Purpose: Demonstrates earthquake location using triangulation on a globe.
Supplies: Seismograms (at least three), travel-time curves, string, globe
Background and Demonstration:
Since P waves travel faster than S waves, the time difference between the arrival of the P wave and the arrival of the S wave depends on the distance the waves traveled from the source (earthquake) to the station (seismograph). Over time, many such measurements have been made, and travel-time curves (time vs. distance plots for P, S and other more complicated waves) have been developed for the Earth. If an earthquake occurred a given distance from a station, it could have been anywhere on a circle whose radius is that distance, centered on the station. If distances from two stations are known, two locations are possible: the two intersection points of two circles. If distances from three stations are known, the earthquake can be unambiguously located. This is the principle of triangulation.
Earthquake location through triangulation is often demonstrated on a map. However, unless the earthquake and station locations are chosen very carefully, the map projection distorts distances and the directions the waves have traveled. This can raise more questions than it answers. Therefore I suggest using a globe. Also, if a source of current seismograms is available (see below), students really enjoy the sense of discovery of locating an earthquake of current interest.
Break the class into groups of three or four students each, with one earthquake per group and each student working on the seismogram from one station. Give each student a seismogram and a string. Students measure the time difference between the P and S wave arrival (they can use the string to transfer this measurement to the time scale to get time in minutes). Then, measuring this time difference on the time scale of the travel-time curves (using the string again), they find the distance (in degrees) that corresponds to this time difference. This can be done by sliding one end of the string along the P-wave curve, keeping the string aligned with the lines of constant distance (parallel to the time axis), until the S-wave curve meets the appropriate length of the string. Then distance can be read from the distance axis of the travel-time curve.
Next, have the student measure this distance on the globe using the string. It is best to make this measurement along the equator or along a meridian line. Distance is not constant along different lines of latitude. Then holding one end of the string at the location of the station (found using the latitude and longitude of the station), the student can swing arcs on the globe at the appropriate distance. It is a valuable learning experience to have students attempt to locate the earthquake using only the distance from their station, and to find how many places the earthquake could have been. After that, encourage two students of the same group to cooperate by measuring distances from each of their stations simultaneously. They should find two possible locations. Finally (and with a tangle of hands of strings), three students can cooperate to locate the earthquake!
Middle-school students enjoy this exercise. They work well in small groups, and if one has difficulty measuring or understanding the instructions, the others can help. This exercise takes about 10-12 minutes to explain and about 20-30 minutes for the students activity.
Where to Get Seismograms: (Note: this needs to be updated)
Seismograms from stations distributed globally may be obtained within a few hours of any significant earthquake from IRIS (Incorporated Research Institutions in Seismology). Follow the links to the IRIS Spyder system, using the login id: bulletin and password: board. You will be prompted for your name, address and other information, some news items will appear, then you will find yourself at a long menu. Select spy (short for "Spyder"). Once again after entering name and address info, you will find yourself at a menu. Follow the instructions to select the earthquake and stations of interest. You will then be connected via ftp to your computer so that the data may be transferred. If you have the SAC (Seismic Analysis Code) program (free software from Lawrence Livermore Lab), it is most convenient to request and plot the data in SAC format. Otherwise, you may request ASCII format and plot the data with your own plotting software.
Travel-time Curves:
The tried-and-true travel-time curves were developed by Sir Harold Jeffries and Keith Bullen in 1940. The original reference is somewhat difficult to find, but plots of the "J-B Curves" may be found in several books, including: Ruth B. Simon, Earthquake Interpretation, A Manual for Reading Seismograms, William Kaufman, Inc., Los Altos, CA, 1981.
The most recent, and therefore not as widely used, set of travel-time curves is the IASPEI-91 model of Kennett and Engdahl, "Traveltimes for global earthquake location and phase identification", Geophysical Journal International, 105: 429-465, 1991.
Jeffrey S. Barker (SUNY Binghamton) Demonstrations of Geophysical Principles Applicable to the Properties and Processes of the Earth's Interior, NE Section GSA Meeting, Binghamton, NY, March 28-30, 1994.
Questions or comments: jbarker@binghamton.edu
Last modified: March 18, 1996 (content), June 6, 2021 (reformatted and moved to Google sites)