Earthquake location using the S minus P
method and magnitude determination ^{1}
(L. Braile, November, 2004)
http://web.ics.purdue.edu/~braile
1. Introduction: This education module uses real seismograms to demonstrate the S minus P earthquake location method and the determination of magnitudes for earthquakes. The seismograms for the S minus P location exercise were recorded at standard GSN (Global Seismographic Network; www.iris.edu) stations and downloaded from The IRIS DMC (Data Management Center) archive using the IRIS DMC online tool WILBER II (instructions for the use of WILBER II are available at:
http://web.ics.purdue.edu/~braile/edumod/as1lessons/UsingAmaSeis/UsingAmaSeis.htm,
see section 5).
The seismograms for the magnitude determination exercise were recorded on an AS1 seismograph.
Additional information about the AS1 seismograph and educational activities for the AS1 can be found at: http://web.ics.purdue.edu/~braile/, select AS1 Seismograph Information, and at the IRIS Education and Outreach website at http://www.iris.edu/about/ENO/. An installation manual for setting up the AS1 seismometer can be found at:
http://www.scieds.com/spinet/ and http://www.iris.edu/about/ENO/AS1AmaSeis.pdf.
Further information on accessing earthquake information can be found at:
http://web.ics.purdue.edu/~braile/edumod/eqdata/eqdata.htm.
The seismograms used in this module can be downloaded to your computer and viewed and interpreted using the AmaSeis software. Alternatively, the activities can be performed using the copies of the seismograms shown here. In addition to the web version of this document, MS Word and PDF versions are available at:
http://web.ics.purdue.edu/~braile/edumod/as1lessons/EQlocation/EQlocation.doc,
and
http://web.ics.purdue.edu/~braile/edumod/as1lessons/EQlocation/EQlocation.pdf.
Using the MS Word version of this document, one can print copies of the seismograms and the S minus P travel time curve at a convenient scale (1 cm = 1 minute) for ease of use with paper copies of the seismograms. For information on installing and using the AmaSeis software, and instructions for downloading seismograms from SpiNet or from the IRIS DMC using the online data access tool WILBER II, see the “Using AmaSeis” tutorial available at:
http://web.ics.purdue.edu/~braile/edumod/as1lessons/UsingAmaSeis/UsingAmaSeis.htm
http://web.ics.purdue.edu/~braile/edumod/as1lessons/UsingAmaSeis/UsingAmaSeis.doc
http://web.ics.purdue.edu/~braile/edumod/as1lessons/UsingAmaSeis/UsingAmaSeis.pdf
Additional technical assistance and a tutorial for the AmaSeis software can be found under the Help menu in AmaSeis. Teaching lessons that use AS1 seismograms and AmaSeis can be found at: http://web.ics.purdue.edu/~braile/edumod/as1lessons/.
2. S minus P location exercise,
http://neic.usgs.gov/neis/travel_times/. For instructions on downloading the seismograms to your computer and using AmaSeis to view and interpret the seismograms, see section 2.2 below.
2.1 Measuring S minus P times of the Seismograms (Paper copies, 20 minute records, Scale: 1 cm = 1 minute): Measure the S minus P times for the 4 seismograms below (Figure 14); then use the standard Earth travel time curves (examples are shown in Figures 5 and 6; for this exercise use the S minus P graph, Figure 7, which is plotted with the same time scale as the seismograms) to infer the distance (in degrees and kilometers) from the epicenter to the station; use Table 1 below to record your results.
To find the
distance corresponding to a given S minus P time, move the metric ruler along
the S minus P travel time graph (keeping the ruler parallel with the time axis)
until the S minus P time matches the time that you entered in the Table 1. The interpreted distance will then be the
position of the ruler on the distance axis (in degrees) as illustrated in
Figure 8. Because the S minus P times
for the velocity structure that best match the Earth, increase consistently
with distance, the observed S minus P time will only match the curves shown in
Figure 7 at one position corresponding to a specific distance (the interpreted
epicentertostation distance). Additional illustrations of this concept are
shown in Figure 8 and 9 for a seismogram (in this case the KIP seismogram for
the
A map of the S minus P results (from Table 1) showing the calculated location of the earthquake (using triangularization) can be made using a globe (see section 3.1, below) or using the online IRIS DMC Event Search mapping tool (see section 3.2, below).
Table 1. Data table for the S minus P earthquake
location information.
Station (Latitude and Longitude, in degrees): 
Measured S minus P times (minutes; measure to nearest tenth of a minute = 1 mm on the seismogram): 
Inferred distance (degrees and kilometers; convert degrees to km by multiplying by 111.19 km/degree): Degrees: Kilometers: 

