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Determining Earth’s
internal structure using
Occam’s Razor
Michael Hubenthal – hubenth@iris.edu
Time – 80-90 Minutes
Suggested Level - 9th Grade Earth Science
5E Phase - Exploration. Students should have already learned about earthquakes and
seismic waves.
Materials List (class of 24)
- 12 Theoretician’s worksheets (Appendix D)
- 12 Seismologist’s worksheets (Appendix E)
- 4 Record sections (See Appendix A for instructions)
- 4 Meter sticks
- 24 Rulers (30cm)
- 24 Scissors
- 4 Earth Scale Model – Both left and right half (Appendix B)
- 24 Earth Scale Model 2 (Appendix C)
- 4 Protractors
- Slide presentation available from http://www.iris.edu
- 1 Blown egg (one for each section you teach as they may break)
- Classroom computer and video projector
- Seismologist/Theoretician spreadsheet available from http://www.iris.edu
- Optional: 1cm graph paper
Content Objectives - By the end of the exercise, students should be able to:
- Demonstrate that Earth can’t be homogenous.
- Explain how the internal structure of Earth (concentric layers of different density
and composition) is inferred through the analysis of seismic data.
- Explain the role models play in the scientific process, especially when used in
combination with observational data.
- Explain how models are refined through the collection of additional data
- Discuss how working in a team to make data-gathering and procedural decisions
provides an efficient means for completing tasks, provides peer support to check
work and to develop conceptual understanding.
Lesson Description
In this activity students examine the evidence
that lead scientists to conclude that the Earth
has a layered internal structure. This
examination occurs by creating a scale model
to develop predictions about seismic wave
propagation and comparing these predictions
to observed data from recent earthquakes.
OPERA
Time (min)
Open
Prior knowledge
Explore/Explain
Reflect
Apply
5
10
30
15
20
80-90
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Open (5 Minutes)
Begin with slide 2 of the presentation and ask students “What is inside the eggs?”
As students are responding, artfully remove a small paper bag or box that contains the
blown egg. Without focusing your attention on the blown egg, carefully remove it form
the bag (with your thumb and index finger covering the holes used to blow the egg) and
show it to the students.
Turn the conversation to explore how they know what is inside the eggs. Ideas will
immediately focus on cracking it open. However, encourage students to consider ways
to do this without opening it, e.g. candling the egg, or spinning the egg (a raw egg won’t
spin up, while a hard boiled egg will stand on its end and spin).
Once these ideas have come out, quickly mention that you like the excitement of
cracking the egg open and toss the blown egg to an unsuspecting student while
switching over to slide 3! (Note: Timing is important here!)
Prior Knowledge (10 Minutes)
Next, show slide 4 of the presentation and ask students “What is inside the Earth?”
Depending on your grade level and your school’s curriculum some students may
suggest a layered Earth (slide 5).
Accept these answers but quickly ask students to Think-Write-Pair-Share about “How
they know, what they know is inside Earth?” as this is the emphasis of the lesson. Here
responses will likely include previous instruction, textbooks, TV shows, the internet.
Encourage students to think about what evidence they have for the idea of a layered
Earth. Next encourage them to think about how evidence they do have for Earth’s
interior. The discussions will likely cover, dirt, rocks (caves, road cuts, quarries etc),
volcanoes etc.
Show slide 6 and explain the concept of Occam’s Razor. Suggest that based on their
“evidence” from life experience Earth is made of rock. Thus the “simplest solution” to
describing Earth’s interior is a homogeneous Earth made of rock.
Ask students how they think we could test this idea. Steer students to see that because
of the size of Earth, we will need a model. Show slide 7 and discuss the role of models
in science (if you haven’t already covered this explicitly in previous instruction).
Explore/Explain (30 Minutes)
Ask students if we created a homogeneous model of Earth, how we might test it. Show
Show slide 8 and ask them if that might help give them evidence? Steer students to
realize that x-rays are energy and that while x-rays can’t penetrate all they way through
Earth, perhaps other types of energy could? Seismic waves?
