How far is the epicenter from the seismic station?

Question

There are two types of seismic waves associated with every earthquake, called P and S waves. They travel in every direction away from the source of an Earthquake called the epicenter. Because they each travel with different speeds, seismologists can determine the distance from a seismic station to an epicenter. An Earthquake occurred in an area where a P wave travels at 5 km/s and the S wave travels at 3 km/s. A seismic station measures an SP lag time of 16.9 seconds (meaning the P wave was detected 16.9 seconds before the S wave).

 

How far is the epicenter from the seismic station?

Answer 1

v_P = 5 km/s

 

v_S = 3 km/s

 

 

Let L the distance from the epicenter.  Then the difference in time for P and S waves is t_S - t_P = 16.9 s.

 

 

The time taken is given by t_P = L/v_P and t_S = L/v_S which in turn gives L/3 - L/5 = 16.9 s.

 

 

Solving for L,

 

L(1/3 - 1/5) = 16.9

 

L = 15/2 * 16.9 = 127 km