Download LOCATION OF A TELESEISMIC EARTHQUAKES – (Keith Priestley

LOCATION OF A TELESEISMIC EARTHQUAKES – (Keith Priestley)
Here we follow a graphical procedure for estimating the epicenter of an earthquake using the
seismograms from just two or three seismographs. More accurate earthquake locations are made
using a least-squares analysis of phase arrival times from many seismographs around the world. To
construct a graphical location, the seismic phases are read and their arrival times noted, without
any prejudice as to the location of the event. The distance of the event, defined as the arc measured
at the center of the Earth of the great circle separating the epicenter and seismograph station, is
then obtained from the relative arrival times using the travel time curves. Once the distance is
obtained, the event is then known to lie on a small circle (lines of latitude) centered on the station
with radius given by the measured angular distance. If two such distances are known then two
possible locations can be obtained. The choice between these two locations can be made using
records from a third station or by examining the particle motion of the P-waves or surface waves.
This practical shows how each of these steps is carried out.
The Records
A seismogram is a recording of surface motion as a function of time. The recording may be made
at various magnifications and recording rates, and over various frequency bands. The seismograms
used in this practical are from the World Wide Standard Seismic Network (WWSSN). This network
of about 100 uniform seismographs was installed in the early 1960’s and a few of these instruments
are still in operation. The first two stations used in this practical are at Shillong (SHL) in India
(25.57o N, 91.88o E), and at Bullowayo (BUL) in Zimbabwe (20.14o S, 28.61o E). The short period
seismograms (components 1, 2, and 3 corresponding to vertical, north-south, and east-west motion,
respectively) have timing marks every minute. The recording drum rotates once in 15 minutes,
therefore timing marks on adjacent lines are 15 minutes apart. The long period seismograms also
have timing marks every minute but the recording drum rotates once an hour. Therefore the time
between timing marks on adjacent traces is one hour.
Reading the Arrival Times
Draw up a table of the arrival times of all the phases you can see in the following way:
Station
component
BUL-1
BUL-2
.
.
.
phase
hour:minute
i
e
.
.
.
5:25
5:33
.
.
.
dist. right
of minute
mark (mm)
31
80
.
.
.
time
(sec)
17
44
.
.
.
time after
1st arrival
0
8:27
.
.
.
time
convert
to mm
0
84.5
.
.
.
Record the station and component in column 1. Record an i in column 2 if the phase is impulsive,
and an e if the phase is emergent. These are subjective terms but you might denote an impulsive
arrival as one which you are confident you can time to ±0.25 seconds and denote emergent as arrivals
where you have less confidence in the arrival time. Later, once you have located the earthquake,
you can add the phase designation (i.e., P, S, PKP, etc.) in this column. Record the time of the
timing mark immediately to the right of the phase in column 3. Measure the distance in millimeters
between the timing mark and the phase onset and record this distance in column 4. Measure the
distance between the timing marks to find the millimeters per second and convert the value in
column 4 to seconds and record this in column 5. Often the drum rotation rate is irregular so the
distance between timing marks can vary. Therefore this factor must be determined for each phase.
Add the time in column 5 to the time of the timing mark in column 3, subtract the time of the first
arrival, and record this time in column 6. Finally, measure the distance between the time marks on
the y-axis of the travel time curve to find the conversion factor between time and distance, convert
the time in column 6 to distance in millimeters and record this value in column 7. Pick the times of
short period body wave phases (i.e. P, PKP) on the short period vertical. Many times it is possible
to time the S-wave arrival on the short period horizontals, but often the S-wave is much clearer on
the long period horizontal components. (Why might the S-wave frequencies be lower than those of
the P-waves?) After you have found at least the P-wave arrival time, (and hopefully the S-wave
arrival time) on the short period seismogram, find the same times on the long period component
seismograms, and examine all the long period components for later phases. Compressional phases
will record best on the vertical and shear phases will record best on the horizontals. The Rayleigh
waves will normally appear on all three long period components but the Love waves will only appear
on the horizontal components. There are several phases to be found on the long period records but
it is difficult to read more than P- and possibly S-arrivals on short period records. Read records
from both seismograph stations before going on to the next part of the practical.
