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# Part Three: Locating an Earthquake using S minus P (Run – Walk) times and Triangulation

**Part Three: Locating an Earthquake using S minus P (Run – Walk) times and Triangulation**

**1. Refer students to Data Table 2, where the next set of data will be recorded. **

**2. Direct the students, who are representing the P and S waves to agree upon an "epicenter" within the area of the field (within a 30 x 30 m square).** (Note to teacher: Be sure to mark this spot, and measure its distance from the timers, or from the edges of the square area, before leaving the field, so that your students will be able to check their accuracy later.) Station three student timers at different positions around the perimeter of the field to represent seismograph stations. Mark the locations of the stations with flags [or masking tape]. A suggested layout for the seismograph stations is illustrated in **Figure 2 (below, right)**. The stations are not required to be at the corners of the square area but this geometry is easy and effective and thus enhances understanding of the triangulation method. This diagram can also be used for plotting the segments of circles to locate the epicenter by triangulation.

**3. Have six students representing P and S waves stand at the epicenter (one P wave and one S wave student facing each of the three stations).** At the signal, "go," all six of the students representing the seismic waves depart from the chosen "epicenter" toward their respective assigned timers ("seismograph stations"), at the speeds that were established in Part One. These students represent the P and S waves that propagate in all directions away from the earthquake focus. By assigning two students to travel to each of the stations, we are representing the P and S propagation paths from the earthquake to the station. *(Note to teacher: Pair a student representing an S wave (Walking) with a student representing a P wave (Running) so as to have 3 pairs of simulated earthquake waves traveling in 3 different directions.)* Observing the pairs of students representing P and S waves traveling from the epicenter to the stations is a very effective visualization of wave propagation and the meaning of the S minus P times used in the earthquake location method using triangulation.

**4. The timers will measure the length of time BETWEEN the arrival of the Running student ("P- wave") and that of the Walking student ("S- wave").** (On the stopwatch, press start at the arrival of the Running student, and press stop at the arrival of the Walking student.)

*These observations are exactly analogous to the arrival times of S and P waves. The time of the earthquake (origin time) is unknown. All that can be determined from the recordings at a single station is the difference between the P wave arrival time and the S wave arrival time. (The absolute times of the P and S arrivals are also known, but the difference between these times is the quantity that is used for triangulation to locate the epicenter.) This time difference is called the S minus P (S – P) time and is like the Walk – Run time of our simulation.*

**5. Record this difference, in seconds, on Data Table 2 (left, click image or here to download). **Repeat this step, and record the difference in arrival times. Recover all materials and return to the classroom.

**Figure 2 (below right, click here or image to download)** is a graph (map view) of station (timer) locations in a 30 x 30 meter area. For convenience, the stations are located at the corners of the square. A scale is provided for the Walk – Run method. Use the graph to plot circular arcs with a compass that correspond to the inferred epicenter to station distances from Data Table 2 and to plot the actual location of the simulated earthquake (epicenter).

**6. Refer to Data Table 2. ** Students should use the graph they constructed earlier to determine the distance to the epicenter from each of the seismograph stations. (Use the Walk minus Run line to correlate the difference in arrival times to the distance in meters by locating each travel difference on the y axis (time axis) and tracing a line horizontally to the Walk minus Run line. From this point, trace a line vertically to the x axis (distance axis). The location on the x axis will be the inferred distance from the corresponding station to the epicenter.)

**7. Construct a "map" of the field on graph paper (Figure 2) with the positions of the stations (timers) marked.** Be sure to establish an appropriate scale for your own activity so that it fits on the graph paper (the attached map with stations, Figure 2, could be used for this step; the scales are given for the 30 x 30 m area for the Walk – Run method). Now the students will use a drafting compass to draw a circle around each timer position (station). The point of the compass should be on the station, and the radius of the circle will be the distance to the epicenter determined previously (see Data Table 2). The point at which the three circles intersect represents the epicenter (see example of triangulation in Figure 3, below).

**A TXESS Revolution teacher uses a drafting compass to triangulate using a "map" of the field on graph paper during PDA3a in 2009.**

*(Photo courtesy of H.C.Olson)*

Because of possible errors in the travel time and distance measurements, the circles may not intersect exactly at one point. Compare the actual location of the epicenter (from distance measurements made in step 8) with the inferred location determined by the triangulation (plot the actual location on the graph). The actual location should be plotted on the graph after the triangulation measurements have been plotted and the estimated epicenter location determined. In this way, the students will be able to compare the location that they found from triangulation with the actual location. Measure the distance on the graph from the actual location to the location determined by triangulation. Check results with teacher. It does not matter if it is not perfect; it is a demonstration of HOW triangulation works. Additional information about earthquakes and earthquake location using the S minus P time method can be found in Bolt (1993, 1999).

An interactive earthquake location program using the same method and actual earthquake data (seismograms) is available on the Internet at the Virtual Earthquake web page (http://www.sciencecourseware.com/VirtualEarthquake/).

Dr. Bridget Smith-Konter, professor of geophysics at UTEP, has many earthquake activities for teachers, including another version of the Walk-Run activity. Please visit for her web site, Earthquakes in Action Teaching Modules at http://www.geo.utep.edu/pub/bkonter/education/index.html

**Figure 3. Example of a completed triangulation graph for the Walk – Run method.** Circular arcs show the inferred distances (from the Walk minus Run times) from each station (timer). The arcs intersect approximately at a point which is the calculated location. The actual location (asterisk) is close to the location determined by the travel time differences and triangulation.

**References**

Bolt, B.A., *Earthquakes and Geological Discovery*, Scientific American Library, W.H. Freeman, New York, 229 pp., 1993.

Bolt, B.A., *Earthquakes*, (4^{th} edition), W.H. Freeman & Co., New York, 366 pp., 1999.

*Virtual Earthquake*, http://www.sciencecourseware.com/VirtualEarthquake/, accessed July 25, 2011.