Finding the epicentre...

On this page, we will see that the distance of the epicentre from the seismometer location, d is proportional to the time difference Dt between the arrivals of the P and S waves.

Given a seismometer trace it is therefore possible to find the distance of the epicentre from the seismometer location.

Seismic trace

From an earlier page, we saw that P waves and S waves travel at different speeds (6.0 km s-1 and 3.5 km s-1 respectively); this means that the P wave and S wave shocks will arrive at the seismology station at different times.

Since velocity = distance / time, we can write equations for the P and S waves thus:

tp = d / vp
(1)
and
ts = d / vs

(2)

where d is the distance from the epicentre, vp and vs are the velocities of the P and S waves respectively, and  tp and ts are the times of arrival (in seconds) of the P and S waves respectively at the seismology station.  As ts is always going to be greater than tp, it is possible to calculate the difference between the two, Dt.

Dt = ts - tp

Substituting from equations (1) and (2) above gives:

Equation 3
(3)
Rearranging in terms of d and substituting values for vs and vp [in km s-1], gives:
Equation 4

(4)

So therefore:

d = 8.4 Dt [km]

where Dt is in s

 

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