HW 5 - Earthquakes

Answer Sheet

This answer sheet is designed to give the answers to the questions in Homework
5. It is
**not**
meant as a substitute for talking to me about the
homework if you have questions. Please ask me after class or send me e-mail
if you still have questions after reading this sheet. My email address is
ganderson@ucsd.edu.

The maximum number of points possible on this assignment was 50.

- Question 1: Worldwide Earthquake Rates (20 points)
- Question 2: Where is that dang quake? (30 points)
- About this document ...

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For this question, I gave you a table which had the number of earthquakes with magnitudes of 7 or larger in each year from 1900 through 1996. You were to make a graph of these numbers with time running along the X axis and the number of earthquakes running along the Y axis. You were then to decide, based on your graph, if the number of large earthquakes worldwide is going up, down, or staying basically the same.

My graph for this question is shown in Figure 1. The red circles are the numbers of earthquakes in each year, while the green line which connects these dots is there to make the trends easier to see. The long-dashed blue line is the mean number of earthquakes of this size worldwide in a given year, which is 20. The blue dotted lines are the maximum number (41 in 1943) and minimum number of quakes (6 in 1986), respectively.

From this graph, my conclusion is that the number of earthquakes of magnitude 7 or larger worldwide varies quite a bit from year to year, but seems to be remaining basically constant. There may also be some sort of cycle of more quakes followed by fewer, but saying anything more than that is pretty risky. It's also clear that the mid-1940s to early 1950s was a pretty active time for large earthquakes, and that the 1980s and early 1990s had fewer earthquakes than the average.

You might argue that, on a smaller scale, the number of earthquakes is going
up (since we are rising out of a dip in the 1980s) and that the number of
earthquakes is actually going down, since there appears to be a *very*
slight ``downhill'' trend over time. I accepted either of these answers,
provided you said *why* you believed the answer to be correct.

The real answer, however, is that even 100 years is probably not a long enough time period to look at the number of large earthquakes to decide if there are any trends over time. The best we can say at the moment is that there is no strong evidence that the number of large earthquakes worldwide is going up over time.

You may well be wondering why I didn't give you a table for smaller
earthquakes. The answer is that it would have been deceptive. Our ability
to detect and locate earthquakes depends on how many seismometers there are
and how well they are scattered about the globe. Due to concerns over
verifying global nuclear test ban treaties, the US Government has spent loads
of money placing seismometers all around the world, and so the number of
seismometers worldwide has steadily gone up over the years. As a result,
the number of earthquakes we can detect has gone up, and the minimum magnitude
earthquake which we can see has gone *down*.

So if you hear people saying very silly things like, ``the world is going to end soon, because there are more and more earthquakes happening all around the world,'' you now can look them in the eye and tell them that's baloney. The number of earthquakes is actually remaining more-or-less constant (to the best of our knowledge), it's just that we are detecting more and more of them. Doomsday may or may not be coming with the new millenium, but seismology certainly doesn't support the idea that the world's going to end anytime soon.

By the way, the next millenium starts on 1 January 2001, **not** on 1 January
2000. I know that people like me will never convince the general population of
that, but it really annoys me to have people get that wrong. So please don't.

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This question was more challenging than Question 1, but most people did well. Cool.

The first step for locating the earthquake is to pick the arrivals for the P and S waves and indicate them with arrows or lines so that I could find your picks easily. Figure 2 shows the traces with my picks marked by dashed lines (with ``P'' and ``S'' as appropriate).

Picking the P and S arrivals correctly is the hardest part of this problem.
The right way to pick P arrivals is to look at the seismogram *before*
the earthquake and see what it looks like, and then to pick the *very
first* instant the record looks significantly different from before the
earthquake. This does not mean that you pick the first large part of the
P wave -- you should pick the very *first* part of the P wave, which
may be much smaller than the big swings a second or so later. For the S
wave, you have a bit tougher of a time, but basically you have to look at
again the *first* instant that the waves look different after the P
wave.

All I can say is that it's tough the first few times you pick the arrivals, but after a while, picking gets easier. I certainly don't expect you to get it perfectly right, and besides, my picks aren't necessarily ``perfect'', either. The fact is that, even when the picking is done by experienced people, using digital recording (rather than paper, like I gave you), the picks made by two people are usually different by as much as a couple tenths of a second for very sharp arrivals, and perhaps by as much as 0.5-1 second for less clear arrivals. So in this case, ``close'' is OK.

Once you have the P and S arrivals located, you need to figure out the times
at which these waves were *first* recorded at the various stations. To
do that, you need to use the time scale on the bottom of the figure. As an
example, let's use the PFO record. The time scale is such that 1.1 centimeters
is the same as 5 seconds. The earliest time mark (on the left edge of the
figure, but it's unlabeled) is 35 seconds after 03:43. So I measure from the
left side of the figure to my dashed line; that distance is roughly 1.1
centimeters. I can use the following equation to work out the time in
seconds:

So the arrival time at PFO is 5.0 seconds *after* 03:43:35, which makes
the PFO P arrival time 03:43:40.0. I can repeat the measurements (distance
is about 2.24 cm) and calculations for the PFO S arrival and I get

So the arrival time at PFO is 10.2 seconds *after* 03:43:35, which makes
the PFO S arrival time 03:43:45.2.