TUC (32.310,
110.785) 



CCM (38.056,
91.245) 



NNA (11.987,
76.842) 



KIP (21.423,
158.015) 



Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5. Standard Earth travel
time curves for a source depth of 0 km (can be used for shallow earthquakes at
distances of ~20 to 120 degrees). Travel
times for many different phases (types of seismic waves and paths through the
Earth) are shown. The first (or direct)
P and S arrival times are shown by heavier lines. Note that the difference between the S and the P times increases smoothly with
distance. Therefore, a seismogram with a
given S minus P time will only match the travel time data at one specific
distance.
Figure 6. Simplified standard Earth travel time curves
showing only the P and S times.
Figure 7. Simplified standard
Earth travel time curves showing only the P and S times (the difference between
the P and S times shown in Figure 6; time scale: 1 cm = 1 minute). To find the distance corresponding to a given
S minus P time, move the metric ruler along the S minus P travel time graph
(keeping the ruler parallel with the time axis) until the S minus P time
matches the time that you entered in the table for a given seismogram. The interpreted distance will then be the
position of the ruler on the distance axis (in degrees).
Figure 8. Illustration of ruler
placed on S minus P travel times graph (Figure 7) showing position
corresponding to 8 minutes (8 cm on the scaled seismograms and S minus P graph
shown above) indicating that the epicentertostation distance for this
seismogram is about 58 degrees.
Figure 9. Overlaying a
seismogram (the KIP seismogram, Figure 4; plotted using the same time scale as
the underlying graph) on the standard Earth model travel time curves. Similar to the measurement illustrated in
Figure9, this diagram shows that the S minus P arrival times indicate an
epicentertostation distance of about 58 degrees. The AmaSeis travel time curve tool provides a
similar display (Figure 10) although the graph is rotated so that the
seismograms are plotted horizontally.
Figure 10. KIP seismogram for
the
2.2
Seismograms (interpreted using AmaSeis):
Sacformat seismograms can be downloaded from SpiNet or from the
IRIS DMC using the WILBER II tool (see the “Using AmaSeis” tutorial referenced
in section 1, above) and interpreted on your computer using the AmaSeis software
to determine the S minus P times and corresponding epicentertostation
distance for each seismogram. For this
exercise, download the
Table 2. The
M7.5 September 30, 1999 Oaxaca, Mexico earthquake recorded at GSN stations CCM (Cathedral Caves, MO), TUC (Tucson, AZ), NNA (Nana, Peru), and KIP (Kipapa, HI) – click on the SAC files below to download . 
Seismograms: CCM.00.BHZ.D.SAC, TUC.00.BHZ.D.SAC, NNA.00.BHZ.D.SAC, KIP.00.BHZ.D.SAC 
Use the AmaSeis program to open and view the seismograms. For each seismogram, use the Pick Arrivals tool to mark the arrival times of the P and S waves on the screen. (The P and S times can be measured individually by placing the mouse cursor on the interpreted arrival and reading the arrival time from the small arrival time window in the lower right hand corner of the screen. The difference between these times, the S minus P time, can then be calculated by subtraction.) Then select the Travel Times Curve tool and enter the depth of 33 km (a “standard” depth if the depth of the earthquake is not known) in the dialog box. The seismogram will appear on the screen (similar to Figure 10). Move the seismogram by dragging with the mouse cursor until the P and S arrivals match the travel time curves (Figure 10). The epicentertostation distance corresponding to the S minus P time will be displayed to the left of the seismogram. Enter these data in Table 1. Further instructions for using AmaSeis in S minus P earthquake location are available in the “Using AmaSeis” tutorial referenced in section 1, above (see section 3.6 in the tutorial). Additional preassembled data sets for S minus P locations are also available in the Using AmaSeis tutorial (section 6).
Using AmaSeis,
three of the traces for the
A map of the S minus P results (from Table 1) showing the calculated location of the earthquake (using triangularization) can be made using a globe (see section 3.1, below) or using the online IRIS DMC Event Search mapping tool (see section 3.2, below).
Figure 11. Threetrace
seismogram display (stations TUC, CCM and NNA) for the
3. Mapping the S minus P
information: Two options for
plotting the S minus P results from the
3.1
S minus P mapping on a globe: The epicenter location can be determined from
the S minus P data by drawing distance circles on a globe as illustrated in
Figures 1315. Use a line of longitude (Figure
13) to provide a distance scale (in degrees) to determine the length of the
string corresponding to the epicentertostation distance for each
seismogram. The distance in degrees (or angular distance or geocentric angle) is illustrated in Figure 12. The distance in km (along the surface) can be
found by multiplying the distance in degrees by 111.19 km/degree. Draw a circle or part of a circle around each
station (Figure 14) using the appropriate string length from your Table 1 data
and the degree scale (Figure 13). The
results should be similar to the map display shown in Figure 15. The circles should approximately intersect at
a point. One can compare the S minus P
determined epicenter with the “official” epicenter (calculated from arrival
times from over a hundred seismograph stations) by plotting the official
