using the seismomter recording shown above determine how far away the epicenter
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using the seismomter recording shown above determine how far away the epicenter of the earthquake was from the seismomterExplanation / Answer
To locate an earthquake, you need the data from at least three seismometer stations. The process is known as triangulation and is described in more detail below.
The seismometer records the time when the P and S-waves arrive at the recording station. P-waves travel faster through the earth than S-waves and so they arrive at the seismometer station before the S-waves and are recorded by the seismometer first.
The difference in arrival time between the two types of seismic wave can be used to calculate the distance of the earthquake's epicentre from the seismometer, as the further away an earthquake is, the greater the lag time between the detection of the S waves relative to the P waves (imagine two cars racing against each other. They both set off at the same time from the same place, but one car has a slightly higher top speed than the other car. At first they will be pretty close together, but the longer the race goes on (as time increases / the further they travel) the faster car will get further and further away, from the slower car). Based on properties of the crust, and many trials, a seismologist can calculate how far away an earthquake is from a station based just on the S-P lag time.
As velocity is equal to distance divided by time, we can write equations for the P and S waves arrival times (TP and TS) as follows:
TP = D / VP (1)
TS = D / VS (2)
Where D is the distance from the epicnetre, VP and VS are the velocitys of the seismic P and S waves. As the S-waves are slower than the P-waves, TS will always be larger than TP. As such it is possible to calculate the difference between the two (DT).
DT = TS - TP
Substituting from equations (1) and (2) above gives:
DT = (D / VS) - (D/VP) = D (1/VS - 1 / VP) = D (VP - VS / VS - VP)
This can then be re-arranged in terms of D(istance) to give the following:
DE = DT x (VP x VS) / (VP - VS)
Where:
DE = Distance to epicentre (km)
DT = Difference between P and S-wave arrival time (s)
VP = P-wave velocity (km/s)
VS = S-wave velocity (km/s)
This can then be plotted on a map, by drawing a circle with a radius equal to the distance to the epicentre around the seismometer station. This is then repeated for the other two seismometer stations and the point where the three circles intersect is the location of the earthquakes epicentre.
The above procedure is commonly automated using computers and numerical techniques so that a large number of differing seismic episodes can be processed efficiently.
It should be noted that this is an imperfect process as a number of assumptions must be made about the material through which the seismic waves travel in order to estimate their speed.
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