Question

PLEASE HELP ME!!!

The further the seismogram is from the epicenter of the earthquake, the more
lag time between the P-waves and the S-waves. Why does this happen?

Answer 1

The reason for that is that P-waves (primary waves) travel faster than S-waves (secondary waves).

If we call
`v_p` the speed of the primary waves and
`v_s` the speed of the secondary waves, and we call
`S` the distance of the seismogram from the epicenter, we can write the time the two waves take to reach the seismogram as

`t_P = (S)/(v_P)`

`t_S= (S)/(v_S)`

So the lag time between the arrival of the P-waves and of the S-waves is

`\Delta t = t_S-t_P= (S)/(v_S)- (S)/(v_P)= S((1)/(v_S)- (1)/(v_P))`
We see that this lag time is proportional to the distance S, therefore the larger the distance, the greater the lag time.