From: The Lahrs (JohnJan@lahr.org)
Date: Fri May 05 2000 - 21:41:53 PDT
Message-Id: <4.2.0.58.20000505191634.00b8c6a0@netmail.home.com> Date: Fri, 05 May 2000 22:41:53 -0600 From: The Lahrs <JohnJan@lahr.org> Subject: Re: Pinhole Digest #399 - 05/05/00
Hi Dillon,
I did this IRIS exercise at a workshop in Yosemite last year. If I remember
correctly you first find out how fast your P-walker and S-walker travel by
measuring them over a known distance. You make this measurement of,
say the time to walk 50 feet, three times. Then put two points on a graph of
time versus distance, the average of the 3 times for the P-walker and the
average for the S-walker. Draw a line from the origin of the graph through
the P-time and another through the S-time. You now have a travel-time
graph to use in locating an "earthquake."
Then you station three people at known locations and pick a forth location
for the earthquake. You need the X and Y coordinates of these four locations.
You're going to figure out the earthquake location, but want the actual
location so you can see how close your estimate is to reality.
Now start the P-walker and the S-walker at the same time from the
earthquake to station 1. Time the difference between the P-walker arrival
and the S-walker arrival. This time interval is S-P(1). Repeat for stations
2 and 3 to get S-P(2) and S-P(3).
You can use your graph to find the distance of the earthquake from
each station. To do this, first, using the time axis of your graph, make two
marks on the edge of a slip of paper so the mark spacing equals S-P(1).
Use the paper to find the place along the distance axis where the vertical
distance (time) between the P curve and the S curve matches the two marks.
This will be the distance to station 1. On a map of the stations, draw a
circle around station 1 with a radius of this distance. Repeat for S-P(2) and
S-P(3) and if everything works out correctly, the three circles will intersect
close to the known location of the earthquake.
You can also use algebra to find the distances. Lets say station 1 is
at unknown distance D1 from the earthquake. The P-walker travel time
from the earthquake to stations 1 will be D1/Vp, where Vp is the velocity of
the P-walker. The S-walker travel time will be D1/Vs, where Vs is the
velocity of the S-walker. Then the measured S-P(1) will equal D1/Vs - D1/Vp
S-P(1)=D1/Vs - D1/Vp
S-P(1) = D1(Vp - Vs)/(Vs*Vp)
D1 = S-P(1)*Vs*Vp/(Vp - Vs)
You can compute what seismologists call the S minus P velocity,
Vs-p = Vs*Vp/(Vp - Vs)
Using this number, it's easy to find the distances.
D1 = S-P(1)*Vs-p
D2 = S-P(2)*Vs-p
D3 = S-P(3)*Vs-p
For real earthquakes in the crust, Vp is about 6.2 km/s and the ratio of Vp to
Vs is about 1.78. Starting with the equation above for Vs-p
Vs-p = Vs*Vp/(Vp - Vs)
Divide the numerator and denominator of the right side by Vs.
Vs-p = Vp/(Vp/Vs - 1)
So, for crustal earthquakes,
Vs-p = 6.2 / (1.78 - 1) = 6.2 / .78 = about 8 km/s
As an example, if the S-P time for a local earthquake is 5 seconds,
the distance to the earthquake is about 5*8 = 40 km. Of course,
for an earthquake, this defines a bowl, not a circle. The earthquake
could 40 km deep directly below the station!
Hope this helps,
John
At 02:20 AM 5/5/00 , you wrote:
>Pinhole Digest #399 - Friday, May 5, 2000
>Date: Wed, 03 May 2000 22:42:18 PDT
>From: Dillon Dutton <drufusd@hotmail.com>
>To: dhunt@exploratorium.edu
>Subject: Need info
>
>Hi,
>
>I was at the AGU teacher's classes in December. They had a
>nice little activity where we played S and P waves and were
>able to locate an earthquake epicenter. I want to do this
>with my students, but can't remember how you convert the
>seconds to distance (seconds = difference between the
>'arrival' of the P wave and the 'arrival' of the S wave.
>
>With three 'stations' one should be able to locate the
>epicenter by the intersection of the circles drawn about
>the stations representing the difference in arrival times.
>But, what distance is used for each second? And what is
>the real distance used for real earthquakes and why?
>
>I'm sure it's quite simple, but I can't figure it out.
>
>Thanks, hope you can help or steer me the right way.
>
>Dillon Dutton (drufusd@hotmail.com)
>________________________________________________________________________
John C. Lahr
1925 Foothills Road
Golden, CO 80402
(303) 215-9913
http://lahr.org/john-jan/science.html
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