## Locating the Epicenter of a Simulated Earthquake by Triangulation

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#### Abstract

Students will learn how earthquake waves travel through the Earth at different speeds. From these speeds, students will be able to locate the epicenter of a simulated earthquake by triangulation.

#### Introduction

This lesson was created in a teacher workshop under the facilitation of Catherine French, University of Minnesota. The authors of this lesson are:

Leslie Bucar, 7-12 Science Teacher, Fond du Lac Ojibwe School, B.S. Biology, B.A.S. Teaching Biology, B.A.S. equiv. Teaching Chemistry

Dan Johnson, 7-12 Math Teacher, Fond du Lac Ojibwe School Teaching Math

#### Earthquake Engineering Component

When an earthquake occurs, vibrations are released into the ground from the starting point of the quake. These vibrations are called *seismic* *waves*. These seismic waves start from the *focus* of the earthquake, which is usually found beneath the Earth's surface. The point on the Earth's surface directly above the focus is called the *epicenter*. When the news reports where an earthquake started from, the epicente*r* is where they are talking about.

There are three different kinds of seismic waves produced by earthquakes. *Primary waves* are the first waves that are detected from the site of an earthquake as they are the fastest. *Secondary waves* are slower than the primary waves thus arrive second at the recording stations. *Surface waves* are formed when both the primary and secondary waves combine at the Earth's surface. These waves are similar to those that are formed when you drop a rock into a pool of water. By calculating the time between the primary and secondary waves*, *we can figure out the location of the epicenter by using a method called triangulation*.*

*Triangulation* is a process by which we can locate a position by using at least 3 reference points. For example, a lost hiker may be found by finding the distance he is from 3 different cell towers to his phone. Once we know the 3 distances, we can use a map and graph the different distance curves. It is the intersection of these three curves that allows us to pinpoint the hikers location. The same principle applies to earthquakes. We can find the epicenter by using the reading from at least 3 different seismographs. We can then plot our findings and locate the starting point of the quake. The more seismographs that we use, the more accurate our location is going to be.

#### Learning Objectives and Standards

National: Understand patterns, relations, functions, and triangulation

Structure of the Earth System

Minnesota State:

History and Nature of Science 7-Scientific World View

History and Nature of Science 8- Scientific World View

History and Nature of Science 7-Scientific Inquiry

History and Nature of Science 8- Scientific Inquiry

Earth and Space Science 8-Earth Structure and Processes

#### Material List

**Materials:**

Piece of rope measured at 30 meters long

Measuring Tape

Stopwatches (3)

Playground or field

Flags or other markers

Graph Paper

Calculator

Ruler/Straight-edge

Pencils

Compass

#### Procedure

**Procedure:**

- Explain to students that they are going to be modeling the speeds of the primary waves and the secondary waves that are produced by an earthquake.

- Outdoors or in a gym, establish a location where students may walk and run without obstacles for 30 meters.

- Measure a 30 meter distance with the pre-measured piece of rope and station a student at 10 meters, one at 20 meters and one at 30 meters. Mark each station with a flag or marker of some sort.

- Establish a speed for 3 students who will walk to stimulate the movement of the slower secondary waves (S waves). Have the timers record the time that it takes each student to reach their specific station and record those in table 1. Have the three students rehearse this walk a few times so that they are all traveling at the same speed.

- Establish a speed for 3 students (use different students than in step two) who will run to stimulate the movement of the faster primary waves (P waves). Have the timers again record the time that it takes each student to reach their specific station and record those in table 1. Have the three students rehearse this run a few times so that they are all traveling at the same speed.

- Outside, mark off an area that is 30 meters by 30 meters. Pick an "epicenter" somewhere within the area of the field. Mark this spot and measure its distance from the timer's locations or from the edges of the square. This measurement will be used for accuracy later.

- Have 3 different students stand at 3 corners of the square with a stopwatch to simulate seismograph locations. Mark the location of these students with a flag.

- Have the 6 students who are representing the S and P waves stand at the epicenter. Assign each P student to a specific seismograph and do the same with the S students. At the signal of "earthquake", have the 6 students move towards their assigned seismograph at their assigned speed. The timers job is to measure the length of time between the arrival of the P wave and the S wave. To do this, they will start their stopwatch when the P wave student arrives and will stop their watch when the S student arrives. They will then record their data in table 2.

- Return to the classroom and have students construct a graph from Table 1. From this graph, students can figure out the distance from a specific seismograph by using the time that was recorded in Table 2.

- Once the students have figured out the estimated distances from the epicenter to the specific seismographs, they can use this information to find the epicenter. To do this, students will need to construct a diagram that represents the 30m x 30m field and that shows all of the seismograph locations. From each station they then take their compass (which is set up to reflect their estimated epicenter distance from table 2) and draw a semicircle from the point of their seismograph. They do this for each of the 3 seismographs. Where the 3 circles intersect is the estimated epicenter of the earthquake.

- Once the students have found their epicenter and have shown it on their scale drawing, they can find out how accurate their estimation was by locating the actual epicenter from the actual measurements that we found in step 6.

**Conclusion:**

From this experiment, we can visually see that primary waves travel faster than secondary waves. Because the primary waves arrive before the secondary, there will be a time difference between the two waves. It is this S - P times that are used to find the epicenter by using triangulation. Triangulation uses the distance from at least 3 points to pinpoint a location.With earthquakes, these distances are from the epicenter to the different seismographs.These distances are found by using the S - P times.

**TABLE 1:**

Travel time observations for Walk and Run times

**TABLE 2:**

Walk minus Run times at three stations and estimated distances to epicenter.

Use the estimated distance to draw your circular arc from the seismograph station on your scale drawing.

**GRAPH OF WALK TIMES AND RUN TIMES**

Mark your distance (m) on the horizontal axis (left to right) and you time (s) on your vertical axis (up and down). Each grid on the horizontal axis will represent 2 meters. Each grid on your vertical axis will represent 1 second. Take and graph the data that is listed in table 1 with different colors for the walk time, run time, and walk-run time. The walk-run time line will be used in step 9. To use this line, find the time on the vertical axis that was recorded in table 2 and draw a horizontal line over to the walk-run time line. From this point, draw a vertical line to the distance axis. This is the distance from the seismograph to the epicenter.

**Example of Graph of Walk Times, Run Times and Walk-Run Times**

**EXAMPLE OF PLOTTING THE ESTIMATED EPICENTER BY TRIANGULATION ON SCALE DRAWING OF FIELD AREA**

Due to experimental error, the epicenter may not be exactly at the intersection of the three circular arcs.

#### Links and Resources

**Bibliography:**

Brecht, W., Ludwig, F., Mann, B., Snyder, R. and Stasik, J. 1991. *Earth Science*. D.C.

Heath and Company, Massachussetts.

http://web.ics.purdue.edu/~braile/edumod/walkrun/walkrun.htm

#### Assessment

**Discussion Questions:**

- If the epicenter that we picked for our simulation was outside of our 30 x 30 field, could we still locate it by triangulation?

- If the primary wave at station 1 arrived 4 hours and 30 minutes local time, what was the origin time of the earthquake?

#### Cite this work

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