Explain that today we will be testing our hypothesis that the Earth is homogeneous. As
we have already mentioned we will do this by creating a homogeneous model of Earth
and comparing observations we make with the model, to observational data we collect
from earthquakes. Thus we will be dividing the class into two groups; Seismologists,
working with seismic observations & Theoreticians who will use a model to create a set
of predictions. Divide the class of 24 into two groups of 12. Then sub-divide each group
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of 12 into teams of three A, B, C, D. Thus you will have a Seismologist A and a
Theoretician A, a Seismologist B and Theoretician B etc that will work together at the
end of the lesson to compare their results.
Once teams have been divided. Show slide 9 and indicate that you will first review the
instructions for the seismologist and then the Theoreticians. This order is ideal because
the Seismologist’s work has the fewest steps to remember (but it takes just as long).
Plus it is very useful for both groups to have a sense of what the other group is doing.
Show slide 10 to set the stage for the observations the Seismologists will be making.
This slide shows the information that is available for the seismologists to work with; a)
we know the location of the earthquake, b) when the earthquake occurred, c) the
location of the station, and d) a seismogram show the seismic waves arriving at the
seismograph. Using a series of questions, guide the students to see the following;
a) we can get distance (in geocentric angle where 1 degree = 111.19km on Earths
surface) between the event and the seismograph, and
b) we can get the length of time it took the seismic waves to travel that distance by
knowing when the earthquake occurred and when the energy arrived at the
seismic station.
Show slide 11 and note that we don’t have to rely on just one seismic station because
the IRIS Consortium maintains a network of seismographs distributed around the world.
Thus, show slide 12, the seismologists will be working with a collection of seismograms,
called a record section, from a single earthquake. A record section is a special ways of
displaying a collection of seismograms from a single earthquake. Each seismogram is
plotted according to its distance from the epicenter x-axis and the time since the
earthquake plotted on the y-axis. In this case, the distance from the seismograph to the
epicenter is provided in degrees as measured by the geocentric angle.
The seismologists will analyze their record section, determine what time the energy
arrived at each station and then record this time and the location of the station in
degrees away from the epicenter in the data table they have been provided.
Next, slide 14, introduce students to the scale model of a homogeneous Earth the
Theoreticians will use.
Note the following
- it is a cut-away
- the location of Earth’s center
- the location of Earth’s surface
- that it lacks layers and we assume the interior white space is all rock
To use this model, we will assume that the focus of our earthquake will occur near the
surface of our scale model at the point on Earth’s surface marked 0°
Next, slide 15, students need to place seismometers on their model by drawing triangles.
Suggested Discussion Questions:
- What range of angles do you want the model to cover?
- What would be “enough” data?
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Slide 16, students will record the location of their seismic stations on their data tables by
measuring the geocentric angle with a protractor.
Slide 17, when the earthquake occurs seismic waves will radiate outwards in all
directions from the earthquake. Because the model is homogeneous, these seismic
waves will travel at a constant speed and will follow a straight path. Students will
represent this dispersion of seismic energy by drawing straight ray-paths from the
earthquake to the seismograph and measure the length of the ray-path with a meter
stick using centimeters (cm). This information will be recorded in the table below.
Slide 18 - Now that students have collected the distance the seismic waves travels in the
models, the will need to convert their data into a form that can be compared to the data
collected by the seismologists. Since we are assuming that our model is homogeneously
rock, we know the seismic waves will travel at a constant velocity. In this case, we will
assume an average velocity of 11km/s (which is close to the average velocity of p-waves
in Earth). Now that students have a distance and a velocity they can solve for time.
Allow the groups time to complete the assignment using the worksheets.
Once students have calculated travel times for various distances both in Earth and the
scale Earth model, there are three ways to close this activity;
- Quick – Groups report out their findings to the teacher who combines the data
into the spreadsheet that graphs automatically. This is done using a video
projector in front of the class. This works best to collect the predicted model
before the observed data.
- Medium – Pair each group of seismologists with a group of theoreticians to
create teams. Each team will then plot their data together onto a preformatted
spreadsheet that automatically graphs the team’s data. Each team then
compares their results with other teams.
