N.Z. Version, 1998
In this activity, the teacher leads the students through a set of tasks and discussions that helps students to: observe that S waves become very weak in (at least some) seismograms recorded more than about 110° from the epicenter; verify that this is a universal, rather than ideosyncratic feature of S waves; generate hypotheses about the reasons for this; pursue the implications of one hypothesis-that S waves encounter a barrier within the earth- to invent a way to calculate the depth of this hypothetical barrier; and, finally to explore the possible relationship between the fuzzy edges of the shadow zone and wave diffraction.
Skills and concepts developed include:
You will need:
Prerequisite concepts:
Show students the following record section. Ask students to look at the marked S waves. What seems to happen to the S waves in seismograms recorded more than about 100 or 110° from the epicenter?
If students made a record section in an earlier activity, have them identify the S waves and connect them with a curve as in the figure above. Do the S waves behave similarly in this record section?
It may be unclear what exactly happens to the S waves--it can appear that they make a jump at about 110°, after which they appear a bit later in the seismograms than one would have predicted. (Note: The S waves that "reappear" have followed a more complicated path through the earth. Students interested in identifying these waves may use the simplified version of the Wave Identifier program. They may become harder to see or change their appearance in the seismograms further than about 100° from the epicenter.
Pose the questions: Is this weakening of S waves a special feature of this event, or is it more common or perhaps universal? If it is common or universal, does it always happen at about 110°, or does the angle change depending on some variable? The most comprehensive way to answer this would be to assemble record sections for a large number of events in different locations, at different depths, generated by different types of seismic motion. That would be time consuming, to say the least. The class may wish to look at a few seismograms, recorded at various angular distances from the epicenter--see below.
Computer Activities (whole class demonstration or small groups)
Your class may wish to investigate other available seismograms,
or, if you have a seismometer,
the seismograms you have recorded. Choose several seismograms of events
at various angular distances from the recording station. Can students identify
S waves for them all? Do they find it easier to identify S waves at angular
distances less than about 110° than at greater angular distances, or
is the situation less clear?
Another way to address the question of whether the S-wave disappearance at this angular distance is a general phenomenon is also use the Wave Identifier program, which produces a list of predicted arrival times for various seismic waves depending only on the depth of the quake and the angular distance between the event and the station. The program was developed by seismologists to reproduce the arrival times found in seismic data collected over many years. It can answer the question of whether the disappearance of the S wave is a general phenomenon.
Invite students to enter a typical earthquake depth on the Wave Identifier form on the Web. (Ask students: What is the most common range of depths?) Now run the program several times, with an increasing angular distance between the epicenter and station. Be sure to include angular distances both less than and greater than the distance at which the S wave disappeared in your record section. Save the results of all your trials.
Discussion Idea
Look over the program's outputs, focusing only on the S wave. Remember,
these are general results for events at a typical depth. What do you conclude?
Tell students that, after looking at seismograms from many events, seismologists have determined that S waves do not appear at stations more than about 110° from the epicenter of an event, regardless of where in the world the event occurs.
Why is this? To help students visualize the possibilities, sketch a cross-section of the earth (omitting the core). Add rays to trace the paths that S waves follow from the epicenter of a seismic event to various locations on the earth's surface-but not to locations more than about 110° from the epicenter.
Discussion Ideas (whole class)
Ask students to look at the sketch, and to suggest ideas about what could
be preventing S waves from reaching the surface further from the epicenter
Record a list of all the hypotheses the class can generate.
Could it be that the earthquake generates S waves only in some directions? Why might this be the case? If, on the other hand, S waves are generated in all directions, what might be happening to the ones that do not reach the surface?
Pursue the implications of each hypothesis the class generates, as far as you can. What does each hypothesis imply about the nature of earthquakes, S waves, or the material inside the earth?
Refer students to the Learning Library page on R. D. Oldham's 1906 paper on what happened to the S waves that failed to appear beyond about 105° from the epicenter. (Pending revision of the Learning Library, you may find a description on pages 8 through 12 of Bruce Bolt's book, Inside The Earth: The Evidence from Earthquakes 1982, W.H. Freeman and Company, San Francisco.) Ask students to compare Oldham's hypothesis to their own.
Paper Activity (individual, small group, or whole class)
Instructions for students:
Now pursue the hypothesis that the missing S waves encounter a barrier of some kind. Can you determine the depth of this barrier? Is it ten kilometers beneath the surface? 100 km? 1000 km? 10000 km?
One way to start is to assume that S waves travel in straight lines inside the earth (for simplicity) and to use the fact that S waves reach the surface of the earth only as far as about 110° away from the epicenter. Estimating the depth will require geometry and either a scale drawing or a sketch and trigonometry. You also must know the radius of the earth.
Given that S waves actually curve gradually toward the surface as they travel, is your estimate too deep or too shallow? Use a sketch to back up your answer.
Can you think of other ways to improve your estimate?
Discussion Ideas (whole class)
If there is such a barrier within the earth, can you determine its shape from what you know? Is it symmetrical? What evidence do you have?
What might happen to the S waves that encounter the barrier?
In evaluating the barrier hypothesis versus the class's other hypotheses, what data could provide evidence either supporting or refuting this hypothesis? Can you acquire these data?
Students may have noticed something that seismologists have long noted: S waves do not entirely disappear exactly at a particular angular distance, such as 104° or 105°. Rather, they weaken over a range of angular distances. (Refer students' attention back to the record sections to see whether these features are apparent. Can they find the same effect in P waves? Sometimes, this is easier.) In other words, the apparent barrier in the earth does not cast a sharp seismic "shadow" with distinct edges. Why is this? Encourage students to offer hypotheses.
Ask: Is this evidence that the barrier itself lacks a distinct edge, perhaps blending into the mantle above it? Does something about the S waves themselves lead to the fuzziness? Is this evidence that the barrier hypothesis is incorrect?
If students have already conducted experiments with the diffraction of waves around barriers, with water tables and with light, remind them of these experiments and ask whether they see any parallels between these experiments and the question at hand. If students have not already conducted such experiments, have them do so now, keeping in mind the question of the "fuzzy edges" of the S-wave shadow zone.
Does the fact that waves bend around the edges of obstacles has implications for the likelihood of each hypothesis above? Check for good scientific thinking by asking students to respond to the statement, "Since waves diffract, the reason for the blurred edges of the shadow zone must be that the seismic waves diffract around the edges of the barrier." If students accept the statement, challenge them to see that the other hypotheses are not ruled out by the fact that waves diffract.
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