EqLocate Tutorial 1
(L. Braile, July 2002, revised November,
2004)
http://web.ics.purdue.edu/~braile
About EqLocate: EqLocate
is an interactive earthquake location program that uses actual seismograms and
user-selected P-wave arrival times to locate the earthquake. The program uses a method that is similar to
the approach that is used by seismologists to routinely determine the location
of earthquakes from around the world. In
the standard method, tens to hundreds of arrival times (each from an individual
seismogram corresponding to a seismograph station) are used by a computer
program to automatically find an optimum solution (location and origin time of
the earthquake determined such that the observed arrival times match the
theoretical arrival times calculated using a well-known seismic velocity model
for the Earth). In EqLocate, a limited
number of seismograms (
Several data sets (seismograms) for selected earthquakes are provided with EqLocate. Additional data can be added to the EqLocate folder at any time. Although EqLocate can be used to locate many earthquakes, and the resulting locations are reasonably accurate, the primary objective of the program is to illustrate the important concepts of earthquake location for educational purposes.
The EqLocate program was written by Alan Jones based on a concept developed by Larry Braile. John Lahr and Larry Braile provided testing and suggestions during program development. Support for development of the program was provided by the NSF-sponsored IRIS (Incorporated Research Institutions for Seismology) Consortium.
Four sections of this tutorial (Running EqLocate, How EqLocate Works, Importing Data into EqLocate, and Data Sets) are provided below to explain the use of the program to locate earthquakes, to understand the method used by the program, and to learn about earthquake data (including importing data into EqLocate) and earthquake location.
List of Contents (click on topic to go directly to that section, use
the red up arrows to return to the List of Contents):
1.4 Opening seismograms from an earthquake folder
1.5 Finding the earthquake epicenter
1.6 Estimating the possible error in the derived epicenter
1.7 Determining the depth of focus of the earthquake
1.8 Checking the accuracy of the solution
2.2 Seismograms recorded at seismograph stations
2.3 Flow chart for the EqLocate program
2.4 An additional example of the use of EqLocate
3. Importing data into EqLocate
1. Running EqLocate: This section describes how to
install and operate the EqLocate program on your computer. EqLocate runs on the Windows operating
system.
1.1 Installing EqLocate: To install EqLocate on your computer, use your Netscape or Internet Explorer browser to link to: www.geol.binghamton.edu/faculty/jones/EqLocateSetup.exe. Download the file EqLocateSetup.exe to your computer (saving it in a folder called “Downloads” is convenient as you can reinstall at some later time or copy or send the file for another computer) and double click on EqLocateSetup.exe. The setup program will install EqLocate on your computer in a folder called EqLocate. In the EqLocate folder, right click on the EqLocate.exe file and create a shortcut to EqLocate.exe. Drag the shortcut to your desktop.
1.2 Starting EqLocate: To start EqLocate, double click on the EqLocate.exe shortcut on your desktop. A “splash screen” with information about the program will appear. Click continue. A world map similar to that shown in Figure 1 will appear. You can change the map view and zoom in using the arrow and plus and minus controls as illustrated in Figure 2. Zoom in on the map and adjust the view to the approximate area of the earthquake that you wish to view. You can select one of the standard earthquake data sets (seismograms located in folders organized by event) provided with the program or generate your own seismogram folder by downloading data from the IRIS Data Management Center using WILBER (see Importing Data Into EqLocate below) or other source of SAC binary seismogram files such as AS-1 or PEPP.
Figure 1.
Screen image of the EqLocate program showing world map display. Any area of the world can be displayed and
the user can zoom in to focus on the area that included the seismograph stations
of interest. Latitude and longitude
lines at 15 degree intervals are shown on the map.
Figure 2. Close-up of the EqLocate controls for moving
around the world map and zooming. The up
arrow causes the world view to move to the north. The down arrow causes the world view to move
to the south. The left arrow causes the
world view to move to the west. The
right arrow causes the world view to move to the east. The plus symbol causes zooming in (smaller
area displayed) on the view. The minus
symbol causes zooming out (larger area displayed).