- Long – Each individual group constructs a graph themselves either by hand or
using spreadsheet software and plots their data on it. Each group should then
compare their data with other groups to see if the predicted model matches the
observations.
Questions for discussion following the graphing of the data
 How does our model data match the observed data?

What does this imply about our assumption that the Earth’s interior might consist
of a homogenous material with a constant velocity of 11 km/s?

How do travel times from the observed stations compare to modeled stations at
similar geocentric angles?

What are the assumptions of your model?

How accurate you think your measurements are and what effect that has on your
results?

Are there any difficulties you had? What were their impact on our results?
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The graphs generated by the groups should look similar to the one shown below. There
are several items that can be discussed with students:
- The model does not match reality and Earth cannot be homogeneous.
- The velocity of seismic waves in the real Earth cannot be constant, as the
observed arrivals are both early and late.
- There is a noticeable unconformity in the observed data at approximately 100
degrees (at 108 in the example below). This of course suggests the presence of
a core in Earth. NOTE: For the purposes of the activity, it is important to highlight
this feature without explaining it at this time. Students will explore this anomaly
further in the next section of the activity.
- The curving points of the model data appear surprising, as this should indicate that
the seismic waves were accelerating in the model despite the assumption of a
constant velocity of 11km/s. This occurs because the distances we are plotting
are on a nearly spherical Earth. Thus, the distance the energy travels to reach
each station becomes proportionally less the close on the far side of Earth. For
example, the distance the energy travels to reach a station on the model at 60
degrees = 19.8cm, 90 degrees = 28.1cm, 120 degrees = 34.2cm. and 150
degrees = 38.2cm. Thus the interval between 60 and 90 is 8.3cm, between 90
and 120 is 6.1cm, and between 120 and 150 is 4cm. Thus the energy is not
accelerating.
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Reflect (15 Minutes)
Students have now concluded that the homogeneous model does not fit the observed
data. In this section students will reflect on the implications of this data and what it
means in terms of reality by defining the P-wave shadow zone on a scale model Earth.
NOTE: The following instructions have been written with the assumption that the steps
will be completed together as a class. However, with minor modification, these could
also be rewritten to create an handout for students to use to complete this section
individually.
Suggested Discussion Questions:
- Begin by asking students to reflect on the anomaly identified previously on their
graphs.
- What does this mean in terms of reality?
- What might this look like on a cross-section of Earth? Lead students to the idea
that another scale model might be useful in helping us visualize both the data
and allow us to further explore its implications.
Thus, the students are able to conclude that Earth cannot be homogeneous. Students
should analyze their data to see where the model and the observations differ
significantly. Students will notice that there is a break in the curve of the observed data
(figure XXX) at approximately 110 degrees away from the epicenter of the earthquake.
The area beyond 110 degrees is called the P-wave shadow zone because no direct pwave energy arrives there.
Step 1: Provide each student with a copy of Earth Scale Model 2 (Appendix XX).
Step 2: Students should indicate the epicenter of an earthquake at 0 degrees on the
right edge of the Earth A model with a dot.
Step 3: Next, have students use the graph of the observed data they previously
generated to determine where there appears to be interference in the propagation of P
waves. In the example below you will note that the last direct arrival occurs at
approximately 108 degrees
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Step 4: Using the protractor, measure a geocentric angle based on their data (108
degrees based on the example data above), to the northern hemisphere and make a
mark on Earth’s surface. Use your ruler to connect the epicenter to the mark you just
drew on Earth’s surface.
Step 5: Repeat the procedure of step 4, but marking the southern hemisphere
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surface.
Sample Discussion Questions:
-
What have we determined so far?
What sort of structure has the seismic data helped us does this scale model of
the P-wave shadow zone help us determine? How?
How have we used the seismic waves to help use develop this picture?
What might this be similar too? Shape the discussion to lead students to the
concept of a shadow.