Now that I have the PFO P and S arrival times, I can compute the PFO S-P time simply by subtracting the PFO P time from the PFO S time. In this case, the answer is 5.2 seconds.

After I have the S-P time, I can go to the table I gave you of distance from S-P time, and find the distance from PFO to the earthquake. In this case, there is no listing in the table for 5.2 seconds, but there are listings for 5.0 and 6.0 seconds (39.2 and 47.1 km, respectively). I can use these distances and times, and my measured time, to get a good estimate for the distance from PFO to the earthquake.

To do so, I first figure out how much the difference in distance is from the smaller time to the larger time (5 seconds to 6 seconds); in this case, it is 47.1-39.2 = 7.9 km. Next, I need to figure out what fraction of a second I am above 5 seconds; in this case, the difference is 0.2 seconds. Finally, I multiply 0.2 by 7.9 and get 1.6 km. I need to add 1.6 km to 39.2 km to get the correct distance; in this case, 40.8 km is the distance from PFO to the earthquake.

Repeating the measurements and calculations for all four stations (both P and S arrivals), I can fill up Table 1. In Table 1, the stations are listed in order of increasing distance from the station to the earthquake. I've listed the arrival times both in the form that I'm used to seeing (like 03:44:01.2) and in the form that most people wrote their times in (like 61.2 seconds).

Once you have filled up your equivalent of Table 1, you need to convert your distances to the radii of the circles you need to draw on your map. To do this, you need to know the scale for your map. For those who got the homework handout in class, the scale was such that 1 centimeter on the map was equal to 25 kilometers in the real world. For those who downloaded the homework from the web page, I couldn't be sure the scale would stay the same, so I made a scale bar; you needed to measure the scale bar to work out your scale (it's different depending on your printer!).

Armed with the map scale, all you have to do is divide the distance in km by the map scale to convert to centimeters on your map. In the case of the handout in class, this means you divide by 25. If you do this for all the stations, you get Table 2.

The final step is to dig out your drawing compass and the map I gave you, and draw circles with the radii in Table 2. If you don't have a compass, you can fake it pretty well using a ruler; draw four or five points at the right radii and connect the dots as smoothly as you can. When you are finished, you should have a map which looks something like Figure 3.

Figure 3. Map showing circles at correct radii from stations BRK, NEE, PFO, and VTV. Asterisk marked "epicenter" is the epicenter calculated by Caltech. Shaded circle is the area in which my estimate of the epicenter lies, counting uncertainties.

If you gave me a table like Table 1, a figure like Figure 2, a map like Figure 3, and your measured P and S arrival times are within a one second of mine, you got full credit. Each arrival time which was off by more than one second dropped one point. If your S-P times didn't match your arrival times, each one like that cost another point. If the distances you listed did not match your S-P times, each discrepancy was another point, and if your circles were the wrong size given your distances, each wrongly-sized circle was another point off. No table cost you five, and no labels for P and S on Figure 2 cost you five. This might seem anal, but it was designed this way so that people wouldn't lose too many points just by having troubles picking the P and S arrivals.

It also occurred to me that you might like to know what the folks at Caltech have to say about this earthquake. This was a pretty fresh quake when the homework was made up --- only about 12 hours old! Your earthquake happened on 22 February at 7:43 pm PST (23 February 03:43 UT) about 18 kilometers (11 miles) north of Mecca in the Little San Bernardino Mountains. It was felt nearby and had a magnitude of 3.8. The Caltech folks have more details available about your earthquake.

Somebody asked about this in lecture, so I thought I would tell you what the three-letter codes mean. Seismologists use three- and four-character station codes to keep the thousands of seismometers straight around the world. There is actually a committee to make sure that no two seismometers get the same name. Most of the time, the names are chosen to be something meaningful geographically (like PAS, which is in Pasadena). But even so, with three- character names, you can have almost 46700 stations before you run out of names. With four-character names, you can have 1,680,000 stations. Needless to say, we won't run out anytime soon, even though there are literally hundreds of seismometers in southern California alone.

In our case, BKR is Baker, NEE is Needles, PFO is the Piñon Flat Geophysical Observatory (I do some research there) between Anza and Palm Desert, and VTV is Victorville. You can find out more details on the Southern California Earthquake Center (SCEC) Southern California Seismographic Network (SCSN) Digital Broadband Stations page at http://www.scecdc.scec.org/terra.html.

I realize this problem was challenging, but I hope you found it at least
somewhat interesting. As I said, nobody *really* locates earthquakes
this way these days, but this is how it used to be done.

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Greg Anderson

ganderson@ucsd.edu

Tue Mar 11 16:37:22 PST 1997