LOCATING EARTHQUAKESMaterials:
Procedure:
The purpose of this activity is to learn how analysis and measurement of seismograms from three or more seismometers can, with relatively simple mathematical calculations, yield the map locations -- the epicenters -- of earthquakes.
The online section of this activity will allow you to interactively analyze real seismic data from several earthquakes that have occurred in southern California. You will be picking the arrival times of the two body waves -- the P wave and the S wave -- and then, using travel-time circles on a map of southern California as your guide, marking the location you believe represents the epicenter of the earthquake. Your wave-arrival picks will also be used to calculate the origin time of the earthquake. Should your first attempt to pick the arrival times produce unsatisfactory results, you will be able to revise them, and see the changes in time and location produced by the changes in your picks. In fact, there is no limit to the number of times you can revise your analysis of the seismograms provided.
This page will help you get started by previewing the basics of the activity. The explanation page will show you the layout and the features of the online portion of the activity; it will also serve as a help page you can bring up in a new window should you need review while you work at locating earthquakes.
Because the online earthquake-locating program uses JavaScript, frames, and layers to manipulate the data appropriately, your browser will need to be capable of handling these features. If it isn't, we apologize; there is no alternate page available. The basic steps for using the program are outlined below:
When the activity first loads, you will see a title frame at upper left, with a button labelled "Quit!" There will also be a data frame to the right of the title; it has five fields of information (all will be blank at first) and a menu bar of four options. Below these two frames is a large frame with a short list of entries -- a date followed by a number of "traces." Above the list are the words "Choose an Event to Locate."
These "events" are earthquakes. You will need to choose one to get the program started. You should also decide, at some point, how many of these earthquakes you intend to locate before you quit the program. There is no upper or lower limit on this, but we recommend you try to locate at least three different earthquakes, including one of the first two on the list. Clicking on a list entry will cause two things to happen. First, the data for that earthquake will fill in the first four fields of the data frame above: Event Number, Date, Number of Traces, and Time. Second, the large frame itself will reload, this time displaying the appropriate number of seismogram traces -- white rectangular boxes with a squiggly black line running the length from left to right.
Atop each seismogram are two items: a red arrow marked "P" and a rectangular button. The red arrow is draggable. To locate earthquakes in this activity, you will need to align the red arrow on each trace with the time of the P-wave arrival. Recall from the text of Section 3 that the arrival of the P wave is generally indicated by the first noticeable deflection of the trace from its position of rest. This at-rest position can be found at the far left edge of each seismogram. All the seismograms for a given earthquake are "aligned" in time -- that is, time elapses from left to right on these records, and the left-hand edge of each starts at the same time, the time given in the "Time" field of the data frame when a new event is first chosen (this changes later).
Picking the arrival times of the P-waves is accomplished by dragging (click and hold down while moving the mouse) the red arrows into position. Depending on your system and browser, you may have trouble dragging the arrows. If you can't seem to get them to drag, try this: instead of clicking on the arrows, try clicking off to either side of them. There are invisible "handles" there that should let you drag the arrows normally. This may take some getting used to.
Once you have picked all the P-wave arrivals, you will need to choose one (and only one) S-wave arrival. You may choose this arrival on whichever trace you feel most confident about identifying the very start of the S wave. Recall that the arrival of the S wave on a waveform is most obviously noted by a sudden increase in the amplitude of trace deflection after the P-wave arrival. There may also be an increase in the wavelength of the oscillations on the waveform associated with the arrival of the S wave. To choose an S-wave arrival, click on the rectangular button labelled "Pick an S arrival" atop that seismogram. A blue arrow marked with an "S" will appear, and the rectangular button will then read "Remove the S arrival." Drag and place the blue arrow as you did the red arrows (but at the point of the S-wave arrival, of course). Should you change your mind, and want to identify the S arrival on a different trace, click the button to remove the S arrow, and click the "Pick an S arrival" atop a different seismogram. Should you change your mind again, and come back to the original trace, you'll find that the arrow reappears right where you left it!
Once you have placed your arrows identifying the P-wave and S-wave arrivals on the seismograms, you are ready to move on to locating the epicenter. Click on the button at the bottom of the screen (scroll down if necessary) that reads "Find Origin Time and Epicenter." When you do, two things will change: the "time" field in the data frame, and the contents of the large frame.