1.3 EqLocate menus: Pull-down menus in EqLocate (at the upper
left hand corner of the screen) provide controls and program information. Using the File menu, one can open or
close seismogram files for events, print the current screen, and exit the
program. In the Controls menu,
one can set the depth of focus (a dialog box appears that allows the user to
select from several standard depths or input an arbitrary depth – the travel
time tables are limited to a maximum depth of about 650 km because only a few
earthquakes deeper than that depth have ever been recorded) of an earthquake to
iteratively determine the depth as well as the epicenter; set the maximum RMS
value for the color coding on the color bar at the lower left hand corner of
the screen – for most regional and distant (teleseismic) events, a value of 30
or 40 works well; use the zoom and arrow controls equivalent to the arrow and
plus/minus symbols in the upper lest hand corner of the screen (Figure 2). In the Options menu, one can turn on
the Hints window that provides a shorter version of the instructions that are
provided here; select multiple seismogram windows (small windows displaying one
seismogram for each station that can be moved to be located adjacent to the
station location), or seismograms in one window. In the Help menu one can determine the
version of EqLocate that is installed and some information about the
program. During program operation, Hints windows appear that help guide
the user through program operation.
1.4 Opening seismograms from an earthquake
folder: To open seismograms
for an earthquake, select Open Event from the File menu and
select the event of interest. The
seismograms for each standard event are saved in a folder named for the
event. Open the folder by double
clicking or selecting and clicking on Open and select the seismograms
using the mouse. Hold the Control
key down to select multiple seismograms.
Hold the Shift key down and select the first seismogram
and the last seismogram to select all seismograms in the folder. Click Open. At least three seismograms should be selected
for each event.
New seismograms for additional
earthquakes can be added. Place
seismograms in folders to organize the data by event as has been done with the
standard earthquakes provided with EqLocate.
Occasionally, an opened seismogram will have an arrival time that cannot
be matched with a theoretical travel time.
In this case, it is possible that a timing error exists with that
seismogram and station and therefore, that seismogram should not be used for
locating the earthquake. For more
information on adding seismograms, see Importing Data Into EqLocate below.
An example of opening seismograms
for an event is shown in Figure 3. In
this example, the
One can also select multiple
seismogram windows (use the Options menu) in which case there will be
one window for each seismogram. The
seismogram windows can be moved around on the screen to place them adjacent to
the corresponding station. Time and
amplitude expansion of the traces is also provided by the arrows in each of the
multiple seismogram windows.
Figure 3. Screen image of the EqLocate program after an
earthquake data set (in this case the
With the single window view, as in Figure 3, one can
enlarge the seismograms window by dragging the lower left hand corner of the
window with the mouse cursor. The time
scale can then be expanded if desired and the amplitude of each trace can be
expanded as needed. Then, placing the
cursor at the interpreted first arrival (P-wave) of each seismogram, clicking
the mouse selects the arrival time (indicated by a red vertical line). The resulting display for the
Figure
4. Screen image of the EqLocate program
seismogram window. The window has been
enlarged on the screen by dragging the lower left hand corner of the window to
the left. Also, the time scale has been
expanded by a factor of 2 using the up arrow in the lower left hand corner of
the seismogram window. Amplitude scales
of some of the seismograms have been enlarged (for easier interpretation of the
first arrival) using the up arrows located to the left of each seismogram. Arrival times for each seismogram have been
picked by clicking the mouse with the cursor positioned at the user-selected
arrival time. The selected arrival times
are marked by a red line extending downward from the seismograms. The scale at the bottom of the window is
relative time in minutes. To the left of
each seismogram is information about the station and seismogram. The station name is a 3, 4 or 5 letter
code. BHZ indicates the vertical
component of motion from a broadband seismograph. The second line of text lists the date
(YYYY/MO/DA) and the time of the start of the seismogram (HR:MN:SS.ss). The next line gives the date (YYYY/MO/DA) and
the arrival time (HR:MN:SS.ss).
