G101, Fall 2022
Worksheet #5: Seismic Waves: distance, timing and velocity; calculating earthquake depth
This worksheet is due by 11:59pm on Tuesday 10/25
For Part A of this worksheet you will work with the graph on ilearn titled “Graph of Earthquake Waves for worksheet #4.”
The graph shows the distance-time relationship for body waves generated by earthquakes. The lower left corner (0,0) indicates the earthquake Focus (point of origin). The Y axis provides the amount of time (in minutes) since the earthquake; the X axis provides the distance (in kilometers) the waves have travelled from the earthquake origin. For the X axis note that each whole number equals 1000km.
The curves labelled “P” and “S” allow us to determine how long it takes the waves to travel a given distance.
For examples of how to use the graph, see the pdf on ilearn titled “Using the graph for Worksheet #4”
Use the graph and material from lecture to answer the following questions.
Part A: Distance, timing and velocity of Body Waves
1. Why are P and S waves referred to as Body Waves?
2. At a distance of 400 km from an earthquake: How long will it take for the P-wave to arrive? How long for the S-wave to arrive?
b. What is the time interval between P and S waves?
3. At a distance of 1200 km from an earthquake: How long will it take for the P-wave to arrive? How long for the S-wave to arrive?
b. What is the time interval between P and S waves?
4. At a distance of 7600 km from an earthquake: How long will it take for the P-wave to arrive? How long for the S-wave to arrive?
b. What is the time interval between P and S waves?
5. Take a close look at your answers for questions 2-4. As distance from the earthquake origin increases, what happens to the time interval between P and S waves?
6. Seismic Stations use the time interval between P and S waves to determine the distance of the station from an earthquake. It is an accurate measurement and allows the Station to determine distance without knowing when the earthquake occurred. We will use this method below:
a. The Station measures the time interval between P and S waves at 4 minutes. How far away did the earthquake occur?
b. The Station measures the time interval between P and S waves at 30 seconds. How far away did the earthquake occur?
7. Because the graph gives us Distance and Time from the earthquake origin, we can calculate the Velocity of the seismic waves using the following formula:
Distance ÷ Time = rate of travel (velocity)
Calculate the velocity of the P and S waves at the following distances from the earthquake origin:
Answers should be in kilometers per minute. (To get credit, you must show your calculations)
Distance 1: 1600km
Distance 2: 5000km
Distance 3: 8800km
8. Look carefully at your answers for #7.
Did the velocity of the P-Wave remain consistent as distance from the earthquake origin increased? What about for the S-Wave?
Describe the pattern/change. Include both P and S waves.
Part B: Using the Properties of a Right Triangle for Earthquake Distances
In this part, we will apply the properties of a Right Triangle to calculate earthquake depth.
As we know from Pythagorean Theorem, if two sides of a triangle form a Right Angle (90°), the relationship between the three sides will be: a²+ b²= c²
a²+ b²= c² allows us to determine the length of any side when the lengths of the two other sides are known. We are going to use this formula to determine the depth of an earthquake when given:
⦁ The distance from epicenter to Seismic Station along the surface
⦁ The distance from the earthquake focus to Seismic Station
To understand how this works, take a look at the diagram on the last page of this worksheet. Make sure you can identify the a, b, and c sides of the triangle. Remember, we are solving for depth, so you will need to rearrange a²+ b²= c² in your calculations.
9. Determine the depth of the earthquake focus for the three earthquakes numbered below :
Earthquake #1:
Epicenter to Seismic Station: 32 km
Focus to Seismic Station: 49 km
Earthquake #2:
Epicenter to Seismic Station: 61 km
Focus to Seismic Station: 74 km
Earthquake #3:
Epicenter to Seismic Station: 101 km
Focus to Seismic Station: 103 km
10. Let’s assume that the Moment Magnitudes of the earthquakes in #11 are the same. Of the three (1, 2 or 3), which one will likely cause the most severe shaking at the surface? Explain why.
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