Contents for Tracing and Naming Waves

N.Z. Version, 1998

Introduction

Seismic waves can travel complicated paths through the interior of the earth. Since every seismic event produces waves traveling away in all directions, some waves travel deep into the earth, while others simply travel directly to the surface. Since seismologists concluded that layers of different materials are responsible for the behaviors of some seismic waves, they have needed a way to indicate where they believe an individual wave traveled between leaving the hypocenter and reaching the station.

If you look at output from the extended version of the Wave Identifier program (with any input values you like), you can see just how complicated the labeling system can be. In addition to P and S, there are waves labeled SKSSKS, pPKiKP, etc. The following table shows how these waves are labeled, and the Learning Library's Ray Tracer page provides animated examples of many of them.

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Wave Table

Letter Type of Wave Travelling Where?
P Compression wave In crust or mantle, (initially traveling down from the hypocenter)
p (lower case) Compression wave In crust or mantle, initially traveling up from the hypocenter
S Shear (transverse) wave In crust or mantle, initially traveling down
s (lower case) Shear wave In crust or mantle, initially traveling up from the hypocenter
Repeated P or S Compression or shear Reflecting off surface of earth
c Compression or shear Reflecting off surface of the outer core
K Compression In outer core
i Compression Reflecting off surface of inner core
I Compression In inner core
J Shear In inner core
Change from P to S or vice versa Changing In reflecting off a surface, a compression wave can generate a shear wave, and vice versa

This last type, in which P waves are converted to S waves or vice versa, are the most complex. You may wish to ignore them for now.

The Learning Library's *(to come)* page shows how the motion of a seismic wave can be represented with a curve or line indicating the wave's ray path. The Ray Tracer page shows animated ray paths for several waves.

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Activity 1: Labeling Ray Paths

The diagram below shows the ray paths of a variety of seismic waves. Use the table to help you label each ray path properly. Note: Rays on the left half of the diagram represent shear waves; rays on the right half represent compressional waves. Assume that none of the waves shown changes from compressional to shear or vice versa.

Figure 1

For the rest of the activities, start with a blank sketch of the cross-section of the earth with a spot just below the surface marked to represent the hypocenter of an earthquake. We have provided you with an example here:

Figure 2.

You can print this figure or draw your own. For your first try at each activity, you may want to draw the ray paths as straight lines or guess at the correct curvature. Once you understand what the activity is about, try our suggested method of approximation in order to draw ray paths with a reasonable approximation of the correct curvature.

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Activity 2: Drawing Ray Paths of P Waves

Draw the ray paths of P waves leaving the hypocenter in all directions: straight up to the surface (call this 0 degrees), straight down toward the earth's center (180 degrees), and also 30, 60, 90, 120, and 150 degrees. What happens to each wave before it reaches the surface? When each wave does reach the surface, label it as P, p, PcP, etc. You can use Figure 2 as a template.

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Activity 3: Drawing Ray Paths of S Waves

Try the previous activity with S waves. What differences will there be?

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Activity 4: Comparing P and S Waves

Mark a location on the surface of the earth to represent a seismic station. Draw the paths of as many P waves as you can that would begin at the hypocenter and eventually reach the station. Label each wave. Now mark a different location and try it again. Try it with S waves. Compare your results with a partner's.

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Activity 5: Drawing and Labeling Complex Wave Paths

Draw a complex wave path. Challenge a partner to label it correctly. Take turns.

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Activity 6: Complex Wave Labels

Write a complex wave label, ensuring that it is physically possible. Challenge a partner to draw it correctly. If your partner believes you have written an impossible label, challenge your partner to prove it. Take turns.

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Activity 7: Estimating Wave Arrival Times

Mark a station location and measure the angular distance between the hypocenter and the station. Repeat the activity of drawing and labeling as many wave paths as you can (P and S) that will reach the station. Next, list the waves in the order in which you believe they will arrive at the station. (Optional: list whether you think each wave will have a large, normal, or small amplitude when it reaches the station.) Now run the Wave Identifier program, choosing coordinates for the station and hypocenter that will produce the same angular distance between them. Compare the output of Wave Identifier to your sequenced list. With a partner, discuss possible reasons for any discrepancies. What assumptions did you use in making your lists? How might you modify those assumptions now?

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Approximating the Curvature of the Ray Paths of Seismic Waves

Within the Mantle:
To draw straight rays inside the Earth's mantle would not be very realistic, since we know the index of refraction for seismic rays increases with depth, causing the rays to follow a curved path. You can get a fairly good approximation of the ray's curvature within the mantle with a simple compass, though. Here is how to do it:

If you do not already have a diagram showing the Earth's core and outer surface, draw one on a piece of paper with a compass, as follows: Draw a small circle on the paper. This is the core of the Earth. Then pull the arms of the compass twice as wide. Use the same center for a second circle. This is the surface of the Earth. Keep the compass as it is.

With the arms of the compass set to draw a circle the same size as the circle representing the surface of the earth, move the centerpoint outside of the Earth, more than half a radius away from the surface. Now draw a part of a circle inside the Earth. This is a seismic ray. You must experiment a bit with placing the center at different locations so as to draw rays that begin at the hypocenter and go where you intend them to go.

When the center of the circle is close to the Earth's surface, the ray hits the Earth's core, where our approximate curvature is not valid. Stop the ray at the boundary with the core, and use the procedure below to continue its path in the correct direction.

Within the Core:
A ray inside the core can be approximated by a straight line, because the index of refraction within the core is nearly constant. To find the appropriate direction of the ray's motion, use Snell's law. Assume that the index of refraction of the mantle is 1.00 at the boundary with the core. Also assume that the core's index of refraction is 1.65.

Draw the appropriately curved ray path through the mantle until it reaches the boundary with the core's surface. Measure the angle of incidence at the core's surface and apply Snell's law. Draw a straight line with the correct angle with the vertical,