epicenter location on the globe (Figure 15).
For the
An additional example of mapping an S minus P earthquake location on a globe is illustrated at:
http://web.ics.purdue.edu/~braile/edumod/as1mag/as1mag2.htm.
Figure 12. Cross section through
the Earth showing the major spherical shells (layers; crust, mantle, outer core
and inner core), selected raypaths of various seismic arrivals (phases), and
the epicentertostation distance.
Figure 13. Determining distance
in degrees on a globe using the lines of latitude. The string is measured for a distance of 40
degrees in this illustration.
Figure 14. Plotting an S minus P
distance circle from a station. The
length of the string is measured to the interpreted epicentertostation
distance (in this case about 35 degrees) for station NNA (yellow dot) and an
arc (circle or part of a circle) is drawn around the station.
Figure 15. Results of S minus P
location. The S minus P estimated
earthquake epicenter is indicated by the intersections of the circles. Station locations are indicated by the yellow
dots. The actual location is indicated
by the red dot.
3.2 S minus P mapping using the Event Search online mapping tool: The IRIS DMC online Event Search tool provides an effective method of plotting the results of an S minus P earthquake location. To access the Event Search tool, go to www.iris.edu, select “Data”, then “Types of Data”, then “Search the catalogs”, then “Event Search”. The Event Search allows one to search the earthquake catalog for events within a selected area, for a specified time period and for a selected range of magnitudes. The results of the search will be a list of earthquakes. On the list page, there is an option to make a map. The resulting map can be modified and optional userdefined data added. Complete instructions for using the optional userdefined data in the Event Search mapping tool are provided at:
http://web.ics.purdue.edu/~braile/edumod/eqdata/eqdata.htm. The online instructions for the optional userdefined data input are available at:
http://www.iris.edu/quakes/eventSearchInstructions.htm. The userdefined data are entered in the Event Search map window illustrated in Figure 16.
The following
data are derived from the 4 seismograms for the
Station coordinates (degrees latitude, degrees longitude): CCM: 38.056, 91.245; TUC: 32.310, 110.785; NNA: 11.987, 76.842; KIP: 21.423, 158.015.
Earthquake epicenter (degrees latitude, degrees longitude): 16.01, 96.93.
Suggested map area (latitude and longitude range, in degrees; for IRIS Event Search and S minus P location map): 15 to 55, 165 to 65.
Figure 16. Userdefined data entered into the IRIS DMC
Event Search mapping tool.
Figure 17. Example of S minus P
location map created with the IRIS DMC Event Search mapping tool. Before entering the optional userdefined
data (Figure 16), an earthquake search was performed to find the epicenters of
events of magnitude 6 and above that occurred in the map area from January 1,
1990 to December 31, 1999. Circles show
the epicentertostation distances interpreted from the S minus P times for
each station. The circles approximately
intersect at a point indicating the epicenter.
The “official” epicenter calculated from seismograms recorded at over
one hundred stations is shown by the red star.
More information about the Event Search mapping tool is provided at: http://web.ics.purdue.edu/~braile/edumod/eqdata/eqdata.htm
(see section 2.3).
4. Magnitude determination: Magnitude determination requires measuring the amplitude and period of specific phases (arrivals) on seismograms, accounting for the epicentertostation distance (because the seismic waves generated by the earthquake spread out and become smaller with distance from the epicenter), and utilizing a magnitude formula. In the exercises provided here, an mb (body wave magnitude using the first arriving P wave arrival) magnitude and an MS (surface wave magnitude using the ~20 s period Rayleigh wave energy) magnitude will be calculated using AS1 seismograms. The measurements on the seismograms can be made on the paper copies (Figures 21 and 24) or by downloading the seismograms (links are listed below) and using AmaSeis to measure the amplitude and the period (the mouse cursor is used to measure amplitude and time; measurements are displayed in the lower right hand corner of the AmaSeis Event screen). Additional information on measuring amplitudes and on magnitudes is available in the Using AmaSeis tutorial (section 3.7; see link in section 1 above), in the MagCalc online AS1 magnitude calculator, and at:
http://web.ics.purdue.edu/~braile/edumod/as1mag/as1mag3.htm.
Measure the amplitude and period
of the P wave (mb magnitude determination; maximum amplitude in the first ~15 s
of the seismogram using the enlarged record; an example of measuring the
amplitude and the period is given in Figure 18) for the San Simeon earthquake
(Figures 1921). Measure the amplitude and period of the ~20 s period
surface waves for the
Links to the two seismograms used in this magnitude calculation exercise are provided below:
To find the official magnitude (for comparison with the magnitude that was determined from the seismograms interpreted here), go to http://earthquake.usgs.gov (for instructions on accessing recent and historical earthquake data, see
http://web.ics.purdue.edu/~braile/edumod/eqdata/eqdata.htm, section 2.3).
Table 3. Data table for the mb and MS magnitude
calculations.
Earthquake 
Magnitude type 
Distance (degrees) 
Amplitude (digital
units) 
Period (s) of arrival
energy 
Magnitude estimate
(from MagCalc) 