Obtaining the Distance
The distance between the station and the epicenter is found using the relative arrival times of
the phases and the travel time curve. Mark a strip of graph paper with the distances from column
7. Align the earliest mark on the graph paper, the mark corresponding to the P-wave arrival time,
with the origin of the travel time curve. Slide the graph paper across the travel time curve in the
direction of increasing distance, keeping the mark on the graph paper denoting the P-wave arrival
time on the travel time curve for the P-wave. Move the graph paper in the direction of increasing
distance until as many of the marks as possible align with travel time curves for various phases.
Remember that you will not have been able to read all the phases shown on the travel time plot,
and the arrival time of some phases is less accurate than others. Place the greatest weight on the
phases you noted as being impulsive in column 2 of the table. The readings of P and S from the
short period should be the most accurate because these records afford better time resolution. You
should therefore take these times in preference to those from other records in determining the final,
accurate, measurement of distance. You may also have identified some wiggles on the seismograms
as phases that are not true arrivals. In addition, inexperienced observer often read arrivals late.
Finding the Two Possible Locations
We need to draw two small circles on a globe, one centered on each station, with radii corresponding to the measured distances. This can be achieved with a globe and two pieces of string,
but a more accurate method is to use a projection of the globe. The stereographic projection is
used because it has the property that small circles plot onto circles on the projection. We can
therefore draw the small circles on the projection with a compass. The distance of a point an
angular distance θ from the center of the projection is at distance 66.5 tan(θ/2) in mm. Take a
piece of A3 tracing paper and put the center of the stereographic net underneath at the center of
the tracing paper. Mark the positions of SHL and BUL using the grid and taking the center of the
grid to be 0o N, 0o E.
The great circle through the origin and BUL maps into a straight line on the projection. Use
the measured angular distance to find the two points where the small circle centered on BUL cuts
this great circle. Although the small circle maps into a circle on the projection, its center does not
map into the center of the circle on the projection. The circle must therefore be drawn using the
mid-point between the two intersections found above as center. Repeat the procedure for SHL.
If you find that one of the intersections is off the grid; its position must be calculated using the
formula d = 66.5 tan(θ/2). The two points of intersection are the two possible locations of the
epicenter. You can decide which is the epicenter by using the phase arrival times from a third
station, or by examining the particle motion of a prominent phase.
The Third Station
The remaining seismograms are from College (COL) in Alaska 64.90o N, 147.79o W. This station
plots on the projection at a distance of 112o from the origin at an azimuth of 345o . Measure the P
and S times at COL and use the difference to measure the angular distance. Work out the position
of the center of the circle as before, which you will find to be very large, and approximate the circle
as a straight line perpendicular to the line joining COL to the origin. Hence find which of the two
possible locations is the true one. How good do you think the location is?
Particle Motion
You could also determine the direction of the event using the particle motion of a prominent
phase. Particle motion plots are important tools for studying the nature of seismic phases. Given
two components, we construct a particle motion plot as follows:
1) Fit a horizontal line through the seismogram.
2) At a set time intervals, measure the amplitude of the seismogram for both components.
3) Plot the points on a pair of linear axes, using arrows to show the trend with time.
The P-wave: The motion of the initial P-wave arrival on the long period seismograms is either
compressional (up and away from the source) or dilatational (down and towards the source). Measure the direction of the first motion on one of the long period vertical component seismograms. If
this is positive, the motion on the horizontals should be away from the source; if the first motion
is negative on the vertical component, the motion on the horizontals should be towards the source.
Does the location indicated by the P-wave particle motion agree with the location found using the
third station?
The Surface Waves: There are two types of surface waves, Rayleigh waves designated LR, and Love
waves designated LQ. Rayleigh waves are longitudinal surface waves and have retrograde elliptical
motion in the direction of propagation. As a consequence, the Rayleigh wave are usually observed
on all three long period components. The Love waves are horizontally polarized transverse surface
waves, that is the particle motion is transverse to the path of propagation. Therefore the Love
waves can only be seen on the horizontal components.
Identify the Rayleigh waves on the the long period seismogram components at BUL. Use the
fact that the Rayleigh waves have retrograde elliptical particle motion to determine the azimuth of
the propagation path. Does this agree with the azimuth of BUL from the epicenter indicated on
the stereographic net?
What are the large waves arriving on the east-west component at BUL between 5:40 and 5:55?
Why is there no corresponding arrivals on the other two long period components?
c 1993 Keith Priestley
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