1.5 Finding the earthquake epicenter: Next, the
initial trial epicenter is selected by clicking on the map display. In practice, any location will work to start
the process, but because we have seismograms that are all recorded and
displayed in absolute time, we know that the epicenter must be closest to the
station corresponding to the seismogram with the earliest travel time. Therefore, one should select an initial trial
epicenter near the station with the earliest arrival time. For the
The degree to which the data from the trial epicenters
fits the observed arrival times (“the quality of the solution”) can be
visualized and understood with three different but related displays. After the trial epicenter is selected, the
epicenter-to-station distances are calculated by the program and theoretical
travel times for each of these distances can be calculated by interpolation of
the standard travel time curves, and an origin time for the earthquake estimated. The theoretical arrival times are then
calculated and compared with the observed (user-selected, or, “picked”) arrival
times. A consistent measure of the fit
of all the arrival time data is the RMS
(Root Mean Square) error (the RMS error is a measure of the average
error of the observed minus theoretical arrival times) shown on the yellow bar
near the upper left hand corner of the map display. For the
Figure 5. Portion of the
EqLocate screen after the initial trial epicenter (small blue star) has been
selected. A depth of 33 km was chosen
for the initial trial epicenter. The
small black triangles and lines extending from the trial epicenter toward the
stations indicate the estimated distance to each station based on the arrival
times and the origin time estimated from an average of the time information
(see How EqLocate Works, section
2, below). The black lines are simply straight lines
connecting the epicenter with the estimated epicenter-to-station distance (from
the observations – not the distance calculated from the coordinates of the
trial epicenter and the stations). These
lines do not represent the paths that the seismic waves would travel. The paths would be slightly curved lines on
this map projection connecting the trial epicenter and the station. The RMS error (in this case 47.74 s)
indicates that our trial epicenter is not a good solution. The fact that the calculated
epicenter-to-station distances (from epicenter to each station – red triangle)
do not match the estimated distances (epicenter to small black triangles) also
indicates that the initial epicenter is not correct. Comparing the observed and theoretical
arrival times in the seismogram window also confirms that the trial epicenter
is not correct.
Theoretical arrival times that are earlier than the observed arrival time indicate that the trial epicenter needs to be moved farther from that station. Similarly, theoretical arrival times that are later than the observed arrival time indicate that the trial epicenter needs to be moved closer to that station.
An additional
display of the fit of the trial epicenter and of the direction to move the
epicenter for a better fit is provided by the black triangles and lines on the
map display. The positions of the small
black triangles and the lengths of the lines are calculated by the program and
represent the expected distance to the corresponding station if the
trial epicenter is correct. A mismatch
in the positions of the triangles means that the trial epicenter needs to be
moved. If the estimated distance is less
than the epicenter-to-station distance (the line connecting the epicenter to
the small black triangle does not reach the station), the epicenter needs to be moved toward that station. Similarly, if the estimated distance is
greater than the epicenter-to-station distance (the line connecting the
epicenter to the small black triangle goes through the station), the epicenter needs to be moved farther
from that station. For example, for
the initial trial epicenter for the
An additional feature appears in the map display for the second trial epicenter (Figure 6). Because the RMS error is less than the maximum RMS error that we have set for the color bar on the map (in this case, 40 s; use the Controls menus to set the maximum RMS error for the color bar display), the second trial epicenter is color-coded, providing a quick, visual indication of the degree of fit of the location. However, in this case, the relatively high RMS error, the mismatch of the estimated and actual station locations, and the mismatch of the observed and theoretical arrival times (visible in the seismogram window) all indicate that the trial epicenter is still not good enough.
The search can
be continued by selecting another trial epicenter using the positions of the
small black triangles as guides to which direction to move the epicenter. A relatively small RMS error solution can usually be found with a few more trials
using this approach. However, a very
effective alternative, and one that provides additional insight into the
solution, is to simply try many epicenters near the location where a relatively
low RMS error solution has been
found. Because the program calculates
new solutions so rapidly, it is very fast and easy to search for the optimum
location using this method. For example,
for the
Figure 6. Portion of the
EqLocate screen after the second trial epicenter (small blue star) has been
selected. The location is improved – the
estimated epicenter-to-station distances derived from the arrival time data (small
black triangles connected to the epicenter by thin lines) are closer to the
theoretical distances (epicenter to station), and the RMS error has decreased
significantly.
Figure 7. Portion of the
EqLocate screen after the best solution has been found for the initial depth of
focus – 33 km. The RMS error has been
reduced but it is still large. This
error corresponds to an average of many seconds of error per station, whereas
arrival time accuracy is about one second or less. The mismatch of the small black triangles and
the station locations also indicates that the solution is not very good. However, by selecting epicenters all around
the lowest RMS error epicenter, the RMS color pattern shows that this epicenter
is optimum for the chosen depth. This
pattern also provides an estimation of the uncertainty in the epicenter
location.