mb 
27.24 



9/25/2003 Hokkaido,

MS 
86.07 



Figure 18. Example of amplitude
and wave period measurement for a seismogram (M7.8 Colima,
Figure 19. AmaSeis 24hour
screen display showing the December 22, 2003 M6.5
Figure 20. AmaSeis event screen
(extracted seismogram) display showing the December 22, 2003 M6.5 San Simeon
earthquake recorded at AS1 station WLIN.
Figure 21. Enlarged (“zoomed
in”) seismogram from Figure 20 showing the first (P) arrivals. Amplitude scale on the left is in digital
units or counts.
Figure 22. AmaSeis 24hour
screen display showing the
Figure 23. AmaSeis event screen
(extracted seismogram) display showing the September 25, 2003 M8.3
Figure 24. Enlarged (“zoomed
in”) seismogram from Figure 23 showing the surface wave arrivals (~20 second
period Rayleigh waves). Amplitude scale
on the left is in digital units or counts.
[1] Last
modified March 13, 2006
The web page for this document is: http://web.ics.purdue.edu/~braile/edumod/as1lessons/EQlocation/EQlocation.htm.
Funding for this development provided by IRIS and the National Science Foundation.
ã Copyright 2004. L. Braile. Permission granted for reproduction for noncommercial uses.