puzzle from the TV show Numbers

In World War II, ships used sonar--P-waves in water—to locate submarines.   In the TV show Numbers, our heroes considered how submarines were able to hide under a cold/warm water boundary.   Seismic waves refract whenever they encounter a boundary between two types of material, like warm and cold water.   Seismic waves travel faster in warm water than cold (just like sound travels faster in warm air than cold air).   To figure out whether the wave refraction in the video is correct, you can imagine arrows showing the direction of wave propagation and think about whether the waves bend toward or away from the normal.   The arrows, showing the direction of propagation, should be drawn perpendicular to the wave-fronts shown in the video.

 

Wave-refraction-puzzle-from-Numbers-- How-do-we-know-Numbers-seismic-video .

(1:06 min)   https://mediaspace.minnstate.edu/media/How-do-we-know-numbers-seismic-video/0_vvt23pzp

 

Write a short report on whether you think the wave refraction in the TV show is illustrated correctly or not.

 

 

 

 

Mirages

  

While we are on the subject of wave refraction, we should talk about another interesting earth science phenomenon caused by refraction—mirages.

  

In general, light travels fastest when it goes through empty space. The more atoms it has to navigate around, the slower it travels (ok—this is a simplification...).

Thus, light travels faster through warm air (which is less dense—fewer molecules) than through cold air (which is more dense—more molecules).

 

There are two prominent kinds of mirages: 1) inferior mirages in which the images appears below the real object, and

2) superior mirages where the image appears above the real object.

 

With inferior mirages, things in the sky appear to be on the ground.

The common "lake on the highway" mirage is this type, where the blue sky appears to be lying on the highway.

 

With superior mirages, things on the ground, or even hidden over the horizon, appear to be much higher than normal, or even floating in the sky.

  

Below, I've sketched an example of each kind of mirage--as they often occur in the Red River Valley near my home--showing the path of light rays. I've drawn horizontal lines to indicate different layers of air. Can you figure out whether the cold or warm air is on the bottom?

 

 

 

 

 

Cool side note:

The mathematical relationship describing how different materials refract light is called Snell's Law, after an early 1600s Dutch Astronomer. However, it was actually first described in 984 by a Baghdad mathematician, Ibn Sahl, in his book On Burning Mirrors and Lenses. One page where he diagrams the mathematics is shown below.

 This image comes from Benjamin Jaffe's interesting article addressing the contributions of artists to optics and optics to art at http://benjaminjaffe.net/digital_institute_of_the_arts/optics.

 

 Last updated July 6, 2015.   All text and pictures are the property of Russ Colson.

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