1.6 Estimating the possible error in the derived epicenter: For the depth of focus that was originally selected (33 km), the best solution found corresponded to an RMS error of 22.8 s (Figure 7). Furthermore, by selecting many trial epicenters, an approximately elliptical-shaped area has been outlined by the colors on the map. The colors show that the lowest RMS error epicenter is near the center of this ellipse and the size of the ellipse gives an indication of the possible error in the derived solution. For example, one can see that the central blue area (corresponding to an RMS error that is somewhat less than the solutions in the surrounding area) is about 600 km wide. Because any epicenter in the blue area has about the same RMS error (in this case, between 20 and 24 s), the different locations are not significantly different in the degree of fit to the observed data. Thus we might conclude that the accuracy of our epicenter is about +/- 300 km. A more complete estimation of the possible inaccuracy of the epicenter is somewhat more complicated and requires the knowledge (or reasonable assumption) of the accuracy of the data including the observed arrival time accuracy, the accuracy of the locations of the stations, and the validity of the Earth model that is used to calculate the travel time curves. However, color-coding of regions of error in the earthquake location, as shown in Figure 7, is at least a useful relative indicator of the accuracy of the solution.
1.7 Determining the depth of focus of the earthquake: The RMS error for the best solution shown in Figure 7 is still relatively large. More data (seismograms from additional stations) might help, but a likely problem that we have not addressed thus far is the depth of focus of this earthquake. The depth of 33 km was chosen arbitrarily as a starting depth because most earthquakes are relatively shallow. However, the large RMS error and the significant mismatch in the distances (as indicated by the triangles on the map in Figure 7) suggest that the depth of focus might be significantly different than 33 km. We can easily test this hypothesis by selecting other depths and then selecting new trial epicenters. Setting the depth is easily accomplished using the Depth window that is opened from the Control menu. Performing multiple epicenter searches as illustrated in Figure 7 for a variety of depths yields locations with RMS errors that are shown in Table 1. The errors decrease significantly for the optimum trial epicenters corresponding to greater depth of focus. The minimum RMS error is found for a depth of focus of 650 km although there is very little difference in the errors found for any depth from about 580 km to 650 km. The resulting solution is shown in Figure 8.
Table 1. Depth of focus and minimum RMS error for the
|
Depth of Focus
(km) |
Minimum RMS Error (s) |
|
33 |
22.8 |
|
100 |
21.1 |
|
200 |
18.9 |
|
300 |
14.5 |
|
400 |
9.3 |
|
500 |
6.7 |
|
600 |
1.8 |
|
650 |
1.7 |
The small RMS error, the comparison of the estimated and calculated distances to each station (correspondence of the small black triangles and the red triangles), and the match of the observed and theoretical arrival times in the seismogram window (Figure 9), all indicate that the epicenter shown in Figure 8 provides a very good fit to the observed arrival times. Furthermore, the small error ellipse (the yellow area outlined in Figure 8 representing epicenters corresponding to RMS errors of less than 4 s) suggests that the derived location is reasonably accurate (about +/- 50 km in epicenter location and +/- 70 km in depth).
Figure
8. Portion of the EqLocate screen after
the final trial epicenter (small blue star) has been selected. Various depth of focus values were tried up
to 650 km (very few earthquakes have been recorded that have depths greater
than 650 km). The small RMS error (1.71
s), the match of the estimated distances and the theoretical distances (black
and red triangles are almost at the same location), the small error ellipse
defined by the colors, and the small observed minus theoretical arrival time
differences seen on the seismogram display, indicate that the earthquake
location (latitude, longitude, depth of focus and origin time) determined using
these seismograms and EqLocate is accurate.
Figure 9. EqLocate seismogram
window (upper diagram) for the
1.8 Checking the accuracy of the solution: To check the accuracy of the location, a comparison between the “official” location and the location determined using the five seismograms and EqLocate is shown in Table 2. As can be seen from Table 2, the EqLocate solution is very good. The official location information for earthquakes can be found from the earthquake search tool on the US Geological Survey web page (http://earthquake.usgs.gov) or using the event search tool on the IRIS DMC web page (http://www.iris.edu). Detailed instructions (including examples) for accessing earthquake information from the Internet for recent and historical events are provided at:
http://web.ics.purdue.edu/~braile/edumod/eqdata/eqdata.htm (see section 2.3).
Table
2. Comparison of the official (USGS)
location (latitude, longitude, depth and origin time) for the Bolivia
earthquake determined from over a hundred arrival times, with the EqLocate
location determined from the five seismograms shown here.
|
|
Official Location
|
EqLocate Location
|
|
Latitude (degrees S) |
13.84 |
13.63 |
|
Longitude (degrees W) |
67.55 |
67.47 |
|
Depth of focus (km) |
631 |
650 |
|
Origin Time (HR:MN:SS, GMT/UTC) |
|