The "Time" field in the data frame will be revised to indicate the origin time of the earthquake, as calculated from the difference in time between the P and S arrivals. The origin time is the time at which the earthquake actually began. This will typically be earlier than the time marking the left-hand edge of the seismograms. The contents of the large frame will change, too. Instead of seismograms, you will see a background map of southern California, overlain with circles and a few other symbols.
The circles are travel-time circles, centered on the seismic stations that recorded the seismograms you used to pick P-wave and S-wave arrivals. How can more than one circle have been calculated when only one S arrival was picked? Because of a clever trick used to simplify things: the one pair of arrivals on a single trace is used to calculate an origin time for the earthquake. Once the origin time is a known quantity, it can be used in place of the S-wave arrival to calculate travel-time circles from seismograms where the time of the P-wave arrival is known.
Hopefully the three or more travel-time circles drawn for you on the map meet in roughly a single point. If so, grab and drag the crosshairs from its position at lower left to the point of the circles' intersection. Then click the "Lock Epicenter" button. In the data frame, the "Epicenter" field will light up with the location of the epicenter you chose, as a distance in kilometers in a certain compass direction from the nearest town labelled on the background map.
Even if the circles fail to intersect in nearly a single point, follow the directions above to mark the place you feel is closest to where the epicenter ought to be, and then use the menu bar in the data frame to "Check Traces." This will take you back to the screen full of seismograms and arrows. Review the arrivals you picked, make modifications if you feel you can improve upon the job you did before, and then once again click on the button marked "Find Origin Time and Epicenter." The screen will again shift, and the origin time will be updated (if necessary) to reflect your changes.
On the map, the old epicentral location you chose will be marked with a faint yellow crosshairs (not draggable). Drag the "active" set of crosshairs to the new (hopefully better) location of intersection for the travel-time circles and "Lock Epicenter" again. Repeat this process as many times as necessary until you are satisfied with the epicentral location. Bear in mind that there will be sources of error in the data and the methods, so trying to get more than three travel-time circles to intersect in exactly one point is probably a waste of time. As long as they come close to intersecting in the same place, that is good enough. (With only three circles, however, you should strive for a "perfect" intersection.)
Once you are fully satisfied that you have located the epicenter as accurately as possible, record this location on a sheet of paper or a whiteboard to check against our suggested solutions later. You can then use the menu bar's "New Event" option to load another set of data for a different earthquake, and start the process all over again.
That's how this activity works. All its features are explained in detail on the explanation page, which can be pulled up as a help page at any point during the activity, using the menu bar's "Help" option. You are now ready to start the activity, though you may wish to more fully orient yourself with the use of the activity by reviewing the explanation page. It covers the same material as above, but organized according to the frames and features of each screen. It also explains the math and models used to calculate origin times and travel-time circles.
When you do begin working on the activity, remember that you are free to locate as many earthquakes as you like, but that once you've finished with them, you should use the button labelled "Quit!" to return to this page and work through the review questions below.
Comparing your results to ours, what is the largest
difference in origin time?
What is the largest difference in epicentral location?
Do the greatest disparities correspond to events
for which there were many traces or for those with few traces --
or did there seem to be no real correlation between these two
factors at all?
Though this locating program should have done a fair job of finding epicenters and origin times, there were many sources of error; you shouldn't feel bad if your results do not match well with the suggested solutions. With the methods you used, the sources of error can be grouped into two classes: human error in picking arrival times, and computer error in calculating travel-time circles based upon the arrival picks and the velocity modelling used.
Imagine a station that records ground motion from an
earthquake roughly 15 seconds after that earthquake's origin time,
which has already been determined with good accuracy.
To calculate a travel-time circle, a P-wave velocity of 6.0 km/sec
is used -- but this velocity has an uncertainty of 10% (0.6 km/sec),
because the geology between the station and the earthquake source
is not well known. Estimate the uncertainty in the radius of a
travel-time circle calculated with this velocity.
(Assume a depth of 0 km.)
What kind of alterations to the computational methods
might reduce the error in the travel-time circles?
There may appear to be a "catch-22" involved in
reducing computational errors: to find the epicentral location
of an earthquake more accurately, you need
to model the wave velocities between the source and the
stations more accurately... but that requires knowing the
epicentral location! Fortunately, this catch can be avoid
by running several iterations when solving
for the location of the earthquake. The first can use a crude
but functional velocity model, like the one this activity
relied upon, to find a general location, and then better
models can be applied to refine this location on successive
iterations. This is essentially how the problem is handled
by the software used for seismic analysis at major research
institutions.
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