NOTE: While no direct P-waves arrive there it is important to emphasize to students that
both P waves and S waves do in-fact arrive in the P-wave shadow zone. The p waves
that do arrive have either been reflected, refracted to arrive in this zone. This is very
similar to a students shadow on the ground. Their shadow is not the absence of all light.
Rather it is an area that is not able to receive direct light but does receive light that has
refracted around the student or has reflected off of nearby objects.
Step 6: Label the area beyond the angle drawn (108 degrees in the example) as the Pwave shadow zone.
NOTE: Irish geologist Richard Oldham discovered the P-wave shadow zone in 1906.
Oldham noted that beyond about 100 degrees from the epicenter the P arrivals rapidly
decayed as a result of what he identified as Earth’s core. Current research now
suggests that P wave shadow zone actually begins at ~98 degrees away from the
epicenter, though strong arrivals from P waves diffracting around the core of the Earth
can be seen out to approximately 104 degrees away before decaying significantly. If
one carefully examines the data used in the example for this exercise, the first arrival of
seismic energy at 108 degrees is slightly delayed and has decayed slightly. Thus this
arrival is actually a P wave that has diffracted around the outer core rather than a direct
P wave. Such an error in interpretation of the data will ultimately result in an error in the
size of the core students will model. However, this is not really significant to the exercise
as the emphasis of this exercise is for students to search for and discover Earth’s core
using real data, rather than precisely solving for the P-wave shadow zone boundaries
and accurately determining the size of Earth’s outer core. Another possible source of
errors for students is simply the lack of a station at around 100 degrees. For example,
students record section might only have data from a station at 92 degrees and then
another at 118 degrees.
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Apply (20 Minutes)
Now that students have developed an model of the P-wave shadow zone. Ask them if it
would be helpful to have the P-wave shadow zone from other earthquakes as well?
How? Lead students to see that with more data, we might develop a more revealing
image.
Step 1: Instruct students to cut out the Pwave shadow zone. This is accomplished
by cutting along the two lines you drew to
connect the epicenter to the surface of the
Earth model and then cutting along the
curvature of Earth’s surface that
connecting them. This wedge shaped cutout represents the portion of Earth where
direct P-waves do not arrive based on your
data.
Step 2: Have direct students to place the point of the wedge shaped cut-out on surface
of Earth B while aligning the curved arc of the wedge with the opposite side of Earth B.
The point on the cone indicates the location of another earthquake epicenter.
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Students should trace the straight edges of the wedge to indicate the area where Pwaves from the earthquake are blocked.
Step 3: Have students repeat this procedure for a number of earthquakes at different
locations around Earth’s surface, each time tracing out the P wave shadow zone. This is
an excellent time to explore the idea of how much data is adequate.
Sample Discussion Questions
- As additional earthquake data is added, what shape is being defined in the interior
of Earth Model B?
- What do you think this new inner circle represents?
Note: This emerging circle represents the mantle-core boundary as revealed by P-wave
propagation. While this exercise reveals a smooth boundary between the core and
mantle current research suggests a boundary that has a substantial amount of
topography that is not represented in this activity.
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Step 4: Direct students to calculate the radius of the core of their Earth Model B using
the scale provided. The scale of the model is 1cm:127,420,000 and there are
100,000cm in 1km. The radius of the outer core of Earth is estimated to be ~3486km.
Sample Discussion Questions
How well do the students estimations for the radius of the outer core match? Where are
there likely sources of error?
NOTE: In addition to errors steming from students work, accuracy of tools used, issues
of scale etc, additional sources of errors (as discussed previously) can be the result of
students miss-interpretation of the seismic data or lack of data. Thus, the accuracy of
their work might be improved by adding additional stations to their record sections to
reveal exactly where the edge of the p wave shadow zone is located.
Step 5: Show students the IRIS poster “Exploring the Earth Using Seismology” to review
the concepts learned in this activity.
Closing thought question for students: Considering the core was discovered only in 1906
is it possible that the current model may have further refinements?
Adapted from Earth’s Interior Structure - Seismic Travel Times in a Constant Velocity Sphere.
(Braile, 2000) and What's THAT Inside our Earth? DLESE Teaching Boxes (2008).
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