Estimating the Distance to an Earthquake from the Interval Between Seismic Waves

 

The primary p waves are compression waves that move relatively fast in the direction of propagation.

 

The secondary s waves (also known as shear waves) move more slowly since they follow a sinusoidal path. They travel at about two thirds the speed of the p waves.

 

distance of an observation point from an earthquake in kilometers =

= (time interval between the arrival of the s and p wave in seconds) * 8

 

Derivation:

(1) distance = (velocity p wave) * T1 = (velocity s wave) * T2

(2) T2 - T1 = ((distance) / (velocity s wave)) - ((distance) / (velocity p wave))

(3) T2 - T1 = (distance) * (( 1 / (velocity s wave)) - ( 1 / (velocity p wave)))

(4) distance = (T2 - T1) * ((velocity of p wave) * (velocity of s wave)) / ((velocity of p wave) - (velocity of s wave))

(5) If the s wave moves at 60% of the p wave, and the p wave moves at about 5.3 km/s then the factor becomes 8.