This is a simple, interactive earthquake location activity developed for use
in introductory earthquake seismology classes. The traditional triangulation
exercises are interesting, and used for a rough estimate of earthquake
location, but they are not how earthquake locations are actually estimated. In
this activity, we use P-arrival times to estimate the location of an
earthquake. Specifically, we use a simple interactive interface to minimize
the misfit between the observed and predicted P wave arrival times.
For details, read the instructions by clicking on the "Instructions" button
below. All the buttons toggle the visibility of the interface. Start by
clicking on the "Observations" button below, enter the observations (or play
with the default values) and click the "Import" button. You will see two views
of the arrival times - one map showing the individual station misfits using
circles, another showing the difference between the travel time curve and the
observed times. A google-map allows you to try different epicenter locations;
when you tap that map, you set the epicenter of the "trial" seismic source
location. The default values are a small earthquake - can you find the
epicenter?
The web-app will NOT work with Internet Explorer;
it seems to work fine with Safari, Chrome, and Firefox on Macs, Safari on ios8,
but has some issues with ios7 on ipads. Firefox appears to work on Windows.
Search for the Source - Minimize the RMS misfit to the P arrival times
The earth model is a very, very crude approximation, a uniform crust
defined by the P-wave speed (Earth is not so simple). The mathematica basis for the
procedure is very simple,
$$Time = \frac{Distance}{Speed}$$
The idea is to move the "source" (an earthquake or quarry balst)
location until the predicted times match the obsered
times.
You can solve the problem more quickly using calculus and algebra, but this
app is designed to give a feel for how those approaches work.
The gold circle represents the epicenter of the source.
The red and blue circles represent the fit to the arrival time at the seismic stations.
If the wave arrives at the station too early, the color is blue.
If the wave arrives at the station too late, the color is red.
The size of the circle size reflects the size the difference between the observed and predicted times (we call the difference a residual).
To try a different source location, click where you want to place the epicenter in the Google Map.
A useful number to watch is the RMS value shown in
the upper left. RMS is an abbreviation for the Root-Mean-Square, which is the
square root of the average value of the squared misfit.
$$RMS = \sqrt{\frac{1}{nobs}~\sum_{i=1}^{nobs}~ \left(t_i^{~observed} - t_i^{~predicted}\right)^2} $$
Try to locate the epicenter with the the fewest number of guesses. To do so,
study the misfit pattern before you make your next location guess.
On the travel-time plot, the thicker, black line shows the times predicted by the
earthquake location model; the thinner, gray line is a least squares fit to the
distance-versus-time values (a guide for adjusting the model).
If enabled in the feedback settings, the parameters at the top of the travel time plot
show the least-squares linear fit (slope is slowness, intercept is a suggested origin time adjustment).
Enter your arrival time measurements in the text area below. The arrival times
should be relative to a uniform and known reference time. For each seismogram,
enter the seismic Station ID, the longitude (in decimal degrees), the latitude
(in decimal degrees), and the arrival time. The data can be space or comma
delimited. Any line beginning with a # will be ignored. The arrival time can
be relative to a specific "reference" time, but all the times should be
relative to the same "reference" time.
The Earth Model
We use a simple, uniform speed to calculate the travel times from a seismic
origin to each observation point. This means that we ignore all variations in
geology (rock type). Enter an average speed to use to calculate the travel
times to the seismic stations.
The units are kilometers per second (km/s).
The Source Depth
We don't know the source depth, so we can try a range of depths. Enter a
source depth and search for a good fit. If you can't find a good fit, try
another depth. Vary the depth systematically.
The units are kilometers (km).
The Origin Time Adjustment
Finally, we don't know when the source initiated, so we may have
to add or subtract a constant to all of our observed arrival times.