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University of Oregon *
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Astronomy
Date
Feb 20, 2024
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9
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Lab #8: Epicenter and magnitude of an Earthquake A) Purpose of the assignment:
In Lab #7, you have learned how to use differences in time of arrival to get distances and found the house of Polly and Salim without knowing where they were coming from. In this lab, you will use measured data to find the epicenter of a real earthquake using the fact that P waves are travelling faster than S waves. You will also calculate the magnitude of the earthquake using amplitude measured on the seismograms. B) Learning objectives and skills •
carefully read instructions •
read graphs and extract data from them •
apply basic graphical and mathematic skills •
provide clear explanation of reasoning and method used C) Tasks Part I: Locating the Epicenter There are hundreds of seismic stations throughout the world. In order to locate the epicenter of an earthquake, you need to estimate the time interval between the arrival of the P and S waves, called the S-P interval, on the seismograms (e.g., Figure 1) from at least three different stations (remember Lab#7). The S-P interval is then converted into a distance to the epicenter. Figure 1:
Example of seismogram. Here vertical blue and black lines are spaced at 2-second intervals so that the S-P time interval is about 36 seconds.
You can now determine the distance from each seismic recording station to the earthquake's epicenter using the known times of travel of the S and P waves. Figure 2:
S and P wave travel-times graphed versus distance, as well as the variation in distance with the difference of the S and P travel times. 1) Approximately, how long does it take for an S wave to travel 300 kilometers? (2 points)
2) Given your answer to question 1), what is the average velocity of S waves in kilometers per second? Explain your calculation. What would be the velocity of S waves in miles per hour (1 mile = 1.61 km)? (2 points)
3) How many times faster are the P waves compared to the S waves? Explain your calculation. (2 points)
4) You determined that the S-P interval is 36 seconds on the seismogram shown in Figure 1. Using Figure 2, what does this S-P interval correspond to in terms of distance? (2 points)
5) Figures 3 and 4 show a map of the Southwestern part of the United States as well as three seismograms recorded during an earthquake that occurred in the area. Using these seismograms together with what you have learned in Lab #7 and in question 1, and the expanded part of Figure 2 provided in Figure 3, locate the epicenter of the earthquake on the map shown in Figure 4. Explain the different steps of your reasoning. (6 points)
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Las Vegas, NV seismograph station Eureka, CA seismograph station Elko, NV seismograph station Figure 3:
(Top) Three seismograms that recorded the earthquake and will allow you to locate the epicenter on the map provided in Figure 4. (Right) expended part of Figure 2 to give you better precision to determine the location of the earthquake. 6) Using just the amplitude (i.e., the vertical axis), which seismograph station is probably closest to the epicenter? Assume all three stations are located on the same type of rocks and that all rocks and Earth’s layers traversed by the seismic waves between the earthquake and all three stations are homogeneous. (2 points)
Figure 4: Map showing the region of the earthquake and the location of the epicenter.
Part II: Determining the Magnitude of the Earthquake So far, you have located the epicenter of an earthquake. Let’s now determine how strong was this particular earthquake. In 1935, Dr. C.F. Richter of the California Institute of Technology introduced a scale, known as the Richter Magnitude Scale, which is used to compare the strengths of earthquakes by using the seismograms of an earthquake (cf. Figure 5). The magnitude of an earthquake is an estimate of the total amount of energy released during fault rupture. The Richter magnitude of an earthquake is a number: about 3 for earthquakes that are strong enough for people to feel, and about 8 or higher for the Earth's strongest earthquakes. Two measurements are needed: The S-P time interval and the Maximum Amplitude of the Seismic waves. Figure 5:
How to make the measurement of the S wave's maximum amplitude. The blue horizontal grid lines are spaced at 10-millimeter intervals, black lines are every 50 mm. In the example above, the maximum amplitude is about 185 mm.
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Figure 6. The Richter Nomogram
: the relationship between Richter magnitude, the measured amplitude, and S-
P interval is complex, but a graphical device (a nomogram) can be used to estimate magnitude from distance and amplitude. Note that a 100 km-away earthquake of magnitude 4 would produce 10 mm of amplitude (line B) and a magnitude 5 would produce 100 mm of amplitude (line C) at the same distance. 1, 10 and 100 are all powers of 10 and this is why the Richter Scale is said to be "exponential." A change of one unit in magnitude (e.g., 4 to 5) increases the maximum amplitude by a factor of 10. The last line drawn, line D, shows the result for an earthquake that produces an amplitude of 150 mm at a distance of 620 km. Although only one amplitude measurement is necessary to estimate the magnitude of an earthquake, it is better to use measurements from several seismograph stations. This allow us to determine an average of several magnitude values, increasing the likelihood that you are accurate in your estimate. 7) Using the Figure 6 and the seismograms provided in Figure 3, provide the amplitude of the earthquake. Briefly explain how you proceeded. (4 points)
Figure 7. Richter Nomogram to use to obtain the magnitude of the earthquake from Figure 3. D) Criteria for Success and grading: This assignment is worth 20 points in total. Questions 1-4 (2 points each):
These four questions are about reading a graph, extracting information, and applying simple math go find the answers. As usual, you need to detail your reasoning and calculation so you can still earn points if your reasoning and math are well detailed and make sense, but you made a mistake in the calculation. Question 5 (6 points):
here, I am looking whether you can read real data and apply a reasoning that you made in Lab#7 on an analog problem to the location of a real earthquake. Question 6 (2 points):
This question is about applying a simple, logical reasoning to find the answer. Only one answer possible. You need to briefly justify your answer.
Question 7 (4 points):
Here I am looking at whether you can apply simple graphical skills and follow the procedure descried in the captions of Figure 5 and 6 to find the magnitude of the earthquake. There is only one possible answer. You need to briefly justify how you found it.
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