Homework 4

Seismology

Greg Anderson

This homework set is worth a total of 100 points. Be sure to read the entire assignment carefully before beginning work on it. You should read pages 73-79 of The Blue Planet and the lecture notes from Lecture 11 before you do Question 2.

Please write your answers on paper other than this assignment, make sure your name is on each page, and staple your pages together. If you have problems with or questions about the homework, please come see me at the discussion section or send me an e-mail. My e-mail address is anderson@python.ucsd.edu; the discussion section will be held on Wednesday evening, 18 February (since Monday 16 February is a holiday) at 6:45 PM in Peterson Hall 104.

One of the most common questions seismologists are asked is: ``I've heard that earthquakes are happening more often these days than they used to. Is that true?'' In this problem, you are going to try to answer that question for yourselves.

Table 1 shows the number of earthquakes with magnitudes of 7.0 or greater which occurred in each year between 1900 and 1997. These numbers come from the United States Geological Survey's National Earthquake Information Center in Golden, Colorado.

Here's what I want you to do:

- Make a graph of the numbers in Table 1.
- Based on your graph, decide for yourself if the number of large earthquakes worldwide per year is increasing, decreasing, or staying relatively constant over time.
- Turn in your graph and your answer to the question ``Is the rate of large earthquakes worldwide on the increase?''

One thing: if you make the graph by hand, *don't* label every year along
the X-axis. Instead, make a tick mark every fifth or tenth year, and just
label those (of course, you still need to plot the numbers for the other years)
-- doing the tick marks this way will make your graph much easier to read.

The single most important thing for this problem is not your answer, but the reasoning behind your answer. Your answer must be supported by your graph and your arguments based on your graph. In other words, I am more interested in how you arrive at your conclusion than what your conclusion is.

In this problem, you get to locate an earthquake here in southern California. Normally, seismologists locate earthquakes with fancy math and fast computers, but we will return to the old days of seismology and locate an earthquake by hand.

Below, you will find a series of figures (Figures
1-5)
with seismograms made by an earthquake here in southern California on Monday, 5
January 1998. These are five *seismograms* made by five different
*seismometers* in locations around southern California. The locations
of the stations which made the recordings are shown on the map in
Figure 6, with the three character
codes (such as EDW) shown both at the right spot on the map and above the
corresponding seismogram.

Look at the seismogram from station GSA (Figure 2). You
will see that
there are two distinct points in the seismogram where the size of the wiggles
(what seismologists call the *amplitude*) goes up compared to the wiggles
around them. The first jump is the arrival of the P wave, which is the
quickest seismic wave. The second jump is the arrival of the S wave. By
measuring the times at which these two jumps occur (called the *arrival
times*) and then taking the difference of these two times (called the
*S-P time*), you can use Table 2
to figure out how far the earthquake is from the station. The procedure of
finding the arrival times for the P and S waves is called ``picking''.

After you know the distance, on your map of Southern California (Figure 6) you draw a circle of the correct radius centered at GSA, and you know the earthquake has to lie somewhere on that circle. After you repeat the above procedure for the other four stations, you will have five different circles, which will overlap one another. There should be a small region where the circles all overlap or are nearly overlapping, and you know the earthquake must be somewhere inside that small region. Ideally, there would actually be only a single point, but small errors in measurements and in Table 2 will cause the circles to overlap rather than just touch in a single spot.

Here's what you are to do:

- Pick your arrivals for the P and S waves at each of the five stations. Indicate your chosen times by drawing an arrow toward the jump on the seismogram, and labeling it ``P'' or ``S'', depending on what type of wave it is.
- Using a ruler and the time scale shown at the bottom of the each figure
calculate the arrival times for the P waves and S waves at each
station.
*Note that the time scale and start time for each seismogram are different.* - From those arrival times, calculate the S-P time.
- Use Table 2 to convert the S-P time to the equivalent distance from the station. You will almost certainly not find an entry in the table which corresponds exactly to your measured S-P times, but you can use the table to make a good guess of the correct distance for your measured times.
- After you have worked out what the correct distances are, use a drawing
compass to draw circles on the map in
Figure 6. Make sure your
circles have the correct radius from each station. To do this
correctly, you need to know that the scale bar shown in the lower left
corner of Figure 6 represents
50 kilometers in the real world.
**If you don't know how to use this map scale information to draw the circles correctly,**.*come see me* - Once you have drawn all five circles at the right radius, you will see that they overlap in a small region. Shade that region in (lightly), so that I can see it.
- Make a small table showing the arrival times of the P and S waves, the S-P time, and the distance to the earthquake from each of the five stations. Look at Table 1 in the notes for Lecture 11 for an example you might follow.

**Be sure to show your work if you want to get credit**. If you don't
show your work, you will get **no credit** for the work you did -- and
if you do something wrong, I won't be able to give you partial credit if I
can't see how you tried it.

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Greg Anderson

anderson@python.ucsd.edu

Tue Feb 10 10:54:40 PST 1998